id	sid	tid	token	lemma	pos
ejpam-5136	1	1	european	european	PROPN
ejpam-5136	1	2	journal	journal	PROPN
ejpam-5136	1	3	of	of	ADP
ejpam-5136	1	4	pure	pure	ADJ
ejpam-5136	1	5	and	and	CCONJ
ejpam-5136	1	6	applied	apply	VERB
ejpam-5136	1	7	mathematics	mathematic	NOUN
ejpam-5136	1	8	vol	vol	NOUN
ejpam-5136	1	9	.	.	PROPN
ejpam-5136	2	1	17	17	NUM
ejpam-5136	2	2	,	,	PUNCT
ejpam-5136	2	3	no	no	INTJ
ejpam-5136	2	4	.	.	NOUN
ejpam-5136	2	5	2	2	NUM
ejpam-5136	2	6	,	,	PUNCT
ejpam-5136	2	7	2024	2024	NUM
ejpam-5136	2	8	,	,	PUNCT
ejpam-5136	2	9	790	790	NUM
ejpam-5136	2	10	-	-	SYM
ejpam-5136	2	11	809	809	NUM
ejpam-5136	2	12	issn	issn	PROPN
ejpam-5136	2	13	1307	1307	NUM
ejpam-5136	2	14	-	-	SYM
ejpam-5136	2	15	5543	5543	NUM
ejpam-5136	2	16	–	–	PUNCT
ejpam-5136	2	17	ejpam.com	ejpam.com	X
ejpam-5136	2	18	published	publish	VERB
ejpam-5136	2	19	by	by	ADP
ejpam-5136	2	20	new	new	PROPN
ejpam-5136	2	21	york	york	PROPN
ejpam-5136	2	22	business	business	PROPN
ejpam-5136	2	23	global	global	PROPN
ejpam-5136	2	24	on	on	ADP
ejpam-5136	2	25	the	the	DET
ejpam-5136	2	26	bivariate	bivariate	ADJ
ejpam-5136	2	27	extension	extension	NOUN
ejpam-5136	2	28	of	of	ADP
ejpam-5136	2	29	the	the	DET
ejpam-5136	2	30	extended	extended	ADJ
ejpam-5136	2	31	standard	standard	ADJ
ejpam-5136	2	32	u	u	ADJ
ejpam-5136	2	33	-	-	ADJ
ejpam-5136	2	34	quadratic	quadratic	ADJ
ejpam-5136	2	35	distribution	distribution	NOUN
ejpam-5136	2	36	idzhar	idzhar	PROPN
ejpam-5136	2	37	a.	a.	PROPN
ejpam-5136	2	38	lakibul1,2,∗	lakibul1,2,∗	PROPN
ejpam-5136	2	39	,	,	PUNCT
ejpam-5136	2	40	daisy	daisy	NOUN
ejpam-5136	2	41	lou	lou	PROPN
ejpam-5136	2	42	l.	l.	PROPN
ejpam-5136	2	43	polestico1,2	polestico1,2	PROPN
ejpam-5136	2	44	,	,	PUNCT
ejpam-5136	2	45	arnulfo	arnulfo	PROPN
ejpam-5136	2	46	p.	p.	NOUN
ejpam-5136	2	47	supe1,2	supe1,2	PROPN
ejpam-5136	2	48	1	1	NUM
ejpam-5136	2	49	department	department	NOUN
ejpam-5136	2	50	of	of	ADP
ejpam-5136	2	51	mathematics	mathematic	NOUN
ejpam-5136	2	52	and	and	CCONJ
ejpam-5136	2	53	statistics	statistic	NOUN
ejpam-5136	2	54	,	,	PUNCT
ejpam-5136	2	55	mindanao	mindanao	PROPN
ejpam-5136	2	56	state	state	PROPN
ejpam-5136	2	57	university	university	PROPN
ejpam-5136	2	58	iligan	iligan	PROPN
ejpam-5136	2	59	institute	institute	PROPN
ejpam-5136	2	60	of	of	ADP
ejpam-5136	2	61	technology	technology	PROPN
ejpam-5136	2	62	,	,	PUNCT
ejpam-5136	2	63	iligan	iligan	PROPN
ejpam-5136	2	64	city	city	PROPN
ejpam-5136	2	65	,	,	PUNCT
ejpam-5136	2	66	philippines	philippine	NOUN
ejpam-5136	2	67	2	2	NUM
ejpam-5136	2	68	premier	premier	PROPN
ejpam-5136	2	69	research	research	PROPN
ejpam-5136	2	70	institute	institute	PROPN
ejpam-5136	2	71	of	of	ADP
ejpam-5136	2	72	science	science	PROPN
ejpam-5136	2	73	and	and	CCONJ
ejpam-5136	2	74	mathematics	mathematic	NOUN
ejpam-5136	2	75	center	center	NOUN
ejpam-5136	2	76	for	for	ADP
ejpam-5136	2	77	computational	computational	ADJ
ejpam-5136	2	78	analytics	analytic	NOUN
ejpam-5136	2	79	and	and	CCONJ
ejpam-5136	2	80	modeling	modeling	NOUN
ejpam-5136	2	81	,	,	PUNCT
ejpam-5136	2	82	mindanao	mindanao	PROPN
ejpam-5136	2	83	state	state	PROPN
ejpam-5136	2	84	university	university	PROPN
ejpam-5136	2	85	iligan	iligan	PROPN
ejpam-5136	2	86	institute	institute	PROPN
ejpam-5136	2	87	of	of	ADP
ejpam-5136	2	88	technology	technology	PROPN
ejpam-5136	2	89	,	,	PUNCT
ejpam-5136	2	90	iligan	iligan	PROPN
ejpam-5136	2	91	city	city	PROPN
ejpam-5136	2	92	,	,	PUNCT
ejpam-5136	3	1	philippines	philippine	NOUN
ejpam-5136	3	2	abstract	abstract	ADJ
ejpam-5136	3	3	.	.	PUNCT
ejpam-5136	4	1	this	this	DET
ejpam-5136	4	2	paper	paper	NOUN
ejpam-5136	4	3	derives	derive	VERB
ejpam-5136	4	4	the	the	DET
ejpam-5136	4	5	bivariate	bivariate	ADJ
ejpam-5136	4	6	version	version	NOUN
ejpam-5136	4	7	of	of	ADP
ejpam-5136	4	8	the	the	DET
ejpam-5136	4	9	extended	extended	ADJ
ejpam-5136	4	10	standard	standard	ADJ
ejpam-5136	4	11	u	u	NOUN
ejpam-5136	4	12	-	-	ADJ
ejpam-5136	4	13	quadratic	quadratic	ADJ
ejpam-5136	4	14	(	(	PUNCT
ejpam-5136	4	15	esu	esu	NOUN
ejpam-5136	4	16	)	)	PUNCT
ejpam-5136	4	17	distribution	distribution	NOUN
ejpam-5136	4	18	using	use	VERB
ejpam-5136	4	19	the	the	DET
ejpam-5136	4	20	compounding	compounding	NOUN
ejpam-5136	4	21	method	method	NOUN
ejpam-5136	4	22	or	or	CCONJ
ejpam-5136	4	23	pseudo	pseudo	NOUN
ejpam-5136	4	24	-	-	NOUN
ejpam-5136	4	25	family	family	NOUN
ejpam-5136	4	26	of	of	ADP
ejpam-5136	4	27	distributions	distribution	NOUN
ejpam-5136	4	28	.	.	PUNCT
ejpam-5136	5	1	the	the	DET
ejpam-5136	5	2	joint	joint	ADJ
ejpam-5136	5	3	probability	probability	NOUN
ejpam-5136	5	4	and	and	CCONJ
ejpam-5136	5	5	cumulative	cumulative	ADJ
ejpam-5136	5	6	distribution	distribution	NOUN
ejpam-5136	5	7	functions	function	NOUN
ejpam-5136	5	8	of	of	ADP
ejpam-5136	5	9	the	the	DET
ejpam-5136	5	10	derived	derive	VERB
ejpam-5136	5	11	distribution	distribution	NOUN
ejpam-5136	5	12	are	be	AUX
ejpam-5136	5	13	obtained	obtain	VERB
ejpam-5136	5	14	and	and	CCONJ
ejpam-5136	5	15	it	it	PRON
ejpam-5136	5	16	is	be	AUX
ejpam-5136	5	17	observed	observe	VERB
ejpam-5136	5	18	that	that	SCONJ
ejpam-5136	5	19	the	the	DET
ejpam-5136	5	20	said	say	VERB
ejpam-5136	5	21	distribution	distribution	NOUN
ejpam-5136	5	22	can	can	AUX
ejpam-5136	5	23	generate	generate	VERB
ejpam-5136	5	24	bivariate	bivariate	ADJ
ejpam-5136	5	25	shape	shape	NOUN
ejpam-5136	5	26	distributions	distribution	NOUN
ejpam-5136	5	27	with	with	ADP
ejpam-5136	5	28	the	the	DET
ejpam-5136	5	29	following	follow	VERB
ejpam-5136	5	30	properties	property	NOUN
ejpam-5136	5	31	:	:	PUNCT
ejpam-5136	5	32	(	(	PUNCT
ejpam-5136	5	33	i	i	NOUN
ejpam-5136	5	34	)	)	PUNCT
ejpam-5136	5	35	x	x	PUNCT
ejpam-5136	6	1	and	and	CCONJ
ejpam-5136	6	2	y	y	PROPN
ejpam-5136	6	3	have	have	VERB
ejpam-5136	6	4	bathtub	bathtub	NOUN
ejpam-5136	6	5	shapes	shape	NOUN
ejpam-5136	6	6	;	;	PUNCT
ejpam-5136	6	7	(	(	PUNCT
ejpam-5136	6	8	ii	ii	NOUN
ejpam-5136	6	9	)	)	PUNCT
ejpam-5136	6	10	x	x	PUNCT
ejpam-5136	6	11	has	have	VERB
ejpam-5136	6	12	a	a	DET
ejpam-5136	6	13	constant	constant	ADJ
ejpam-5136	6	14	distribution	distribution	NOUN
ejpam-5136	6	15	and	and	CCONJ
ejpam-5136	6	16	y	y	PROPN
ejpam-5136	6	17	has	have	VERB
ejpam-5136	6	18	a	a	DET
ejpam-5136	6	19	bathtub	bathtub	ADJ
ejpam-5136	6	20	shape	shape	NOUN
ejpam-5136	6	21	;	;	PUNCT
ejpam-5136	6	22	and	and	CCONJ
ejpam-5136	6	23	(	(	PUNCT
ejpam-5136	6	24	iii	iii	X
ejpam-5136	6	25	)	)	PUNCT
ejpam-5136	6	26	x	x	PUNCT
ejpam-5136	6	27	has	have	VERB
ejpam-5136	6	28	an	an	DET
ejpam-5136	6	29	inverted	inverted	ADJ
ejpam-5136	6	30	bathtub	bathtub	NOUN
ejpam-5136	6	31	and	and	CCONJ
ejpam-5136	6	32	y	y	PROPN
ejpam-5136	6	33	has	have	VERB
ejpam-5136	6	34	a	a	DET
ejpam-5136	6	35	bathtub	bathtub	ADJ
ejpam-5136	6	36	shape	shape	NOUN
ejpam-5136	6	37	.	.	PUNCT
ejpam-5136	7	1	moreover	moreover	ADV
ejpam-5136	7	2	,	,	PUNCT
ejpam-5136	7	3	some	some	DET
ejpam-5136	7	4	properties	property	NOUN
ejpam-5136	7	5	of	of	ADP
ejpam-5136	7	6	this	this	DET
ejpam-5136	7	7	proposed	propose	VERB
ejpam-5136	7	8	distribution	distribution	NOUN
ejpam-5136	7	9	are	be	AUX
ejpam-5136	7	10	derived	derive	VERB
ejpam-5136	7	11	such	such	ADJ
ejpam-5136	7	12	as	as	ADP
ejpam-5136	7	13	the	the	DET
ejpam-5136	7	14	marginal	marginal	ADJ
ejpam-5136	7	15	distribution	distribution	NOUN
ejpam-5136	7	16	,	,	PUNCT
ejpam-5136	7	17	conditional	conditional	ADJ
ejpam-5136	7	18	distribution	distribution	NOUN
ejpam-5136	7	19	,	,	PUNCT
ejpam-5136	7	20	conditional	conditional	ADJ
ejpam-5136	7	21	moments	moment	NOUN
ejpam-5136	7	22	,	,	PUNCT
ejpam-5136	7	23	product	product	NOUN
ejpam-5136	7	24	and	and	CCONJ
ejpam-5136	7	25	ratio	ratio	NOUN
ejpam-5136	7	26	moments	moment	NOUN
ejpam-5136	7	27	,	,	PUNCT
ejpam-5136	7	28	pearson	pearson	PROPN
ejpam-5136	7	29	correlation	correlation	NOUN
ejpam-5136	7	30	coefficient	coefficient	NOUN
ejpam-5136	7	31	,	,	PUNCT
ejpam-5136	7	32	joint	joint	ADJ
ejpam-5136	7	33	moment	moment	NOUN
ejpam-5136	7	34	generating	generate	VERB
ejpam-5136	7	35	function	function	NOUN
ejpam-5136	7	36	,	,	PUNCT
ejpam-5136	7	37	and	and	CCONJ
ejpam-5136	7	38	the	the	DET
ejpam-5136	7	39	stress	stress	NOUN
ejpam-5136	7	40	strength	strength	NOUN
ejpam-5136	7	41	parameter	parameter	NOUN
ejpam-5136	7	42	.	.	PUNCT
ejpam-5136	8	1	further	far	ADV
ejpam-5136	8	2	,	,	PUNCT
ejpam-5136	8	3	the	the	DET
ejpam-5136	8	4	maximum	maximum	ADJ
ejpam-5136	8	5	likelihood	likelihood	NOUN
ejpam-5136	8	6	estimation	estimation	NOUN
ejpam-5136	8	7	is	be	AUX
ejpam-5136	8	8	performed	perform	VERB
ejpam-5136	8	9	to	to	PART
ejpam-5136	8	10	estimate	estimate	VERB
ejpam-5136	8	11	the	the	DET
ejpam-5136	8	12	parameters	parameter	NOUN
ejpam-5136	8	13	of	of	ADP
ejpam-5136	8	14	the	the	DET
ejpam-5136	8	15	derived	derive	VERB
ejpam-5136	8	16	distribution	distribution	NOUN
ejpam-5136	8	17	.	.	PUNCT
ejpam-5136	9	1	a	a	DET
ejpam-5136	9	2	simulation	simulation	NOUN
ejpam-5136	9	3	study	study	NOUN
ejpam-5136	9	4	is	be	AUX
ejpam-5136	9	5	carried	carry	VERB
ejpam-5136	9	6	out	out	ADP
ejpam-5136	9	7	to	to	PART
ejpam-5136	9	8	evaluate	evaluate	VERB
ejpam-5136	9	9	the	the	DET
ejpam-5136	9	10	behavior	behavior	NOUN
ejpam-5136	9	11	of	of	ADP
ejpam-5136	9	12	the	the	DET
ejpam-5136	9	13	estimates	estimate	NOUN
ejpam-5136	9	14	of	of	ADP
ejpam-5136	9	15	the	the	DET
ejpam-5136	9	16	parameters	parameter	NOUN
ejpam-5136	9	17	.	.	PUNCT
ejpam-5136	10	1	a	a	DET
ejpam-5136	10	2	new	new	ADJ
ejpam-5136	10	3	bivariate	bivariate	ADJ
ejpam-5136	10	4	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	10	5	distribution	distribution	NOUN
ejpam-5136	10	6	is	be	AUX
ejpam-5136	10	7	derived	derive	VERB
ejpam-5136	10	8	and	and	CCONJ
ejpam-5136	10	9	used	use	VERB
ejpam-5136	10	10	to	to	PART
ejpam-5136	10	11	simulate	simulate	VERB
ejpam-5136	10	12	bivariate	bivariate	ADJ
ejpam-5136	10	13	data	datum	NOUN
ejpam-5136	10	14	with	with	ADP
ejpam-5136	10	15	x	x	PUNCT
ejpam-5136	10	16	and	and	CCONJ
ejpam-5136	10	17	y	y	PROPN
ejpam-5136	10	18	having	have	VERB
ejpam-5136	10	19	bathtub	bathtub	NOUN
ejpam-5136	10	20	shapes	shape	NOUN
ejpam-5136	10	21	.	.	PUNCT
ejpam-5136	11	1	a	a	DET
ejpam-5136	11	2	new	new	ADJ
ejpam-5136	11	3	bivariate	bivariate	ADJ
ejpam-5136	11	4	version	version	NOUN
ejpam-5136	11	5	of	of	ADP
ejpam-5136	11	6	the	the	DET
ejpam-5136	11	7	cubic	cubic	ADJ
ejpam-5136	11	8	transmuted	transmuted	ADJ
ejpam-5136	11	9	uniform	uniform	NOUN
ejpam-5136	11	10	(	(	PUNCT
ejpam-5136	11	11	ctu	ctu	NOUN
ejpam-5136	11	12	)	)	PUNCT
ejpam-5136	11	13	distribution	distribution	NOUN
ejpam-5136	11	14	is	be	AUX
ejpam-5136	11	15	also	also	ADV
ejpam-5136	11	16	derived	derive	VERB
ejpam-5136	11	17	.	.	PUNCT
ejpam-5136	12	1	finally	finally	ADV
ejpam-5136	12	2	,	,	PUNCT
ejpam-5136	12	3	the	the	DET
ejpam-5136	12	4	proposed	propose	VERB
ejpam-5136	12	5	bivariate	bivariate	ADJ
ejpam-5136	12	6	esu	esu	NOUN
ejpam-5136	12	7	distribution	distribution	NOUN
ejpam-5136	12	8	is	be	AUX
ejpam-5136	12	9	applied	apply	VERB
ejpam-5136	12	10	to	to	ADP
ejpam-5136	12	11	simulated	simulated	ADJ
ejpam-5136	12	12	data	datum	NOUN
ejpam-5136	12	13	and	and	CCONJ
ejpam-5136	12	14	compared	compare	VERB
ejpam-5136	12	15	with	with	ADP
ejpam-5136	12	16	the	the	DET
ejpam-5136	12	17	bivarite	bivarite	NOUN
ejpam-5136	12	18	cubic	cubic	ADJ
ejpam-5136	12	19	transmuted	transmuted	ADJ
ejpam-5136	12	20	uniform	uniform	ADJ
ejpam-5136	12	21	distribution	distribution	NOUN
ejpam-5136	12	22	.	.	PUNCT
ejpam-5136	13	1	the	the	DET
ejpam-5136	13	2	results	result	NOUN
ejpam-5136	13	3	show	show	VERB
ejpam-5136	13	4	that	that	SCONJ
ejpam-5136	13	5	the	the	DET
ejpam-5136	13	6	proposed	propose	VERB
ejpam-5136	13	7	bivariate	bivariate	ADJ
ejpam-5136	13	8	esu	esu	NOUN
ejpam-5136	13	9	distribution	distribution	NOUN
ejpam-5136	13	10	provides	provide	VERB
ejpam-5136	13	11	a	a	DET
ejpam-5136	13	12	better	well	ADJ
ejpam-5136	13	13	fit	fit	NOUN
ejpam-5136	13	14	on	on	ADP
ejpam-5136	13	15	the	the	DET
ejpam-5136	13	16	simulated	simulate	VERB
ejpam-5136	13	17	dataset	dataset	NOUN
ejpam-5136	13	18	compared	compare	VERB
ejpam-5136	13	19	with	with	ADP
ejpam-5136	13	20	the	the	DET
ejpam-5136	13	21	bivariate	bivariate	ADJ
ejpam-5136	13	22	ctu	ctu	ADJ
ejpam-5136	13	23	distribution	distribution	NOUN
ejpam-5136	13	24	.	.	PUNCT
ejpam-5136	14	1	2020	2020	NUM
ejpam-5136	14	2	mathematics	mathematic	NOUN
ejpam-5136	14	3	subject	subject	NOUN
ejpam-5136	14	4	classifications	classification	NOUN
ejpam-5136	14	5	:	:	PUNCT
ejpam-5136	14	6	60e05	60e05	NUM
ejpam-5136	14	7	,	,	PUNCT
ejpam-5136	14	8	62e10	62e10	NUM
ejpam-5136	14	9	,	,	PUNCT
ejpam-5136	14	10	65c10	65c10	NUM
ejpam-5136	14	11	key	key	ADJ
ejpam-5136	14	12	words	word	NOUN
ejpam-5136	14	13	and	and	CCONJ
ejpam-5136	14	14	phrases	phrase	NOUN
ejpam-5136	14	15	:	:	PUNCT
ejpam-5136	14	16	standard	standard	ADJ
ejpam-5136	14	17	u	u	ADJ
ejpam-5136	14	18	-	-	ADJ
ejpam-5136	14	19	quadratic	quadratic	ADJ
ejpam-5136	14	20	distribution	distribution	NOUN
ejpam-5136	14	21	,	,	PUNCT
ejpam-5136	14	22	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	14	23	distribution	distribution	NOUN
ejpam-5136	14	24	,	,	PUNCT
ejpam-5136	14	25	bivariate	bivariate	ADJ
ejpam-5136	14	26	distribution	distribution	NOUN
ejpam-5136	14	27	,	,	PUNCT
ejpam-5136	14	28	bivariate	bivariate	ADJ
ejpam-5136	14	29	pseudo	pseudo	NOUN
ejpam-5136	14	30	family	family	NOUN
ejpam-5136	14	31	,	,	PUNCT
ejpam-5136	14	32	bathtub	bathtub	NOUN
ejpam-5136	14	33	shape	shape	NOUN
ejpam-5136	14	34	distribution	distribution	NOUN
ejpam-5136	14	35	∗corresponding	∗corresponde	VERB
ejpam-5136	14	36	author	author	NOUN
ejpam-5136	14	37	.	.	PUNCT
ejpam-5136	15	1	doi	doi	NOUN
ejpam-5136	15	2	:	:	PUNCT
ejpam-5136	15	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5136	https://doi.org/10.29020/nybg.ejpam.v17i2.5136	ADJ
ejpam-5136	15	4	email	email	NOUN
ejpam-5136	15	5	addresses	address	NOUN
ejpam-5136	15	6	:	:	PUNCT
ejpam-5136	15	7	idzhar.lakibul@g.msuiit.edu.ph	idzhar.lakibul@g.msuiit.edu.ph	PROPN
ejpam-5136	15	8	(	(	PUNCT
ejpam-5136	15	9	i.	i.	PROPN
ejpam-5136	15	10	a.	a.	PROPN
ejpam-5136	15	11	lakibul	lakibul	PROPN
ejpam-5136	15	12	)	)	PUNCT
ejpam-5136	15	13	,	,	PUNCT
ejpam-5136	15	14	daisylou.polestico@g.msuiit.edu.ph	daisylou.polestico@g.msuiit.edu.ph	PROPN
ejpam-5136	15	15	(	(	PUNCT
ejpam-5136	15	16	d.	d.	PROPN
ejpam-5136	15	17	l.	l.	PROPN
ejpam-5136	15	18	polestico	polestico	PROPN
ejpam-5136	15	19	)	)	PUNCT
ejpam-5136	15	20	,	,	PUNCT
ejpam-5136	15	21	arnulfo.supe@g.msuiit.edu.ph	arnulfo.supe@g.msuiit.edu.ph	PROPN
ejpam-5136	15	22	(	(	PUNCT
ejpam-5136	15	23	a.	a.	PROPN
ejpam-5136	15	24	p.	p.	NOUN
ejpam-5136	15	25	supe	supe	PROPN
ejpam-5136	15	26	)	)	PUNCT
ejpam-5136	15	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5136	16	1	790	790	NUM
ejpam-5136	16	2	©	©	ADP
ejpam-5136	16	3	2024	2024	NUM
ejpam-5136	16	4	ejpam	ejpam	NOUN
ejpam-5136	16	5	all	all	DET
ejpam-5136	16	6	rights	right	NOUN
ejpam-5136	16	7	reserved	reserve	VERB
ejpam-5136	16	8	.	.	PUNCT
ejpam-5136	17	1	i.	i.	PROPN
ejpam-5136	17	2	a.	a.	PROPN
ejpam-5136	17	3	lakibul	lakibul	PROPN
ejpam-5136	17	4	,	,	PUNCT
ejpam-5136	17	5	d.	d.	PROPN
ejpam-5136	17	6	l.	l.	PROPN
ejpam-5136	17	7	polestico	polestico	PROPN
ejpam-5136	17	8	,	,	PUNCT
ejpam-5136	17	9	a.	a.	PROPN
ejpam-5136	17	10	p.	p.	NOUN
ejpam-5136	17	11	supe	supe	PROPN
ejpam-5136	17	12	/	/	SYM
ejpam-5136	17	13	eur	eur	PROPN
ejpam-5136	17	14	.	.	PUNCT
ejpam-5136	18	1	j.	j.	PROPN
ejpam-5136	18	2	pure	pure	PROPN
ejpam-5136	18	3	appl	appl	PROPN
ejpam-5136	18	4	.	.	PROPN
ejpam-5136	18	5	math	math	PROPN
ejpam-5136	18	6	,	,	PUNCT
ejpam-5136	18	7	17	17	NUM
ejpam-5136	18	8	(	(	PUNCT
ejpam-5136	18	9	2	2	NUM
ejpam-5136	18	10	)	)	PUNCT
ejpam-5136	18	11	(	(	PUNCT
ejpam-5136	18	12	2024	2024	NUM
ejpam-5136	18	13	)	)	PUNCT
ejpam-5136	18	14	,	,	PUNCT
ejpam-5136	18	15	790	790	NUM
ejpam-5136	18	16	-	-	SYM
ejpam-5136	18	17	809	809	NUM
ejpam-5136	18	18	791	791	NUM
ejpam-5136	18	19	1	1	NUM
ejpam-5136	18	20	.	.	PUNCT
ejpam-5136	19	1	introduction	introduction	NOUN
ejpam-5136	19	2	nowadays	nowadays	ADV
ejpam-5136	19	3	,	,	PUNCT
ejpam-5136	19	4	one	one	NUM
ejpam-5136	19	5	of	of	ADP
ejpam-5136	19	6	the	the	DET
ejpam-5136	19	7	developing	develop	VERB
ejpam-5136	19	8	research	research	NOUN
ejpam-5136	19	9	areas	area	NOUN
ejpam-5136	19	10	in	in	ADP
ejpam-5136	19	11	the	the	DET
ejpam-5136	19	12	field	field	NOUN
ejpam-5136	19	13	of	of	ADP
ejpam-5136	19	14	distribution	distribution	NOUN
ejpam-5136	19	15	theory	theory	NOUN
ejpam-5136	19	16	is	be	AUX
ejpam-5136	19	17	the	the	DET
ejpam-5136	19	18	generalization	generalization	NOUN
ejpam-5136	19	19	of	of	ADP
ejpam-5136	19	20	existing	exist	VERB
ejpam-5136	19	21	univariate	univariate	ADJ
ejpam-5136	19	22	distribution	distribution	NOUN
ejpam-5136	19	23	into	into	ADP
ejpam-5136	19	24	a	a	DET
ejpam-5136	19	25	bivariate	bivariate	ADJ
ejpam-5136	19	26	case	case	NOUN
ejpam-5136	19	27	.	.	PUNCT
ejpam-5136	20	1	a	a	DET
ejpam-5136	20	2	bivariate	bivariate	ADJ
ejpam-5136	20	3	distribution	distribution	NOUN
ejpam-5136	20	4	is	be	AUX
ejpam-5136	20	5	useful	useful	ADJ
ejpam-5136	20	6	for	for	ADP
ejpam-5136	20	7	modeling	model	VERB
ejpam-5136	20	8	two	two	NUM
ejpam-5136	20	9	related	relate	VERB
ejpam-5136	20	10	random	random	ADJ
ejpam-5136	20	11	variables	variable	NOUN
ejpam-5136	20	12	.	.	PUNCT
ejpam-5136	21	1	filus	filus	NOUN
ejpam-5136	21	2	and	and	CCONJ
ejpam-5136	21	3	filus	filus	NOUN
ejpam-5136	22	1	[	[	X
ejpam-5136	22	2	1	1	X
ejpam-5136	22	3	]	]	PUNCT
ejpam-5136	22	4	proposed	propose	VERB
ejpam-5136	22	5	a	a	DET
ejpam-5136	22	6	method	method	NOUN
ejpam-5136	22	7	of	of	ADP
ejpam-5136	22	8	generating	generate	VERB
ejpam-5136	22	9	bivariate	bivariate	ADJ
ejpam-5136	22	10	or	or	CCONJ
ejpam-5136	22	11	multivariate	multivariate	NOUN
ejpam-5136	22	12	distributions	distribution	NOUN
ejpam-5136	22	13	as	as	ADP
ejpam-5136	22	14	the	the	DET
ejpam-5136	22	15	linear	linear	ADJ
ejpam-5136	22	16	combinations	combination	NOUN
ejpam-5136	22	17	of	of	ADP
ejpam-5136	22	18	two	two	NUM
ejpam-5136	22	19	or	or	CCONJ
ejpam-5136	22	20	more	more	ADV
ejpam-5136	22	21	random	random	ADJ
ejpam-5136	22	22	variables	variable	NOUN
ejpam-5136	22	23	.	.	PUNCT
ejpam-5136	23	1	in	in	ADP
ejpam-5136	23	2	particular	particular	ADJ
ejpam-5136	23	3	,	,	PUNCT
ejpam-5136	23	4	they	they	PRON
ejpam-5136	23	5	derived	derive	VERB
ejpam-5136	23	6	the	the	DET
ejpam-5136	23	7	pseudo	pseudo	NOUN
ejpam-5136	23	8	-	-	NOUN
ejpam-5136	23	9	weibull	weibull	ADJ
ejpam-5136	23	10	and	and	CCONJ
ejpam-5136	23	11	pseudo	pseudo	NOUN
ejpam-5136	23	12	-	-	NOUN
ejpam-5136	23	13	gamma	gamma	NOUN
ejpam-5136	23	14	distributions	distribution	NOUN
ejpam-5136	23	15	as	as	ADP
ejpam-5136	23	16	the	the	DET
ejpam-5136	23	17	linear	linear	ADJ
ejpam-5136	23	18	combinations	combination	NOUN
ejpam-5136	23	19	of	of	ADP
ejpam-5136	23	20	the	the	DET
ejpam-5136	23	21	weibull	weibull	NOUN
ejpam-5136	23	22	and	and	CCONJ
ejpam-5136	23	23	gamma	gamma	NOUN
ejpam-5136	23	24	random	random	ADJ
ejpam-5136	23	25	variables	variable	NOUN
ejpam-5136	23	26	,	,	PUNCT
ejpam-5136	23	27	respectively	respectively	ADV
ejpam-5136	23	28	.	.	PUNCT
ejpam-5136	24	1	shahbaz	shahbaz	PROPN
ejpam-5136	24	2	et	et	PROPN
ejpam-5136	24	3	al	al	PROPN
ejpam-5136	24	4	.	.	PUNCT
ejpam-5136	25	1	[	[	X
ejpam-5136	25	2	10	10	NUM
ejpam-5136	25	3	]	]	PUNCT
ejpam-5136	25	4	formed	form	VERB
ejpam-5136	25	5	a	a	DET
ejpam-5136	25	6	bivariate	bivariate	ADJ
ejpam-5136	25	7	exponential	exponential	ADJ
ejpam-5136	25	8	distribution	distribution	NOUN
ejpam-5136	25	9	as	as	ADP
ejpam-5136	25	10	the	the	DET
ejpam-5136	25	11	compound	compound	NOUN
ejpam-5136	25	12	distribution	distribution	NOUN
ejpam-5136	25	13	of	of	ADP
ejpam-5136	25	14	two	two	NUM
ejpam-5136	25	15	exponential	exponential	ADJ
ejpam-5136	25	16	random	random	ADJ
ejpam-5136	25	17	variables	variable	NOUN
ejpam-5136	25	18	.	.	PUNCT
ejpam-5136	26	1	aside	aside	ADV
ejpam-5136	26	2	from	from	ADP
ejpam-5136	26	3	the	the	DET
ejpam-5136	26	4	bivariate	bivariate	ADJ
ejpam-5136	26	5	exponential	exponential	ADJ
ejpam-5136	26	6	distribution	distribution	NOUN
ejpam-5136	26	7	,	,	PUNCT
ejpam-5136	26	8	many	many	ADJ
ejpam-5136	26	9	derived	derive	VERB
ejpam-5136	26	10	bivariate	bivariate	ADJ
ejpam-5136	26	11	distributions	distribution	NOUN
ejpam-5136	26	12	were	be	AUX
ejpam-5136	26	13	formulated	formulate	VERB
ejpam-5136	26	14	using	use	VERB
ejpam-5136	26	15	this	this	DET
ejpam-5136	26	16	idea	idea	NOUN
ejpam-5136	26	17	such	such	ADJ
ejpam-5136	26	18	as	as	ADP
ejpam-5136	26	19	the	the	DET
ejpam-5136	26	20	bivariate	bivariate	ADJ
ejpam-5136	26	21	pseudo	pseudo	NOUN
ejpam-5136	26	22	-	-	ADJ
ejpam-5136	26	23	weibull	weibull	ADJ
ejpam-5136	26	24	distribution	distribution	NOUN
ejpam-5136	27	1	[	[	X
ejpam-5136	27	2	9	9	NUM
ejpam-5136	27	3	]	]	PUNCT
ejpam-5136	27	4	,	,	PUNCT
ejpam-5136	27	5	bivariate	bivariate	ADJ
ejpam-5136	27	6	pseudo	pseudo	ADJ
ejpam-5136	27	7	-	-	ADJ
ejpam-5136	27	8	rayleigh	rayleigh	ADJ
ejpam-5136	27	9	distribution	distribution	NOUN
ejpam-5136	27	10	[	[	X
ejpam-5136	27	11	7	7	NUM
ejpam-5136	27	12	]	]	PUNCT
ejpam-5136	27	13	,	,	PUNCT
ejpam-5136	27	14	bivariate	bivariate	ADJ
ejpam-5136	27	15	pseudo	pseudo	NOUN
ejpam-5136	27	16	-	-	ADJ
ejpam-5136	27	17	inverse	inverse	ADJ
ejpam-5136	27	18	rayleigh	rayleigh	NOUN
ejpam-5136	27	19	distribution	distribution	NOUN
ejpam-5136	27	20	[	[	X
ejpam-5136	27	21	5	5	NUM
ejpam-5136	27	22	]	]	PUNCT
ejpam-5136	27	23	,	,	PUNCT
ejpam-5136	27	24	bivariate	bivariate	ADJ
ejpam-5136	27	25	pseudo	pseudo	NOUN
ejpam-5136	27	26	-	-	NOUN
ejpam-5136	27	27	gumbel	gumbel	NOUN
ejpam-5136	27	28	distribution	distribution	NOUN
ejpam-5136	27	29	[	[	X
ejpam-5136	27	30	8	8	NUM
ejpam-5136	27	31	]	]	PUNCT
ejpam-5136	27	32	,	,	PUNCT
ejpam-5136	27	33	bivariate	bivariate	ADJ
ejpam-5136	27	34	inverse	inverse	ADJ
ejpam-5136	27	35	exponential	exponential	ADJ
ejpam-5136	27	36	distribution	distribution	NOUN
ejpam-5136	27	37	[	[	X
ejpam-5136	27	38	11	11	NUM
ejpam-5136	27	39	]	]	PUNCT
ejpam-5136	27	40	,	,	PUNCT
ejpam-5136	27	41	among	among	ADP
ejpam-5136	27	42	others	other	NOUN
ejpam-5136	27	43	.	.	PUNCT
ejpam-5136	28	1	lakibul	lakibul	PROPN
ejpam-5136	28	2	and	and	CCONJ
ejpam-5136	28	3	tubo	tubo	VERB
ejpam-5136	28	4	[	[	X
ejpam-5136	28	5	4	4	NUM
ejpam-5136	28	6	]	]	PUNCT
ejpam-5136	28	7	developed	develop	VERB
ejpam-5136	28	8	a	a	DET
ejpam-5136	28	9	probability	probability	NOUN
ejpam-5136	28	10	distribution	distribution	NOUN
ejpam-5136	28	11	called	call	VERB
ejpam-5136	28	12	the	the	DET
ejpam-5136	28	13	extended	extended	ADJ
ejpam-5136	28	14	standard	standard	ADJ
ejpam-5136	28	15	u	u	ADJ
ejpam-5136	28	16	-	-	ADJ
ejpam-5136	28	17	quadratic	quadratic	ADJ
ejpam-5136	28	18	distribution	distribution	NOUN
ejpam-5136	28	19	with	with	ADP
ejpam-5136	28	20	support	support	NOUN
ejpam-5136	28	21	on	on	ADP
ejpam-5136	28	22	[	[	X
ejpam-5136	28	23	0	0	NUM
ejpam-5136	28	24	,	,	PUNCT
ejpam-5136	28	25	1	1	NUM
ejpam-5136	28	26	]	]	PUNCT
ejpam-5136	28	27	and	and	CCONJ
ejpam-5136	28	28	it	it	PRON
ejpam-5136	28	29	is	be	AUX
ejpam-5136	28	30	given	give	VERB
ejpam-5136	28	31	in	in	ADP
ejpam-5136	28	32	the	the	DET
ejpam-5136	28	33	following	follow	VERB
ejpam-5136	28	34	definition	definition	NOUN
ejpam-5136	28	35	.	.	PUNCT
ejpam-5136	29	1	a	a	DET
ejpam-5136	29	2	random	random	ADJ
ejpam-5136	29	3	variable	variable	NOUN
ejpam-5136	29	4	x	x	PUNCT
ejpam-5136	29	5	is	be	AUX
ejpam-5136	29	6	said	say	VERB
ejpam-5136	29	7	to	to	PART
ejpam-5136	29	8	have	have	VERB
ejpam-5136	29	9	an	an	DET
ejpam-5136	29	10	extended	extended	ADJ
ejpam-5136	29	11	standard	standard	ADJ
ejpam-5136	29	12	u	u	ADJ
ejpam-5136	29	13	-	-	ADJ
ejpam-5136	29	14	quadratic	quadratic	ADJ
ejpam-5136	29	15	distribution	distribution	NOUN
ejpam-5136	29	16	denoted	denote	VERB
ejpam-5136	29	17	by	by	ADP
ejpam-5136	29	18	”	"	PUNCT
ejpam-5136	29	19	esu	esu	NOUN
ejpam-5136	29	20	”	"	PUNCT
ejpam-5136	29	21	if	if	SCONJ
ejpam-5136	29	22	the	the	DET
ejpam-5136	29	23	probability	probability	NOUN
ejpam-5136	29	24	density	density	NOUN
ejpam-5136	29	25	function	function	NOUN
ejpam-5136	29	26	(	(	PUNCT
ejpam-5136	29	27	pdf	pdf	NOUN
ejpam-5136	29	28	)	)	PUNCT
ejpam-5136	29	29	of	of	ADP
ejpam-5136	29	30	x	x	PRON
ejpam-5136	29	31	is	be	AUX
ejpam-5136	29	32	given	give	VERB
ejpam-5136	29	33	by	by	ADP
ejpam-5136	29	34	f(x	f(x	PROPN
ejpam-5136	29	35	)	)	PUNCT
ejpam-5136	29	36	=	=	SYM
ejpam-5136	30	1	1−	1−	NUM
ejpam-5136	30	2	λ+	λ+	PUNCT
ejpam-5136	30	3	3λ(2x−	3λ(2x−	NUM
ejpam-5136	30	4	1)2	1)2	NUM
ejpam-5136	30	5	,	,	PUNCT
ejpam-5136	30	6	x	x	SYM
ejpam-5136	30	7	∈	∈	PROPN
ejpam-5136	31	1	[	[	X
ejpam-5136	31	2	0	0	NUM
ejpam-5136	31	3	,	,	PUNCT
ejpam-5136	31	4	1	1	NUM
ejpam-5136	31	5	]	]	PUNCT
ejpam-5136	31	6	,	,	PUNCT
ejpam-5136	31	7	(	(	PUNCT
ejpam-5136	31	8	1	1	X
ejpam-5136	31	9	)	)	PUNCT
ejpam-5136	31	10	where	where	SCONJ
ejpam-5136	31	11	λ	λ	PROPN
ejpam-5136	31	12	∈	∈	PROPN
ejpam-5136	32	1	[	[	X
ejpam-5136	32	2	−0.5	−0.5	PROPN
ejpam-5136	32	3	,	,	PUNCT
ejpam-5136	32	4	1	1	NUM
ejpam-5136	32	5	]	]	PUNCT
ejpam-5136	32	6	.	.	PUNCT
ejpam-5136	33	1	it	it	PRON
ejpam-5136	33	2	was	be	AUX
ejpam-5136	33	3	observed	observe	VERB
ejpam-5136	33	4	that	that	SCONJ
ejpam-5136	33	5	this	this	DET
ejpam-5136	33	6	distribution	distribution	NOUN
ejpam-5136	33	7	can	can	AUX
ejpam-5136	33	8	generate	generate	VERB
ejpam-5136	33	9	three	three	NUM
ejpam-5136	33	10	different	different	ADJ
ejpam-5136	33	11	types	type	NOUN
ejpam-5136	33	12	of	of	ADP
ejpam-5136	33	13	shape	shape	NOUN
ejpam-5136	33	14	for	for	ADP
ejpam-5136	33	15	its	its	PRON
ejpam-5136	33	16	pdf	pdf	NOUN
ejpam-5136	33	17	,	,	PUNCT
ejpam-5136	33	18	namely	namely	ADV
ejpam-5136	33	19	,	,	PUNCT
ejpam-5136	33	20	inverted	inverted	ADJ
ejpam-5136	33	21	bathtub	bathtub	NOUN
ejpam-5136	33	22	for	for	ADP
ejpam-5136	33	23	λ	λ	PROPN
ejpam-5136	33	24	∈	∈	PROPN
ejpam-5136	34	1	[	[	X
ejpam-5136	34	2	−0.5	−0.5	PROPN
ejpam-5136	34	3	,	,	PUNCT
ejpam-5136	34	4	0	0	NUM
ejpam-5136	34	5	)	)	PUNCT
ejpam-5136	34	6	,	,	PUNCT
ejpam-5136	34	7	constant	constant	ADJ
ejpam-5136	34	8	for	for	ADP
ejpam-5136	34	9	λ	λ	X
ejpam-5136	34	10	=	=	SYM
ejpam-5136	34	11	0	0	NUM
ejpam-5136	34	12	and	and	CCONJ
ejpam-5136	34	13	bathtub	bathtub	VERB
ejpam-5136	34	14	for	for	ADP
ejpam-5136	34	15	λ	λ	PROPN
ejpam-5136	34	16	∈	∈	PROPN
ejpam-5136	34	17	(	(	PUNCT
ejpam-5136	34	18	0	0	NUM
ejpam-5136	34	19	,	,	PUNCT
ejpam-5136	34	20	1	1	NUM
ejpam-5136	34	21	]	]	PUNCT
ejpam-5136	34	22	.	.	PUNCT
ejpam-5136	35	1	in	in	ADP
ejpam-5136	35	2	addition	addition	NOUN
ejpam-5136	35	3	,	,	PUNCT
ejpam-5136	35	4	some	some	DET
ejpam-5136	35	5	properties	property	NOUN
ejpam-5136	35	6	of	of	ADP
ejpam-5136	35	7	this	this	DET
ejpam-5136	35	8	distribution	distribution	NOUN
ejpam-5136	35	9	can	can	AUX
ejpam-5136	35	10	be	be	AUX
ejpam-5136	35	11	found	find	VERB
ejpam-5136	35	12	in	in	ADP
ejpam-5136	35	13	the	the	DET
ejpam-5136	35	14	paper	paper	NOUN
ejpam-5136	35	15	of	of	ADP
ejpam-5136	35	16	lakibul	lakibul	PROPN
ejpam-5136	35	17	and	and	CCONJ
ejpam-5136	35	18	tubo	tubo	VERB
ejpam-5136	35	19	[	[	X
ejpam-5136	35	20	3	3	NUM
ejpam-5136	35	21	]	]	PUNCT
ejpam-5136	35	22	.	.	PUNCT
ejpam-5136	36	1	this	this	DET
ejpam-5136	36	2	distribution	distribution	NOUN
ejpam-5136	36	3	can	can	AUX
ejpam-5136	36	4	be	be	AUX
ejpam-5136	36	5	used	use	VERB
ejpam-5136	36	6	as	as	ADP
ejpam-5136	36	7	an	an	DET
ejpam-5136	36	8	alternative	alternative	NOUN
ejpam-5136	36	9	to	to	ADP
ejpam-5136	36	10	the	the	DET
ejpam-5136	36	11	beta	beta	ADJ
ejpam-5136	36	12	distribution	distribution	NOUN
ejpam-5136	36	13	and	and	CCONJ
ejpam-5136	36	14	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	36	15	[	[	X
ejpam-5136	36	16	2	2	NUM
ejpam-5136	36	17	]	]	PUNCT
ejpam-5136	36	18	distribution	distribution	NOUN
ejpam-5136	36	19	for	for	ADP
ejpam-5136	36	20	modeling	model	VERB
ejpam-5136	36	21	data	datum	NOUN
ejpam-5136	36	22	with	with	ADP
ejpam-5136	36	23	support	support	NOUN
ejpam-5136	36	24	on	on	ADP
ejpam-5136	36	25	[	[	X
ejpam-5136	36	26	0	0	NUM
ejpam-5136	36	27	,	,	PUNCT
ejpam-5136	36	28	1	1	NUM
ejpam-5136	36	29	]	]	PUNCT
ejpam-5136	36	30	,	,	PUNCT
ejpam-5136	36	31	particularly	particularly	ADV
ejpam-5136	36	32	,	,	PUNCT
ejpam-5136	36	33	those	those	DET
ejpam-5136	36	34	data	datum	NOUN
ejpam-5136	36	35	follow	follow	VERB
ejpam-5136	36	36	bathtub	bathtub	PROPN
ejpam-5136	36	37	,	,	PUNCT
ejpam-5136	36	38	inverted	inverted	ADJ
ejpam-5136	36	39	bathtub	bathtub	PROPN
ejpam-5136	36	40	,	,	PUNCT
ejpam-5136	36	41	and	and	CCONJ
ejpam-5136	36	42	constant	constant	ADJ
ejpam-5136	36	43	behavior	behavior	NOUN
ejpam-5136	36	44	.	.	PUNCT
ejpam-5136	37	1	however	however	ADV
ejpam-5136	37	2	,	,	PUNCT
ejpam-5136	37	3	if	if	SCONJ
ejpam-5136	37	4	we	we	PRON
ejpam-5136	37	5	want	want	VERB
ejpam-5136	37	6	to	to	PART
ejpam-5136	37	7	model	model	VERB
ejpam-5136	37	8	simultaneously	simultaneously	ADV
ejpam-5136	37	9	two	two	NUM
ejpam-5136	37	10	related	relate	VERB
ejpam-5136	37	11	random	random	ADJ
ejpam-5136	37	12	variables	variable	NOUN
ejpam-5136	37	13	where	where	SCONJ
ejpam-5136	37	14	each	each	PRON
ejpam-5136	37	15	of	of	ADP
ejpam-5136	37	16	the	the	DET
ejpam-5136	37	17	variables	variable	NOUN
ejpam-5136	37	18	has	have	VERB
ejpam-5136	37	19	a	a	DET
ejpam-5136	37	20	bathtub	bathtub	ADJ
ejpam-5136	37	21	shape	shape	NOUN
ejpam-5136	37	22	then	then	ADV
ejpam-5136	37	23	the	the	DET
ejpam-5136	37	24	esu	esu	NOUN
ejpam-5136	37	25	distribution	distribution	NOUN
ejpam-5136	37	26	can	can	AUX
ejpam-5136	37	27	not	not	PART
ejpam-5136	37	28	be	be	AUX
ejpam-5136	37	29	used	use	VERB
ejpam-5136	37	30	.	.	PUNCT
ejpam-5136	38	1	thus	thus	ADV
ejpam-5136	38	2	,	,	PUNCT
ejpam-5136	38	3	there	there	PRON
ejpam-5136	38	4	is	be	VERB
ejpam-5136	38	5	a	a	DET
ejpam-5136	38	6	need	need	NOUN
ejpam-5136	38	7	to	to	PART
ejpam-5136	38	8	extend	extend	VERB
ejpam-5136	38	9	this	this	DET
ejpam-5136	38	10	distribution	distribution	NOUN
ejpam-5136	38	11	into	into	ADP
ejpam-5136	38	12	the	the	DET
ejpam-5136	38	13	bivariate	bivariate	ADJ
ejpam-5136	38	14	case	case	NOUN
ejpam-5136	38	15	.	.	PUNCT
ejpam-5136	39	1	in	in	ADP
ejpam-5136	39	2	this	this	DET
ejpam-5136	39	3	paper	paper	NOUN
ejpam-5136	39	4	,	,	PUNCT
ejpam-5136	39	5	we	we	PRON
ejpam-5136	39	6	will	will	AUX
ejpam-5136	39	7	follow	follow	VERB
ejpam-5136	39	8	the	the	DET
ejpam-5136	39	9	idea	idea	NOUN
ejpam-5136	39	10	of	of	ADP
ejpam-5136	39	11	shahbaz	shahbaz	PROPN
ejpam-5136	39	12	et	et	PROPN
ejpam-5136	39	13	al	al	PROPN
ejpam-5136	39	14	.	.	PUNCT
ejpam-5136	40	1	[	[	X
ejpam-5136	40	2	10	10	NUM
ejpam-5136	40	3	]	]	PUNCT
ejpam-5136	40	4	to	to	PART
ejpam-5136	40	5	expand	expand	VERB
ejpam-5136	40	6	the	the	DET
ejpam-5136	40	7	extended	extended	ADJ
ejpam-5136	40	8	standard	standard	ADJ
ejpam-5136	40	9	u	u	ADJ
ejpam-5136	40	10	-	-	ADJ
ejpam-5136	40	11	quadratic	quadratic	ADJ
ejpam-5136	40	12	distribution	distribution	NOUN
ejpam-5136	40	13	into	into	ADP
ejpam-5136	40	14	a	a	DET
ejpam-5136	40	15	bivariate	bivariate	ADJ
ejpam-5136	40	16	case	case	NOUN
ejpam-5136	40	17	.	.	PUNCT
ejpam-5136	41	1	we	we	PRON
ejpam-5136	41	2	will	will	AUX
ejpam-5136	41	3	also	also	ADV
ejpam-5136	41	4	derive	derive	VERB
ejpam-5136	41	5	some	some	DET
ejpam-5136	41	6	properties	property	NOUN
ejpam-5136	41	7	of	of	ADP
ejpam-5136	41	8	the	the	DET
ejpam-5136	41	9	proposed	propose	VERB
ejpam-5136	41	10	distribution	distribution	NOUN
ejpam-5136	41	11	such	such	ADJ
ejpam-5136	41	12	as	as	ADP
ejpam-5136	41	13	the	the	DET
ejpam-5136	41	14	marginal	marginal	ADJ
ejpam-5136	41	15	distribution	distribution	NOUN
ejpam-5136	41	16	,	,	PUNCT
ejpam-5136	41	17	conditional	conditional	ADJ
ejpam-5136	41	18	distribution	distribution	NOUN
ejpam-5136	41	19	,	,	PUNCT
ejpam-5136	41	20	conditional	conditional	ADJ
ejpam-5136	41	21	moments	moment	NOUN
ejpam-5136	41	22	,	,	PUNCT
ejpam-5136	41	23	product	product	NOUN
ejpam-5136	41	24	and	and	CCONJ
ejpam-5136	41	25	ratio	ratio	NOUN
ejpam-5136	41	26	moments	moment	NOUN
ejpam-5136	41	27	,	,	PUNCT
ejpam-5136	41	28	pearson	pearson	PROPN
ejpam-5136	41	29	correlation	correlation	NOUN
ejpam-5136	41	30	coefficient	coefficient	NOUN
ejpam-5136	41	31	,	,	PUNCT
ejpam-5136	41	32	joint	joint	ADJ
ejpam-5136	41	33	moment	moment	NOUN
ejpam-5136	41	34	generating	generate	VERB
ejpam-5136	41	35	function	function	NOUN
ejpam-5136	41	36	,	,	PUNCT
ejpam-5136	41	37	and	and	CCONJ
ejpam-5136	41	38	the	the	DET
ejpam-5136	41	39	stress	stress	NOUN
ejpam-5136	41	40	strength	strength	NOUN
ejpam-5136	41	41	parameter	parameter	PROPN
ejpam-5136	41	42	.	.	PUNCT
ejpam-5136	42	1	investigation	investigation	NOUN
ejpam-5136	42	2	on	on	ADP
ejpam-5136	42	3	the	the	DET
ejpam-5136	42	4	performance	performance	NOUN
ejpam-5136	42	5	of	of	ADP
ejpam-5136	42	6	the	the	DET
ejpam-5136	42	7	proposed	propose	VERB
ejpam-5136	42	8	distribution	distribution	NOUN
ejpam-5136	42	9	is	be	AUX
ejpam-5136	42	10	done	do	VERB
ejpam-5136	42	11	by	by	ADP
ejpam-5136	42	12	applying	apply	VERB
ejpam-5136	42	13	it	it	PRON
ejpam-5136	42	14	on	on	ADP
ejpam-5136	42	15	a	a	DET
ejpam-5136	42	16	simulated	simulate	VERB
ejpam-5136	42	17	dataset	dataset	NOUN
ejpam-5136	42	18	.	.	PUNCT
ejpam-5136	43	1	the	the	DET
ejpam-5136	43	2	rest	rest	NOUN
ejpam-5136	43	3	of	of	ADP
ejpam-5136	43	4	the	the	DET
ejpam-5136	43	5	paper	paper	NOUN
ejpam-5136	43	6	is	be	AUX
ejpam-5136	43	7	structured	structure	VERB
ejpam-5136	43	8	as	as	SCONJ
ejpam-5136	43	9	follows	follow	VERB
ejpam-5136	43	10	:	:	PUNCT
ejpam-5136	43	11	section	section	NOUN
ejpam-5136	43	12	2	2	NUM
ejpam-5136	43	13	presents	present	VERB
ejpam-5136	43	14	the	the	DET
ejpam-5136	43	15	construction	construction	NOUN
ejpam-5136	43	16	of	of	ADP
ejpam-5136	43	17	the	the	DET
ejpam-5136	43	18	bivariate	bivariate	ADJ
ejpam-5136	43	19	extended	extend	VERB
ejpam-5136	43	20	standard	standard	ADJ
ejpam-5136	43	21	u	u	NOUN
ejpam-5136	43	22	-	-	ADJ
ejpam-5136	43	23	quadratic	quadratic	ADJ
ejpam-5136	43	24	(	(	PUNCT
ejpam-5136	43	25	besu	besu	NOUN
ejpam-5136	43	26	)	)	PUNCT
ejpam-5136	43	27	distribution	distribution	NOUN
ejpam-5136	43	28	.	.	PUNCT
ejpam-5136	44	1	section	section	NOUN
ejpam-5136	44	2	3	3	NUM
ejpam-5136	44	3	provides	provide	VERB
ejpam-5136	44	4	derivations	derivation	NOUN
ejpam-5136	44	5	of	of	ADP
ejpam-5136	44	6	some	some	DET
ejpam-5136	44	7	properties	property	NOUN
ejpam-5136	44	8	of	of	ADP
ejpam-5136	44	9	the	the	DET
ejpam-5136	44	10	proposed	propose	VERB
ejpam-5136	44	11	besu	besu	NOUN
ejpam-5136	44	12	distribution	distribution	NOUN
ejpam-5136	44	13	.	.	PUNCT
ejpam-5136	45	1	section	section	NOUN
ejpam-5136	45	2	4	4	NUM
ejpam-5136	45	3	discusses	discuss	VERB
ejpam-5136	45	4	the	the	DET
ejpam-5136	45	5	maximum	maximum	ADJ
ejpam-5136	45	6	likelihood	likelihood	NOUN
ejpam-5136	45	7	estimation	estimation	NOUN
ejpam-5136	45	8	for	for	ADP
ejpam-5136	45	9	estimating	estimate	VERB
ejpam-5136	45	10	the	the	DET
ejpam-5136	45	11	proposed	propose	VERB
ejpam-5136	45	12	bivariate	bivariate	ADJ
ejpam-5136	45	13	distribution	distribution	NOUN
ejpam-5136	45	14	’s	’s	PART
ejpam-5136	45	15	parameter	parameter	NOUN
ejpam-5136	45	16	.	.	PUNCT
ejpam-5136	46	1	section	section	NOUN
ejpam-5136	46	2	5	5	NUM
ejpam-5136	46	3	deals	deal	NOUN
ejpam-5136	46	4	with	with	ADP
ejpam-5136	46	5	the	the	DET
ejpam-5136	46	6	random	random	ADJ
ejpam-5136	46	7	number	number	NOUN
ejpam-5136	46	8	generation	generation	NOUN
ejpam-5136	46	9	of	of	ADP
ejpam-5136	46	10	the	the	DET
ejpam-5136	46	11	proposed	propose	VERB
ejpam-5136	46	12	bivariate	bivariate	ADJ
ejpam-5136	46	13	distribution	distribution	NOUN
ejpam-5136	46	14	.	.	PUNCT
ejpam-5136	47	1	section	section	NOUN
ejpam-5136	47	2	6	6	NUM
ejpam-5136	47	3	presents	present	VERB
ejpam-5136	47	4	the	the	DET
ejpam-5136	47	5	simulation	simulation	NOUN
ejpam-5136	47	6	results	result	VERB
ejpam-5136	47	7	for	for	ADP
ejpam-5136	47	8	assessing	assess	VERB
ejpam-5136	47	9	the	the	DET
ejpam-5136	47	10	behavior	behavior	NOUN
ejpam-5136	47	11	of	of	ADP
ejpam-5136	47	12	the	the	DET
ejpam-5136	47	13	maximum	maximum	ADJ
ejpam-5136	47	14	likelihood	likelihood	NOUN
ejpam-5136	47	15	estimate	estimate	NOUN
ejpam-5136	47	16	of	of	ADP
ejpam-5136	47	17	the	the	DET
ejpam-5136	47	18	proposed	propose	VERB
ejpam-5136	47	19	bivariate	bivariate	ADJ
ejpam-5136	47	20	distribution	distribution	NOUN
ejpam-5136	47	21	’s	’s	PART
ejpam-5136	47	22	parameter	parameter	NOUN
ejpam-5136	47	23	.	.	PUNCT
ejpam-5136	48	1	section	section	PROPN
ejpam-5136	48	2	i.	i.	PROPN
ejpam-5136	48	3	a.	a.	PROPN
ejpam-5136	48	4	lakibul	lakibul	PROPN
ejpam-5136	48	5	,	,	PUNCT
ejpam-5136	48	6	d.	d.	PROPN
ejpam-5136	48	7	l.	l.	PROPN
ejpam-5136	48	8	polestico	polestico	PROPN
ejpam-5136	48	9	,	,	PUNCT
ejpam-5136	48	10	a.	a.	PROPN
ejpam-5136	48	11	p.	p.	NOUN
ejpam-5136	48	12	supe	supe	PROPN
ejpam-5136	48	13	/	/	SYM
ejpam-5136	48	14	eur	eur	PROPN
ejpam-5136	48	15	.	.	PUNCT
ejpam-5136	49	1	j.	j.	PROPN
ejpam-5136	49	2	pure	pure	PROPN
ejpam-5136	49	3	appl	appl	PROPN
ejpam-5136	49	4	.	.	PROPN
ejpam-5136	49	5	math	math	PROPN
ejpam-5136	49	6	,	,	PUNCT
ejpam-5136	49	7	17	17	NUM
ejpam-5136	49	8	(	(	PUNCT
ejpam-5136	49	9	2	2	NUM
ejpam-5136	49	10	)	)	PUNCT
ejpam-5136	49	11	(	(	PUNCT
ejpam-5136	49	12	2024	2024	NUM
ejpam-5136	49	13	)	)	PUNCT
ejpam-5136	49	14	,	,	PUNCT
ejpam-5136	49	15	790	790	NUM
ejpam-5136	49	16	-	-	SYM
ejpam-5136	49	17	809	809	NUM
ejpam-5136	49	18	792	792	NUM
ejpam-5136	49	19	7	7	NUM
ejpam-5136	49	20	presents	present	VERB
ejpam-5136	49	21	the	the	DET
ejpam-5136	49	22	application	application	NOUN
ejpam-5136	49	23	of	of	ADP
ejpam-5136	49	24	the	the	DET
ejpam-5136	49	25	proposed	propose	VERB
ejpam-5136	49	26	bivariate	bivariate	ADJ
ejpam-5136	49	27	distribution	distribution	NOUN
ejpam-5136	49	28	on	on	ADP
ejpam-5136	49	29	a	a	DET
ejpam-5136	49	30	simulated	simulate	VERB
ejpam-5136	49	31	dataset	dataset	NOUN
ejpam-5136	49	32	.	.	PUNCT
ejpam-5136	50	1	section	section	NOUN
ejpam-5136	50	2	8	8	NUM
ejpam-5136	50	3	gives	give	VERB
ejpam-5136	50	4	some	some	DET
ejpam-5136	50	5	concluding	conclude	VERB
ejpam-5136	50	6	remarks	remark	NOUN
ejpam-5136	50	7	about	about	ADP
ejpam-5136	50	8	the	the	DET
ejpam-5136	50	9	paper	paper	NOUN
ejpam-5136	50	10	and	and	CCONJ
ejpam-5136	50	11	recommendations	recommendation	NOUN
ejpam-5136	50	12	for	for	ADP
ejpam-5136	50	13	future	future	ADJ
ejpam-5136	50	14	studies	study	NOUN
ejpam-5136	50	15	.	.	PUNCT
ejpam-5136	51	1	2	2	X
ejpam-5136	51	2	.	.	X
ejpam-5136	51	3	the	the	DET
ejpam-5136	51	4	bivariate	bivariate	ADJ
ejpam-5136	51	5	extended	extended	ADJ
ejpam-5136	51	6	standard	standard	ADJ
ejpam-5136	51	7	u	u	ADJ
ejpam-5136	51	8	-	-	ADJ
ejpam-5136	51	9	quadratic	quadratic	ADJ
ejpam-5136	51	10	distribution	distribution	NOUN
ejpam-5136	51	11	this	this	DET
ejpam-5136	51	12	section	section	NOUN
ejpam-5136	51	13	presents	present	VERB
ejpam-5136	51	14	the	the	DET
ejpam-5136	51	15	derivation	derivation	NOUN
ejpam-5136	51	16	of	of	ADP
ejpam-5136	51	17	the	the	DET
ejpam-5136	51	18	new	new	ADJ
ejpam-5136	51	19	bivariate	bivariate	ADJ
ejpam-5136	51	20	distribution	distribution	NOUN
ejpam-5136	51	21	with	with	ADP
ejpam-5136	51	22	support	support	NOUN
ejpam-5136	51	23	on	on	ADP
ejpam-5136	51	24	[	[	X
ejpam-5136	51	25	0	0	NUM
ejpam-5136	51	26	,	,	PUNCT
ejpam-5136	51	27	1]×	1]×	NUM
ejpam-5136	51	28	[	[	X
ejpam-5136	51	29	0	0	NUM
ejpam-5136	51	30	,	,	PUNCT
ejpam-5136	51	31	1	1	NUM
ejpam-5136	51	32	]	]	PUNCT
ejpam-5136	51	33	.	.	PUNCT
ejpam-5136	52	1	letx	letx	PROPN
ejpam-5136	52	2	be	be	AUX
ejpam-5136	52	3	a	a	DET
ejpam-5136	52	4	random	random	ADJ
ejpam-5136	52	5	variable	variable	NOUN
ejpam-5136	52	6	that	that	PRON
ejpam-5136	52	7	follows	follow	VERB
ejpam-5136	52	8	an	an	DET
ejpam-5136	52	9	extended	extended	ADJ
ejpam-5136	52	10	standard	standard	ADJ
ejpam-5136	52	11	u	u	ADJ
ejpam-5136	52	12	-	-	ADJ
ejpam-5136	52	13	quadratic	quadratic	ADJ
ejpam-5136	52	14	distribution	distribution	NOUN
ejpam-5136	52	15	with	with	ADP
ejpam-5136	52	16	pdf	pdf	NOUN
ejpam-5136	52	17	given	give	VERB
ejpam-5136	52	18	in	in	ADP
ejpam-5136	52	19	equation	equation	NOUN
ejpam-5136	52	20	(	(	PUNCT
ejpam-5136	52	21	1	1	NUM
ejpam-5136	52	22	)	)	PUNCT
ejpam-5136	52	23	.	.	PUNCT
ejpam-5136	53	1	let	let	VERB
ejpam-5136	53	2	y	y	PRON
ejpam-5136	53	3	be	be	AUX
ejpam-5136	53	4	another	another	DET
ejpam-5136	53	5	random	random	ADJ
ejpam-5136	53	6	variable	variable	NOUN
ejpam-5136	53	7	such	such	ADJ
ejpam-5136	53	8	that	that	SCONJ
ejpam-5136	53	9	the	the	DET
ejpam-5136	53	10	conditional	conditional	ADJ
ejpam-5136	53	11	probability	probability	NOUN
ejpam-5136	53	12	density	density	NOUN
ejpam-5136	53	13	function	function	NOUN
ejpam-5136	53	14	of	of	ADP
ejpam-5136	53	15	y	y	PROPN
ejpam-5136	53	16	given	give	VERB
ejpam-5136	53	17	x	x	PUNCT
ejpam-5136	53	18	=	=	PUNCT
ejpam-5136	53	19	x	x	PRON
ejpam-5136	53	20	follows	follow	VERB
ejpam-5136	53	21	an	an	DET
ejpam-5136	53	22	extended	extended	ADJ
ejpam-5136	53	23	standard	standard	ADJ
ejpam-5136	53	24	u	u	ADJ
ejpam-5136	53	25	-	-	ADJ
ejpam-5136	53	26	quadratic	quadratic	ADJ
ejpam-5136	53	27	distribution	distribution	NOUN
ejpam-5136	53	28	,	,	PUNCT
ejpam-5136	53	29	that	that	ADV
ejpam-5136	53	30	is	is	ADV
ejpam-5136	53	31	,	,	PUNCT
ejpam-5136	53	32	f(y|x	f(y|x	NOUN
ejpam-5136	53	33	)	)	PUNCT
ejpam-5136	53	34	=	=	SYM
ejpam-5136	54	1	1−	1−	NUM
ejpam-5136	54	2	v(x	v(x	NOUN
ejpam-5136	54	3	)	)	PUNCT
ejpam-5136	55	1	+	+	CCONJ
ejpam-5136	56	1	3v(x)(2y	3v(x)(2y	PROPN
ejpam-5136	56	2	−	−	PROPN
ejpam-5136	57	1	1)2	1)2	NUM
ejpam-5136	57	2	,	,	PUNCT
ejpam-5136	57	3	y	y	PROPN
ejpam-5136	57	4	∈	∈	PROPN
ejpam-5136	58	1	[	[	X
ejpam-5136	58	2	0	0	NUM
ejpam-5136	58	3	,	,	PUNCT
ejpam-5136	58	4	1	1	NUM
ejpam-5136	58	5	]	]	PUNCT
ejpam-5136	58	6	,	,	PUNCT
ejpam-5136	58	7	(	(	PUNCT
ejpam-5136	58	8	2	2	X
ejpam-5136	58	9	)	)	PUNCT
ejpam-5136	58	10	where	where	SCONJ
ejpam-5136	58	11	v(x	v(x	NOUN
ejpam-5136	58	12	)	)	PUNCT
ejpam-5136	58	13	∈	∈	PROPN
ejpam-5136	59	1	[	[	X
ejpam-5136	59	2	−0.5	−0.5	PROPN
ejpam-5136	59	3	,	,	PUNCT
ejpam-5136	59	4	1	1	NUM
ejpam-5136	59	5	]	]	PUNCT
ejpam-5136	59	6	.	.	PUNCT
ejpam-5136	60	1	following	follow	VERB
ejpam-5136	60	2	the	the	DET
ejpam-5136	60	3	idea	idea	NOUN
ejpam-5136	60	4	of	of	ADP
ejpam-5136	60	5	shahbaz	shahbaz	PROPN
ejpam-5136	60	6	[	[	X
ejpam-5136	60	7	10	10	NUM
ejpam-5136	60	8	]	]	PUNCT
ejpam-5136	60	9	and	and	CCONJ
ejpam-5136	60	10	by	by	ADP
ejpam-5136	60	11	the	the	DET
ejpam-5136	60	12	definition	definition	NOUN
ejpam-5136	60	13	of	of	ADP
ejpam-5136	60	14	the	the	DET
ejpam-5136	60	15	conditional	conditional	ADJ
ejpam-5136	60	16	probability	probability	NOUN
ejpam-5136	60	17	,	,	PUNCT
ejpam-5136	60	18	the	the	DET
ejpam-5136	60	19	joint	joint	ADJ
ejpam-5136	60	20	probability	probability	NOUN
ejpam-5136	60	21	distribution	distribution	NOUN
ejpam-5136	60	22	function	function	NOUN
ejpam-5136	60	23	of	of	ADP
ejpam-5136	60	24	x	x	PUNCT
ejpam-5136	60	25	and	and	CCONJ
ejpam-5136	60	26	y	y	PROPN
ejpam-5136	60	27	is	be	AUX
ejpam-5136	60	28	given	give	VERB
ejpam-5136	60	29	by	by	ADP
ejpam-5136	60	30	f(x	f(x	PROPN
ejpam-5136	60	31	,	,	PUNCT
ejpam-5136	60	32	y	y	NOUN
ejpam-5136	60	33	)	)	PUNCT
ejpam-5136	60	34	=	=	PUNCT
ejpam-5136	61	1	[	[	PUNCT
ejpam-5136	61	2	1−	1−	NUM
ejpam-5136	61	3	v(x	v(x	NOUN
ejpam-5136	61	4	)	)	PUNCT
ejpam-5136	62	1	+	+	CCONJ
ejpam-5136	63	1	3v(x)(2y	3v(x)(2y	ADJ
ejpam-5136	63	2	−	−	PROPN
ejpam-5136	64	1	1)2	1)2	NUM
ejpam-5136	64	2	]	]	PUNCT
ejpam-5136	65	1	[	[	PUNCT
ejpam-5136	65	2	1−	1−	NUM
ejpam-5136	65	3	λ+	λ+	PUNCT
ejpam-5136	65	4	3λ(2x−	3λ(2x−	NUM
ejpam-5136	65	5	1)2	1)2	NUM
ejpam-5136	65	6	]	]	PUNCT
ejpam-5136	65	7	.	.	PUNCT
ejpam-5136	66	1	note	note	VERB
ejpam-5136	66	2	that	that	SCONJ
ejpam-5136	66	3	,	,	PUNCT
ejpam-5136	66	4	v(x	v(x	PROPN
ejpam-5136	66	5	)	)	PUNCT
ejpam-5136	66	6	∈	∈	PROPN
ejpam-5136	67	1	[	[	X
ejpam-5136	67	2	−0.5	−0.5	PROPN
ejpam-5136	67	3	,	,	PUNCT
ejpam-5136	67	4	1	1	NUM
ejpam-5136	67	5	]	]	PUNCT
ejpam-5136	67	6	,	,	PUNCT
ejpam-5136	67	7	then	then	ADV
ejpam-5136	67	8	v(x	v(x	PROPN
ejpam-5136	67	9	)	)	PUNCT
ejpam-5136	67	10	can	can	AUX
ejpam-5136	67	11	be	be	AUX
ejpam-5136	67	12	defined	define	VERB
ejpam-5136	67	13	in	in	ADP
ejpam-5136	67	14	many	many	ADJ
ejpam-5136	67	15	ways	way	NOUN
ejpam-5136	67	16	.	.	PUNCT
ejpam-5136	68	1	for	for	ADP
ejpam-5136	68	2	example	example	NOUN
ejpam-5136	68	3	,	,	PUNCT
ejpam-5136	68	4	for	for	ADP
ejpam-5136	68	5	x	x	PROPN
ejpam-5136	68	6	∈	∈	PROPN
ejpam-5136	69	1	[	[	X
ejpam-5136	69	2	0	0	NUM
ejpam-5136	69	3	,	,	PUNCT
ejpam-5136	69	4	1	1	NUM
ejpam-5136	69	5	]	]	PUNCT
ejpam-5136	69	6	,	,	PUNCT
ejpam-5136	69	7	v(x	v(x	PROPN
ejpam-5136	69	8	)	)	PUNCT
ejpam-5136	69	9	can	can	AUX
ejpam-5136	69	10	be	be	AUX
ejpam-5136	69	11	defined	define	VERB
ejpam-5136	69	12	as	as	ADP
ejpam-5136	69	13	v(x	v(x	NOUN
ejpam-5136	69	14	)	)	PUNCT
ejpam-5136	70	1	=	=	SYM
ejpam-5136	70	2	1.5xτ−0.5	1.5xτ−0.5	NUM
ejpam-5136	70	3	,	,	PUNCT
ejpam-5136	70	4	τ	τ	PROPN
ejpam-5136	70	5	>	>	X
ejpam-5136	70	6	0	0	NUM
ejpam-5136	70	7	or	or	CCONJ
ejpam-5136	70	8	v(x	v(x	NUM
ejpam-5136	70	9	)	)	PUNCT
ejpam-5136	71	1	=	=	SYM
ejpam-5136	71	2	1.5(1−(1−x)a)b−0.5	1.5(1−(1−x)a)b−0.5	NUM
ejpam-5136	71	3	,	,	PUNCT
ejpam-5136	71	4	a	a	PRON
ejpam-5136	71	5	>	>	X
ejpam-5136	71	6	0	0	NUM
ejpam-5136	71	7	,	,	PUNCT
ejpam-5136	71	8	b	b	X
ejpam-5136	71	9	>	>	X
ejpam-5136	71	10	0	0	NUM
ejpam-5136	71	11	.	.	PUNCT
ejpam-5136	72	1	in	in	ADP
ejpam-5136	72	2	this	this	DET
ejpam-5136	72	3	paper	paper	NOUN
ejpam-5136	72	4	,	,	PUNCT
ejpam-5136	72	5	we	we	PRON
ejpam-5136	72	6	focus	focus	VERB
ejpam-5136	72	7	on	on	ADP
ejpam-5136	72	8	the	the	DET
ejpam-5136	72	9	special	special	ADJ
ejpam-5136	72	10	case	case	NOUN
ejpam-5136	72	11	where	where	SCONJ
ejpam-5136	72	12	we	we	PRON
ejpam-5136	72	13	have	have	VERB
ejpam-5136	72	14	no	no	DET
ejpam-5136	72	15	additional	additional	ADJ
ejpam-5136	72	16	parameter	parameter	NOUN
ejpam-5136	72	17	in	in	ADP
ejpam-5136	72	18	the	the	DET
ejpam-5136	72	19	model	model	NOUN
ejpam-5136	72	20	to	to	PART
ejpam-5136	72	21	have	have	VERB
ejpam-5136	72	22	a	a	DET
ejpam-5136	72	23	simple	simple	ADJ
ejpam-5136	72	24	bivariate	bivariate	ADJ
ejpam-5136	72	25	model	model	NOUN
ejpam-5136	72	26	with	with	ADP
ejpam-5136	72	27	a	a	DET
ejpam-5136	72	28	single	single	ADJ
ejpam-5136	72	29	parameter	parameter	NOUN
ejpam-5136	72	30	.	.	PUNCT
ejpam-5136	73	1	a	a	DET
ejpam-5136	73	2	simple	simple	ADJ
ejpam-5136	73	3	bivariate	bivariate	ADJ
ejpam-5136	73	4	model	model	NOUN
ejpam-5136	73	5	with	with	ADP
ejpam-5136	73	6	a	a	DET
ejpam-5136	73	7	single	single	ADJ
ejpam-5136	73	8	parameter	parameter	NOUN
ejpam-5136	73	9	is	be	AUX
ejpam-5136	73	10	usually	usually	ADV
ejpam-5136	73	11	preferred	prefer	VERB
ejpam-5136	73	12	for	for	ADP
ejpam-5136	73	13	modeling	model	VERB
ejpam-5136	73	14	some	some	DET
ejpam-5136	73	15	bivariate	bivariate	ADJ
ejpam-5136	73	16	data	datum	NOUN
ejpam-5136	73	17	than	than	ADP
ejpam-5136	73	18	a	a	DET
ejpam-5136	73	19	bivariate	bivariate	ADJ
ejpam-5136	73	20	model	model	NOUN
ejpam-5136	73	21	with	with	ADP
ejpam-5136	73	22	more	more	ADJ
ejpam-5136	73	23	parameters	parameter	NOUN
ejpam-5136	73	24	because	because	SCONJ
ejpam-5136	73	25	sometimes	sometimes	ADV
ejpam-5136	73	26	a	a	DET
ejpam-5136	73	27	model	model	NOUN
ejpam-5136	73	28	with	with	ADP
ejpam-5136	73	29	more	more	ADJ
ejpam-5136	73	30	parameters	parameter	NOUN
ejpam-5136	73	31	will	will	AUX
ejpam-5136	73	32	over	over	AUX
ejpam-5136	73	33	parameterize	parameterize	VERB
ejpam-5136	73	34	the	the	DET
ejpam-5136	73	35	data	datum	NOUN
ejpam-5136	73	36	.	.	PUNCT
ejpam-5136	74	1	hence	hence	ADV
ejpam-5136	74	2	,	,	PUNCT
ejpam-5136	74	3	we	we	PRON
ejpam-5136	74	4	define	define	VERB
ejpam-5136	74	5	v(x	v(x	NOUN
ejpam-5136	74	6	)	)	PUNCT
ejpam-5136	74	7	as	as	ADP
ejpam-5136	74	8	v(x	v(x	NOUN
ejpam-5136	74	9	)	)	PUNCT
ejpam-5136	75	1	=	=	SYM
ejpam-5136	75	2	1.5x	1.5x	NUM
ejpam-5136	75	3	−	−	NOUN
ejpam-5136	75	4	0.5	0.5	NUM
ejpam-5136	75	5	,	,	PUNCT
ejpam-5136	75	6	where	where	SCONJ
ejpam-5136	76	1	x	x	PUNCT
ejpam-5136	76	2	∈	∈	PROPN
ejpam-5136	77	1	[	[	X
ejpam-5136	77	2	0	0	NUM
ejpam-5136	77	3	,	,	PUNCT
ejpam-5136	77	4	1	1	NUM
ejpam-5136	77	5	]	]	PUNCT
ejpam-5136	77	6	.	.	PUNCT
ejpam-5136	78	1	thus	thus	ADV
ejpam-5136	78	2	,	,	PUNCT
ejpam-5136	78	3	the	the	DET
ejpam-5136	78	4	joint	joint	ADJ
ejpam-5136	78	5	pdf	pdf	NOUN
ejpam-5136	78	6	of	of	ADP
ejpam-5136	78	7	x	x	PUNCT
ejpam-5136	78	8	and	and	CCONJ
ejpam-5136	78	9	y	y	PROPN
ejpam-5136	78	10	is	be	AUX
ejpam-5136	78	11	given	give	VERB
ejpam-5136	78	12	by	by	ADP
ejpam-5136	78	13	f(x	f(x	PROPN
ejpam-5136	78	14	,	,	PUNCT
ejpam-5136	78	15	y	y	NOUN
ejpam-5136	78	16	)	)	PUNCT
ejpam-5136	78	17	=	=	PUNCT
ejpam-5136	79	1	[	[	PUNCT
ejpam-5136	79	2	1.5−	1.5−	NUM
ejpam-5136	79	3	1.5x+	1.5x+	NUM
ejpam-5136	79	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	79	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	79	6	−	−	PROPN
ejpam-5136	79	7	1)2	1)2	NUM
ejpam-5136	79	8	]	]	PUNCT
ejpam-5136	79	9	[	[	PUNCT
ejpam-5136	79	10	1−	1−	NUM
ejpam-5136	79	11	λ+	λ+	PUNCT
ejpam-5136	79	12	3λ(2x−	3λ(2x−	NUM
ejpam-5136	79	13	1)2	1)2	NUM
ejpam-5136	79	14	]	]	PUNCT
ejpam-5136	79	15	.	.	PUNCT
ejpam-5136	80	1	definition	definition	NOUN
ejpam-5136	80	2	1	1	NUM
ejpam-5136	80	3	.	.	PUNCT
ejpam-5136	81	1	a	a	DET
ejpam-5136	81	2	bivariate	bivariate	ADJ
ejpam-5136	81	3	random	random	ADJ
ejpam-5136	81	4	vector	vector	NOUN
ejpam-5136	81	5	(	(	PUNCT
ejpam-5136	81	6	x	x	X
ejpam-5136	81	7	,	,	PUNCT
ejpam-5136	81	8	y	y	PROPN
ejpam-5136	81	9	)	)	PUNCT
ejpam-5136	81	10	is	be	AUX
ejpam-5136	81	11	said	say	VERB
ejpam-5136	81	12	to	to	PART
ejpam-5136	81	13	have	have	VERB
ejpam-5136	81	14	a	a	DET
ejpam-5136	81	15	bivariate	bivariate	ADJ
ejpam-5136	81	16	extended	extend	VERB
ejpam-5136	81	17	standard	standard	ADJ
ejpam-5136	81	18	u	u	NOUN
ejpam-5136	81	19	-	-	ADJ
ejpam-5136	81	20	quadratic	quadratic	ADJ
ejpam-5136	81	21	(	(	PUNCT
ejpam-5136	81	22	besu	besu	NOUN
ejpam-5136	81	23	)	)	PUNCT
ejpam-5136	81	24	distribution	distribution	NOUN
ejpam-5136	81	25	if	if	SCONJ
ejpam-5136	81	26	the	the	DET
ejpam-5136	81	27	joint	joint	ADJ
ejpam-5136	81	28	pdf	pdf	NOUN
ejpam-5136	81	29	of	of	ADP
ejpam-5136	81	30	x	x	PUNCT
ejpam-5136	81	31	and	and	CCONJ
ejpam-5136	81	32	y	y	PROPN
ejpam-5136	81	33	is	be	AUX
ejpam-5136	81	34	given	give	VERB
ejpam-5136	81	35	by	by	ADP
ejpam-5136	81	36	f(x	f(x	PROPN
ejpam-5136	81	37	,	,	PUNCT
ejpam-5136	81	38	y	y	NOUN
ejpam-5136	81	39	)	)	PUNCT
ejpam-5136	81	40	=	=	PUNCT
ejpam-5136	82	1	[	[	PUNCT
ejpam-5136	82	2	1.5−	1.5−	NUM
ejpam-5136	82	3	1.5x+	1.5x+	NUM
ejpam-5136	82	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	82	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	82	6	−	−	PROPN
ejpam-5136	82	7	1)2	1)2	NUM
ejpam-5136	82	8	]	]	PUNCT
ejpam-5136	82	9	[	[	PUNCT
ejpam-5136	82	10	1−	1−	NUM
ejpam-5136	82	11	λ+	λ+	PUNCT
ejpam-5136	82	12	3λ(2x−	3λ(2x−	NUM
ejpam-5136	82	13	1)2	1)2	NUM
ejpam-5136	82	14	]	]	PUNCT
ejpam-5136	82	15	,	,	PUNCT
ejpam-5136	82	16	(	(	PUNCT
ejpam-5136	82	17	3	3	X
ejpam-5136	82	18	)	)	PUNCT
ejpam-5136	82	19	where	where	SCONJ
ejpam-5136	82	20	0	0	NUM
ejpam-5136	82	21	≤	≤	NOUN
ejpam-5136	82	22	(	(	PUNCT
ejpam-5136	82	23	x	x	X
ejpam-5136	82	24	,	,	PUNCT
ejpam-5136	82	25	y	y	NOUN
ejpam-5136	82	26	)	)	PUNCT
ejpam-5136	82	27	≤	≤	NOUN
ejpam-5136	82	28	1	1	NUM
ejpam-5136	82	29	and	and	CCONJ
ejpam-5136	82	30	λ	λ	X
ejpam-5136	82	31	∈	∈	PROPN
ejpam-5136	83	1	[	[	X
ejpam-5136	83	2	−0.5	−0.5	PROPN
ejpam-5136	83	3	,	,	PUNCT
ejpam-5136	83	4	1	1	NUM
ejpam-5136	83	5	]	]	PUNCT
ejpam-5136	83	6	.	.	PUNCT
ejpam-5136	84	1	theorem	theorem	NOUN
ejpam-5136	84	2	1	1	X
ejpam-5136	84	3	.	.	PUNCT
ejpam-5136	85	1	let	let	AUX
ejpam-5136	85	2	(	(	PUNCT
ejpam-5136	85	3	x	x	X
ejpam-5136	85	4	,	,	PUNCT
ejpam-5136	85	5	y	y	PROPN
ejpam-5136	85	6	)	)	PUNCT
ejpam-5136	85	7	be	be	AUX
ejpam-5136	85	8	the	the	DET
ejpam-5136	85	9	bivariate	bivariate	ADJ
ejpam-5136	85	10	random	random	ADJ
ejpam-5136	85	11	vector	vector	NOUN
ejpam-5136	85	12	with	with	ADP
ejpam-5136	85	13	joint	joint	ADJ
ejpam-5136	85	14	pdf	pdf	NOUN
ejpam-5136	85	15	given	give	VERB
ejpam-5136	85	16	in	in	ADP
ejpam-5136	85	17	equation	equation	NOUN
ejpam-5136	85	18	(	(	PUNCT
ejpam-5136	85	19	3	3	NUM
ejpam-5136	85	20	)	)	PUNCT
ejpam-5136	85	21	,	,	PUNCT
ejpam-5136	85	22	then	then	ADV
ejpam-5136	85	23	the	the	DET
ejpam-5136	85	24	joint	joint	ADJ
ejpam-5136	85	25	cdf	cdf	PROPN
ejpam-5136	85	26	of	of	ADP
ejpam-5136	85	27	(	(	PUNCT
ejpam-5136	85	28	x	x	PROPN
ejpam-5136	85	29	,	,	PUNCT
ejpam-5136	85	30	y	y	PROPN
ejpam-5136	85	31	)	)	PUNCT
ejpam-5136	85	32	is	be	AUX
ejpam-5136	85	33	given	give	VERB
ejpam-5136	85	34	by	by	ADP
ejpam-5136	85	35	f	f	PROPN
ejpam-5136	85	36	(	(	PUNCT
ejpam-5136	85	37	x	x	PROPN
ejpam-5136	85	38	,	,	PUNCT
ejpam-5136	85	39	y	y	NOUN
ejpam-5136	85	40	)	)	PUNCT
ejpam-5136	85	41	=	=	SYM
ejpam-5136	86	1	3y	3y	NUM
ejpam-5136	86	2	(	(	PUNCT
ejpam-5136	86	3	2y2	2y2	NUM
ejpam-5136	86	4	−	−	NOUN
ejpam-5136	86	5	3y	3y	NUM
ejpam-5136	86	6	+	+	NOUN
ejpam-5136	86	7	1	1	X
ejpam-5136	86	8	)	)	PUNCT
ejpam-5136	86	9	m(x)−	m(x)−	NOUN
ejpam-5136	86	10	(	(	PUNCT
ejpam-5136	86	11	2y	2y	PROPN
ejpam-5136	86	12	−	−	PROPN
ejpam-5136	86	13	3)y2f	3)y2f	NUM
ejpam-5136	86	14	(	(	PUNCT
ejpam-5136	86	15	x	x	NOUN
ejpam-5136	86	16	)	)	PUNCT
ejpam-5136	86	17	,	,	PUNCT
ejpam-5136	86	18	(	(	PUNCT
ejpam-5136	86	19	4	4	X
ejpam-5136	86	20	)	)	PUNCT
ejpam-5136	86	21	where	where	SCONJ
ejpam-5136	86	22	m(x	m(x	X
ejpam-5136	86	23	)	)	PUNCT
ejpam-5136	86	24	=	=	PUNCT
ejpam-5136	87	1	(	(	PUNCT
ejpam-5136	87	2	1	1	NUM
ejpam-5136	87	3	+	+	NUM
ejpam-5136	87	4	2λ	2λ	NOUN
ejpam-5136	87	5	)	)	PUNCT
ejpam-5136	87	6	2	2	NUM
ejpam-5136	87	7	x2	x2	NOUN
ejpam-5136	87	8	−	−	PROPN
ejpam-5136	87	9	4λx3	4λx3	NUM
ejpam-5136	87	10	+	+	CCONJ
ejpam-5136	87	11	3λx4	3λx4	NUM
ejpam-5136	87	12	,	,	PUNCT
ejpam-5136	87	13	and	and	CCONJ
ejpam-5136	87	14	f	f	PROPN
ejpam-5136	87	15	(	(	PUNCT
ejpam-5136	87	16	x	x	X
ejpam-5136	87	17	)	)	PUNCT
ejpam-5136	87	18	=	=	SYM
ejpam-5136	88	1	(	(	PUNCT
ejpam-5136	88	2	1	1	NUM
ejpam-5136	88	3	+	+	NUM
ejpam-5136	88	4	2λ)x−	2λ)x−	NUM
ejpam-5136	88	5	6λx2	6λx2	NUM
ejpam-5136	88	6	+	+	SYM
ejpam-5136	88	7	4λx3	4λx3	NUM
ejpam-5136	88	8	.	.	PUNCT
ejpam-5136	88	9	i.	i.	PROPN
ejpam-5136	88	10	a.	a.	PROPN
ejpam-5136	88	11	lakibul	lakibul	PROPN
ejpam-5136	88	12	,	,	PUNCT
ejpam-5136	88	13	d.	d.	PROPN
ejpam-5136	88	14	l.	l.	PROPN
ejpam-5136	88	15	polestico	polestico	PROPN
ejpam-5136	88	16	,	,	PUNCT
ejpam-5136	88	17	a.	a.	PROPN
ejpam-5136	88	18	p.	p.	NOUN
ejpam-5136	88	19	supe	supe	PROPN
ejpam-5136	88	20	/	/	SYM
ejpam-5136	88	21	eur	eur	PROPN
ejpam-5136	88	22	.	.	PUNCT
ejpam-5136	89	1	j.	j.	PROPN
ejpam-5136	89	2	pure	pure	PROPN
ejpam-5136	89	3	appl	appl	PROPN
ejpam-5136	89	4	.	.	PROPN
ejpam-5136	89	5	math	math	PROPN
ejpam-5136	89	6	,	,	PUNCT
ejpam-5136	89	7	17	17	NUM
ejpam-5136	89	8	(	(	PUNCT
ejpam-5136	89	9	2	2	NUM
ejpam-5136	89	10	)	)	PUNCT
ejpam-5136	89	11	(	(	PUNCT
ejpam-5136	89	12	2024	2024	NUM
ejpam-5136	89	13	)	)	PUNCT
ejpam-5136	89	14	,	,	PUNCT
ejpam-5136	89	15	790	790	NUM
ejpam-5136	89	16	-	-	SYM
ejpam-5136	89	17	809	809	NUM
ejpam-5136	89	18	793	793	NUM
ejpam-5136	89	19	proof	proof	NOUN
ejpam-5136	89	20	.	.	PUNCT
ejpam-5136	90	1	the	the	DET
ejpam-5136	90	2	joint	joint	ADJ
ejpam-5136	90	3	cumulative	cumulative	ADJ
ejpam-5136	90	4	distribution	distribution	NOUN
ejpam-5136	90	5	function	function	NOUN
ejpam-5136	90	6	of	of	ADP
ejpam-5136	90	7	x	x	PUNCT
ejpam-5136	90	8	and	and	CCONJ
ejpam-5136	90	9	y	y	PROPN
ejpam-5136	90	10	is	be	AUX
ejpam-5136	90	11	defined	define	VERB
ejpam-5136	90	12	as	as	ADP
ejpam-5136	90	13	f	f	PROPN
ejpam-5136	90	14	(	(	PUNCT
ejpam-5136	90	15	x	x	PROPN
ejpam-5136	90	16	,	,	PUNCT
ejpam-5136	90	17	y	y	NOUN
ejpam-5136	90	18	)	)	PUNCT
ejpam-5136	90	19	=	=	SYM
ejpam-5136	91	1	∫	∫	PUNCT
ejpam-5136	91	2	x	x	SYM
ejpam-5136	91	3	0	0	NUM
ejpam-5136	91	4	∫	∫	PROPN
ejpam-5136	91	5	y	y	PROPN
ejpam-5136	91	6	0	0	PROPN
ejpam-5136	91	7	f(u	f(u	PROPN
ejpam-5136	91	8	,	,	PUNCT
ejpam-5136	91	9	v)dvdu	v)dvdu	PROPN
ejpam-5136	91	10	=	=	SYM
ejpam-5136	92	1	∫	∫	PROPN
ejpam-5136	92	2	x	x	SYM
ejpam-5136	92	3	0	0	PROPN
ejpam-5136	92	4	f(u	f(u	PROPN
ejpam-5136	92	5	)	)	PUNCT
ejpam-5136	93	1	[	[	X
ejpam-5136	93	2	∫	∫	X
ejpam-5136	93	3	y	y	PROPN
ejpam-5136	93	4	0	0	NUM
ejpam-5136	93	5	f(v|u)dv	f(v|u)dv	PROPN
ejpam-5136	93	6	]	]	PUNCT
ejpam-5136	93	7	du	du	AUX
ejpam-5136	93	8	.	.	PROPN
ejpam-5136	93	9	observe	observe	VERB
ejpam-5136	93	10	that	that	SCONJ
ejpam-5136	93	11	,	,	PUNCT
ejpam-5136	93	12	∫	∫	PROPN
ejpam-5136	93	13	y	y	PROPN
ejpam-5136	93	14	0	0	NUM
ejpam-5136	93	15	f(v|u)dv	f(v|u)dv	PROPN
ejpam-5136	93	16	=	=	SYM
ejpam-5136	93	17	∫	∫	PROPN
ejpam-5136	93	18	y	y	NOUN
ejpam-5136	93	19	0	0	NUM
ejpam-5136	94	1	[	[	PUNCT
ejpam-5136	94	2	1.5−	1.5−	NUM
ejpam-5136	94	3	1.5u+	1.5u+	NUM
ejpam-5136	94	4	3(1.5u−	3(1.5u−	NUM
ejpam-5136	94	5	0.5)(2v	0.5)(2v	NOUN
ejpam-5136	95	1	−	−	PROPN
ejpam-5136	95	2	1)2	1)2	NUM
ejpam-5136	95	3	]	]	PUNCT
ejpam-5136	95	4	dv	dv	PROPN
ejpam-5136	95	5	=	=	X
ejpam-5136	95	6	(	(	PUNCT
ejpam-5136	95	7	6y3	6y3	NUM
ejpam-5136	95	8	−	−	NUM
ejpam-5136	95	9	9y2	9y2	NUM
ejpam-5136	95	10	+	+	CCONJ
ejpam-5136	95	11	3y	3y	NUM
ejpam-5136	95	12	)	)	PUNCT
ejpam-5136	95	13	u−	u−	PROPN
ejpam-5136	95	14	(	(	PUNCT
ejpam-5136	95	15	2y3	2y3	NUM
ejpam-5136	95	16	−	−	PROPN
ejpam-5136	95	17	3y2	3y2	NUM
ejpam-5136	95	18	)	)	PUNCT
ejpam-5136	95	19	.	.	PUNCT
ejpam-5136	96	1	thus	thus	ADV
ejpam-5136	96	2	,	,	PUNCT
ejpam-5136	96	3	f	f	PROPN
ejpam-5136	96	4	(	(	PUNCT
ejpam-5136	96	5	x	x	PROPN
ejpam-5136	96	6	,	,	PUNCT
ejpam-5136	96	7	y	y	NOUN
ejpam-5136	96	8	)	)	PUNCT
ejpam-5136	96	9	=	=	SYM
ejpam-5136	97	1	∫	∫	PROPN
ejpam-5136	97	2	x	x	SYM
ejpam-5136	97	3	0	0	PUNCT
ejpam-5136	97	4	(	(	PUNCT
ejpam-5136	97	5	1−	1−	NUM
ejpam-5136	97	6	λ+	λ+	PUNCT
ejpam-5136	97	7	3λ(2u−	3λ(2u−	NUM
ejpam-5136	97	8	1)2	1)2	NUM
ejpam-5136	97	9	)	)	PUNCT
ejpam-5136	98	1	[	[	X
ejpam-5136	98	2	(	(	PUNCT
ejpam-5136	98	3	6y3	6y3	NUM
ejpam-5136	98	4	−	−	NUM
ejpam-5136	98	5	9y2	9y2	NUM
ejpam-5136	98	6	+	+	CCONJ
ejpam-5136	98	7	3y	3y	NUM
ejpam-5136	98	8	)	)	PUNCT
ejpam-5136	98	9	u−	u−	PROPN
ejpam-5136	98	10	(	(	PUNCT
ejpam-5136	98	11	2y3	2y3	NUM
ejpam-5136	98	12	−	−	PROPN
ejpam-5136	98	13	3y2	3y2	NUM
ejpam-5136	98	14	)	)	PUNCT
ejpam-5136	98	15	]	]	PUNCT
ejpam-5136	98	16	du	du	PROPN
ejpam-5136	98	17	=	=	NOUN
ejpam-5136	98	18	3y	3y	X
ejpam-5136	98	19	(	(	PUNCT
ejpam-5136	98	20	2y2	2y2	NUM
ejpam-5136	98	21	−	−	NOUN
ejpam-5136	98	22	3y	3y	NUM
ejpam-5136	98	23	+	+	NOUN
ejpam-5136	98	24	1	1	X
ejpam-5136	98	25	)	)	PUNCT
ejpam-5136	98	26	m(x)−	m(x)−	NOUN
ejpam-5136	98	27	(	(	PUNCT
ejpam-5136	98	28	2y	2y	PROPN
ejpam-5136	98	29	−	−	PROPN
ejpam-5136	98	30	3)y2f	3)y2f	NUM
ejpam-5136	98	31	(	(	PUNCT
ejpam-5136	98	32	x	x	NOUN
ejpam-5136	98	33	)	)	PUNCT
ejpam-5136	98	34	,	,	PUNCT
ejpam-5136	98	35	where	where	SCONJ
ejpam-5136	98	36	m(x	m(x	X
ejpam-5136	98	37	)	)	PUNCT
ejpam-5136	98	38	=	=	PUNCT
ejpam-5136	98	39	(	(	PUNCT
ejpam-5136	98	40	1	1	NUM
ejpam-5136	98	41	+	+	SYM
ejpam-5136	98	42	2λ)x2	2λ)x2	NUM
ejpam-5136	98	43	2	2	NUM
ejpam-5136	98	44	−	−	NOUN
ejpam-5136	98	45	4λx3	4λx3	NUM
ejpam-5136	98	46	+	+	CCONJ
ejpam-5136	98	47	3λx4	3λx4	NUM
ejpam-5136	98	48	,	,	PUNCT
ejpam-5136	98	49	and	and	CCONJ
ejpam-5136	98	50	f	f	PROPN
ejpam-5136	98	51	(	(	PUNCT
ejpam-5136	98	52	x	x	NOUN
ejpam-5136	98	53	)	)	PUNCT
ejpam-5136	98	54	=(	=(	NOUN
ejpam-5136	98	55	1	1	NUM
ejpam-5136	98	56	+	+	NUM
ejpam-5136	98	57	2λ)x−	2λ)x−	NUM
ejpam-5136	98	58	6λx2	6λx2	NUM
ejpam-5136	98	59	+	+	CCONJ
ejpam-5136	98	60	4λx3	4λx3	NUM
ejpam-5136	98	61	.	.	PUNCT
ejpam-5136	99	1	this	this	DET
ejpam-5136	99	2	besu	besu	NOUN
ejpam-5136	99	3	distribution	distribution	NOUN
ejpam-5136	99	4	can	can	AUX
ejpam-5136	99	5	be	be	AUX
ejpam-5136	99	6	used	use	VERB
ejpam-5136	99	7	to	to	PART
ejpam-5136	99	8	model	model	VERB
ejpam-5136	99	9	the	the	DET
ejpam-5136	99	10	lifetimes	lifetime	NOUN
ejpam-5136	99	11	of	of	ADP
ejpam-5136	99	12	two	two	NUM
ejpam-5136	99	13	related	relate	VERB
ejpam-5136	99	14	electronic	electronic	ADJ
ejpam-5136	99	15	devices	device	NOUN
ejpam-5136	99	16	where	where	SCONJ
ejpam-5136	99	17	the	the	DET
ejpam-5136	99	18	distributions	distribution	NOUN
ejpam-5136	99	19	of	of	ADP
ejpam-5136	99	20	the	the	DET
ejpam-5136	99	21	lifetimes	lifetime	NOUN
ejpam-5136	99	22	of	of	ADP
ejpam-5136	99	23	two	two	NUM
ejpam-5136	99	24	related	relate	VERB
ejpam-5136	99	25	devices	device	NOUN
ejpam-5136	99	26	follow	follow	VERB
ejpam-5136	99	27	the	the	DET
ejpam-5136	99	28	bathtub	bathtub	ADJ
ejpam-5136	99	29	shape	shape	NOUN
ejpam-5136	99	30	.	.	PUNCT
ejpam-5136	100	1	an	an	DET
ejpam-5136	100	2	example	example	NOUN
ejpam-5136	100	3	of	of	ADP
ejpam-5136	100	4	the	the	DET
ejpam-5136	100	5	electronic	electronic	ADJ
ejpam-5136	100	6	dataset	dataset	NOUN
ejpam-5136	100	7	that	that	PRON
ejpam-5136	100	8	follows	follow	VERB
ejpam-5136	100	9	a	a	DET
ejpam-5136	100	10	bathtub	bathtub	ADJ
ejpam-5136	100	11	shape	shape	NOUN
ejpam-5136	100	12	is	be	AUX
ejpam-5136	100	13	the	the	DET
ejpam-5136	100	14	dataset	dataset	NOUN
ejpam-5136	100	15	used	use	VERB
ejpam-5136	100	16	by	by	ADP
ejpam-5136	100	17	rahman	rahman	PROPN
ejpam-5136	100	18	et	et	PROPN
ejpam-5136	100	19	al	al	PROPN
ejpam-5136	100	20	.	.	PUNCT
ejpam-5136	101	1	[	[	X
ejpam-5136	101	2	6	6	NUM
ejpam-5136	101	3	]	]	PUNCT
ejpam-5136	101	4	in	in	ADP
ejpam-5136	101	5	their	their	PRON
ejpam-5136	101	6	study	study	NOUN
ejpam-5136	101	7	and	and	CCONJ
ejpam-5136	101	8	that	that	SCONJ
ejpam-5136	101	9	data	data	NOUN
ejpam-5136	101	10	is	be	AUX
ejpam-5136	101	11	about	about	ADP
ejpam-5136	101	12	the	the	DET
ejpam-5136	101	13	lifetimes	lifetime	NOUN
ejpam-5136	101	14	of	of	ADP
ejpam-5136	101	15	30	30	NUM
ejpam-5136	101	16	electronic	electronic	ADJ
ejpam-5136	101	17	devices	device	NOUN
ejpam-5136	101	18	.	.	PUNCT
ejpam-5136	102	1	3	3	X
ejpam-5136	102	2	.	.	X
ejpam-5136	103	1	some	some	DET
ejpam-5136	103	2	properties	property	NOUN
ejpam-5136	103	3	of	of	ADP
ejpam-5136	103	4	the	the	DET
ejpam-5136	103	5	bivariate	bivariate	ADJ
ejpam-5136	103	6	extended	extend	VERB
ejpam-5136	103	7	standard	standard	ADJ
ejpam-5136	103	8	u	u	ADJ
ejpam-5136	103	9	-	-	ADJ
ejpam-5136	103	10	quadratic	quadratic	ADJ
ejpam-5136	103	11	distribution	distribution	NOUN
ejpam-5136	103	12	theorem	theorem	NOUN
ejpam-5136	103	13	2	2	X
ejpam-5136	103	14	.	.	X
ejpam-5136	104	1	let	let	VERB
ejpam-5136	104	2	(	(	PUNCT
ejpam-5136	104	3	x	x	X
ejpam-5136	104	4	,	,	PUNCT
ejpam-5136	104	5	y	y	PROPN
ejpam-5136	104	6	)	)	PUNCT
ejpam-5136	104	7	be	be	AUX
ejpam-5136	104	8	a	a	DET
ejpam-5136	104	9	bivariate	bivariate	ADJ
ejpam-5136	104	10	random	random	ADJ
ejpam-5136	104	11	vector	vector	NOUN
ejpam-5136	104	12	with	with	ADP
ejpam-5136	104	13	joint	joint	ADJ
ejpam-5136	104	14	probability	probability	NOUN
ejpam-5136	104	15	density	density	NOUN
ejpam-5136	104	16	function	function	NOUN
ejpam-5136	104	17	given	give	VERB
ejpam-5136	104	18	in	in	ADP
ejpam-5136	104	19	equation	equation	NOUN
ejpam-5136	104	20	(	(	PUNCT
ejpam-5136	104	21	3	3	NUM
ejpam-5136	104	22	)	)	PUNCT
ejpam-5136	104	23	,	,	PUNCT
ejpam-5136	104	24	then	then	ADV
ejpam-5136	104	25	the	the	DET
ejpam-5136	104	26	marginal	marginal	ADJ
ejpam-5136	104	27	density	density	NOUN
ejpam-5136	104	28	function	function	NOUN
ejpam-5136	104	29	of	of	ADP
ejpam-5136	104	30	y	y	PROPN
ejpam-5136	104	31	follows	follow	VERB
ejpam-5136	104	32	an	an	DET
ejpam-5136	104	33	extended	extended	ADJ
ejpam-5136	104	34	standard	standard	ADJ
ejpam-5136	104	35	u	u	NOUN
ejpam-5136	104	36	-	-	ADJ
ejpam-5136	104	37	quadratic	quadratic	ADJ
ejpam-5136	104	38	(	(	PUNCT
ejpam-5136	104	39	esu	esu	NOUN
ejpam-5136	104	40	)	)	PUNCT
ejpam-5136	104	41	distribution	distribution	NOUN
ejpam-5136	104	42	with	with	ADP
ejpam-5136	104	43	parameter	parameter	NOUN
ejpam-5136	104	44	λ∗	λ∗	PROPN
ejpam-5136	104	45	=	=	PUNCT
ejpam-5136	105	1	0.25	0.25	NUM
ejpam-5136	105	2	.	.	PUNCT
ejpam-5136	106	1	proof	proof	NOUN
ejpam-5136	106	2	.	.	PUNCT
ejpam-5136	107	1	the	the	DET
ejpam-5136	107	2	marginal	marginal	ADJ
ejpam-5136	107	3	distribution	distribution	NOUN
ejpam-5136	107	4	of	of	ADP
ejpam-5136	107	5	y	y	PROPN
ejpam-5136	107	6	is	be	AUX
ejpam-5136	107	7	defined	define	VERB
ejpam-5136	107	8	as	as	ADP
ejpam-5136	107	9	f(y	f(y	NOUN
ejpam-5136	107	10	)	)	PUNCT
ejpam-5136	108	1	=	=	SYM
ejpam-5136	108	2	∫	∫	PROPN
ejpam-5136	108	3	1	1	NUM
ejpam-5136	108	4	0	0	NUM
ejpam-5136	108	5	f(x	f(x	PROPN
ejpam-5136	108	6	,	,	PUNCT
ejpam-5136	108	7	y)dx	y)dx	PROPN
ejpam-5136	108	8	=	=	SYM
ejpam-5136	108	9	∫	∫	PROPN
ejpam-5136	108	10	1	1	NUM
ejpam-5136	108	11	0	0	NUM
ejpam-5136	109	1	[	[	PUNCT
ejpam-5136	109	2	1.5−	1.5−	NUM
ejpam-5136	109	3	1.5x+	1.5x+	NUM
ejpam-5136	109	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	109	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	109	6	−	−	PROPN
ejpam-5136	109	7	1)2	1)2	NUM
ejpam-5136	109	8	]	]	PUNCT
ejpam-5136	109	9	f(x)dx	f(x)dx	VERB
ejpam-5136	109	10	i.	i.	NOUN
ejpam-5136	109	11	a.	a.	PROPN
ejpam-5136	109	12	lakibul	lakibul	PROPN
ejpam-5136	109	13	,	,	PUNCT
ejpam-5136	109	14	d.	d.	PROPN
ejpam-5136	109	15	l.	l.	PROPN
ejpam-5136	109	16	polestico	polestico	PROPN
ejpam-5136	109	17	,	,	PUNCT
ejpam-5136	109	18	a.	a.	PROPN
ejpam-5136	109	19	p.	p.	NOUN
ejpam-5136	109	20	supe	supe	PROPN
ejpam-5136	109	21	/	/	SYM
ejpam-5136	109	22	eur	eur	PROPN
ejpam-5136	109	23	.	.	PUNCT
ejpam-5136	110	1	j.	j.	PROPN
ejpam-5136	110	2	pure	pure	PROPN
ejpam-5136	110	3	appl	appl	PROPN
ejpam-5136	110	4	.	.	PROPN
ejpam-5136	110	5	math	math	PROPN
ejpam-5136	110	6	,	,	PUNCT
ejpam-5136	110	7	17	17	NUM
ejpam-5136	110	8	(	(	PUNCT
ejpam-5136	110	9	2	2	NUM
ejpam-5136	110	10	)	)	PUNCT
ejpam-5136	110	11	(	(	PUNCT
ejpam-5136	110	12	2024	2024	NUM
ejpam-5136	110	13	)	)	PUNCT
ejpam-5136	110	14	,	,	PUNCT
ejpam-5136	110	15	790	790	NUM
ejpam-5136	110	16	-	-	SYM
ejpam-5136	110	17	809	809	NUM
ejpam-5136	110	18	794	794	NUM
ejpam-5136	110	19	f(y	f(y	NOUN
ejpam-5136	110	20	)	)	PUNCT
ejpam-5136	111	1	=	=	NOUN
ejpam-5136	111	2	1.5	1.5	NUM
ejpam-5136	111	3	[	[	PUNCT
ejpam-5136	111	4	1−	1−	NUM
ejpam-5136	111	5	(	(	PUNCT
ejpam-5136	111	6	2y	2y	NOUN
ejpam-5136	111	7	−	−	PROPN
ejpam-5136	111	8	1)2	1)2	NUM
ejpam-5136	111	9	]	]	PUNCT
ejpam-5136	111	10	∫	∫	PROPN
ejpam-5136	111	11	1	1	NUM
ejpam-5136	111	12	0	0	NUM
ejpam-5136	112	1	f(x)dx−	f(x)dx−	PROPN
ejpam-5136	112	2	1.5	1.5	NUM
ejpam-5136	112	3	[	[	PUNCT
ejpam-5136	112	4	1−	1−	NUM
ejpam-5136	112	5	3(2y	3(2y	NUM
ejpam-5136	112	6	−	−	PROPN
ejpam-5136	113	1	1)2	1)2	NUM
ejpam-5136	113	2	]	]	PUNCT
ejpam-5136	113	3	∫	∫	PROPN
ejpam-5136	113	4	1	1	NUM
ejpam-5136	113	5	0	0	NUM
ejpam-5136	113	6	xf(x)dx	xf(x)dx	NOUN
ejpam-5136	113	7	.	.	PUNCT
ejpam-5136	114	1	(	(	PUNCT
ejpam-5136	114	2	5	5	X
ejpam-5136	114	3	)	)	PUNCT
ejpam-5136	114	4	observe	observe	VERB
ejpam-5136	114	5	that	that	SCONJ
ejpam-5136	114	6	the	the	DET
ejpam-5136	114	7	first	first	ADJ
ejpam-5136	114	8	part	part	NOUN
ejpam-5136	114	9	of	of	ADP
ejpam-5136	114	10	equation	equation	NOUN
ejpam-5136	114	11	(	(	PUNCT
ejpam-5136	114	12	5	5	X
ejpam-5136	114	13	)	)	PUNCT
ejpam-5136	114	14	simplifies	simplifie	NOUN
ejpam-5136	114	15	to	to	ADP
ejpam-5136	114	16	1.5	1.5	NUM
ejpam-5136	114	17	[	[	PUNCT
ejpam-5136	114	18	1−	1−	NUM
ejpam-5136	114	19	(	(	PUNCT
ejpam-5136	114	20	2y	2y	NOUN
ejpam-5136	114	21	−	−	PROPN
ejpam-5136	114	22	1)2	1)2	NUM
ejpam-5136	114	23	]	]	PUNCT
ejpam-5136	114	24	since	since	SCONJ
ejpam-5136	114	25	f(x	f(x	PROPN
ejpam-5136	114	26	)	)	PUNCT
ejpam-5136	114	27	is	be	AUX
ejpam-5136	114	28	a	a	DET
ejpam-5136	114	29	pdf	pdf	NOUN
ejpam-5136	114	30	of	of	ADP
ejpam-5136	114	31	an	an	DET
ejpam-5136	114	32	esu	esu	NOUN
ejpam-5136	114	33	distribution	distribution	NOUN
ejpam-5136	114	34	for	for	ADP
ejpam-5136	114	35	a	a	DET
ejpam-5136	114	36	random	random	ADJ
ejpam-5136	114	37	variable	variable	NOUN
ejpam-5136	114	38	x.	x.	NOUN
ejpam-5136	114	39	furthermore,∫	furthermore,∫	VERB
ejpam-5136	115	1	1	1	NUM
ejpam-5136	115	2	0	0	NUM
ejpam-5136	115	3	xf(x)dx	xf(x)dx	NOUN
ejpam-5136	115	4	=	=	SYM
ejpam-5136	115	5	∫	∫	PROPN
ejpam-5136	115	6	1	1	NUM
ejpam-5136	115	7	0	0	NUM
ejpam-5136	115	8	x	x	SYM
ejpam-5136	115	9	[	[	PUNCT
ejpam-5136	115	10	(	(	PUNCT
ejpam-5136	115	11	1−	1−	NUM
ejpam-5136	115	12	λ	λ	NOUN
ejpam-5136	115	13	)	)	PUNCT
ejpam-5136	115	14	+	+	NUM
ejpam-5136	115	15	3λ(2x−	3λ(2x−	NUM
ejpam-5136	115	16	1)2	1)2	NUM
ejpam-5136	115	17	]	]	PUNCT
ejpam-5136	115	18	dx	dx	PROPN
ejpam-5136	115	19	=	=	SYM
ejpam-5136	115	20	1	1	NUM
ejpam-5136	115	21	2	2	NUM
ejpam-5136	115	22	.	.	PUNCT
ejpam-5136	116	1	it	it	PRON
ejpam-5136	116	2	follows	follow	VERB
ejpam-5136	116	3	that	that	SCONJ
ejpam-5136	116	4	equation	equation	NOUN
ejpam-5136	116	5	(	(	PUNCT
ejpam-5136	116	6	5	5	X
ejpam-5136	116	7	)	)	PUNCT
ejpam-5136	116	8	simplifies	simplifie	NOUN
ejpam-5136	116	9	to	to	PART
ejpam-5136	116	10	f(y	f(y	VERB
ejpam-5136	116	11	)	)	PUNCT
ejpam-5136	117	1	=	=	PROPN
ejpam-5136	117	2	1−	1−	NUM
ejpam-5136	117	3	λ∗	λ∗	NOUN
ejpam-5136	118	1	+	+	CCONJ
ejpam-5136	118	2	3λ∗(2y	3λ∗(2y	NUM
ejpam-5136	118	3	−	−	NOUN
ejpam-5136	119	1	1)2	1)2	NUM
ejpam-5136	119	2	,	,	PUNCT
ejpam-5136	119	3	where	where	SCONJ
ejpam-5136	119	4	y	y	PROPN
ejpam-5136	119	5	∈	∈	PROPN
ejpam-5136	120	1	[	[	X
ejpam-5136	120	2	0	0	NUM
ejpam-5136	120	3	,	,	PUNCT
ejpam-5136	120	4	1	1	NUM
ejpam-5136	120	5	]	]	PUNCT
ejpam-5136	120	6	and	and	CCONJ
ejpam-5136	120	7	λ∗	λ∗	NOUN
ejpam-5136	120	8	=	=	PUNCT
ejpam-5136	120	9	0.25	0.25	NUM
ejpam-5136	120	10	.	.	PUNCT
ejpam-5136	121	1	thus	thus	ADV
ejpam-5136	121	2	,	,	PUNCT
ejpam-5136	121	3	the	the	DET
ejpam-5136	121	4	marginal	marginal	ADJ
ejpam-5136	121	5	distribution	distribution	NOUN
ejpam-5136	121	6	of	of	ADP
ejpam-5136	121	7	y	y	PROPN
ejpam-5136	121	8	is	be	AUX
ejpam-5136	121	9	esu	esu	NOUN
ejpam-5136	121	10	distributed	distribute	VERB
ejpam-5136	121	11	with	with	ADP
ejpam-5136	121	12	parameter	parameter	NOUN
ejpam-5136	121	13	λ∗	λ∗	PROPN
ejpam-5136	121	14	=	=	PUNCT
ejpam-5136	122	1	0.25	0.25	NUM
ejpam-5136	122	2	.	.	PUNCT
ejpam-5136	122	3	figure	figure	NOUN
ejpam-5136	122	4	1	1	NUM
ejpam-5136	122	5	:	:	PUNCT
ejpam-5136	122	6	joint	joint	ADJ
ejpam-5136	122	7	pdf	pdf	NOUN
ejpam-5136	122	8	plot	plot	NOUN
ejpam-5136	122	9	of	of	ADP
ejpam-5136	122	10	the	the	DET
ejpam-5136	122	11	bivariate	bivariate	ADJ
ejpam-5136	122	12	extended	extend	VERB
ejpam-5136	122	13	standard	standard	ADJ
ejpam-5136	122	14	u	u	ADJ
ejpam-5136	122	15	-	-	ADJ
ejpam-5136	122	16	quadratic	quadratic	ADJ
ejpam-5136	122	17	distribution	distribution	NOUN
ejpam-5136	122	18	for	for	ADP
ejpam-5136	122	19	λ	λ	X
ejpam-5136	122	20	=	=	SYM
ejpam-5136	122	21	−0.5	−0.5	PROPN
ejpam-5136	122	22	.	.	PUNCT
ejpam-5136	122	23	figure	figure	NOUN
ejpam-5136	122	24	1	1	NUM
ejpam-5136	122	25	presents	present	VERB
ejpam-5136	122	26	the	the	DET
ejpam-5136	122	27	joint	joint	ADJ
ejpam-5136	122	28	pdf	pdf	NOUN
ejpam-5136	122	29	of	of	ADP
ejpam-5136	122	30	the	the	DET
ejpam-5136	122	31	bivariate	bivariate	ADJ
ejpam-5136	122	32	extended	extend	VERB
ejpam-5136	122	33	standard	standard	ADJ
ejpam-5136	122	34	u	u	ADJ
ejpam-5136	122	35	-	-	ADJ
ejpam-5136	122	36	quadratic	quadratic	ADJ
ejpam-5136	122	37	distribution	distribution	NOUN
ejpam-5136	122	38	and	and	CCONJ
ejpam-5136	122	39	it	it	PRON
ejpam-5136	122	40	shows	show	VERB
ejpam-5136	122	41	that	that	SCONJ
ejpam-5136	122	42	this	this	DET
ejpam-5136	122	43	distribution	distribution	NOUN
ejpam-5136	122	44	can	can	AUX
ejpam-5136	122	45	generate	generate	VERB
ejpam-5136	122	46	a	a	DET
ejpam-5136	122	47	combination	combination	NOUN
ejpam-5136	122	48	of	of	ADP
ejpam-5136	122	49	the	the	DET
ejpam-5136	122	50	inverted	inverted	ADJ
ejpam-5136	122	51	bathtub	bathtub	NOUN
ejpam-5136	122	52	shape	shape	NOUN
ejpam-5136	122	53	for	for	ADP
ejpam-5136	122	54	x	x	PUNCT
ejpam-5136	122	55	and	and	CCONJ
ejpam-5136	122	56	bathtub	bathtub	ADJ
ejpam-5136	122	57	shape	shape	NOUN
ejpam-5136	122	58	for	for	ADP
ejpam-5136	122	59	y	y	PROPN
ejpam-5136	122	60	.	.	PUNCT
ejpam-5136	123	1	figure	figure	VERB
ejpam-5136	123	2	2	2	NUM
ejpam-5136	123	3	presents	present	VERB
ejpam-5136	123	4	the	the	DET
ejpam-5136	123	5	joint	joint	ADJ
ejpam-5136	123	6	pdf	pdf	NOUN
ejpam-5136	123	7	of	of	ADP
ejpam-5136	123	8	the	the	DET
ejpam-5136	123	9	bivariate	bivariate	ADJ
ejpam-5136	123	10	extended	extend	VERB
ejpam-5136	123	11	standard	standard	ADJ
ejpam-5136	123	12	u	u	ADJ
ejpam-5136	123	13	-	-	ADJ
ejpam-5136	123	14	quadratic	quadratic	ADJ
ejpam-5136	123	15	distribution	distribution	NOUN
ejpam-5136	123	16	and	and	CCONJ
ejpam-5136	123	17	it	it	PRON
ejpam-5136	123	18	shows	show	VERB
ejpam-5136	123	19	that	that	SCONJ
ejpam-5136	123	20	this	this	DET
ejpam-5136	123	21	distribution	distribution	NOUN
ejpam-5136	123	22	can	can	AUX
ejpam-5136	123	23	generate	generate	VERB
ejpam-5136	123	24	a	a	DET
ejpam-5136	123	25	combination	combination	NOUN
ejpam-5136	123	26	of	of	ADP
ejpam-5136	123	27	the	the	DET
ejpam-5136	123	28	constant	constant	ADJ
ejpam-5136	123	29	shape	shape	NOUN
ejpam-5136	123	30	for	for	ADP
ejpam-5136	123	31	x	x	PUNCT
ejpam-5136	123	32	and	and	CCONJ
ejpam-5136	123	33	bathtub	bathtub	ADJ
ejpam-5136	123	34	shape	shape	NOUN
ejpam-5136	123	35	for	for	ADP
ejpam-5136	123	36	y	y	PROPN
ejpam-5136	123	37	.	.	PUNCT
ejpam-5136	124	1	figure	figure	VERB
ejpam-5136	124	2	3	3	NUM
ejpam-5136	124	3	presents	present	VERB
ejpam-5136	124	4	the	the	DET
ejpam-5136	124	5	joint	joint	ADJ
ejpam-5136	124	6	pdf	pdf	NOUN
ejpam-5136	124	7	of	of	ADP
ejpam-5136	124	8	the	the	DET
ejpam-5136	124	9	bivariate	bivariate	ADJ
ejpam-5136	124	10	extended	extend	VERB
ejpam-5136	124	11	standard	standard	ADJ
ejpam-5136	124	12	u	u	ADJ
ejpam-5136	124	13	-	-	ADJ
ejpam-5136	124	14	quadratic	quadratic	ADJ
ejpam-5136	124	15	distribution	distribution	NOUN
ejpam-5136	124	16	and	and	CCONJ
ejpam-5136	124	17	it	it	PRON
ejpam-5136	124	18	shows	show	VERB
ejpam-5136	124	19	that	that	SCONJ
ejpam-5136	124	20	this	this	DET
ejpam-5136	124	21	distribution	distribution	NOUN
ejpam-5136	124	22	can	can	AUX
ejpam-5136	124	23	generate	generate	VERB
ejpam-5136	124	24	a	a	DET
ejpam-5136	124	25	combination	combination	NOUN
ejpam-5136	124	26	of	of	ADP
ejpam-5136	124	27	a	a	DET
ejpam-5136	124	28	bathtub	bathtub	NOUN
ejpam-5136	124	29	shape	shape	NOUN
ejpam-5136	124	30	for	for	ADP
ejpam-5136	124	31	x	x	PUNCT
ejpam-5136	124	32	and	and	CCONJ
ejpam-5136	124	33	a	a	DET
ejpam-5136	124	34	bathtub	bathtub	NOUN
ejpam-5136	124	35	shape	shape	NOUN
ejpam-5136	124	36	for	for	ADP
ejpam-5136	124	37	y	y	PROPN
ejpam-5136	124	38	.	.	PUNCT
ejpam-5136	125	1	i.	i.	PROPN
ejpam-5136	125	2	a.	a.	PROPN
ejpam-5136	125	3	lakibul	lakibul	PROPN
ejpam-5136	125	4	,	,	PUNCT
ejpam-5136	125	5	d.	d.	PROPN
ejpam-5136	125	6	l.	l.	PROPN
ejpam-5136	125	7	polestico	polestico	PROPN
ejpam-5136	125	8	,	,	PUNCT
ejpam-5136	125	9	a.	a.	PROPN
ejpam-5136	125	10	p.	p.	NOUN
ejpam-5136	125	11	supe	supe	PROPN
ejpam-5136	125	12	/	/	SYM
ejpam-5136	125	13	eur	eur	PROPN
ejpam-5136	125	14	.	.	PUNCT
ejpam-5136	126	1	j.	j.	PROPN
ejpam-5136	126	2	pure	pure	PROPN
ejpam-5136	126	3	appl	appl	PROPN
ejpam-5136	126	4	.	.	PROPN
ejpam-5136	126	5	math	math	PROPN
ejpam-5136	126	6	,	,	PUNCT
ejpam-5136	126	7	17	17	NUM
ejpam-5136	126	8	(	(	PUNCT
ejpam-5136	126	9	2	2	NUM
ejpam-5136	126	10	)	)	PUNCT
ejpam-5136	126	11	(	(	PUNCT
ejpam-5136	126	12	2024	2024	NUM
ejpam-5136	126	13	)	)	PUNCT
ejpam-5136	126	14	,	,	PUNCT
ejpam-5136	126	15	790	790	NUM
ejpam-5136	126	16	-	-	SYM
ejpam-5136	126	17	809	809	NUM
ejpam-5136	126	18	795	795	NUM
ejpam-5136	126	19	figure	figure	NOUN
ejpam-5136	126	20	2	2	NUM
ejpam-5136	126	21	:	:	PUNCT
ejpam-5136	126	22	joint	joint	ADJ
ejpam-5136	126	23	pdf	pdf	NOUN
ejpam-5136	126	24	plot	plot	NOUN
ejpam-5136	126	25	of	of	ADP
ejpam-5136	126	26	the	the	DET
ejpam-5136	126	27	bivariate	bivariate	ADJ
ejpam-5136	126	28	extended	extend	VERB
ejpam-5136	126	29	standard	standard	ADJ
ejpam-5136	126	30	u	u	ADJ
ejpam-5136	126	31	-	-	ADJ
ejpam-5136	126	32	quadratic	quadratic	ADJ
ejpam-5136	126	33	distribution	distribution	NOUN
ejpam-5136	126	34	for	for	ADP
ejpam-5136	126	35	λ	λ	X
ejpam-5136	126	36	=	=	SYM
ejpam-5136	126	37	0	0	PROPN
ejpam-5136	126	38	.	.	PUNCT
ejpam-5136	126	39	theorem	theorem	NOUN
ejpam-5136	126	40	3	3	X
ejpam-5136	126	41	.	.	PUNCT
ejpam-5136	127	1	let	let	VERB
ejpam-5136	127	2	x	x	PRON
ejpam-5136	127	3	and	and	CCONJ
ejpam-5136	127	4	y	y	PROPN
ejpam-5136	127	5	be	be	AUX
ejpam-5136	127	6	any	any	DET
ejpam-5136	127	7	two	two	NUM
ejpam-5136	127	8	random	random	ADJ
ejpam-5136	127	9	variables	variable	NOUN
ejpam-5136	127	10	with	with	ADP
ejpam-5136	127	11	joint	joint	ADJ
ejpam-5136	127	12	pdf	pdf	NOUN
ejpam-5136	127	13	given	give	VERB
ejpam-5136	127	14	in	in	ADP
ejpam-5136	127	15	equation	equation	NOUN
ejpam-5136	127	16	(	(	PUNCT
ejpam-5136	127	17	3	3	NUM
ejpam-5136	127	18	)	)	PUNCT
ejpam-5136	127	19	.	.	PUNCT
ejpam-5136	128	1	if	if	SCONJ
ejpam-5136	128	2	the	the	DET
ejpam-5136	128	3	marginal	marginal	ADJ
ejpam-5136	128	4	distribution	distribution	NOUN
ejpam-5136	128	5	of	of	ADP
ejpam-5136	128	6	y	y	PROPN
ejpam-5136	128	7	is	be	AUX
ejpam-5136	128	8	given	give	VERB
ejpam-5136	128	9	in	in	ADP
ejpam-5136	128	10	theorem	theorem	ADJ
ejpam-5136	128	11	2	2	NUM
ejpam-5136	128	12	,	,	PUNCT
ejpam-5136	128	13	then	then	ADV
ejpam-5136	128	14	the	the	DET
ejpam-5136	128	15	conditional	conditional	ADJ
ejpam-5136	128	16	distribution	distribution	NOUN
ejpam-5136	128	17	of	of	ADP
ejpam-5136	128	18	x	x	PUNCT
ejpam-5136	128	19	given	give	VERB
ejpam-5136	128	20	y	y	PROPN
ejpam-5136	128	21	=	=	PUNCT
ejpam-5136	128	22	y	y	PROPN
ejpam-5136	128	23	is	be	AUX
ejpam-5136	128	24	f(x|y	f(x|y	PROPN
ejpam-5136	128	25	=	=	SYM
ejpam-5136	128	26	y	y	NOUN
ejpam-5136	128	27	)	)	PUNCT
ejpam-5136	128	28	=	=	PUNCT
ejpam-5136	129	1	[	[	PUNCT
ejpam-5136	129	2	1.5−	1.5−	NUM
ejpam-5136	129	3	1.5x+	1.5x+	NUM
ejpam-5136	129	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	129	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	129	6	−	−	PROPN
ejpam-5136	129	7	1)2	1)2	NUM
ejpam-5136	129	8	]	]	PUNCT
ejpam-5136	129	9	[	[	PUNCT
ejpam-5136	129	10	1−	1−	NUM
ejpam-5136	129	11	λ+	λ+	PUNCT
ejpam-5136	129	12	3λ(2x−	3λ(2x−	NUM
ejpam-5136	129	13	1)2	1)2	NUM
ejpam-5136	129	14	]	]	PUNCT
ejpam-5136	129	15	0.75	0.75	NUM
ejpam-5136	129	16	+	+	CCONJ
ejpam-5136	129	17	0.75(2y	0.75(2y	VERB
ejpam-5136	129	18	−	−	PROPN
ejpam-5136	129	19	1)2	1)2	NUM
ejpam-5136	129	20	,	,	PUNCT
ejpam-5136	129	21	(	(	PUNCT
ejpam-5136	129	22	6	6	NUM
ejpam-5136	129	23	)	)	PUNCT
ejpam-5136	129	24	where	where	SCONJ
ejpam-5136	129	25	λ	λ	PROPN
ejpam-5136	129	26	∈	∈	PROPN
ejpam-5136	130	1	[	[	X
ejpam-5136	130	2	−0.5	−0.5	PROPN
ejpam-5136	130	3	,	,	PUNCT
ejpam-5136	130	4	1	1	NUM
ejpam-5136	130	5	]	]	PUNCT
ejpam-5136	130	6	.	.	PUNCT
ejpam-5136	131	1	the	the	DET
ejpam-5136	131	2	proof	proof	NOUN
ejpam-5136	131	3	follows	follow	VERB
ejpam-5136	131	4	directly	directly	ADV
ejpam-5136	131	5	from	from	ADP
ejpam-5136	131	6	the	the	DET
ejpam-5136	131	7	definition	definition	NOUN
ejpam-5136	131	8	of	of	ADP
ejpam-5136	131	9	the	the	DET
ejpam-5136	131	10	conditional	conditional	ADJ
ejpam-5136	131	11	distribution	distribution	NOUN
ejpam-5136	131	12	of	of	ADP
ejpam-5136	131	13	x	x	PUNCT
ejpam-5136	131	14	given	give	VERB
ejpam-5136	131	15	y	y	PROPN
ejpam-5136	131	16	=	=	SYM
ejpam-5136	131	17	y.	y.	PROPN
ejpam-5136	131	18	theorem	theorem	VERB
ejpam-5136	131	19	4	4	NUM
ejpam-5136	131	20	.	.	PUNCT
ejpam-5136	132	1	let	let	VERB
ejpam-5136	132	2	x	x	PRON
ejpam-5136	132	3	and	and	CCONJ
ejpam-5136	132	4	y	y	PROPN
ejpam-5136	132	5	be	be	AUX
ejpam-5136	132	6	any	any	DET
ejpam-5136	132	7	two	two	NUM
ejpam-5136	132	8	random	random	ADJ
ejpam-5136	132	9	variables	variable	NOUN
ejpam-5136	132	10	with	with	ADP
ejpam-5136	132	11	joint	joint	ADJ
ejpam-5136	132	12	pdf	pdf	NOUN
ejpam-5136	132	13	given	give	VERB
ejpam-5136	132	14	in	in	ADP
ejpam-5136	132	15	equation	equation	NOUN
ejpam-5136	132	16	(	(	PUNCT
ejpam-5136	132	17	3	3	NUM
ejpam-5136	132	18	)	)	PUNCT
ejpam-5136	132	19	.	.	PUNCT
ejpam-5136	133	1	if	if	SCONJ
ejpam-5136	133	2	the	the	DET
ejpam-5136	133	3	marginal	marginal	ADJ
ejpam-5136	133	4	distribution	distribution	NOUN
ejpam-5136	133	5	of	of	ADP
ejpam-5136	133	6	y	y	PROPN
ejpam-5136	133	7	is	be	AUX
ejpam-5136	133	8	given	give	VERB
ejpam-5136	133	9	in	in	ADP
ejpam-5136	133	10	theorem	theorem	ADJ
ejpam-5136	133	11	2	2	NUM
ejpam-5136	133	12	then	then	ADV
ejpam-5136	133	13	the	the	DET
ejpam-5136	133	14	rth	rth	ADJ
ejpam-5136	133	15	conditional	conditional	ADJ
ejpam-5136	133	16	moment	moment	NOUN
ejpam-5136	133	17	of	of	ADP
ejpam-5136	133	18	x	x	PUNCT
ejpam-5136	133	19	given	give	VERB
ejpam-5136	133	20	y	y	PROPN
ejpam-5136	133	21	=	=	PUNCT
ejpam-5136	133	22	y	y	PROPN
ejpam-5136	133	23	is	be	AUX
ejpam-5136	133	24	e	e	NOUN
ejpam-5136	133	25	[	[	NOUN
ejpam-5136	133	26	xr|y	xr|y	X
ejpam-5136	133	27	]	]	X
ejpam-5136	133	28	=	=	SYM
ejpam-5136	133	29	1.5	1.5	NUM
ejpam-5136	133	30	{	{	PUNCT
ejpam-5136	133	31	[	[	PUNCT
ejpam-5136	133	32	1−	1−	NUM
ejpam-5136	133	33	(	(	PUNCT
ejpam-5136	133	34	2y	2y	NOUN
ejpam-5136	133	35	−	−	PROPN
ejpam-5136	133	36	1)2	1)2	NUM
ejpam-5136	133	37	]	]	PUNCT
ejpam-5136	133	38	e	e	X
ejpam-5136	134	1	[	[	X
ejpam-5136	134	2	xr]−	xr]−	PROPN
ejpam-5136	134	3	[	[	PUNCT
ejpam-5136	134	4	1−	1−	NUM
ejpam-5136	134	5	3(2y	3(2y	NUM
ejpam-5136	135	1	−	−	PROPN
ejpam-5136	135	2	1)2	1)2	NUM
ejpam-5136	136	1	]	]	PUNCT
ejpam-5136	136	2	e	e	X
ejpam-5136	136	3	[	[	PUNCT
ejpam-5136	136	4	xr+1	xr+1	X
ejpam-5136	136	5	]	]	X
ejpam-5136	136	6	}	}	PUNCT
ejpam-5136	136	7	0.75	0.75	NUM
ejpam-5136	136	8	+	+	CCONJ
ejpam-5136	136	9	0.75(2y	0.75(2y	VERB
ejpam-5136	136	10	−	−	PROPN
ejpam-5136	136	11	1)2	1)2	NUM
ejpam-5136	136	12	,	,	PUNCT
ejpam-5136	136	13	(	(	PUNCT
ejpam-5136	136	14	7	7	X
ejpam-5136	136	15	)	)	PUNCT
ejpam-5136	136	16	where	where	SCONJ
ejpam-5136	136	17	e	e	X
ejpam-5136	136	18	[	[	X
ejpam-5136	136	19	xr	xr	X
ejpam-5136	136	20	]	]	X
ejpam-5136	136	21	=	=	X
ejpam-5136	136	22	(	(	PUNCT
ejpam-5136	136	23	1	1	NUM
ejpam-5136	136	24	+	+	CCONJ
ejpam-5136	136	25	2λ)r2	2λ)r2	NUM
ejpam-5136	136	26	+	+	CCONJ
ejpam-5136	136	27	(	(	PUNCT
ejpam-5136	136	28	5−	5−	NUM
ejpam-5136	136	29	2λ)r	2λ)r	NUM
ejpam-5136	136	30	+	+	CCONJ
ejpam-5136	136	31	6	6	NUM
ejpam-5136	136	32	(	(	PUNCT
ejpam-5136	136	33	r	r	NOUN
ejpam-5136	136	34	+	+	NUM
ejpam-5136	136	35	1)(r	1)(r	NUM
ejpam-5136	136	36	+	+	SYM
ejpam-5136	136	37	2)(r	2)(r	NUM
ejpam-5136	136	38	+	+	CCONJ
ejpam-5136	136	39	3	3	NUM
ejpam-5136	136	40	)	)	PUNCT
ejpam-5136	136	41	,	,	PUNCT
ejpam-5136	136	42	and	and	CCONJ
ejpam-5136	136	43	e	e	X
ejpam-5136	136	44	[	[	PUNCT
ejpam-5136	136	45	xr+1	xr+1	X
ejpam-5136	136	46	]	]	X
ejpam-5136	136	47	=	=	PUNCT
ejpam-5136	136	48	(	(	PUNCT
ejpam-5136	136	49	1	1	NUM
ejpam-5136	136	50	+	+	NUM
ejpam-5136	136	51	2λ)(r	2λ)(r	NUM
ejpam-5136	136	52	+	+	CCONJ
ejpam-5136	136	53	1)2	1)2	NUM
ejpam-5136	136	54	+	+	CCONJ
ejpam-5136	136	55	(	(	PUNCT
ejpam-5136	136	56	5−	5−	NUM
ejpam-5136	136	57	2λ)(r	2λ)(r	NUM
ejpam-5136	136	58	+	+	CCONJ
ejpam-5136	136	59	1	1	X
ejpam-5136	136	60	)	)	PUNCT
ejpam-5136	136	61	+	+	CCONJ
ejpam-5136	136	62	6	6	NUM
ejpam-5136	136	63	(	(	PUNCT
ejpam-5136	136	64	r	r	NOUN
ejpam-5136	136	65	+	+	NUM
ejpam-5136	136	66	2)(r	2)(r	NUM
ejpam-5136	136	67	+	+	CCONJ
ejpam-5136	136	68	3)(r	3)(r	NUM
ejpam-5136	136	69	+	+	NUM
ejpam-5136	136	70	4	4	NUM
ejpam-5136	136	71	)	)	PUNCT
ejpam-5136	136	72	.	.	PUNCT
ejpam-5136	137	1	proof	proof	NOUN
ejpam-5136	137	2	.	.	PUNCT
ejpam-5136	138	1	the	the	DET
ejpam-5136	138	2	rth	rth	PROPN
ejpam-5136	138	3	conditional	conditional	ADJ
ejpam-5136	138	4	moment	moment	NOUN
ejpam-5136	138	5	of	of	ADP
ejpam-5136	138	6	x	x	PUNCT
ejpam-5136	138	7	given	give	VERB
ejpam-5136	138	8	y	y	PROPN
ejpam-5136	138	9	=	=	PUNCT
ejpam-5136	138	10	y	y	PROPN
ejpam-5136	138	11	is	be	AUX
ejpam-5136	138	12	defined	define	VERB
ejpam-5136	138	13	as	as	ADP
ejpam-5136	138	14	e	e	NOUN
ejpam-5136	138	15	[	[	NOUN
ejpam-5136	138	16	xr|y	xr|y	X
ejpam-5136	138	17	]	]	X
ejpam-5136	138	18	=	=	SYM
ejpam-5136	138	19	∫	∫	PROPN
ejpam-5136	138	20	1	1	NUM
ejpam-5136	138	21	0	0	NUM
ejpam-5136	138	22	xrf(x|y	xrf(x|y	PROPN
ejpam-5136	139	1	=	=	SYM
ejpam-5136	139	2	y)dx	y)dx	PROPN
ejpam-5136	139	3	i.	i.	NOUN
ejpam-5136	139	4	a.	a.	NOUN
ejpam-5136	139	5	lakibul	lakibul	PROPN
ejpam-5136	139	6	,	,	PUNCT
ejpam-5136	139	7	d.	d.	PROPN
ejpam-5136	139	8	l.	l.	PROPN
ejpam-5136	139	9	polestico	polestico	PROPN
ejpam-5136	139	10	,	,	PUNCT
ejpam-5136	139	11	a.	a.	PROPN
ejpam-5136	139	12	p.	p.	NOUN
ejpam-5136	139	13	supe	supe	PROPN
ejpam-5136	139	14	/	/	SYM
ejpam-5136	139	15	eur	eur	PROPN
ejpam-5136	139	16	.	.	PUNCT
ejpam-5136	140	1	j.	j.	PROPN
ejpam-5136	140	2	pure	pure	PROPN
ejpam-5136	140	3	appl	appl	PROPN
ejpam-5136	140	4	.	.	PROPN
ejpam-5136	140	5	math	math	PROPN
ejpam-5136	140	6	,	,	PUNCT
ejpam-5136	140	7	17	17	NUM
ejpam-5136	140	8	(	(	PUNCT
ejpam-5136	140	9	2	2	NUM
ejpam-5136	140	10	)	)	PUNCT
ejpam-5136	140	11	(	(	PUNCT
ejpam-5136	140	12	2024	2024	NUM
ejpam-5136	140	13	)	)	PUNCT
ejpam-5136	140	14	,	,	PUNCT
ejpam-5136	140	15	790	790	NUM
ejpam-5136	140	16	-	-	SYM
ejpam-5136	140	17	809	809	NUM
ejpam-5136	140	18	796	796	NUM
ejpam-5136	140	19	figure	figure	NOUN
ejpam-5136	140	20	3	3	NUM
ejpam-5136	140	21	:	:	PUNCT
ejpam-5136	140	22	joint	joint	ADJ
ejpam-5136	140	23	pdf	pdf	NOUN
ejpam-5136	140	24	plot	plot	NOUN
ejpam-5136	140	25	of	of	ADP
ejpam-5136	140	26	the	the	DET
ejpam-5136	140	27	bivariate	bivariate	ADJ
ejpam-5136	140	28	extended	extend	VERB
ejpam-5136	140	29	standard	standard	ADJ
ejpam-5136	140	30	u	u	ADJ
ejpam-5136	140	31	-	-	ADJ
ejpam-5136	140	32	quadratic	quadratic	ADJ
ejpam-5136	140	33	distribution	distribution	NOUN
ejpam-5136	140	34	for	for	ADP
ejpam-5136	140	35	λ	λ	NOUN
ejpam-5136	140	36	=	=	SYM
ejpam-5136	140	37	0.5	0.5	NUM
ejpam-5136	140	38	.	.	PUNCT
ejpam-5136	141	1	e	e	X
ejpam-5136	141	2	[	[	X
ejpam-5136	141	3	xr|y	xr|y	X
ejpam-5136	141	4	]	]	X
ejpam-5136	141	5	=	=	SYM
ejpam-5136	141	6	∫	∫	PROPN
ejpam-5136	141	7	1	1	NUM
ejpam-5136	141	8	0	0	NUM
ejpam-5136	141	9	xr	xr	PROPN
ejpam-5136	141	10	f(x	f(x	PROPN
ejpam-5136	141	11	,	,	PUNCT
ejpam-5136	141	12	y	y	NOUN
ejpam-5136	141	13	)	)	PUNCT
ejpam-5136	141	14	f(y	f(y	NOUN
ejpam-5136	141	15	)	)	PUNCT
ejpam-5136	141	16	dx	dx	PROPN
ejpam-5136	141	17	.	.	PUNCT
ejpam-5136	142	1	it	it	PRON
ejpam-5136	142	2	follows	follow	VERB
ejpam-5136	142	3	that	that	SCONJ
ejpam-5136	142	4	the	the	DET
ejpam-5136	142	5	rth	rth	PROPN
ejpam-5136	142	6	conditional	conditional	ADJ
ejpam-5136	142	7	moment	moment	NOUN
ejpam-5136	142	8	of	of	ADP
ejpam-5136	142	9	x	x	PUNCT
ejpam-5136	142	10	given	give	VERB
ejpam-5136	142	11	y	y	PROPN
ejpam-5136	142	12	=	=	SYM
ejpam-5136	142	13	y	y	PROPN
ejpam-5136	142	14	becomes	become	VERB
ejpam-5136	142	15	e	e	NOUN
ejpam-5136	142	16	[	[	NOUN
ejpam-5136	142	17	xr|y	xr|y	X
ejpam-5136	142	18	]	]	X
ejpam-5136	142	19	=	=	SYM
ejpam-5136	142	20	1	1	NUM
ejpam-5136	142	21	f(y	f(y	NOUN
ejpam-5136	142	22	)	)	PUNCT
ejpam-5136	142	23	∫	∫	PROPN
ejpam-5136	142	24	1	1	NUM
ejpam-5136	142	25	0	0	NUM
ejpam-5136	142	26	xr	xr	PROPN
ejpam-5136	142	27	[	[	PUNCT
ejpam-5136	142	28	1.5	1.5	NUM
ejpam-5136	142	29	(	(	PUNCT
ejpam-5136	142	30	1−	1−	NUM
ejpam-5136	142	31	(	(	PUNCT
ejpam-5136	142	32	2y	2y	PROPN
ejpam-5136	142	33	−	−	PROPN
ejpam-5136	142	34	1)2	1)2	NUM
ejpam-5136	142	35	)	)	PUNCT
ejpam-5136	143	1	−	−	PROPN
ejpam-5136	143	2	1.5x	1.5x	NUM
ejpam-5136	143	3	(	(	PUNCT
ejpam-5136	143	4	1−	1−	NUM
ejpam-5136	143	5	3(2y	3(2y	NUM
ejpam-5136	143	6	−	−	PROPN
ejpam-5136	143	7	1)2	1)2	NUM
ejpam-5136	143	8	)	)	PUNCT
ejpam-5136	143	9	]	]	PUNCT
ejpam-5136	144	1	f(x|λ)dx	f(x|λ)dx	ADJ
ejpam-5136	144	2	=	=	SYM
ejpam-5136	144	3	1.5	1.5	NUM
ejpam-5136	144	4	(	(	PUNCT
ejpam-5136	144	5	1−	1−	NUM
ejpam-5136	144	6	(	(	PUNCT
ejpam-5136	144	7	2y	2y	PROPN
ejpam-5136	144	8	−	−	PROPN
ejpam-5136	144	9	1)2	1)2	NUM
ejpam-5136	144	10	)	)	PUNCT
ejpam-5136	144	11	f(y	f(y	NOUN
ejpam-5136	144	12	)	)	PUNCT
ejpam-5136	144	13	[	[	PUNCT
ejpam-5136	144	14	(	(	PUNCT
ejpam-5136	144	15	1	1	NUM
ejpam-5136	144	16	+	+	X
ejpam-5136	144	17	2λ)r2	2λ)r2	NUM
ejpam-5136	144	18	+	+	CCONJ
ejpam-5136	144	19	(	(	PUNCT
ejpam-5136	144	20	5−	5−	NUM
ejpam-5136	144	21	2λ)r	2λ)r	NUM
ejpam-5136	144	22	+	+	CCONJ
ejpam-5136	144	23	6	6	NUM
ejpam-5136	144	24	(	(	PUNCT
ejpam-5136	144	25	r	r	NOUN
ejpam-5136	144	26	+	+	NUM
ejpam-5136	144	27	1)(r	1)(r	NUM
ejpam-5136	144	28	+	+	SYM
ejpam-5136	144	29	2)(r	2)(r	NUM
ejpam-5136	144	30	+	+	CCONJ
ejpam-5136	144	31	3	3	NUM
ejpam-5136	144	32	)	)	PUNCT
ejpam-5136	144	33	]	]	PUNCT
ejpam-5136	145	1	−	−	PROPN
ejpam-5136	145	2	1.5	1.5	NUM
ejpam-5136	145	3	(	(	PUNCT
ejpam-5136	145	4	1−	1−	NUM
ejpam-5136	145	5	3(2y	3(2y	NUM
ejpam-5136	145	6	−	−	PROPN
ejpam-5136	145	7	1)2	1)2	NUM
ejpam-5136	145	8	)	)	PUNCT
ejpam-5136	145	9	f(y	f(y	NOUN
ejpam-5136	145	10	)	)	PUNCT
ejpam-5136	145	11	[	[	PUNCT
ejpam-5136	145	12	(	(	PUNCT
ejpam-5136	145	13	1	1	NUM
ejpam-5136	145	14	+	+	NUM
ejpam-5136	145	15	2λ)(r	2λ)(r	NUM
ejpam-5136	146	1	+	+	CCONJ
ejpam-5136	146	2	1)2	1)2	NUM
ejpam-5136	146	3	+	+	CCONJ
ejpam-5136	146	4	(	(	PUNCT
ejpam-5136	146	5	5−	5−	NUM
ejpam-5136	146	6	2λ)(r	2λ)(r	NUM
ejpam-5136	146	7	+	+	CCONJ
ejpam-5136	146	8	1	1	X
ejpam-5136	146	9	)	)	PUNCT
ejpam-5136	147	1	+	+	CCONJ
ejpam-5136	147	2	6	6	NUM
ejpam-5136	147	3	(	(	PUNCT
ejpam-5136	147	4	r	r	NOUN
ejpam-5136	147	5	+	+	NUM
ejpam-5136	147	6	2)(r	2)(r	NUM
ejpam-5136	147	7	+	+	CCONJ
ejpam-5136	147	8	3)(r	3)(r	NUM
ejpam-5136	147	9	+	+	NUM
ejpam-5136	147	10	4	4	NUM
ejpam-5136	147	11	)	)	PUNCT
ejpam-5136	147	12	]	]	PUNCT
ejpam-5136	148	1	=	=	SYM
ejpam-5136	148	2	1.5	1.5	NUM
ejpam-5136	148	3	f(y	f(y	NOUN
ejpam-5136	148	4	)	)	PUNCT
ejpam-5136	148	5	{	{	PUNCT
ejpam-5136	148	6	[	[	PUNCT
ejpam-5136	148	7	1−	1−	NUM
ejpam-5136	148	8	(	(	PUNCT
ejpam-5136	148	9	2y	2y	NOUN
ejpam-5136	148	10	−	−	PROPN
ejpam-5136	148	11	1)2	1)2	NUM
ejpam-5136	148	12	]	]	PUNCT
ejpam-5136	148	13	e	e	X
ejpam-5136	149	1	[	[	X
ejpam-5136	149	2	xr]−	xr]−	PROPN
ejpam-5136	149	3	[	[	PUNCT
ejpam-5136	149	4	1−	1−	NUM
ejpam-5136	149	5	3(2y	3(2y	NUM
ejpam-5136	150	1	−	−	PROPN
ejpam-5136	150	2	1)2	1)2	NUM
ejpam-5136	151	1	]	]	PUNCT
ejpam-5136	151	2	e	e	X
ejpam-5136	151	3	[	[	PUNCT
ejpam-5136	151	4	xr+1	xr+1	X
ejpam-5136	151	5	]	]	X
ejpam-5136	151	6	}	}	PUNCT
ejpam-5136	151	7	,	,	PUNCT
ejpam-5136	151	8	where	where	SCONJ
ejpam-5136	151	9	e	e	X
ejpam-5136	151	10	[	[	X
ejpam-5136	151	11	xr	xr	X
ejpam-5136	151	12	]	]	X
ejpam-5136	151	13	=	=	X
ejpam-5136	151	14	(	(	PUNCT
ejpam-5136	151	15	1	1	NUM
ejpam-5136	151	16	+	+	CCONJ
ejpam-5136	151	17	2λ)r2	2λ)r2	NUM
ejpam-5136	151	18	+	+	CCONJ
ejpam-5136	151	19	(	(	PUNCT
ejpam-5136	151	20	5−	5−	NUM
ejpam-5136	151	21	2λ)r	2λ)r	NUM
ejpam-5136	151	22	+	+	CCONJ
ejpam-5136	151	23	6	6	NUM
ejpam-5136	151	24	(	(	PUNCT
ejpam-5136	151	25	r	r	NOUN
ejpam-5136	151	26	+	+	NUM
ejpam-5136	151	27	1)(r	1)(r	NUM
ejpam-5136	151	28	+	+	SYM
ejpam-5136	151	29	2)(r	2)(r	NUM
ejpam-5136	151	30	+	+	CCONJ
ejpam-5136	151	31	3	3	NUM
ejpam-5136	151	32	)	)	PUNCT
ejpam-5136	151	33	,	,	PUNCT
ejpam-5136	151	34	and	and	CCONJ
ejpam-5136	151	35	e	e	X
ejpam-5136	151	36	[	[	PUNCT
ejpam-5136	151	37	xr+1	xr+1	X
ejpam-5136	151	38	]	]	X
ejpam-5136	151	39	=	=	PUNCT
ejpam-5136	151	40	(	(	PUNCT
ejpam-5136	151	41	1	1	NUM
ejpam-5136	151	42	+	+	NUM
ejpam-5136	151	43	2λ)(r	2λ)(r	NUM
ejpam-5136	151	44	+	+	CCONJ
ejpam-5136	151	45	1)2	1)2	NUM
ejpam-5136	151	46	+	+	CCONJ
ejpam-5136	151	47	(	(	PUNCT
ejpam-5136	151	48	5−	5−	NUM
ejpam-5136	151	49	2λ)(r	2λ)(r	NUM
ejpam-5136	151	50	+	+	CCONJ
ejpam-5136	151	51	1	1	X
ejpam-5136	151	52	)	)	PUNCT
ejpam-5136	151	53	+	+	CCONJ
ejpam-5136	151	54	6	6	NUM
ejpam-5136	151	55	(	(	PUNCT
ejpam-5136	151	56	r	r	NOUN
ejpam-5136	151	57	+	+	NUM
ejpam-5136	151	58	2)(r	2)(r	NUM
ejpam-5136	151	59	+	+	CCONJ
ejpam-5136	151	60	3)(r	3)(r	NUM
ejpam-5136	151	61	+	+	NUM
ejpam-5136	151	62	4	4	NUM
ejpam-5136	151	63	)	)	PUNCT
ejpam-5136	151	64	.	.	PUNCT
ejpam-5136	152	1	remark	remark	NOUN
ejpam-5136	152	2	1	1	NUM
ejpam-5136	152	3	.	.	PUNCT
ejpam-5136	153	1	the	the	DET
ejpam-5136	153	2	conditional	conditional	ADJ
ejpam-5136	153	3	mean	mean	NOUN
ejpam-5136	153	4	of	of	ADP
ejpam-5136	153	5	x	x	PUNCT
ejpam-5136	153	6	given	give	VERB
ejpam-5136	153	7	y	y	PROPN
ejpam-5136	153	8	is	be	AUX
ejpam-5136	153	9	given	give	VERB
ejpam-5136	153	10	by	by	ADP
ejpam-5136	153	11	e[x|y	e[x|y	NOUN
ejpam-5136	153	12	]	]	X
ejpam-5136	153	13	=	=	SYM
ejpam-5136	153	14	1.5{0.5[1−	1.5{0.5[1−	NOUN
ejpam-5136	153	15	(	(	PUNCT
ejpam-5136	153	16	2y	2y	PROPN
ejpam-5136	153	17	−	−	PROPN
ejpam-5136	153	18	1)2]−	1)2]−	NUM
ejpam-5136	153	19	(	(	PUNCT
ejpam-5136	153	20	5+λ	5+λ	NUM
ejpam-5136	153	21	15	15	NUM
ejpam-5136	153	22	)	)	PUNCT
ejpam-5136	154	1	[	[	X
ejpam-5136	154	2	1−	1−	NUM
ejpam-5136	154	3	3(2y	3(2y	NUM
ejpam-5136	154	4	−	−	PROPN
ejpam-5136	154	5	1)2	1)2	NUM
ejpam-5136	154	6	]	]	PUNCT
ejpam-5136	154	7	}	}	PUNCT
ejpam-5136	154	8	0.75	0.75	NUM
ejpam-5136	154	9	+	+	CCONJ
ejpam-5136	154	10	0.75(2y	0.75(2y	VERB
ejpam-5136	154	11	−	−	PROPN
ejpam-5136	154	12	1)2	1)2	NUM
ejpam-5136	154	13	.	.	PUNCT
ejpam-5136	155	1	(	(	PUNCT
ejpam-5136	155	2	8)	8)	NUM
ejpam-5136	155	3	i.	i.	PROPN
ejpam-5136	155	4	a.	a.	PROPN
ejpam-5136	155	5	lakibul	lakibul	PROPN
ejpam-5136	155	6	,	,	PUNCT
ejpam-5136	155	7	d.	d.	PROPN
ejpam-5136	155	8	l.	l.	PROPN
ejpam-5136	155	9	polestico	polestico	PROPN
ejpam-5136	155	10	,	,	PUNCT
ejpam-5136	155	11	a.	a.	PROPN
ejpam-5136	155	12	p.	p.	NOUN
ejpam-5136	155	13	supe	supe	PROPN
ejpam-5136	155	14	/	/	SYM
ejpam-5136	155	15	eur	eur	PROPN
ejpam-5136	155	16	.	.	PUNCT
ejpam-5136	156	1	j.	j.	PROPN
ejpam-5136	156	2	pure	pure	PROPN
ejpam-5136	156	3	appl	appl	PROPN
ejpam-5136	156	4	.	.	PROPN
ejpam-5136	156	5	math	math	PROPN
ejpam-5136	156	6	,	,	PUNCT
ejpam-5136	156	7	17	17	NUM
ejpam-5136	156	8	(	(	PUNCT
ejpam-5136	156	9	2	2	NUM
ejpam-5136	156	10	)	)	PUNCT
ejpam-5136	156	11	(	(	PUNCT
ejpam-5136	156	12	2024	2024	NUM
ejpam-5136	156	13	)	)	PUNCT
ejpam-5136	156	14	,	,	PUNCT
ejpam-5136	156	15	790	790	NUM
ejpam-5136	156	16	-	-	SYM
ejpam-5136	156	17	809	809	NUM
ejpam-5136	156	18	797	797	NUM
ejpam-5136	156	19	remark	remark	NOUN
ejpam-5136	156	20	2	2	NUM
ejpam-5136	156	21	.	.	PUNCT
ejpam-5136	157	1	the	the	DET
ejpam-5136	157	2	conditional	conditional	ADJ
ejpam-5136	157	3	variance	variance	NOUN
ejpam-5136	157	4	of	of	ADP
ejpam-5136	157	5	x	x	PUNCT
ejpam-5136	157	6	given	give	VERB
ejpam-5136	157	7	y	y	PROPN
ejpam-5136	157	8	is	be	AUX
ejpam-5136	157	9	given	give	VERB
ejpam-5136	157	10	by	by	ADP
ejpam-5136	157	11	v	v	NOUN
ejpam-5136	157	12	ar(x|y	ar(x|y	NUM
ejpam-5136	157	13	)	)	PUNCT
ejpam-5136	157	14	=	=	X
ejpam-5136	157	15	e[x2|y]−	e[x2|y]−	NOUN
ejpam-5136	157	16	(	(	PUNCT
ejpam-5136	157	17	e[x|y])2	e[x|y])2	VERB
ejpam-5136	157	18	,	,	PUNCT
ejpam-5136	157	19	(	(	PUNCT
ejpam-5136	157	20	9	9	NUM
ejpam-5136	157	21	)	)	PUNCT
ejpam-5136	157	22	where	where	SCONJ
ejpam-5136	157	23	e[x|y	e[x|y	NOUN
ejpam-5136	157	24	]	]	X
ejpam-5136	157	25	is	be	AUX
ejpam-5136	157	26	the	the	DET
ejpam-5136	157	27	conditional	conditional	ADJ
ejpam-5136	157	28	mean	mean	NOUN
ejpam-5136	157	29	of	of	ADP
ejpam-5136	157	30	x	x	PUNCT
ejpam-5136	157	31	given	give	VERB
ejpam-5136	157	32	y	y	PROPN
ejpam-5136	157	33	,	,	PUNCT
ejpam-5136	157	34	and	and	CCONJ
ejpam-5136	157	35	e[x2|y	e[x2|y	VERB
ejpam-5136	157	36	]	]	X
ejpam-5136	157	37	=	=	SYM
ejpam-5136	157	38	1.5	1.5	NUM
ejpam-5136	157	39	{	{	PUNCT
ejpam-5136	157	40	(	(	PUNCT
ejpam-5136	157	41	5+λ	5+λ	NUM
ejpam-5136	157	42	15	15	NUM
ejpam-5136	157	43	)	)	PUNCT
ejpam-5136	158	1	[	[	X
ejpam-5136	158	2	1−	1−	NUM
ejpam-5136	158	3	(	(	PUNCT
ejpam-5136	158	4	2y	2y	PROPN
ejpam-5136	158	5	−	−	PROPN
ejpam-5136	158	6	1)2]−	1)2]−	NUM
ejpam-5136	158	7	(	(	PUNCT
ejpam-5136	158	8	5	5	NUM
ejpam-5136	158	9	+	+	NOUN
ejpam-5136	158	10	2λ	2λ	NUM
ejpam-5136	158	11	20	20	NUM
ejpam-5136	158	12	)	)	PUNCT
ejpam-5136	159	1	[	[	X
ejpam-5136	159	2	1−	1−	NUM
ejpam-5136	159	3	3(2y	3(2y	NUM
ejpam-5136	159	4	−	−	PROPN
ejpam-5136	159	5	1)2	1)2	NUM
ejpam-5136	159	6	]	]	PUNCT
ejpam-5136	159	7	}	}	PUNCT
ejpam-5136	159	8	0.75	0.75	NUM
ejpam-5136	159	9	+	+	CCONJ
ejpam-5136	159	10	0.75(2y	0.75(2y	VERB
ejpam-5136	159	11	−	−	PROPN
ejpam-5136	160	1	1)2	1)2	NUM
ejpam-5136	160	2	.	.	PUNCT
ejpam-5136	161	1	(	(	PUNCT
ejpam-5136	161	2	10	10	NUM
ejpam-5136	161	3	)	)	PUNCT
ejpam-5136	161	4	theorem	theorem	NOUN
ejpam-5136	161	5	5	5	NUM
ejpam-5136	161	6	.	.	PUNCT
ejpam-5136	162	1	let	let	VERB
ejpam-5136	162	2	x	x	PRON
ejpam-5136	162	3	and	and	CCONJ
ejpam-5136	162	4	y	y	PROPN
ejpam-5136	162	5	be	be	AUX
ejpam-5136	162	6	any	any	DET
ejpam-5136	162	7	two	two	NUM
ejpam-5136	162	8	random	random	ADJ
ejpam-5136	162	9	variables	variable	NOUN
ejpam-5136	162	10	with	with	ADP
ejpam-5136	162	11	joint	joint	ADJ
ejpam-5136	162	12	pdf	pdf	NOUN
ejpam-5136	162	13	given	give	VERB
ejpam-5136	162	14	in	in	ADP
ejpam-5136	162	15	equation	equation	NOUN
ejpam-5136	162	16	(	(	PUNCT
ejpam-5136	162	17	3	3	NUM
ejpam-5136	162	18	)	)	PUNCT
ejpam-5136	162	19	.	.	PUNCT
ejpam-5136	163	1	if	if	SCONJ
ejpam-5136	163	2	the	the	DET
ejpam-5136	163	3	conditional	conditional	ADJ
ejpam-5136	163	4	distribution	distribution	NOUN
ejpam-5136	163	5	of	of	ADP
ejpam-5136	163	6	y	y	PROPN
ejpam-5136	163	7	given	give	VERB
ejpam-5136	163	8	x	x	PUNCT
ejpam-5136	163	9	=	=	PUNCT
ejpam-5136	163	10	x	x	X
ejpam-5136	163	11	has	have	VERB
ejpam-5136	163	12	an	an	DET
ejpam-5136	163	13	esu	esu	NOUN
ejpam-5136	163	14	distribution	distribution	NOUN
ejpam-5136	163	15	with	with	ADP
ejpam-5136	163	16	parameter	parameter	NOUN
ejpam-5136	163	17	v(x	v(x	NOUN
ejpam-5136	163	18	)	)	PUNCT
ejpam-5136	164	1	=	=	NOUN
ejpam-5136	164	2	1.5x−	1.5x−	NUM
ejpam-5136	164	3	0.5	0.5	NUM
ejpam-5136	164	4	,	,	PUNCT
ejpam-5136	164	5	then	then	ADV
ejpam-5136	164	6	the	the	DET
ejpam-5136	164	7	sth	sth	PROPN
ejpam-5136	164	8	conditional	conditional	ADJ
ejpam-5136	164	9	moment	moment	NOUN
ejpam-5136	164	10	of	of	ADP
ejpam-5136	164	11	y	y	PROPN
ejpam-5136	164	12	given	give	VERB
ejpam-5136	164	13	x	x	PUNCT
ejpam-5136	164	14	=	=	PUNCT
ejpam-5136	164	15	x	x	PUNCT
ejpam-5136	164	16	is	be	AUX
ejpam-5136	164	17	e[y	e[y	ADJ
ejpam-5136	164	18	s|x	s|x	NOUN
ejpam-5136	165	1	=	=	PUNCT
ejpam-5136	165	2	x	x	X
ejpam-5136	165	3	]	]	X
ejpam-5136	165	4	=	=	PUNCT
ejpam-5136	165	5	6(s+	6(s+	NOUN
ejpam-5136	165	6	1	1	NUM
ejpam-5136	165	7	)	)	PUNCT
ejpam-5136	165	8	+	+	CCONJ
ejpam-5136	165	9	3s(s−	3s(s−	NUM
ejpam-5136	165	10	1)x	1)x	NUM
ejpam-5136	165	11	(	(	PUNCT
ejpam-5136	165	12	s+	s+	NUM
ejpam-5136	165	13	1)(s+	1)(s+	NUM
ejpam-5136	165	14	2)(s+	2)(s+	NUM
ejpam-5136	165	15	3	3	NUM
ejpam-5136	165	16	)	)	PUNCT
ejpam-5136	165	17	.	.	PUNCT
ejpam-5136	166	1	(	(	PUNCT
ejpam-5136	166	2	11	11	NUM
ejpam-5136	166	3	)	)	PUNCT
ejpam-5136	166	4	proof	proof	NOUN
ejpam-5136	166	5	.	.	PUNCT
ejpam-5136	167	1	the	the	DET
ejpam-5136	167	2	sth	sth	PROPN
ejpam-5136	167	3	conditional	conditional	ADJ
ejpam-5136	167	4	moment	moment	NOUN
ejpam-5136	167	5	of	of	ADP
ejpam-5136	167	6	y	y	PROPN
ejpam-5136	167	7	given	give	VERB
ejpam-5136	167	8	x	x	PUNCT
ejpam-5136	167	9	=	=	PUNCT
ejpam-5136	167	10	x	x	PUNCT
ejpam-5136	167	11	is	be	AUX
ejpam-5136	167	12	defined	define	VERB
ejpam-5136	167	13	as	as	ADP
ejpam-5136	167	14	e[y	e[y	ADJ
ejpam-5136	167	15	s|x	s|x	NOUN
ejpam-5136	168	1	=	=	PUNCT
ejpam-5136	168	2	x	x	X
ejpam-5136	168	3	]	]	X
ejpam-5136	168	4	=	=	SYM
ejpam-5136	168	5	∫	∫	PROPN
ejpam-5136	168	6	1	1	NUM
ejpam-5136	168	7	0	0	NUM
ejpam-5136	168	8	ysf(y|x)dy	ysf(y|x)dy	NOUN
ejpam-5136	168	9	.	.	PUNCT
ejpam-5136	169	1	recall	recall	NOUN
ejpam-5136	169	2	from	from	ADP
ejpam-5136	169	3	[	[	X
ejpam-5136	169	4	3	3	X
ejpam-5136	169	5	]	]	PUNCT
ejpam-5136	169	6	that	that	SCONJ
ejpam-5136	169	7	the	the	DET
ejpam-5136	169	8	rth	rth	PROPN
ejpam-5136	169	9	moment	moment	NOUN
ejpam-5136	169	10	of	of	ADP
ejpam-5136	169	11	an	an	DET
ejpam-5136	169	12	esu	esu	NOUN
ejpam-5136	169	13	distribution	distribution	NOUN
ejpam-5136	169	14	is	be	AUX
ejpam-5136	169	15	given	give	VERB
ejpam-5136	169	16	by	by	ADP
ejpam-5136	169	17	e[xr	e[xr	PROPN
ejpam-5136	169	18	]	]	X
ejpam-5136	169	19	=	=	PUNCT
ejpam-5136	169	20	(	(	PUNCT
ejpam-5136	169	21	1	1	NUM
ejpam-5136	169	22	+	+	CCONJ
ejpam-5136	169	23	2λ)r2	2λ)r2	NUM
ejpam-5136	169	24	+	+	CCONJ
ejpam-5136	169	25	(	(	PUNCT
ejpam-5136	169	26	5−	5−	NUM
ejpam-5136	169	27	2λ)r	2λ)r	NUM
ejpam-5136	170	1	+	+	CCONJ
ejpam-5136	171	1	6	6	NUM
ejpam-5136	171	2	(	(	PUNCT
ejpam-5136	171	3	r	r	NOUN
ejpam-5136	171	4	+	+	NUM
ejpam-5136	171	5	1)(r	1)(r	NUM
ejpam-5136	171	6	+	+	SYM
ejpam-5136	171	7	2)(r	2)(r	NUM
ejpam-5136	171	8	+	+	CCONJ
ejpam-5136	171	9	3	3	NUM
ejpam-5136	171	10	)	)	PUNCT
ejpam-5136	171	11	,	,	PUNCT
ejpam-5136	171	12	(	(	PUNCT
ejpam-5136	171	13	12	12	NUM
ejpam-5136	171	14	)	)	PUNCT
ejpam-5136	171	15	where	where	SCONJ
ejpam-5136	171	16	λ	λ	PROPN
ejpam-5136	171	17	∈	∈	PROPN
ejpam-5136	172	1	[	[	X
ejpam-5136	172	2	−0.5	−0.5	PROPN
ejpam-5136	172	3	,	,	PUNCT
ejpam-5136	172	4	1	1	NUM
ejpam-5136	172	5	]	]	PUNCT
ejpam-5136	172	6	.	.	PUNCT
ejpam-5136	173	1	using	use	VERB
ejpam-5136	173	2	equation	equation	NOUN
ejpam-5136	173	3	(	(	PUNCT
ejpam-5136	173	4	12	12	NUM
ejpam-5136	173	5	)	)	PUNCT
ejpam-5136	173	6	for	for	ADP
ejpam-5136	173	7	the	the	DET
ejpam-5136	173	8	sth	sth	PROPN
ejpam-5136	173	9	moment	moment	NOUN
ejpam-5136	173	10	of	of	ADP
ejpam-5136	173	11	y	y	PROPN
ejpam-5136	173	12	|x	|x	PROPN
ejpam-5136	173	13	,	,	PUNCT
ejpam-5136	173	14	we	we	PRON
ejpam-5136	173	15	have	have	VERB
ejpam-5136	173	16	e[y	e[y	VERB
ejpam-5136	173	17	s|x	s|x	NOUN
ejpam-5136	174	1	=	=	PUNCT
ejpam-5136	174	2	x	x	X
ejpam-5136	174	3	]	]	X
ejpam-5136	174	4	=	=	X
ejpam-5136	174	5	(	(	PUNCT
ejpam-5136	174	6	1	1	NUM
ejpam-5136	174	7	+	+	SYM
ejpam-5136	174	8	2v(x))s2	2v(x))s2	NUM
ejpam-5136	174	9	+	+	SYM
ejpam-5136	174	10	(	(	PUNCT
ejpam-5136	174	11	5−	5−	NUM
ejpam-5136	174	12	2v(x))s+	2v(x))s+	NUM
ejpam-5136	174	13	6	6	NUM
ejpam-5136	174	14	(	(	PUNCT
ejpam-5136	174	15	s+	s+	NUM
ejpam-5136	174	16	1)(s+	1)(s+	NUM
ejpam-5136	174	17	2)(s+	2)(s+	NUM
ejpam-5136	174	18	3	3	NUM
ejpam-5136	174	19	)	)	PUNCT
ejpam-5136	174	20	=	=	SYM
ejpam-5136	175	1	6(s+	6(s+	NOUN
ejpam-5136	175	2	1	1	X
ejpam-5136	175	3	)	)	PUNCT
ejpam-5136	175	4	+	+	CCONJ
ejpam-5136	175	5	3s(s−	3s(s−	NUM
ejpam-5136	175	6	1)x	1)x	NUM
ejpam-5136	175	7	(	(	PUNCT
ejpam-5136	175	8	s+	s+	NUM
ejpam-5136	175	9	1)(s+	1)(s+	NUM
ejpam-5136	175	10	2)(s+	2)(s+	NUM
ejpam-5136	175	11	3	3	NUM
ejpam-5136	175	12	)	)	PUNCT
ejpam-5136	175	13	.	.	PUNCT
ejpam-5136	176	1	theorem	theorem	ADJ
ejpam-5136	176	2	6	6	NUM
ejpam-5136	176	3	.	.	PUNCT
ejpam-5136	177	1	let	let	VERB
ejpam-5136	177	2	x	x	PRON
ejpam-5136	177	3	and	and	CCONJ
ejpam-5136	177	4	y	y	PROPN
ejpam-5136	177	5	be	be	AUX
ejpam-5136	177	6	any	any	DET
ejpam-5136	177	7	two	two	NUM
ejpam-5136	177	8	random	random	ADJ
ejpam-5136	177	9	variables	variable	NOUN
ejpam-5136	177	10	with	with	ADP
ejpam-5136	177	11	joint	joint	ADJ
ejpam-5136	177	12	pdf	pdf	NOUN
ejpam-5136	177	13	given	give	VERB
ejpam-5136	177	14	in	in	ADP
ejpam-5136	177	15	equation	equation	NOUN
ejpam-5136	177	16	(	(	PUNCT
ejpam-5136	177	17	3	3	NUM
ejpam-5136	177	18	)	)	PUNCT
ejpam-5136	177	19	,	,	PUNCT
ejpam-5136	177	20	then	then	ADV
ejpam-5136	177	21	the	the	DET
ejpam-5136	177	22	product	product	NOUN
ejpam-5136	177	23	and	and	CCONJ
ejpam-5136	177	24	ratio	ratio	NOUN
ejpam-5136	177	25	moments	moment	NOUN
ejpam-5136	177	26	are	be	AUX
ejpam-5136	177	27	given	give	VERB
ejpam-5136	177	28	by	by	ADP
ejpam-5136	177	29	e	e	PROPN
ejpam-5136	177	30	[	[	X
ejpam-5136	177	31	xry	xry	X
ejpam-5136	177	32	s	s	X
ejpam-5136	177	33	]	]	X
ejpam-5136	177	34	=	=	SYM
ejpam-5136	177	35	1	1	NUM
ejpam-5136	177	36	(	(	PUNCT
ejpam-5136	177	37	s+	s+	NUM
ejpam-5136	177	38	1)(s+	1)(s+	NUM
ejpam-5136	177	39	2)(s+	2)(s+	NUM
ejpam-5136	177	40	3	3	NUM
ejpam-5136	177	41	)	)	PUNCT
ejpam-5136	177	42	[	[	PUNCT
ejpam-5136	177	43	6(s+	6(s+	NUM
ejpam-5136	177	44	1)e[xr	1)e[xr	NOUN
ejpam-5136	177	45	]	]	X
ejpam-5136	178	1	+	+	CCONJ
ejpam-5136	178	2	3s(s−	3s(s−	NUM
ejpam-5136	178	3	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	178	4	]	]	X
ejpam-5136	178	5	]	]	PUNCT
ejpam-5136	178	6	,	,	PUNCT
ejpam-5136	178	7	(	(	PUNCT
ejpam-5136	178	8	13	13	NUM
ejpam-5136	178	9	)	)	PUNCT
ejpam-5136	178	10	and	and	CCONJ
ejpam-5136	178	11	e	e	X
ejpam-5136	178	12	[	[	PUNCT
ejpam-5136	178	13	xry	xry	PROPN
ejpam-5136	178	14	−s	−s	NOUN
ejpam-5136	178	15	]	]	X
ejpam-5136	178	16	=	=	SYM
ejpam-5136	178	17	1	1	NUM
ejpam-5136	178	18	(	(	PUNCT
ejpam-5136	178	19	1−	1−	NUM
ejpam-5136	178	20	s)(2−	s)(2−	PROPN
ejpam-5136	178	21	s)(3−	s)(3−	PROPN
ejpam-5136	178	22	s	s	NOUN
ejpam-5136	178	23	)	)	PUNCT
ejpam-5136	178	24	[	[	PUNCT
ejpam-5136	178	25	6(1−	6(1−	NUM
ejpam-5136	178	26	s)e[xr	s)e[xr	PROPN
ejpam-5136	178	27	]	]	X
ejpam-5136	178	28	+	+	CCONJ
ejpam-5136	178	29	3s(s+	3s(s+	PROPN
ejpam-5136	178	30	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	178	31	]	]	PUNCT
ejpam-5136	178	32	]	]	PUNCT
ejpam-5136	178	33	,	,	PUNCT
ejpam-5136	178	34	(	(	PUNCT
ejpam-5136	178	35	14	14	NUM
ejpam-5136	178	36	)	)	PUNCT
ejpam-5136	178	37	where	where	SCONJ
ejpam-5136	178	38	e[xr	e[xr	PROPN
ejpam-5136	178	39	]	]	X
ejpam-5136	178	40	=	=	PUNCT
ejpam-5136	178	41	(	(	PUNCT
ejpam-5136	178	42	1	1	NUM
ejpam-5136	178	43	+	+	CCONJ
ejpam-5136	178	44	2λ)r2	2λ)r2	NUM
ejpam-5136	178	45	+	+	CCONJ
ejpam-5136	178	46	(	(	PUNCT
ejpam-5136	178	47	5−	5−	NUM
ejpam-5136	178	48	2λ)r	2λ)r	NUM
ejpam-5136	179	1	+	+	CCONJ
ejpam-5136	180	1	6	6	NUM
ejpam-5136	180	2	(	(	PUNCT
ejpam-5136	180	3	r	r	NOUN
ejpam-5136	180	4	+	+	NUM
ejpam-5136	180	5	1)(r	1)(r	NUM
ejpam-5136	180	6	+	+	SYM
ejpam-5136	180	7	2)(r	2)(r	NUM
ejpam-5136	180	8	+	+	CCONJ
ejpam-5136	180	9	3	3	NUM
ejpam-5136	180	10	)	)	PUNCT
ejpam-5136	180	11	,	,	PUNCT
ejpam-5136	180	12	and	and	CCONJ
ejpam-5136	180	13	e[xr+1	e[xr+1	X
ejpam-5136	180	14	]	]	X
ejpam-5136	180	15	=	=	PUNCT
ejpam-5136	180	16	(	(	PUNCT
ejpam-5136	180	17	1	1	NUM
ejpam-5136	180	18	+	+	NUM
ejpam-5136	180	19	2λ)(r	2λ)(r	NUM
ejpam-5136	180	20	+	+	CCONJ
ejpam-5136	180	21	1)2	1)2	NUM
ejpam-5136	180	22	+	+	CCONJ
ejpam-5136	180	23	(	(	PUNCT
ejpam-5136	180	24	5−	5−	NUM
ejpam-5136	180	25	2λ)(r	2λ)(r	NUM
ejpam-5136	180	26	+	+	CCONJ
ejpam-5136	180	27	1	1	X
ejpam-5136	180	28	)	)	PUNCT
ejpam-5136	180	29	+	+	CCONJ
ejpam-5136	180	30	6	6	NUM
ejpam-5136	180	31	(	(	PUNCT
ejpam-5136	180	32	r	r	NOUN
ejpam-5136	180	33	+	+	NUM
ejpam-5136	180	34	2)(r	2)(r	NUM
ejpam-5136	180	35	+	+	SYM
ejpam-5136	180	36	2)(r	2)(r	NUM
ejpam-5136	180	37	+	+	CCONJ
ejpam-5136	180	38	4	4	NUM
ejpam-5136	180	39	)	)	PUNCT
ejpam-5136	180	40	.	.	PUNCT
ejpam-5136	181	1	i.	i.	PROPN
ejpam-5136	181	2	a.	a.	PROPN
ejpam-5136	181	3	lakibul	lakibul	PROPN
ejpam-5136	181	4	,	,	PUNCT
ejpam-5136	181	5	d.	d.	PROPN
ejpam-5136	181	6	l.	l.	PROPN
ejpam-5136	181	7	polestico	polestico	PROPN
ejpam-5136	181	8	,	,	PUNCT
ejpam-5136	181	9	a.	a.	PROPN
ejpam-5136	181	10	p.	p.	NOUN
ejpam-5136	181	11	supe	supe	PROPN
ejpam-5136	181	12	/	/	SYM
ejpam-5136	181	13	eur	eur	PROPN
ejpam-5136	181	14	.	.	PUNCT
ejpam-5136	182	1	j.	j.	PROPN
ejpam-5136	182	2	pure	pure	PROPN
ejpam-5136	182	3	appl	appl	PROPN
ejpam-5136	182	4	.	.	PROPN
ejpam-5136	182	5	math	math	PROPN
ejpam-5136	182	6	,	,	PUNCT
ejpam-5136	182	7	17	17	NUM
ejpam-5136	182	8	(	(	PUNCT
ejpam-5136	182	9	2	2	NUM
ejpam-5136	182	10	)	)	PUNCT
ejpam-5136	182	11	(	(	PUNCT
ejpam-5136	182	12	2024	2024	NUM
ejpam-5136	182	13	)	)	PUNCT
ejpam-5136	182	14	,	,	PUNCT
ejpam-5136	182	15	790	790	NUM
ejpam-5136	182	16	-	-	SYM
ejpam-5136	182	17	809	809	NUM
ejpam-5136	182	18	798	798	NUM
ejpam-5136	182	19	proof	proof	NOUN
ejpam-5136	182	20	.	.	PUNCT
ejpam-5136	183	1	the	the	DET
ejpam-5136	183	2	product	product	NOUN
ejpam-5136	183	3	moment	moment	NOUN
ejpam-5136	183	4	of	of	ADP
ejpam-5136	183	5	x	x	PUNCT
ejpam-5136	183	6	and	and	CCONJ
ejpam-5136	183	7	y	y	PROPN
ejpam-5136	183	8	is	be	AUX
ejpam-5136	183	9	defined	define	VERB
ejpam-5136	183	10	as	as	ADP
ejpam-5136	183	11	e	e	PROPN
ejpam-5136	183	12	[	[	X
ejpam-5136	183	13	xry	xry	X
ejpam-5136	183	14	s	s	X
ejpam-5136	183	15	]	]	X
ejpam-5136	183	16	=	=	SYM
ejpam-5136	183	17	∫	∫	PROPN
ejpam-5136	183	18	1	1	NUM
ejpam-5136	183	19	0	0	NUM
ejpam-5136	183	20	∫	∫	PROPN
ejpam-5136	183	21	1	1	NUM
ejpam-5136	183	22	0	0	NUM
ejpam-5136	183	23	xrysf(x	xrysf(x	PROPN
ejpam-5136	183	24	,	,	PUNCT
ejpam-5136	183	25	y)dxdy	y)dxdy	X
ejpam-5136	184	1	=	=	SYM
ejpam-5136	184	2	1	1	NUM
ejpam-5136	184	3	(	(	PUNCT
ejpam-5136	184	4	s+	s+	NUM
ejpam-5136	184	5	1)(s+	1)(s+	NUM
ejpam-5136	184	6	2)(s+	2)(s+	NUM
ejpam-5136	184	7	3	3	NUM
ejpam-5136	184	8	)	)	PUNCT
ejpam-5136	184	9	[	[	PUNCT
ejpam-5136	184	10	6(s+	6(s+	NOUN
ejpam-5136	184	11	1	1	NUM
ejpam-5136	184	12	)	)	PUNCT
ejpam-5136	184	13	∫	∫	PROPN
ejpam-5136	184	14	1	1	NUM
ejpam-5136	184	15	0	0	NUM
ejpam-5136	184	16	xrf(x)dx	xrf(x)dx	PUNCT
ejpam-5136	184	17	+	+	CCONJ
ejpam-5136	184	18	3s(s−	3s(s−	NUM
ejpam-5136	184	19	1	1	NUM
ejpam-5136	184	20	)	)	PUNCT
ejpam-5136	184	21	∫	∫	PROPN
ejpam-5136	185	1	1	1	NUM
ejpam-5136	185	2	0	0	NUM
ejpam-5136	185	3	xr+1f(x)dx	xr+1f(x)dx	NUM
ejpam-5136	185	4	]	]	PUNCT
ejpam-5136	186	1	=	=	SYM
ejpam-5136	186	2	1	1	NUM
ejpam-5136	186	3	(	(	PUNCT
ejpam-5136	186	4	s+	s+	NUM
ejpam-5136	186	5	1)(s+	1)(s+	NUM
ejpam-5136	186	6	2)(s+	2)(s+	NUM
ejpam-5136	186	7	3	3	NUM
ejpam-5136	186	8	)	)	PUNCT
ejpam-5136	186	9	[	[	PUNCT
ejpam-5136	186	10	6(s+	6(s+	NUM
ejpam-5136	186	11	1)e[xr	1)e[xr	NOUN
ejpam-5136	186	12	]	]	X
ejpam-5136	187	1	+	+	CCONJ
ejpam-5136	187	2	3s(s−	3s(s−	NUM
ejpam-5136	187	3	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	187	4	]	]	X
ejpam-5136	187	5	]	]	PUNCT
ejpam-5136	187	6	,	,	PUNCT
ejpam-5136	187	7	where	where	SCONJ
ejpam-5136	187	8	e[xr	e[xr	PROPN
ejpam-5136	187	9	]	]	X
ejpam-5136	187	10	=	=	PUNCT
ejpam-5136	187	11	(	(	PUNCT
ejpam-5136	187	12	1	1	NUM
ejpam-5136	187	13	+	+	CCONJ
ejpam-5136	187	14	2λ)r2	2λ)r2	NUM
ejpam-5136	187	15	+	+	CCONJ
ejpam-5136	187	16	(	(	PUNCT
ejpam-5136	187	17	5−	5−	NUM
ejpam-5136	187	18	2λ)r	2λ)r	NUM
ejpam-5136	187	19	+	+	CCONJ
ejpam-5136	187	20	6	6	NUM
ejpam-5136	187	21	(	(	PUNCT
ejpam-5136	187	22	r	r	NOUN
ejpam-5136	187	23	+	+	NUM
ejpam-5136	187	24	1)(r	1)(r	NUM
ejpam-5136	187	25	+	+	SYM
ejpam-5136	187	26	2)(r	2)(r	NUM
ejpam-5136	187	27	+	+	CCONJ
ejpam-5136	187	28	3	3	NUM
ejpam-5136	187	29	)	)	PUNCT
ejpam-5136	187	30	,	,	PUNCT
ejpam-5136	187	31	and	and	CCONJ
ejpam-5136	187	32	e[xr+1	e[xr+1	X
ejpam-5136	187	33	]	]	X
ejpam-5136	187	34	=	=	PUNCT
ejpam-5136	187	35	(	(	PUNCT
ejpam-5136	187	36	1	1	NUM
ejpam-5136	187	37	+	+	NUM
ejpam-5136	187	38	2λ)(r	2λ)(r	NUM
ejpam-5136	188	1	+	+	CCONJ
ejpam-5136	188	2	1)2	1)2	NUM
ejpam-5136	188	3	+	+	CCONJ
ejpam-5136	188	4	(	(	PUNCT
ejpam-5136	188	5	5−	5−	NUM
ejpam-5136	188	6	2λ)(r	2λ)(r	NUM
ejpam-5136	188	7	+	+	CCONJ
ejpam-5136	188	8	1	1	X
ejpam-5136	188	9	)	)	PUNCT
ejpam-5136	189	1	+	+	CCONJ
ejpam-5136	189	2	6	6	NUM
ejpam-5136	189	3	(	(	PUNCT
ejpam-5136	189	4	r	r	NOUN
ejpam-5136	189	5	+	+	NUM
ejpam-5136	189	6	2)(r	2)(r	NUM
ejpam-5136	189	7	+	+	CCONJ
ejpam-5136	189	8	3)(r	3)(r	NUM
ejpam-5136	189	9	+	+	NUM
ejpam-5136	189	10	4	4	NUM
ejpam-5136	189	11	)	)	PUNCT
ejpam-5136	189	12	.	.	PUNCT
ejpam-5136	190	1	next	next	ADV
ejpam-5136	190	2	,	,	PUNCT
ejpam-5136	190	3	the	the	DET
ejpam-5136	190	4	ratio	ratio	NOUN
ejpam-5136	190	5	moment	moment	NOUN
ejpam-5136	190	6	of	of	ADP
ejpam-5136	190	7	x	x	X
ejpam-5136	190	8	and	and	CCONJ
ejpam-5136	190	9	y	y	PROPN
ejpam-5136	190	10	is	be	AUX
ejpam-5136	190	11	defined	define	VERB
ejpam-5136	190	12	as	as	ADP
ejpam-5136	190	13	e	e	PROPN
ejpam-5136	190	14	[	[	PUNCT
ejpam-5136	190	15	xr	xr	PROPN
ejpam-5136	190	16	y	y	PROPN
ejpam-5136	190	17	s	s	PART
ejpam-5136	190	18	]	]	PUNCT
ejpam-5136	190	19	=	=	SYM
ejpam-5136	190	20	e	e	X
ejpam-5136	190	21	[	[	PUNCT
ejpam-5136	190	22	xry	xry	PROPN
ejpam-5136	190	23	−s	−s	NOUN
ejpam-5136	190	24	]	]	X
ejpam-5136	191	1	=	=	SYM
ejpam-5136	191	2	1	1	NUM
ejpam-5136	191	3	(	(	PUNCT
ejpam-5136	191	4	1−	1−	NUM
ejpam-5136	191	5	s)(2−	s)(2−	PROPN
ejpam-5136	191	6	s)(3−	s)(3−	PROPN
ejpam-5136	191	7	s	s	NOUN
ejpam-5136	191	8	)	)	PUNCT
ejpam-5136	191	9	[	[	PUNCT
ejpam-5136	191	10	6(1−	6(1−	NUM
ejpam-5136	191	11	s)e[xr	s)e[xr	PROPN
ejpam-5136	191	12	]	]	X
ejpam-5136	191	13	+	+	CCONJ
ejpam-5136	191	14	3s(s+	3s(s+	PROPN
ejpam-5136	191	15	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	191	16	]	]	PUNCT
ejpam-5136	191	17	]	]	PUNCT
ejpam-5136	191	18	.	.	PUNCT
ejpam-5136	192	1	remark	remark	PROPN
ejpam-5136	192	2	3	3	NUM
ejpam-5136	192	3	.	.	PUNCT
ejpam-5136	193	1	the	the	DET
ejpam-5136	193	2	covariance	covariance	NOUN
ejpam-5136	193	3	of	of	ADP
ejpam-5136	193	4	x	x	PUNCT
ejpam-5136	193	5	and	and	CCONJ
ejpam-5136	193	6	y	y	PROPN
ejpam-5136	193	7	is	be	AUX
ejpam-5136	193	8	given	give	VERB
ejpam-5136	193	9	by	by	ADP
ejpam-5136	193	10	cov(x	cov(x	PROPN
ejpam-5136	193	11	,	,	PUNCT
ejpam-5136	193	12	y	y	PROPN
ejpam-5136	193	13	)	)	PUNCT
ejpam-5136	194	1	=	=	NOUN
ejpam-5136	194	2	e[xy	e[xy	ADJ
ejpam-5136	194	3	]	]	PUNCT
ejpam-5136	194	4	−	−	NOUN
ejpam-5136	194	5	e[x]e[y	e[x]e[y	NOUN
ejpam-5136	194	6	]	]	X
ejpam-5136	194	7	=	=	SYM
ejpam-5136	194	8	1	1	NUM
ejpam-5136	194	9	4	4	NUM
ejpam-5136	194	10	−	−	NOUN
ejpam-5136	194	11	1	1	NUM
ejpam-5136	194	12	2	2	NUM
ejpam-5136	194	13	(	(	PUNCT
ejpam-5136	194	14	1	1	NUM
ejpam-5136	194	15	2	2	NUM
ejpam-5136	194	16	)	)	PUNCT
ejpam-5136	194	17	=	=	SYM
ejpam-5136	195	1	0	0	X
ejpam-5136	195	2	.	.	PUNCT
ejpam-5136	195	3	remark	remark	PROPN
ejpam-5136	195	4	4	4	NUM
ejpam-5136	195	5	.	.	PUNCT
ejpam-5136	196	1	the	the	DET
ejpam-5136	196	2	pearson	pearson	PROPN
ejpam-5136	196	3	correlation	correlation	NOUN
ejpam-5136	196	4	or	or	CCONJ
ejpam-5136	196	5	correlation	correlation	NOUN
ejpam-5136	196	6	coefficient	coefficient	NOUN
ejpam-5136	196	7	of	of	ADP
ejpam-5136	196	8	x	x	PUNCT
ejpam-5136	196	9	and	and	CCONJ
ejpam-5136	196	10	y	y	PROPN
ejpam-5136	196	11	is	be	AUX
ejpam-5136	196	12	zero	zero	NUM
ejpam-5136	196	13	.	.	PUNCT
ejpam-5136	197	1	note	note	VERB
ejpam-5136	197	2	that	that	SCONJ
ejpam-5136	197	3	the	the	DET
ejpam-5136	197	4	correlation	correlation	NOUN
ejpam-5136	197	5	coefficient	coefficient	NOUN
ejpam-5136	197	6	of	of	ADP
ejpam-5136	197	7	x	x	PUNCT
ejpam-5136	197	8	and	and	CCONJ
ejpam-5136	197	9	y	y	PROPN
ejpam-5136	197	10	is	be	AUX
ejpam-5136	197	11	zero	zero	NUM
ejpam-5136	197	12	since	since	SCONJ
ejpam-5136	197	13	the	the	DET
ejpam-5136	197	14	covariance	covariance	NOUN
ejpam-5136	197	15	of	of	ADP
ejpam-5136	197	16	x	x	PUNCT
ejpam-5136	197	17	and	and	CCONJ
ejpam-5136	197	18	y	y	PROPN
ejpam-5136	197	19	is	be	AUX
ejpam-5136	197	20	zero	zero	NUM
ejpam-5136	197	21	.	.	PUNCT
ejpam-5136	198	1	this	this	PRON
ejpam-5136	198	2	implies	imply	VERB
ejpam-5136	198	3	that	that	SCONJ
ejpam-5136	198	4	there	there	PRON
ejpam-5136	198	5	is	be	VERB
ejpam-5136	198	6	no	no	DET
ejpam-5136	198	7	linear	linear	ADJ
ejpam-5136	198	8	relationship	relationship	NOUN
ejpam-5136	198	9	between	between	ADP
ejpam-5136	198	10	x	x	PROPN
ejpam-5136	198	11	and	and	CCONJ
ejpam-5136	198	12	y	y	PROPN
ejpam-5136	198	13	.	.	PUNCT
ejpam-5136	199	1	a	a	DET
ejpam-5136	199	2	nonlinear	nonlinear	ADJ
ejpam-5136	199	3	form	form	NOUN
ejpam-5136	199	4	may	may	AUX
ejpam-5136	199	5	best	well	ADV
ejpam-5136	199	6	describe	describe	VERB
ejpam-5136	199	7	the	the	DET
ejpam-5136	199	8	relationship	relationship	NOUN
ejpam-5136	199	9	between	between	ADP
ejpam-5136	199	10	x	x	PROPN
ejpam-5136	199	11	and	and	CCONJ
ejpam-5136	199	12	y	y	PROPN
ejpam-5136	199	13	.	.	PUNCT
ejpam-5136	200	1	theorem	theorem	VERB
ejpam-5136	200	2	7	7	NUM
ejpam-5136	200	3	.	.	PUNCT
ejpam-5136	201	1	let	let	VERB
ejpam-5136	201	2	(	(	PUNCT
ejpam-5136	201	3	x	x	X
ejpam-5136	201	4	,	,	PUNCT
ejpam-5136	201	5	y	y	PROPN
ejpam-5136	201	6	)	)	PUNCT
ejpam-5136	201	7	be	be	AUX
ejpam-5136	201	8	a	a	DET
ejpam-5136	201	9	bivariate	bivariate	ADJ
ejpam-5136	201	10	random	random	ADJ
ejpam-5136	201	11	vector	vector	NOUN
ejpam-5136	201	12	that	that	PRON
ejpam-5136	201	13	follows	follow	VERB
ejpam-5136	201	14	a	a	DET
ejpam-5136	201	15	bivariate	bivariate	ADJ
ejpam-5136	201	16	extended	extended	ADJ
ejpam-5136	201	17	standard	standard	ADJ
ejpam-5136	201	18	u	u	ADJ
ejpam-5136	201	19	-	-	ADJ
ejpam-5136	201	20	quadratic	quadratic	ADJ
ejpam-5136	201	21	distribution	distribution	NOUN
ejpam-5136	201	22	,	,	PUNCT
ejpam-5136	201	23	then	then	ADV
ejpam-5136	201	24	the	the	DET
ejpam-5136	201	25	joint	joint	ADJ
ejpam-5136	201	26	moment	moment	NOUN
ejpam-5136	201	27	generating	generate	VERB
ejpam-5136	201	28	function	function	NOUN
ejpam-5136	201	29	of	of	ADP
ejpam-5136	201	30	x	x	PUNCT
ejpam-5136	201	31	and	and	CCONJ
ejpam-5136	201	32	y	y	PROPN
ejpam-5136	201	33	is	be	AUX
ejpam-5136	201	34	given	give	VERB
ejpam-5136	201	35	by	by	ADP
ejpam-5136	201	36	mx	mx	PROPN
ejpam-5136	201	37	,	,	PUNCT
ejpam-5136	201	38	y	y	PROPN
ejpam-5136	201	39	(	(	PUNCT
ejpam-5136	201	40	t1	t1	PROPN
ejpam-5136	201	41	,	,	PUNCT
ejpam-5136	201	42	t2	t2	NOUN
ejpam-5136	201	43	)	)	PUNCT
ejpam-5136	201	44	=	=	SYM
ejpam-5136	201	45	3	3	NUM
ejpam-5136	201	46	(	(	PUNCT
ejpam-5136	201	47	s+	s+	NUM
ejpam-5136	201	48	2)(s+	2)(s+	NUM
ejpam-5136	201	49	3	3	NUM
ejpam-5136	201	50	)	)	PUNCT
ejpam-5136	201	51	∞∑	∞∑	NUM
ejpam-5136	201	52	r=0	r=0	ADJ
ejpam-5136	201	53	tr1	tr1	NOUN
ejpam-5136	201	54	r	r	NOUN
ejpam-5136	201	55	!	!	PUNCT
ejpam-5136	202	1	∞∑	∞∑	NUM
ejpam-5136	202	2	s=0	s=0	PROPN
ejpam-5136	202	3	ts2	ts2	PROPN
ejpam-5136	202	4	s	s	PART
ejpam-5136	202	5	!	!	PUNCT
ejpam-5136	203	1	[	[	PUNCT
ejpam-5136	203	2	2e[xr	2e[xr	NUM
ejpam-5136	203	3	]	]	X
ejpam-5136	204	1	+	+	CCONJ
ejpam-5136	204	2	s(s−	s(s−	PROPN
ejpam-5136	204	3	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	204	4	]	]	X
ejpam-5136	204	5	(	(	PUNCT
ejpam-5136	204	6	s+	s+	X
ejpam-5136	204	7	1	1	NUM
ejpam-5136	204	8	)	)	PUNCT
ejpam-5136	204	9	]	]	PUNCT
ejpam-5136	204	10	,	,	PUNCT
ejpam-5136	204	11	(	(	PUNCT
ejpam-5136	204	12	15	15	X
ejpam-5136	204	13	)	)	PUNCT
ejpam-5136	204	14	i.	i.	NOUN
ejpam-5136	204	15	a.	a.	PROPN
ejpam-5136	204	16	lakibul	lakibul	PROPN
ejpam-5136	204	17	,	,	PUNCT
ejpam-5136	204	18	d.	d.	PROPN
ejpam-5136	204	19	l.	l.	PROPN
ejpam-5136	204	20	polestico	polestico	PROPN
ejpam-5136	204	21	,	,	PUNCT
ejpam-5136	204	22	a.	a.	PROPN
ejpam-5136	204	23	p.	p.	NOUN
ejpam-5136	204	24	supe	supe	PROPN
ejpam-5136	204	25	/	/	SYM
ejpam-5136	204	26	eur	eur	PROPN
ejpam-5136	204	27	.	.	PUNCT
ejpam-5136	205	1	j.	j.	PROPN
ejpam-5136	205	2	pure	pure	PROPN
ejpam-5136	205	3	appl	appl	PROPN
ejpam-5136	205	4	.	.	PROPN
ejpam-5136	205	5	math	math	PROPN
ejpam-5136	205	6	,	,	PUNCT
ejpam-5136	205	7	17	17	NUM
ejpam-5136	205	8	(	(	PUNCT
ejpam-5136	205	9	2	2	NUM
ejpam-5136	205	10	)	)	PUNCT
ejpam-5136	205	11	(	(	PUNCT
ejpam-5136	205	12	2024	2024	NUM
ejpam-5136	205	13	)	)	PUNCT
ejpam-5136	205	14	,	,	PUNCT
ejpam-5136	205	15	790	790	NUM
ejpam-5136	205	16	-	-	SYM
ejpam-5136	205	17	809	809	NUM
ejpam-5136	205	18	799	799	NUM
ejpam-5136	205	19	where	where	SCONJ
ejpam-5136	205	20	e[xr	e[xr	PROPN
ejpam-5136	205	21	]	]	X
ejpam-5136	205	22	=	=	PUNCT
ejpam-5136	205	23	(	(	PUNCT
ejpam-5136	205	24	1	1	NUM
ejpam-5136	206	1	+	+	CCONJ
ejpam-5136	206	2	2λ)r2	2λ)r2	NUM
ejpam-5136	206	3	+	+	CCONJ
ejpam-5136	206	4	(	(	PUNCT
ejpam-5136	206	5	5−	5−	NUM
ejpam-5136	206	6	2λ)r	2λ)r	NUM
ejpam-5136	207	1	+	+	CCONJ
ejpam-5136	208	1	6	6	NUM
ejpam-5136	208	2	(	(	PUNCT
ejpam-5136	208	3	r	r	NOUN
ejpam-5136	208	4	+	+	NUM
ejpam-5136	208	5	1)(r	1)(r	NUM
ejpam-5136	208	6	+	+	SYM
ejpam-5136	208	7	2)(r	2)(r	NUM
ejpam-5136	208	8	+	+	CCONJ
ejpam-5136	208	9	3	3	NUM
ejpam-5136	208	10	)	)	PUNCT
ejpam-5136	208	11	,	,	PUNCT
ejpam-5136	208	12	and	and	CCONJ
ejpam-5136	208	13	e[xr+1	e[xr+1	X
ejpam-5136	208	14	]	]	X
ejpam-5136	208	15	=	=	PUNCT
ejpam-5136	208	16	(	(	PUNCT
ejpam-5136	208	17	1	1	NUM
ejpam-5136	208	18	+	+	NUM
ejpam-5136	208	19	2λ)(r	2λ)(r	NUM
ejpam-5136	208	20	+	+	CCONJ
ejpam-5136	208	21	1)2	1)2	NUM
ejpam-5136	208	22	+	+	CCONJ
ejpam-5136	208	23	(	(	PUNCT
ejpam-5136	208	24	5−	5−	NUM
ejpam-5136	208	25	2λ)(r	2λ)(r	NUM
ejpam-5136	208	26	+	+	CCONJ
ejpam-5136	208	27	1	1	X
ejpam-5136	208	28	)	)	PUNCT
ejpam-5136	208	29	+	+	CCONJ
ejpam-5136	208	30	6	6	NUM
ejpam-5136	208	31	(	(	PUNCT
ejpam-5136	208	32	r	r	NOUN
ejpam-5136	208	33	+	+	NUM
ejpam-5136	208	34	2)(r	2)(r	NUM
ejpam-5136	208	35	+	+	CCONJ
ejpam-5136	208	36	3)(r	3)(r	NUM
ejpam-5136	208	37	+	+	NUM
ejpam-5136	208	38	4	4	NUM
ejpam-5136	208	39	)	)	PUNCT
ejpam-5136	208	40	.	.	PUNCT
ejpam-5136	209	1	proof	proof	NOUN
ejpam-5136	209	2	.	.	PUNCT
ejpam-5136	210	1	the	the	DET
ejpam-5136	210	2	joint	joint	ADJ
ejpam-5136	210	3	moment	moment	NOUN
ejpam-5136	210	4	generating	generate	VERB
ejpam-5136	210	5	function	function	NOUN
ejpam-5136	210	6	of	of	ADP
ejpam-5136	210	7	x	x	PUNCT
ejpam-5136	210	8	and	and	CCONJ
ejpam-5136	210	9	y	y	PROPN
ejpam-5136	210	10	is	be	AUX
ejpam-5136	210	11	defined	define	VERB
ejpam-5136	210	12	as	as	ADP
ejpam-5136	210	13	mx	mx	PROPN
ejpam-5136	210	14	,	,	PUNCT
ejpam-5136	210	15	y	y	PROPN
ejpam-5136	210	16	(	(	PUNCT
ejpam-5136	210	17	t1	t1	PROPN
ejpam-5136	210	18	,	,	PUNCT
ejpam-5136	210	19	t2	t2	NOUN
ejpam-5136	210	20	)	)	PUNCT
ejpam-5136	211	1	=	=	SYM
ejpam-5136	211	2	∫	∫	PROPN
ejpam-5136	211	3	1	1	NUM
ejpam-5136	211	4	0	0	NUM
ejpam-5136	211	5	∫	∫	PROPN
ejpam-5136	211	6	1	1	NUM
ejpam-5136	211	7	0	0	NUM
ejpam-5136	211	8	et1x+t2yf(x	et1x+t2yf(x	NOUN
ejpam-5136	211	9	,	,	PUNCT
ejpam-5136	211	10	y)dydx	y)dydx	PROPN
ejpam-5136	212	1	=	=	SYM
ejpam-5136	212	2	∫	∫	PROPN
ejpam-5136	212	3	1	1	NUM
ejpam-5136	212	4	0	0	NUM
ejpam-5136	212	5	∫	∫	PROPN
ejpam-5136	212	6	1	1	NUM
ejpam-5136	212	7	0	0	NUM
ejpam-5136	212	8	et1xet2y	et1xet2y	PROPN
ejpam-5136	212	9	[	[	PUNCT
ejpam-5136	212	10	1.5−	1.5−	NUM
ejpam-5136	212	11	1.5x+	1.5x+	NUM
ejpam-5136	212	12	3(1.5x−	3(1.5x−	NUM
ejpam-5136	212	13	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	213	1	−	−	PROPN
ejpam-5136	213	2	1)2	1)2	NUM
ejpam-5136	213	3	]	]	PUNCT
ejpam-5136	213	4	f(x)dydx	f(x)dydx	PROPN
ejpam-5136	213	5	.	.	PUNCT
ejpam-5136	214	1	recall	recall	VERB
ejpam-5136	214	2	that	that	DET
ejpam-5136	214	3	etx	etx	NOUN
ejpam-5136	215	1	=	=	SYM
ejpam-5136	215	2	∑∞	∑∞	NOUN
ejpam-5136	216	1	r=0	r=0	VERB
ejpam-5136	216	2	tr	tr	NOUN
ejpam-5136	216	3	r!x	r!x	PROPN
ejpam-5136	216	4	r	r	NOUN
ejpam-5136	216	5	,	,	PUNCT
ejpam-5136	216	6	then	then	ADV
ejpam-5136	216	7	we	we	PRON
ejpam-5136	216	8	have	have	VERB
ejpam-5136	216	9	mx	mx	PROPN
ejpam-5136	216	10	,	,	PUNCT
ejpam-5136	216	11	y	y	PROPN
ejpam-5136	216	12	(	(	PUNCT
ejpam-5136	216	13	t1	t1	PROPN
ejpam-5136	216	14	,	,	PUNCT
ejpam-5136	216	15	t2	t2	NOUN
ejpam-5136	216	16	)	)	PUNCT
ejpam-5136	216	17	=	=	SYM
ejpam-5136	217	1	∫	∫	PROPN
ejpam-5136	217	2	1	1	NUM
ejpam-5136	217	3	0	0	NUM
ejpam-5136	217	4	∫	∫	PROPN
ejpam-5136	217	5	1	1	NUM
ejpam-5136	217	6	0	0	NUM
ejpam-5136	217	7	∞∑	∞∑	NUM
ejpam-5136	217	8	r=0	r=0	ADJ
ejpam-5136	217	9	tr1	tr1	NOUN
ejpam-5136	217	10	r	r	NOUN
ejpam-5136	217	11	!	!	PUNCT
ejpam-5136	217	12	xr	xr	PROPN
ejpam-5136	218	1	∞∑	∞∑	PROPN
ejpam-5136	218	2	s=0	s=0	PROPN
ejpam-5136	218	3	ts2	ts2	PROPN
ejpam-5136	218	4	s	s	PART
ejpam-5136	218	5	!	!	PUNCT
ejpam-5136	218	6	ys	ys	PROPN
ejpam-5136	219	1	[	[	PUNCT
ejpam-5136	219	2	1.5−	1.5−	NUM
ejpam-5136	219	3	1.5x+	1.5x+	NUM
ejpam-5136	219	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	219	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	219	6	−	−	PROPN
ejpam-5136	219	7	1)2	1)2	NUM
ejpam-5136	219	8	]	]	PUNCT
ejpam-5136	219	9	f(x)dydx	f(x)dydx	PROPN
ejpam-5136	220	1	=	=	SYM
ejpam-5136	220	2	∫	∫	PROPN
ejpam-5136	220	3	1	1	NUM
ejpam-5136	220	4	0	0	NUM
ejpam-5136	221	1	∞∑	∞∑	NUM
ejpam-5136	221	2	r1=0	r1=0	PROPN
ejpam-5136	221	3	tr1	tr1	NOUN
ejpam-5136	221	4	r	r	NOUN
ejpam-5136	221	5	!	!	PUNCT
ejpam-5136	221	6	xr	xr	PROPN
ejpam-5136	221	7	{	{	PUNCT
ejpam-5136	221	8	∫	∫	PROPN
ejpam-5136	221	9	1	1	NUM
ejpam-5136	221	10	0	0	NUM
ejpam-5136	222	1	∞∑	∞∑	NUM
ejpam-5136	222	2	s=0	s=0	ADJ
ejpam-5136	222	3	ts2	ts2	PROPN
ejpam-5136	222	4	s	s	PART
ejpam-5136	222	5	!	!	PUNCT
ejpam-5136	222	6	ys	ys	PROPN
ejpam-5136	223	1	[	[	PUNCT
ejpam-5136	223	2	1.5−	1.5−	NUM
ejpam-5136	223	3	1.5x+	1.5x+	NUM
ejpam-5136	223	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	223	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	223	6	−	−	PROPN
ejpam-5136	223	7	1)2	1)2	NUM
ejpam-5136	223	8	]	]	PUNCT
ejpam-5136	223	9	dy	dy	NOUN
ejpam-5136	223	10	}	}	PUNCT
ejpam-5136	223	11	f(x)dx	f(x)dx	NOUN
ejpam-5136	223	12	=	=	NOUN
ejpam-5136	223	13	3	3	NUM
ejpam-5136	223	14	(	(	PUNCT
ejpam-5136	223	15	s+	s+	NUM
ejpam-5136	223	16	2)(s+	2)(s+	NUM
ejpam-5136	223	17	3	3	NUM
ejpam-5136	223	18	)	)	PUNCT
ejpam-5136	223	19	∞∑	∞∑	NUM
ejpam-5136	223	20	r=0	r=0	ADJ
ejpam-5136	223	21	tr1	tr1	NOUN
ejpam-5136	223	22	r	r	NOUN
ejpam-5136	223	23	!	!	PUNCT
ejpam-5136	224	1	∞∑	∞∑	NUM
ejpam-5136	224	2	s=0	s=0	PROPN
ejpam-5136	224	3	ts2	ts2	PROPN
ejpam-5136	224	4	s	s	PART
ejpam-5136	224	5	!	!	PUNCT
ejpam-5136	225	1	[	[	PUNCT
ejpam-5136	225	2	2e[xr	2e[xr	NUM
ejpam-5136	225	3	]	]	X
ejpam-5136	226	1	+	+	CCONJ
ejpam-5136	226	2	s(s−	s(s−	PROPN
ejpam-5136	226	3	1)e[xr+1	1)e[xr+1	PROPN
ejpam-5136	226	4	]	]	X
ejpam-5136	226	5	(	(	PUNCT
ejpam-5136	226	6	s+	s+	X
ejpam-5136	226	7	1	1	NUM
ejpam-5136	226	8	)	)	PUNCT
ejpam-5136	226	9	]	]	PUNCT
ejpam-5136	226	10	,	,	PUNCT
ejpam-5136	226	11	where	where	SCONJ
ejpam-5136	226	12	e[xr	e[xr	PROPN
ejpam-5136	226	13	]	]	X
ejpam-5136	226	14	=	=	PUNCT
ejpam-5136	226	15	(	(	PUNCT
ejpam-5136	226	16	1	1	NUM
ejpam-5136	226	17	+	+	CCONJ
ejpam-5136	226	18	2λ)r2	2λ)r2	NUM
ejpam-5136	226	19	+	+	CCONJ
ejpam-5136	226	20	(	(	PUNCT
ejpam-5136	226	21	5−	5−	NUM
ejpam-5136	226	22	2λ)r	2λ)r	NUM
ejpam-5136	227	1	+	+	CCONJ
ejpam-5136	228	1	6	6	NUM
ejpam-5136	228	2	(	(	PUNCT
ejpam-5136	228	3	r	r	NOUN
ejpam-5136	228	4	+	+	NUM
ejpam-5136	228	5	1)(r	1)(r	NUM
ejpam-5136	228	6	+	+	SYM
ejpam-5136	228	7	2)(r	2)(r	NUM
ejpam-5136	228	8	+	+	CCONJ
ejpam-5136	228	9	3	3	NUM
ejpam-5136	228	10	)	)	PUNCT
ejpam-5136	228	11	,	,	PUNCT
ejpam-5136	228	12	and	and	CCONJ
ejpam-5136	228	13	e[xr+1	e[xr+1	X
ejpam-5136	228	14	]	]	X
ejpam-5136	228	15	=	=	PUNCT
ejpam-5136	228	16	(	(	PUNCT
ejpam-5136	228	17	1	1	NUM
ejpam-5136	228	18	+	+	NUM
ejpam-5136	228	19	2λ)(r	2λ)(r	NUM
ejpam-5136	228	20	+	+	CCONJ
ejpam-5136	228	21	1)2	1)2	NUM
ejpam-5136	228	22	+	+	CCONJ
ejpam-5136	228	23	(	(	PUNCT
ejpam-5136	228	24	5−	5−	NUM
ejpam-5136	228	25	2λ)(r	2λ)(r	NUM
ejpam-5136	228	26	+	+	CCONJ
ejpam-5136	228	27	1	1	X
ejpam-5136	228	28	)	)	PUNCT
ejpam-5136	228	29	+	+	CCONJ
ejpam-5136	228	30	6	6	NUM
ejpam-5136	228	31	(	(	PUNCT
ejpam-5136	228	32	r	r	NOUN
ejpam-5136	228	33	+	+	NUM
ejpam-5136	228	34	2)(r	2)(r	NUM
ejpam-5136	228	35	+	+	CCONJ
ejpam-5136	228	36	3)(r	3)(r	NUM
ejpam-5136	228	37	+	+	NUM
ejpam-5136	228	38	4	4	NUM
ejpam-5136	228	39	)	)	PUNCT
ejpam-5136	228	40	.	.	PUNCT
ejpam-5136	229	1	theorem	theorem	ADJ
ejpam-5136	229	2	8	8	NUM
ejpam-5136	229	3	.	.	PUNCT
ejpam-5136	230	1	let	let	AUX
ejpam-5136	230	2	(	(	PUNCT
ejpam-5136	230	3	x	x	X
ejpam-5136	230	4	,	,	PUNCT
ejpam-5136	230	5	y	y	PROPN
ejpam-5136	230	6	)	)	PUNCT
ejpam-5136	230	7	be	be	AUX
ejpam-5136	230	8	a	a	DET
ejpam-5136	230	9	bivariate	bivariate	ADJ
ejpam-5136	230	10	random	random	ADJ
ejpam-5136	230	11	vector	vector	NOUN
ejpam-5136	230	12	that	that	PRON
ejpam-5136	230	13	follows	follow	VERB
ejpam-5136	230	14	a	a	DET
ejpam-5136	230	15	bivariate	bivariate	ADJ
ejpam-5136	230	16	extended	extended	ADJ
ejpam-5136	230	17	standard	standard	ADJ
ejpam-5136	230	18	u	u	ADJ
ejpam-5136	230	19	-	-	ADJ
ejpam-5136	230	20	quadratic	quadratic	ADJ
ejpam-5136	230	21	distribution	distribution	NOUN
ejpam-5136	230	22	,	,	PUNCT
ejpam-5136	230	23	then	then	ADV
ejpam-5136	230	24	the	the	DET
ejpam-5136	230	25	stress	stress	NOUN
ejpam-5136	230	26	strength	strength	NOUN
ejpam-5136	230	27	parameter	parameter	NOUN
ejpam-5136	230	28	of	of	ADP
ejpam-5136	230	29	x	x	PUNCT
ejpam-5136	230	30	and	and	CCONJ
ejpam-5136	230	31	y	y	PROPN
ejpam-5136	230	32	is	be	AUX
ejpam-5136	230	33	given	give	VERB
ejpam-5136	230	34	by	by	ADP
ejpam-5136	230	35	p(y	p(y	PROPN
ejpam-5136	230	36	<	<	X
ejpam-5136	230	37	x	x	X
ejpam-5136	230	38	)	)	PUNCT
ejpam-5136	230	39	=	=	SYM
ejpam-5136	230	40	1	1	NUM
ejpam-5136	230	41	70	70	NUM
ejpam-5136	230	42	(	(	PUNCT
ejpam-5136	230	43	63	63	NUM
ejpam-5136	230	44	2	2	NUM
ejpam-5136	230	45	−	−	PROPN
ejpam-5136	230	46	λ	λ	PROPN
ejpam-5136	230	47	)	)	PUNCT
ejpam-5136	230	48	,	,	PUNCT
ejpam-5136	230	49	(	(	PUNCT
ejpam-5136	230	50	16	16	NUM
ejpam-5136	230	51	)	)	PUNCT
ejpam-5136	230	52	where	where	SCONJ
ejpam-5136	230	53	λ	λ	PROPN
ejpam-5136	230	54	∈	∈	PROPN
ejpam-5136	231	1	[	[	X
ejpam-5136	231	2	−0.5	−0.5	PROPN
ejpam-5136	231	3	,	,	PUNCT
ejpam-5136	231	4	1	1	NUM
ejpam-5136	231	5	]	]	PUNCT
ejpam-5136	231	6	.	.	PUNCT
ejpam-5136	232	1	i.	i.	PROPN
ejpam-5136	232	2	a.	a.	PROPN
ejpam-5136	232	3	lakibul	lakibul	PROPN
ejpam-5136	232	4	,	,	PUNCT
ejpam-5136	232	5	d.	d.	PROPN
ejpam-5136	232	6	l.	l.	PROPN
ejpam-5136	232	7	polestico	polestico	PROPN
ejpam-5136	232	8	,	,	PUNCT
ejpam-5136	232	9	a.	a.	PROPN
ejpam-5136	232	10	p.	p.	NOUN
ejpam-5136	232	11	supe	supe	PROPN
ejpam-5136	232	12	/	/	SYM
ejpam-5136	232	13	eur	eur	PROPN
ejpam-5136	232	14	.	.	PUNCT
ejpam-5136	233	1	j.	j.	PROPN
ejpam-5136	233	2	pure	pure	PROPN
ejpam-5136	233	3	appl	appl	PROPN
ejpam-5136	233	4	.	.	PROPN
ejpam-5136	233	5	math	math	PROPN
ejpam-5136	233	6	,	,	PUNCT
ejpam-5136	233	7	17	17	NUM
ejpam-5136	233	8	(	(	PUNCT
ejpam-5136	233	9	2	2	NUM
ejpam-5136	233	10	)	)	PUNCT
ejpam-5136	233	11	(	(	PUNCT
ejpam-5136	233	12	2024	2024	NUM
ejpam-5136	233	13	)	)	PUNCT
ejpam-5136	233	14	,	,	PUNCT
ejpam-5136	233	15	790	790	NUM
ejpam-5136	233	16	-	-	SYM
ejpam-5136	233	17	809	809	NUM
ejpam-5136	233	18	800	800	NUM
ejpam-5136	233	19	proof	proof	NOUN
ejpam-5136	233	20	.	.	PUNCT
ejpam-5136	234	1	the	the	DET
ejpam-5136	234	2	stress	stress	NOUN
ejpam-5136	234	3	strength	strength	NOUN
ejpam-5136	234	4	parameter	parameter	NOUN
ejpam-5136	234	5	of	of	ADP
ejpam-5136	234	6	random	random	ADJ
ejpam-5136	234	7	variables	variable	NOUN
ejpam-5136	234	8	x	x	PUNCT
ejpam-5136	234	9	and	and	CCONJ
ejpam-5136	234	10	y	y	PROPN
ejpam-5136	234	11	is	be	AUX
ejpam-5136	234	12	defined	define	VERB
ejpam-5136	234	13	by	by	ADP
ejpam-5136	234	14	p(y	p(y	PROPN
ejpam-5136	234	15	<	<	X
ejpam-5136	234	16	x	x	X
ejpam-5136	234	17	)	)	PUNCT
ejpam-5136	235	1	=	=	SYM
ejpam-5136	235	2	∫	∫	PROPN
ejpam-5136	235	3	1	1	NUM
ejpam-5136	235	4	0	0	NUM
ejpam-5136	235	5	∫	∫	PROPN
ejpam-5136	235	6	x	x	SYM
ejpam-5136	235	7	0	0	NUM
ejpam-5136	235	8	f(x	f(x	PROPN
ejpam-5136	235	9	,	,	PUNCT
ejpam-5136	235	10	y)dydx	y)dydx	PROPN
ejpam-5136	236	1	=	=	SYM
ejpam-5136	236	2	∫	∫	PROPN
ejpam-5136	236	3	1	1	NUM
ejpam-5136	236	4	0	0	NUM
ejpam-5136	236	5	∫	∫	PROPN
ejpam-5136	236	6	x	x	SYM
ejpam-5136	236	7	0	0	PUNCT
ejpam-5136	237	1	[	[	PUNCT
ejpam-5136	237	2	1.5−	1.5−	NUM
ejpam-5136	237	3	1.5x+	1.5x+	NUM
ejpam-5136	237	4	3(1.5x−	3(1.5x−	NUM
ejpam-5136	237	5	0.5)(2y	0.5)(2y	NOUN
ejpam-5136	237	6	−	−	PROPN
ejpam-5136	237	7	1)2	1)2	NUM
ejpam-5136	237	8	]	]	PUNCT
ejpam-5136	238	1	[	[	PUNCT
ejpam-5136	238	2	1−	1−	NUM
ejpam-5136	238	3	λ+	λ+	PUNCT
ejpam-5136	238	4	3λ(2x−	3λ(2x−	NUM
ejpam-5136	238	5	1)2	1)2	NUM
ejpam-5136	238	6	]	]	PUNCT
ejpam-5136	238	7	dydx	dydx	NOUN
ejpam-5136	238	8	=	=	NOUN
ejpam-5136	238	9	6e[x2]−	6e[x2]−	NOUN
ejpam-5136	238	10	11e[x3	11e[x3	NUM
ejpam-5136	238	11	]	]	X
ejpam-5136	239	1	+	+	CCONJ
ejpam-5136	239	2	6e[x4	6e[x4	NOUN
ejpam-5136	239	3	]	]	X
ejpam-5136	239	4	=	=	SYM
ejpam-5136	239	5	1	1	NUM
ejpam-5136	239	6	70	70	NUM
ejpam-5136	239	7	(	(	PUNCT
ejpam-5136	239	8	63	63	NUM
ejpam-5136	239	9	2	2	NUM
ejpam-5136	239	10	−	−	PROPN
ejpam-5136	239	11	λ	λ	PROPN
ejpam-5136	239	12	)	)	PUNCT
ejpam-5136	239	13	.	.	PUNCT
ejpam-5136	240	1	table	table	NOUN
ejpam-5136	240	2	1	1	NUM
ejpam-5136	240	3	:	:	PUNCT
ejpam-5136	240	4	some	some	DET
ejpam-5136	240	5	values	value	NOUN
ejpam-5136	240	6	of	of	ADP
ejpam-5136	240	7	the	the	DET
ejpam-5136	240	8	stress	stress	NOUN
ejpam-5136	240	9	strength	strength	NOUN
ejpam-5136	240	10	parameter	parameter	NOUN
ejpam-5136	240	11	for	for	ADP
ejpam-5136	240	12	different	different	ADJ
ejpam-5136	240	13	values	value	NOUN
ejpam-5136	240	14	of	of	ADP
ejpam-5136	240	15	λ	λ	PROPN
ejpam-5136	240	16	.	.	PUNCT
ejpam-5136	241	1	λ	λ	PROPN
ejpam-5136	241	2	p(y	p(y	PROPN
ejpam-5136	241	3	<	<	X
ejpam-5136	241	4	x	x	X
ejpam-5136	241	5	)	)	PUNCT
ejpam-5136	241	6	λ	λ	NOUN
ejpam-5136	241	7	p(y	p(y	NOUN
ejpam-5136	241	8	<	<	X
ejpam-5136	241	9	x	x	X
ejpam-5136	241	10	)	)	PUNCT
ejpam-5136	241	11	−0.5	−0.5	PROPN
ejpam-5136	242	1	0.4571429	0.4571429	NUM
ejpam-5136	242	2	0.3	0.3	NUM
ejpam-5136	242	3	0.4457143	0.4457143	NUM
ejpam-5136	242	4	−0.4	−0.4	NUM
ejpam-5136	243	1	0.4557143	0.4557143	NUM
ejpam-5136	243	2	0.4	0.4	NUM
ejpam-5136	243	3	0.4442857	0.4442857	NUM
ejpam-5136	243	4	−0.3	−0.3	PROPN
ejpam-5136	243	5	0.4542857	0.4542857	NUM
ejpam-5136	243	6	0.5	0.5	NUM
ejpam-5136	243	7	0.4428571	0.4428571	NUM
ejpam-5136	243	8	−0.2	−0.2	PROPN
ejpam-5136	243	9	0.4528571	0.4528571	NUM
ejpam-5136	243	10	0.6	0.6	NUM
ejpam-5136	243	11	0.4414286	0.4414286	NUM
ejpam-5136	243	12	−0.1	−0.1	PROPN
ejpam-5136	243	13	0.4514286	0.4514286	NUM
ejpam-5136	243	14	0.7	0.7	NUM
ejpam-5136	243	15	0.4400000	0.4400000	NUM
ejpam-5136	243	16	0.0	0.0	NUM
ejpam-5136	243	17	0.4500000	0.4500000	NUM
ejpam-5136	243	18	0.8	0.8	NUM
ejpam-5136	243	19	0.4385714	0.4385714	NUM
ejpam-5136	243	20	0.1	0.1	NUM
ejpam-5136	243	21	0.4485714	0.4485714	NUM
ejpam-5136	243	22	0.9	0.9	NUM
ejpam-5136	243	23	0.4371429	0.4371429	NUM
ejpam-5136	243	24	0.2	0.2	NUM
ejpam-5136	243	25	0.4471429	0.4471429	NUM
ejpam-5136	243	26	1.0	1.0	NUM
ejpam-5136	243	27	0.4357143	0.4357143	NUM
ejpam-5136	243	28	from	from	ADP
ejpam-5136	243	29	table	table	NOUN
ejpam-5136	243	30	1	1	NUM
ejpam-5136	243	31	we	we	PRON
ejpam-5136	243	32	can	can	AUX
ejpam-5136	243	33	see	see	VERB
ejpam-5136	243	34	that	that	PRON
ejpam-5136	243	35	as	as	ADP
ejpam-5136	243	36	λ	λ	NOUN
ejpam-5136	243	37	increases	increase	NOUN
ejpam-5136	243	38	,	,	PUNCT
ejpam-5136	243	39	the	the	DET
ejpam-5136	243	40	stress	stress	NOUN
ejpam-5136	243	41	strength	strength	NOUN
ejpam-5136	243	42	seems	seem	VERB
ejpam-5136	243	43	to	to	PART
ejpam-5136	243	44	decrease	decrease	VERB
ejpam-5136	243	45	.	.	PUNCT
ejpam-5136	244	1	4	4	X
ejpam-5136	244	2	.	.	X
ejpam-5136	244	3	maximum	maximum	ADJ
ejpam-5136	244	4	likelihood	likelihood	NOUN
ejpam-5136	244	5	estimation	estimation	NOUN
ejpam-5136	244	6	let	let	VERB
ejpam-5136	244	7	(	(	PUNCT
ejpam-5136	244	8	x1	x1	ADJ
ejpam-5136	244	9	,	,	PUNCT
ejpam-5136	244	10	y1),(x2	y1),(x2	PROPN
ejpam-5136	244	11	,	,	PUNCT
ejpam-5136	244	12	y2),	y2),	PROPN
ejpam-5136	244	13	...	...	PUNCT
ejpam-5136	244	14	,(xn	,(xn	PUNCT
ejpam-5136	244	15	,	,	PUNCT
ejpam-5136	244	16	yn	yn	PROPN
ejpam-5136	244	17	)	)	PUNCT
ejpam-5136	244	18	be	be	VERB
ejpam-5136	244	19	a	a	DET
ejpam-5136	244	20	random	random	ADJ
ejpam-5136	244	21	sample	sample	NOUN
ejpam-5136	244	22	of	of	ADP
ejpam-5136	244	23	size	size	NOUN
ejpam-5136	244	24	n	n	CCONJ
ejpam-5136	244	25	from	from	ADP
ejpam-5136	244	26	a	a	DET
ejpam-5136	244	27	bivariate	bivariate	ADJ
ejpam-5136	244	28	extended	extend	VERB
ejpam-5136	244	29	standard	standard	ADJ
ejpam-5136	244	30	u	u	NOUN
ejpam-5136	244	31	-	-	ADJ
ejpam-5136	244	32	quadratic	quadratic	ADJ
ejpam-5136	244	33	(	(	PUNCT
ejpam-5136	244	34	besu	besu	ADJ
ejpam-5136	244	35	)	)	PUNCT
ejpam-5136	244	36	distribution	distribution	NOUN
ejpam-5136	244	37	.	.	PUNCT
ejpam-5136	245	1	then	then	ADV
ejpam-5136	245	2	the	the	DET
ejpam-5136	245	3	likelihood	likelihood	NOUN
ejpam-5136	245	4	function	function	NOUN
ejpam-5136	245	5	is	be	AUX
ejpam-5136	245	6	defined	define	VERB
ejpam-5136	245	7	by	by	ADP
ejpam-5136	245	8	l	l	NOUN
ejpam-5136	245	9	=	=	PUNCT
ejpam-5136	245	10	n∏	n∏	PROPN
ejpam-5136	245	11	i	i	PRON
ejpam-5136	245	12	[	[	PUNCT
ejpam-5136	245	13	1.5−	1.5−	NUM
ejpam-5136	245	14	1.5xi	1.5xi	NUM
ejpam-5136	246	1	+	+	NOUN
ejpam-5136	246	2	3(1.5xi	3(1.5xi	NUM
ejpam-5136	246	3	−	−	NOUN
ejpam-5136	246	4	0.5)(2yi	0.5)(2yi	ADV
ejpam-5136	247	1	−	−	PROPN
ejpam-5136	247	2	1)2	1)2	NUM
ejpam-5136	247	3	]	]	PUNCT
ejpam-5136	248	1	[	[	PUNCT
ejpam-5136	248	2	1−	1−	NUM
ejpam-5136	248	3	λ+	λ+	PUNCT
ejpam-5136	248	4	3λ(2xi	3λ(2xi	NUM
ejpam-5136	248	5	−	−	PROPN
ejpam-5136	248	6	1)2	1)2	NUM
ejpam-5136	248	7	]	]	PUNCT
ejpam-5136	248	8	,	,	PUNCT
ejpam-5136	248	9	with	with	ADP
ejpam-5136	248	10	its	its	PRON
ejpam-5136	248	11	log	log	NOUN
ejpam-5136	248	12	-	-	PUNCT
ejpam-5136	248	13	likelihood	likelihood	NOUN
ejpam-5136	248	14	function	function	NOUN
ejpam-5136	248	15	is	be	AUX
ejpam-5136	248	16	given	give	VERB
ejpam-5136	248	17	by	by	ADP
ejpam-5136	248	18	logl	logl	NOUN
ejpam-5136	248	19	=	=	SYM
ejpam-5136	248	20	n∑	n∑	NOUN
ejpam-5136	249	1	i	i	PRON
ejpam-5136	249	2	log	log	VERB
ejpam-5136	249	3	[	[	PUNCT
ejpam-5136	249	4	1.5−	1.5−	NUM
ejpam-5136	249	5	1.5xi	1.5xi	NUM
ejpam-5136	250	1	+	+	NOUN
ejpam-5136	250	2	3(1.5xi	3(1.5xi	NUM
ejpam-5136	250	3	−	−	NOUN
ejpam-5136	250	4	0.5)(2yi	0.5)(2yi	ADV
ejpam-5136	251	1	−	−	PROPN
ejpam-5136	251	2	1)2	1)2	NUM
ejpam-5136	251	3	]	]	PUNCT
ejpam-5136	252	1	+	+	CCONJ
ejpam-5136	252	2	n∑	n∑	INTJ
ejpam-5136	252	3	i	i	PRON
ejpam-5136	252	4	log	log	VERB
ejpam-5136	252	5	[	[	PUNCT
ejpam-5136	252	6	1−	1−	NUM
ejpam-5136	252	7	λ+	λ+	PUNCT
ejpam-5136	252	8	3λ(2xi	3λ(2xi	NUM
ejpam-5136	252	9	−	−	PROPN
ejpam-5136	252	10	1)2	1)2	NUM
ejpam-5136	252	11	]	]	PUNCT
ejpam-5136	252	12	.	.	PUNCT
ejpam-5136	253	1	the	the	DET
ejpam-5136	253	2	partial	partial	ADJ
ejpam-5136	253	3	derivative	derivative	NOUN
ejpam-5136	253	4	of	of	ADP
ejpam-5136	253	5	logl	logl	NOUN
ejpam-5136	253	6	with	with	ADP
ejpam-5136	253	7	respect	respect	NOUN
ejpam-5136	253	8	to	to	ADP
ejpam-5136	253	9	the	the	DET
ejpam-5136	253	10	parameter	parameter	NOUN
ejpam-5136	253	11	λ	λ	PROPN
ejpam-5136	253	12	is	be	AUX
ejpam-5136	253	13	given	give	VERB
ejpam-5136	253	14	by	by	ADP
ejpam-5136	253	15	∂	∂	NUM
ejpam-5136	254	1	logl	logl	NOUN
ejpam-5136	254	2	∂λ	∂λ	PROPN
ejpam-5136	254	3	=	=	SYM
ejpam-5136	254	4	n∑	n∑	PROPN
ejpam-5136	254	5	i	i	VERB
ejpam-5136	255	1	3(2xi	3(2xi	NUM
ejpam-5136	255	2	−	−	NOUN
ejpam-5136	256	1	1)2	1)2	NUM
ejpam-5136	256	2	−	−	NOUN
ejpam-5136	256	3	1	1	NUM
ejpam-5136	256	4	1−	1−	NUM
ejpam-5136	256	5	λ+	λ+	PUNCT
ejpam-5136	256	6	3λ(2xi	3λ(2xi	NUM
ejpam-5136	256	7	−	−	PROPN
ejpam-5136	256	8	1)2	1)2	NUM
ejpam-5136	256	9	.	.	PUNCT
ejpam-5136	257	1	i.	i.	PROPN
ejpam-5136	257	2	a.	a.	PROPN
ejpam-5136	257	3	lakibul	lakibul	PROPN
ejpam-5136	257	4	,	,	PUNCT
ejpam-5136	257	5	d.	d.	PROPN
ejpam-5136	257	6	l.	l.	PROPN
ejpam-5136	257	7	polestico	polestico	PROPN
ejpam-5136	257	8	,	,	PUNCT
ejpam-5136	257	9	a.	a.	PROPN
ejpam-5136	257	10	p.	p.	NOUN
ejpam-5136	257	11	supe	supe	PROPN
ejpam-5136	257	12	/	/	SYM
ejpam-5136	257	13	eur	eur	PROPN
ejpam-5136	257	14	.	.	PUNCT
ejpam-5136	258	1	j.	j.	PROPN
ejpam-5136	258	2	pure	pure	PROPN
ejpam-5136	258	3	appl	appl	PROPN
ejpam-5136	258	4	.	.	PROPN
ejpam-5136	258	5	math	math	PROPN
ejpam-5136	258	6	,	,	PUNCT
ejpam-5136	258	7	17	17	NUM
ejpam-5136	258	8	(	(	PUNCT
ejpam-5136	258	9	2	2	NUM
ejpam-5136	258	10	)	)	PUNCT
ejpam-5136	258	11	(	(	PUNCT
ejpam-5136	258	12	2024	2024	NUM
ejpam-5136	258	13	)	)	PUNCT
ejpam-5136	258	14	,	,	PUNCT
ejpam-5136	258	15	790	790	NUM
ejpam-5136	258	16	-	-	SYM
ejpam-5136	258	17	809	809	NUM
ejpam-5136	258	18	801	801	NUM
ejpam-5136	258	19	the	the	DET
ejpam-5136	258	20	maximum	maximum	ADJ
ejpam-5136	258	21	likelihood	likelihood	NOUN
ejpam-5136	258	22	estimate	estimate	NOUN
ejpam-5136	258	23	of	of	ADP
ejpam-5136	258	24	the	the	DET
ejpam-5136	258	25	parameter	parameter	NOUN
ejpam-5136	258	26	λ	λ	PROPN
ejpam-5136	258	27	of	of	ADP
ejpam-5136	258	28	the	the	DET
ejpam-5136	258	29	besu	besu	NOUN
ejpam-5136	258	30	distribution	distribution	NOUN
ejpam-5136	258	31	is	be	AUX
ejpam-5136	258	32	computed	compute	VERB
ejpam-5136	258	33	by	by	ADP
ejpam-5136	258	34	solving	solve	VERB
ejpam-5136	258	35	n∑	n∑	PROPN
ejpam-5136	258	36	i	i	NOUN
ejpam-5136	259	1	3(2xi	3(2xi	NUM
ejpam-5136	259	2	−	−	NOUN
ejpam-5136	260	1	1)2	1)2	NUM
ejpam-5136	260	2	−	−	NOUN
ejpam-5136	260	3	1	1	NUM
ejpam-5136	260	4	1−	1−	NUM
ejpam-5136	260	5	λ+	λ+	PUNCT
ejpam-5136	260	6	3λ(2xi	3λ(2xi	NUM
ejpam-5136	260	7	−	−	PROPN
ejpam-5136	260	8	1)2	1)2	NUM
ejpam-5136	260	9	=	=	SYM
ejpam-5136	260	10	0	0	NUM
ejpam-5136	260	11	.	.	NOUN
ejpam-5136	260	12	5	5	NUM
ejpam-5136	260	13	.	.	X
ejpam-5136	260	14	random	random	ADJ
ejpam-5136	260	15	number	number	NOUN
ejpam-5136	260	16	generation	generation	NOUN
ejpam-5136	260	17	this	this	DET
ejpam-5136	260	18	section	section	NOUN
ejpam-5136	260	19	presents	present	VERB
ejpam-5136	260	20	the	the	DET
ejpam-5136	260	21	algorithm	algorithm	NOUN
ejpam-5136	260	22	for	for	ADP
ejpam-5136	260	23	the	the	DET
ejpam-5136	260	24	generation	generation	NOUN
ejpam-5136	260	25	of	of	ADP
ejpam-5136	260	26	bivariate	bivariate	ADJ
ejpam-5136	260	27	random	random	ADJ
ejpam-5136	260	28	numbers	number	NOUN
ejpam-5136	260	29	from	from	ADP
ejpam-5136	260	30	the	the	DET
ejpam-5136	260	31	bivariate	bivariate	ADJ
ejpam-5136	260	32	extended	extend	VERB
ejpam-5136	260	33	standard	standard	ADJ
ejpam-5136	260	34	u	u	NOUN
ejpam-5136	260	35	-	-	ADJ
ejpam-5136	260	36	quadratic	quadratic	ADJ
ejpam-5136	260	37	(	(	PUNCT
ejpam-5136	260	38	besu	besu	ADJ
ejpam-5136	260	39	)	)	PUNCT
ejpam-5136	260	40	distribution	distribution	NOUN
ejpam-5136	260	41	.	.	PUNCT
ejpam-5136	261	1	consider	consider	VERB
ejpam-5136	261	2	the	the	DET
ejpam-5136	261	3	algorithm	algorithm	NOUN
ejpam-5136	261	4	of	of	ADP
ejpam-5136	261	5	lakibul	lakibul	PROPN
ejpam-5136	261	6	and	and	CCONJ
ejpam-5136	261	7	tubo	tubo	ADJ
ejpam-5136	261	8	[	[	X
ejpam-5136	261	9	4	4	NUM
ejpam-5136	261	10	]	]	PUNCT
ejpam-5136	261	11	for	for	ADP
ejpam-5136	261	12	generating	generate	VERB
ejpam-5136	261	13	random	random	ADJ
ejpam-5136	261	14	numbers	number	NOUN
ejpam-5136	261	15	from	from	ADP
ejpam-5136	261	16	a	a	DET
ejpam-5136	261	17	textended	textende	VERB
ejpam-5136	261	18	standard	standard	ADJ
ejpam-5136	261	19	u	u	NOUN
ejpam-5136	261	20	-	-	ADJ
ejpam-5136	261	21	quadratic	quadratic	ADJ
ejpam-5136	261	22	(	(	PUNCT
ejpam-5136	261	23	tesu	tesu	NOUN
ejpam-5136	261	24	)	)	PUNCT
ejpam-5136	262	1	g	g	PROPN
ejpam-5136	262	2	family	family	NOUN
ejpam-5136	262	3	of	of	ADP
ejpam-5136	262	4	distributions	distribution	NOUN
ejpam-5136	262	5	.	.	PUNCT
ejpam-5136	263	1	the	the	DET
ejpam-5136	263	2	cumulative	cumulative	ADJ
ejpam-5136	263	3	distribution	distribution	NOUN
ejpam-5136	263	4	function	function	NOUN
ejpam-5136	263	5	of	of	ADP
ejpam-5136	263	6	the	the	DET
ejpam-5136	263	7	tesu	tesu	PROPN
ejpam-5136	263	8	-	-	PUNCT
ejpam-5136	263	9	g	g	NOUN
ejpam-5136	263	10	family	family	NOUN
ejpam-5136	263	11	is	be	AUX
ejpam-5136	263	12	given	give	VERB
ejpam-5136	263	13	by	by	ADP
ejpam-5136	263	14	f	f	PROPN
ejpam-5136	263	15	(	(	PUNCT
ejpam-5136	263	16	x	x	NOUN
ejpam-5136	263	17	)	)	PUNCT
ejpam-5136	263	18	=	=	SYM
ejpam-5136	263	19	(	(	PUNCT
ejpam-5136	264	1	1	1	NUM
ejpam-5136	264	2	+	+	NUM
ejpam-5136	264	3	2λ)g(x)−	2λ)g(x)−	NUM
ejpam-5136	264	4	6λ(g(x))2	6λ(g(x))2	NOUN
ejpam-5136	264	5	+	+	CCONJ
ejpam-5136	264	6	4λ(g(x))3	4λ(g(x))3	NUM
ejpam-5136	264	7	,	,	PUNCT
ejpam-5136	264	8	(	(	PUNCT
ejpam-5136	264	9	17	17	NUM
ejpam-5136	264	10	)	)	PUNCT
ejpam-5136	264	11	where	where	SCONJ
ejpam-5136	264	12	λ	λ	PROPN
ejpam-5136	264	13	∈	∈	PROPN
ejpam-5136	265	1	[	[	X
ejpam-5136	265	2	−0.5	−0.5	PROPN
ejpam-5136	265	3	,	,	PUNCT
ejpam-5136	265	4	1	1	NUM
ejpam-5136	265	5	]	]	PUNCT
ejpam-5136	265	6	and	and	CCONJ
ejpam-5136	265	7	g(x	g(x	NOUN
ejpam-5136	265	8	)	)	PUNCT
ejpam-5136	265	9	is	be	AUX
ejpam-5136	265	10	any	any	DET
ejpam-5136	265	11	baseline	baseline	ADJ
ejpam-5136	265	12	cumulative	cumulative	ADJ
ejpam-5136	265	13	distribution	distribution	NOUN
ejpam-5136	265	14	function	function	NOUN
ejpam-5136	265	15	.	.	PUNCT
ejpam-5136	266	1	the	the	DET
ejpam-5136	266	2	algorithm	algorithm	NOUN
ejpam-5136	266	3	to	to	PART
ejpam-5136	266	4	generate	generate	VERB
ejpam-5136	266	5	random	random	ADJ
ejpam-5136	266	6	numbers	number	NOUN
ejpam-5136	266	7	from	from	ADP
ejpam-5136	266	8	tesu	tesu	NOUN
ejpam-5136	266	9	-	-	PUNCT
ejpam-5136	266	10	g	g	NOUN
ejpam-5136	266	11	family	family	NOUN
ejpam-5136	266	12	is	be	AUX
ejpam-5136	266	13	given	give	VERB
ejpam-5136	266	14	as	as	SCONJ
ejpam-5136	266	15	follows	follow	VERB
ejpam-5136	266	16	.	.	PUNCT
ejpam-5136	267	1	let	let	VERB
ejpam-5136	267	2	v	v	PART
ejpam-5136	267	3	follow	follow	VERB
ejpam-5136	267	4	a	a	DET
ejpam-5136	267	5	uniform	uniform	ADJ
ejpam-5136	267	6	distribution	distribution	NOUN
ejpam-5136	267	7	(	(	PUNCT
ejpam-5136	267	8	0	0	NUM
ejpam-5136	267	9	,	,	PUNCT
ejpam-5136	267	10	1	1	NUM
ejpam-5136	267	11	)	)	PUNCT
ejpam-5136	267	12	.	.	PUNCT
ejpam-5136	268	1	step	step	NOUN
ejpam-5136	268	2	1	1	NUM
ejpam-5136	268	3	.	.	PUNCT
ejpam-5136	269	1	compute	compute	PROPN
ejpam-5136	269	2	q	q	NOUN
ejpam-5136	270	1	=	=	NOUN
ejpam-5136	270	2	1	1	NUM
ejpam-5136	270	3	2	2	NUM
ejpam-5136	270	4	(	(	PUNCT
ejpam-5136	270	5	1−	1−	NUM
ejpam-5136	270	6	1	1	NUM
ejpam-5136	270	7	λ	λ	NOUN
ejpam-5136	270	8	)	)	PUNCT
ejpam-5136	270	9	,	,	PUNCT
ejpam-5136	270	10	λ	λ	X
ejpam-5136	270	11	̸=	̸=	PROPN
ejpam-5136	270	12	0	0	NUM
ejpam-5136	270	13	;	;	PUNCT
ejpam-5136	270	14	r	r	NOUN
ejpam-5136	270	15	=	=	SYM
ejpam-5136	270	16	1−	1−	NUM
ejpam-5136	270	17	2v	2v	PROPN
ejpam-5136	270	18	16λ	16λ	PROPN
ejpam-5136	270	19	.	.	PUNCT
ejpam-5136	271	1	step	step	NOUN
ejpam-5136	271	2	2	2	NUM
ejpam-5136	271	3	.	.	PUNCT
ejpam-5136	272	1	if	if	SCONJ
ejpam-5136	272	2	r2	r2	PROPN
ejpam-5136	272	3	>	>	X
ejpam-5136	272	4	q3	q3	PROPN
ejpam-5136	272	5	,	,	PUNCT
ejpam-5136	272	6	then	then	ADV
ejpam-5136	272	7	compute	compute	VERB
ejpam-5136	272	8	a	a	DET
ejpam-5136	272	9	=	=	SYM
ejpam-5136	272	10	−sign(r	−sign(r	NUM
ejpam-5136	272	11	)	)	PUNCT
ejpam-5136	272	12	(	(	PUNCT
ejpam-5136	272	13	|r|+	|r|+	NOUN
ejpam-5136	272	14	√	√	PROPN
ejpam-5136	272	15	r2	r2	PROPN
ejpam-5136	272	16	−q3	−q3	PROPN
ejpam-5136	272	17	)	)	PUNCT
ejpam-5136	272	18	1	1	NUM
ejpam-5136	272	19	3	3	NUM
ejpam-5136	272	20	;	;	PUNCT
ejpam-5136	272	21	b	b	X
ejpam-5136	272	22	=	=	SYM
ejpam-5136	272	23	a	a	PROPN
ejpam-5136	272	24	,	,	PUNCT
ejpam-5136	272	25	ifa	ifa	PROPN
ejpam-5136	272	26	=	=	PUNCT
ejpam-5136	272	27	0	0	PROPN
ejpam-5136	273	1	q	q	PROPN
ejpam-5136	274	1	a	a	INTJ
ejpam-5136	274	2	,	,	PUNCT
ejpam-5136	274	3	otherwise	otherwise	ADV
ejpam-5136	274	4	;	;	PUNCT
ejpam-5136	274	5	x	x	X
ejpam-5136	274	6	=	=	SYM
ejpam-5136	274	7	g−1	g−1	X
ejpam-5136	274	8	(	(	PUNCT
ejpam-5136	274	9	a+b	a+b	X
ejpam-5136	274	10	+	+	CCONJ
ejpam-5136	274	11	1	1	NUM
ejpam-5136	274	12	2	2	NUM
ejpam-5136	274	13	)	)	PUNCT
ejpam-5136	274	14	.	.	PUNCT
ejpam-5136	275	1	otherwise	otherwise	ADV
ejpam-5136	275	2	,	,	PUNCT
ejpam-5136	275	3	θ	θ	PROPN
ejpam-5136	275	4	=	=	SYM
ejpam-5136	275	5	arccos	arcco	NOUN
ejpam-5136	275	6	(	(	PUNCT
ejpam-5136	275	7	r√	r√	NOUN
ejpam-5136	275	8	q3	q3	PROPN
ejpam-5136	275	9	)	)	PUNCT
ejpam-5136	275	10	;	;	PUNCT
ejpam-5136	275	11	x	x	X
ejpam-5136	275	12	=	=	SYM
ejpam-5136	275	13	g−1	g−1	X
ejpam-5136	275	14	(	(	PUNCT
ejpam-5136	275	15	1	1	NUM
ejpam-5136	275	16	2	2	NUM
ejpam-5136	275	17	−	−	NUM
ejpam-5136	275	18	2	2	NUM
ejpam-5136	275	19	√	√	PROPN
ejpam-5136	275	20	q	q	PROPN
ejpam-5136	275	21	cos	cos	PROPN
ejpam-5136	275	22	(	(	PUNCT
ejpam-5136	275	23	θ	θ	PROPN
ejpam-5136	275	24	−	−	PROPN
ejpam-5136	275	25	2π	2π	PROPN
ejpam-5136	275	26	3	3	NUM
ejpam-5136	275	27	)	)	PUNCT
ejpam-5136	275	28	)	)	PUNCT
ejpam-5136	275	29	,	,	PUNCT
ejpam-5136	275	30	where	where	SCONJ
ejpam-5136	275	31	g−1(x	g−1(x	NOUN
ejpam-5136	275	32	)	)	PUNCT
ejpam-5136	275	33	is	be	AUX
ejpam-5136	275	34	the	the	DET
ejpam-5136	275	35	inverse	inverse	ADJ
ejpam-5136	275	36	function	function	NOUN
ejpam-5136	275	37	of	of	ADP
ejpam-5136	275	38	any	any	DET
ejpam-5136	275	39	baseline	baseline	ADJ
ejpam-5136	275	40	distribution	distribution	NOUN
ejpam-5136	275	41	function	function	NOUN
ejpam-5136	275	42	g(x	g(x	NOUN
ejpam-5136	275	43	)	)	PUNCT
ejpam-5136	275	44	.	.	PUNCT
ejpam-5136	276	1	if	if	SCONJ
ejpam-5136	276	2	λ	λ	X
ejpam-5136	276	3	=	=	SYM
ejpam-5136	276	4	0	0	NUM
ejpam-5136	276	5	,	,	PUNCT
ejpam-5136	276	6	then	then	ADV
ejpam-5136	276	7	x	x	NOUN
ejpam-5136	276	8	=	=	SYM
ejpam-5136	276	9	g−1(v	g−1(v	PROPN
ejpam-5136	276	10	)	)	PUNCT
ejpam-5136	276	11	.	.	PUNCT
ejpam-5136	277	1	note	note	VERB
ejpam-5136	277	2	that	that	SCONJ
ejpam-5136	277	3	,	,	PUNCT
ejpam-5136	277	4	the	the	DET
ejpam-5136	277	5	extended	extended	ADJ
ejpam-5136	277	6	standard	standard	ADJ
ejpam-5136	277	7	u	u	ADJ
ejpam-5136	277	8	-	-	ADJ
ejpam-5136	277	9	quadratic	quadratic	ADJ
ejpam-5136	277	10	distribution	distribution	NOUN
ejpam-5136	277	11	is	be	AUX
ejpam-5136	277	12	derived	derive	VERB
ejpam-5136	277	13	i.	i.	NOUN
ejpam-5136	277	14	a.	a.	PROPN
ejpam-5136	277	15	lakibul	lakibul	PROPN
ejpam-5136	277	16	,	,	PUNCT
ejpam-5136	277	17	d.	d.	PROPN
ejpam-5136	277	18	l.	l.	PROPN
ejpam-5136	277	19	polestico	polestico	PROPN
ejpam-5136	277	20	,	,	PUNCT
ejpam-5136	277	21	a.	a.	PROPN
ejpam-5136	277	22	p.	p.	NOUN
ejpam-5136	277	23	supe	supe	PROPN
ejpam-5136	277	24	/	/	SYM
ejpam-5136	277	25	eur	eur	PROPN
ejpam-5136	277	26	.	.	PUNCT
ejpam-5136	278	1	j.	j.	PROPN
ejpam-5136	278	2	pure	pure	PROPN
ejpam-5136	278	3	appl	appl	PROPN
ejpam-5136	278	4	.	.	PROPN
ejpam-5136	278	5	math	math	PROPN
ejpam-5136	278	6	,	,	PUNCT
ejpam-5136	278	7	17	17	NUM
ejpam-5136	278	8	(	(	PUNCT
ejpam-5136	278	9	2	2	NUM
ejpam-5136	278	10	)	)	PUNCT
ejpam-5136	278	11	(	(	PUNCT
ejpam-5136	278	12	2024	2024	NUM
ejpam-5136	278	13	)	)	PUNCT
ejpam-5136	278	14	,	,	PUNCT
ejpam-5136	278	15	790	790	NUM
ejpam-5136	278	16	-	-	SYM
ejpam-5136	278	17	809	809	NUM
ejpam-5136	278	18	802	802	NUM
ejpam-5136	278	19	from	from	ADP
ejpam-5136	278	20	the	the	DET
ejpam-5136	278	21	t	t	PROPN
ejpam-5136	278	22	-	-	PUNCT
ejpam-5136	278	23	extended	extend	VERB
ejpam-5136	278	24	standard	standard	ADJ
ejpam-5136	278	25	u	u	ADJ
ejpam-5136	278	26	-	-	ADJ
ejpam-5136	278	27	quadratic	quadratic	ADJ
ejpam-5136	278	28	g	g	PROPN
ejpam-5136	278	29	family	family	NOUN
ejpam-5136	278	30	of	of	ADP
ejpam-5136	278	31	distributions	distribution	NOUN
ejpam-5136	278	32	by	by	ADP
ejpam-5136	278	33	taking	take	VERB
ejpam-5136	278	34	g(x	g(x	NOUN
ejpam-5136	278	35	)	)	PUNCT
ejpam-5136	279	1	=	=	PUNCT
ejpam-5136	279	2	x.	x.	PUNCT
ejpam-5136	279	3	thus	thus	ADV
ejpam-5136	279	4	,	,	PUNCT
ejpam-5136	279	5	we	we	PRON
ejpam-5136	279	6	have	have	VERB
ejpam-5136	279	7	the	the	DET
ejpam-5136	279	8	following	follow	VERB
ejpam-5136	279	9	modified	modified	ADJ
ejpam-5136	279	10	algorithm	algorithm	NOUN
ejpam-5136	279	11	to	to	PART
ejpam-5136	279	12	generate	generate	VERB
ejpam-5136	279	13	random	random	ADJ
ejpam-5136	279	14	numbers	number	NOUN
ejpam-5136	279	15	from	from	ADP
ejpam-5136	279	16	an	an	DET
ejpam-5136	279	17	extended	extended	ADJ
ejpam-5136	279	18	standard	standard	ADJ
ejpam-5136	279	19	u	u	ADJ
ejpam-5136	279	20	-	-	ADJ
ejpam-5136	279	21	quadratic	quadratic	ADJ
ejpam-5136	279	22	distribution	distribution	NOUN
ejpam-5136	279	23	.	.	PUNCT
ejpam-5136	280	1	let	let	VERB
ejpam-5136	280	2	v	v	PART
ejpam-5136	280	3	follow	follow	VERB
ejpam-5136	280	4	a	a	DET
ejpam-5136	280	5	uniform	uniform	ADJ
ejpam-5136	280	6	distribution	distribution	NOUN
ejpam-5136	280	7	(	(	PUNCT
ejpam-5136	280	8	0	0	NUM
ejpam-5136	280	9	,	,	PUNCT
ejpam-5136	280	10	1	1	NUM
ejpam-5136	280	11	)	)	PUNCT
ejpam-5136	280	12	.	.	PUNCT
ejpam-5136	281	1	if	if	SCONJ
ejpam-5136	281	2	λ	λ	X
ejpam-5136	281	3	=	=	SYM
ejpam-5136	281	4	0	0	NUM
ejpam-5136	281	5	,	,	PUNCT
ejpam-5136	281	6	then	then	ADV
ejpam-5136	281	7	x	x	X
ejpam-5136	282	1	=	=	NOUN
ejpam-5136	282	2	v.	v.	CCONJ
ejpam-5136	282	3	otherwise	otherwise	ADV
ejpam-5136	282	4	,	,	PUNCT
ejpam-5136	282	5	it	it	PRON
ejpam-5136	282	6	is	be	AUX
ejpam-5136	282	7	given	give	VERB
ejpam-5136	282	8	as	as	SCONJ
ejpam-5136	282	9	follows	follow	VERB
ejpam-5136	282	10	:	:	PUNCT
ejpam-5136	282	11	step	step	NOUN
ejpam-5136	282	12	1	1	NUM
ejpam-5136	282	13	.	.	PUNCT
ejpam-5136	282	14	*	*	PUNCT
ejpam-5136	282	15	compute	compute	NOUN
ejpam-5136	282	16	q	q	NOUN
ejpam-5136	282	17	=	=	NOUN
ejpam-5136	282	18	1	1	NUM
ejpam-5136	282	19	2	2	NUM
ejpam-5136	282	20	(	(	PUNCT
ejpam-5136	282	21	1−	1−	NUM
ejpam-5136	282	22	1	1	NUM
ejpam-5136	282	23	λ	λ	NOUN
ejpam-5136	282	24	)	)	PUNCT
ejpam-5136	282	25	,	,	PUNCT
ejpam-5136	283	1	λ	λ	X
ejpam-5136	283	2	̸=	̸=	PROPN
ejpam-5136	283	3	0	0	NUM
ejpam-5136	283	4	;	;	PUNCT
ejpam-5136	283	5	r	r	NOUN
ejpam-5136	283	6	=	=	SYM
ejpam-5136	283	7	1−	1−	NUM
ejpam-5136	283	8	2v	2v	PROPN
ejpam-5136	283	9	16λ	16λ	PROPN
ejpam-5136	283	10	.	.	PUNCT
ejpam-5136	284	1	step	step	NOUN
ejpam-5136	284	2	2	2	NUM
ejpam-5136	284	3	.	.	PUNCT
ejpam-5136	285	1	*	*	PUNCT
ejpam-5136	286	1	if	if	SCONJ
ejpam-5136	286	2	r2	r2	PROPN
ejpam-5136	286	3	>	>	X
ejpam-5136	286	4	q3	q3	PROPN
ejpam-5136	286	5	,	,	PUNCT
ejpam-5136	286	6	then	then	ADV
ejpam-5136	286	7	a	a	DET
ejpam-5136	286	8	=	=	SYM
ejpam-5136	286	9	−sign(r	−sign(r	NUM
ejpam-5136	286	10	)	)	PUNCT
ejpam-5136	286	11	(	(	PUNCT
ejpam-5136	286	12	|r|+	|r|+	NOUN
ejpam-5136	286	13	√	√	PROPN
ejpam-5136	286	14	r2	r2	PROPN
ejpam-5136	286	15	−q3	−q3	PROPN
ejpam-5136	286	16	)	)	PUNCT
ejpam-5136	286	17	1	1	NUM
ejpam-5136	286	18	3	3	NUM
ejpam-5136	286	19	;	;	PUNCT
ejpam-5136	286	20	b	b	X
ejpam-5136	286	21	=	=	SYM
ejpam-5136	286	22	a	a	PROPN
ejpam-5136	286	23	,	,	PUNCT
ejpam-5136	286	24	ifa	ifa	PROPN
ejpam-5136	286	25	=	=	PUNCT
ejpam-5136	286	26	0	0	PROPN
ejpam-5136	287	1	q	q	PROPN
ejpam-5136	287	2	a	a	INTJ
ejpam-5136	287	3	,	,	PUNCT
ejpam-5136	287	4	otherwise	otherwise	ADV
ejpam-5136	287	5	;	;	PUNCT
ejpam-5136	287	6	x	x	SYM
ejpam-5136	287	7	=	=	PUNCT
ejpam-5136	287	8	a+b	a+b	X
ejpam-5136	287	9	+	+	NUM
ejpam-5136	287	10	1	1	NUM
ejpam-5136	287	11	2	2	NUM
ejpam-5136	287	12	.	.	PUNCT
ejpam-5136	288	1	otherwise	otherwise	ADV
ejpam-5136	288	2	,	,	PUNCT
ejpam-5136	288	3	θ	θ	PROPN
ejpam-5136	288	4	=	=	SYM
ejpam-5136	288	5	arccos	arcco	NOUN
ejpam-5136	288	6	(	(	PUNCT
ejpam-5136	288	7	r√	r√	NOUN
ejpam-5136	288	8	q3	q3	PROPN
ejpam-5136	288	9	)	)	PUNCT
ejpam-5136	288	10	;	;	PUNCT
ejpam-5136	288	11	x	x	X
ejpam-5136	288	12	=	=	SYM
ejpam-5136	288	13	1	1	NUM
ejpam-5136	288	14	2	2	NUM
ejpam-5136	288	15	−	−	NUM
ejpam-5136	288	16	2	2	NUM
ejpam-5136	288	17	√	√	PROPN
ejpam-5136	288	18	q	q	PROPN
ejpam-5136	288	19	cos	cos	PROPN
ejpam-5136	288	20	(	(	PUNCT
ejpam-5136	288	21	θ	θ	PROPN
ejpam-5136	288	22	−	−	PROPN
ejpam-5136	288	23	2π	2π	PROPN
ejpam-5136	288	24	3	3	NUM
ejpam-5136	288	25	)	)	PUNCT
ejpam-5136	288	26	.	.	PUNCT
ejpam-5136	289	1	in	in	ADP
ejpam-5136	289	2	addition	addition	NOUN
ejpam-5136	289	3	,	,	PUNCT
ejpam-5136	289	4	to	to	PART
ejpam-5136	289	5	generate	generate	VERB
ejpam-5136	289	6	a	a	DET
ejpam-5136	289	7	random	random	ADJ
ejpam-5136	289	8	sample	sample	NOUN
ejpam-5136	289	9	from	from	ADP
ejpam-5136	289	10	the	the	DET
ejpam-5136	289	11	bivariate	bivariate	ADJ
ejpam-5136	289	12	extended	extended	ADJ
ejpam-5136	289	13	standard	standard	ADJ
ejpam-5136	289	14	uquadratic	uquadratic	ADJ
ejpam-5136	289	15	distribution	distribution	NOUN
ejpam-5136	289	16	,	,	PUNCT
ejpam-5136	289	17	we	we	PRON
ejpam-5136	289	18	use	use	VERB
ejpam-5136	289	19	the	the	DET
ejpam-5136	289	20	conditional	conditional	ADJ
ejpam-5136	289	21	approach	approach	NOUN
ejpam-5136	289	22	given	give	VERB
ejpam-5136	289	23	in	in	ADP
ejpam-5136	289	24	the	the	DET
ejpam-5136	289	25	following	follow	VERB
ejpam-5136	289	26	algorithm	algorithm	NOUN
ejpam-5136	289	27	:	:	PUNCT
ejpam-5136	289	28	step	step	NOUN
ejpam-5136	289	29	1	1	NUM
ejpam-5136	289	30	.	.	PUNCT
ejpam-5136	290	1	*	*	PUNCT
ejpam-5136	290	2	*	*	PUNCT
ejpam-5136	290	3	draw	draw	VERB
ejpam-5136	290	4	a	a	DET
ejpam-5136	290	5	random	random	ADJ
ejpam-5136	290	6	sample	sample	NOUN
ejpam-5136	290	7	x	x	PUNCT
ejpam-5136	290	8	of	of	ADP
ejpam-5136	290	9	size	size	NOUN
ejpam-5136	290	10	n	n	CCONJ
ejpam-5136	290	11	from	from	ADP
ejpam-5136	290	12	an	an	DET
ejpam-5136	290	13	extended	extended	ADJ
ejpam-5136	290	14	standard	standard	ADJ
ejpam-5136	290	15	u	u	ADJ
ejpam-5136	290	16	-	-	ADJ
ejpam-5136	290	17	quadratic	quadratic	ADJ
ejpam-5136	290	18	distribution	distribution	NOUN
ejpam-5136	290	19	with	with	ADP
ejpam-5136	290	20	parameter	parameter	PROPN
ejpam-5136	290	21	λ	λ	PROPN
ejpam-5136	290	22	.	.	PROPN
ejpam-5136	290	23	step	step	NOUN
ejpam-5136	290	24	2	2	NUM
ejpam-5136	290	25	.	.	PUNCT
ejpam-5136	291	1	*	*	PUNCT
ejpam-5136	291	2	*	*	PUNCT
ejpam-5136	291	3	for	for	ADP
ejpam-5136	291	4	each	each	DET
ejpam-5136	291	5	observation	observation	NOUN
ejpam-5136	291	6	of	of	ADP
ejpam-5136	291	7	x	x	PRON
ejpam-5136	291	8	,	,	PUNCT
ejpam-5136	291	9	draw	draw	VERB
ejpam-5136	291	10	a	a	DET
ejpam-5136	291	11	sample	sample	NOUN
ejpam-5136	291	12	of	of	ADP
ejpam-5136	291	13	size	size	NOUN
ejpam-5136	291	14	1	1	NUM
ejpam-5136	291	15	from	from	ADP
ejpam-5136	291	16	an	an	DET
ejpam-5136	291	17	extended	extended	ADJ
ejpam-5136	291	18	standard	standard	ADJ
ejpam-5136	291	19	u	u	ADJ
ejpam-5136	291	20	-	-	ADJ
ejpam-5136	291	21	quadratic	quadratic	ADJ
ejpam-5136	291	22	distribution	distribution	NOUN
ejpam-5136	291	23	with	with	ADP
ejpam-5136	291	24	parameter	parameter	NOUN
ejpam-5136	291	25	1.5x	1.5x	NUM
ejpam-5136	291	26	−	−	NOUN
ejpam-5136	291	27	0.5	0.5	NUM
ejpam-5136	291	28	.	.	PUNCT
ejpam-5136	292	1	repeat	repeat	VERB
ejpam-5136	292	2	this	this	DET
ejpam-5136	292	3	process	process	NOUN
ejpam-5136	292	4	for	for	ADP
ejpam-5136	292	5	all	all	DET
ejpam-5136	292	6	observations	observation	NOUN
ejpam-5136	292	7	of	of	ADP
ejpam-5136	292	8	x.	x.	NOUN
ejpam-5136	292	9	denote	denote	VERB
ejpam-5136	292	10	this	this	DET
ejpam-5136	292	11	sample	sample	NOUN
ejpam-5136	292	12	as	as	ADP
ejpam-5136	292	13	y	y	PROPN
ejpam-5136	292	14	.	.	PUNCT
ejpam-5136	293	1	step	step	NOUN
ejpam-5136	293	2	3	3	NUM
ejpam-5136	293	3	.	.	PUNCT
ejpam-5136	294	1	*	*	PUNCT
ejpam-5136	294	2	*	*	PUNCT
ejpam-5136	294	3	finally	finally	ADV
ejpam-5136	294	4	,	,	PUNCT
ejpam-5136	294	5	the	the	DET
ejpam-5136	294	6	desired	desire	VERB
ejpam-5136	294	7	random	random	ADJ
ejpam-5136	294	8	sample	sample	NOUN
ejpam-5136	294	9	is	be	AUX
ejpam-5136	294	10	(	(	PUNCT
ejpam-5136	294	11	x	x	NOUN
ejpam-5136	294	12	,	,	PUNCT
ejpam-5136	294	13	y	y	PROPN
ejpam-5136	294	14	)	)	PUNCT
ejpam-5136	294	15	.	.	PUNCT
ejpam-5136	295	1	i.	i.	PROPN
ejpam-5136	295	2	a.	a.	PROPN
ejpam-5136	295	3	lakibul	lakibul	PROPN
ejpam-5136	295	4	,	,	PUNCT
ejpam-5136	295	5	d.	d.	PROPN
ejpam-5136	295	6	l.	l.	PROPN
ejpam-5136	295	7	polestico	polestico	PROPN
ejpam-5136	295	8	,	,	PUNCT
ejpam-5136	295	9	a.	a.	PROPN
ejpam-5136	295	10	p.	p.	NOUN
ejpam-5136	295	11	supe	supe	PROPN
ejpam-5136	295	12	/	/	SYM
ejpam-5136	295	13	eur	eur	PROPN
ejpam-5136	295	14	.	.	PUNCT
ejpam-5136	296	1	j.	j.	PROPN
ejpam-5136	296	2	pure	pure	PROPN
ejpam-5136	296	3	appl	appl	PROPN
ejpam-5136	296	4	.	.	PROPN
ejpam-5136	296	5	math	math	PROPN
ejpam-5136	296	6	,	,	PUNCT
ejpam-5136	296	7	17	17	NUM
ejpam-5136	296	8	(	(	PUNCT
ejpam-5136	296	9	2	2	NUM
ejpam-5136	296	10	)	)	PUNCT
ejpam-5136	296	11	(	(	PUNCT
ejpam-5136	296	12	2024	2024	NUM
ejpam-5136	296	13	)	)	PUNCT
ejpam-5136	296	14	,	,	PUNCT
ejpam-5136	296	15	790	790	NUM
ejpam-5136	296	16	-	-	SYM
ejpam-5136	296	17	809	809	NUM
ejpam-5136	296	18	803	803	NUM
ejpam-5136	296	19	6	6	NUM
ejpam-5136	296	20	.	.	PUNCT
ejpam-5136	297	1	simulation	simulation	NOUN
ejpam-5136	297	2	study	study	VERB
ejpam-5136	297	3	this	this	DET
ejpam-5136	297	4	section	section	NOUN
ejpam-5136	297	5	presents	present	VERB
ejpam-5136	297	6	the	the	DET
ejpam-5136	297	7	simulation	simulation	NOUN
ejpam-5136	297	8	results	result	VERB
ejpam-5136	297	9	to	to	PART
ejpam-5136	297	10	assess	assess	VERB
ejpam-5136	297	11	the	the	DET
ejpam-5136	297	12	behavior	behavior	NOUN
ejpam-5136	297	13	of	of	ADP
ejpam-5136	297	14	the	the	DET
ejpam-5136	297	15	maximum	maximum	ADJ
ejpam-5136	297	16	likelihood	likelihood	NOUN
ejpam-5136	297	17	estimate	estimate	NOUN
ejpam-5136	297	18	of	of	ADP
ejpam-5136	297	19	the	the	DET
ejpam-5136	297	20	parameter	parameter	NOUN
ejpam-5136	297	21	of	of	ADP
ejpam-5136	297	22	the	the	DET
ejpam-5136	297	23	proposed	propose	VERB
ejpam-5136	297	24	bivariate	bivariate	ADJ
ejpam-5136	297	25	distribution	distribution	NOUN
ejpam-5136	297	26	.	.	PUNCT
ejpam-5136	298	1	the	the	DET
ejpam-5136	298	2	simulation	simulation	NOUN
ejpam-5136	298	3	algorithm	algorithm	NOUN
ejpam-5136	298	4	is	be	AUX
ejpam-5136	298	5	given	give	VERB
ejpam-5136	298	6	as	as	SCONJ
ejpam-5136	298	7	follows	follow	VERB
ejpam-5136	298	8	:	:	PUNCT
ejpam-5136	298	9	step	step	NOUN
ejpam-5136	298	10	1	1	NUM
ejpam-5136	298	11	.	.	PUNCT
ejpam-5136	299	1	*	*	PUNCT
ejpam-5136	299	2	*	*	PUNCT
ejpam-5136	299	3	*	*	PUNCT
ejpam-5136	299	4	draw	draw	VERB
ejpam-5136	299	5	sample	sample	NOUN
ejpam-5136	299	6	of	of	ADP
ejpam-5136	299	7	size	size	NOUN
ejpam-5136	299	8	n	n	CCONJ
ejpam-5136	299	9	,	,	PUNCT
ejpam-5136	299	10	n	n	NOUN
ejpam-5136	299	11	=	=	SYM
ejpam-5136	299	12	50	50	NUM
ejpam-5136	299	13	,	,	PUNCT
ejpam-5136	299	14	100	100	NUM
ejpam-5136	299	15	,	,	PUNCT
ejpam-5136	299	16	200	200	NUM
ejpam-5136	299	17	,	,	PUNCT
ejpam-5136	299	18	500	500	NUM
ejpam-5136	299	19	,	,	PUNCT
ejpam-5136	299	20	1000	1000	NUM
ejpam-5136	299	21	,	,	PUNCT
ejpam-5136	299	22	from	from	ADP
ejpam-5136	299	23	a	a	DET
ejpam-5136	299	24	bivariate	bivariate	ADJ
ejpam-5136	299	25	extended	extend	VERB
ejpam-5136	299	26	standard	standard	ADJ
ejpam-5136	299	27	u	u	ADJ
ejpam-5136	299	28	-	-	ADJ
ejpam-5136	299	29	quadratic	quadratic	ADJ
ejpam-5136	299	30	distribution	distribution	NOUN
ejpam-5136	299	31	with	with	ADP
ejpam-5136	299	32	parameter	parameter	NOUN
ejpam-5136	299	33	λ	λ	PROPN
ejpam-5136	299	34	using	use	VERB
ejpam-5136	299	35	the	the	DET
ejpam-5136	299	36	algorithm	algorithm	NOUN
ejpam-5136	299	37	given	give	VERB
ejpam-5136	299	38	in	in	ADP
ejpam-5136	299	39	section	section	NOUN
ejpam-5136	299	40	5	5	NUM
ejpam-5136	299	41	.	.	PUNCT
ejpam-5136	299	42	step	step	NOUN
ejpam-5136	299	43	2	2	NUM
ejpam-5136	299	44	.	.	PUNCT
ejpam-5136	300	1	*	*	PUNCT
ejpam-5136	300	2	*	*	PUNCT
ejpam-5136	300	3	*	*	PUNCT
ejpam-5136	300	4	using	use	VERB
ejpam-5136	300	5	the	the	DET
ejpam-5136	300	6	bivariate	bivariate	ADJ
ejpam-5136	300	7	sample	sample	NOUN
ejpam-5136	300	8	(	(	PUNCT
ejpam-5136	300	9	x	x	NOUN
ejpam-5136	300	10	,	,	PUNCT
ejpam-5136	300	11	y	y	PROPN
ejpam-5136	300	12	)	)	PUNCT
ejpam-5136	300	13	obtained	obtain	VERB
ejpam-5136	300	14	in	in	ADP
ejpam-5136	300	15	step	step	NOUN
ejpam-5136	300	16	1	1	NUM
ejpam-5136	300	17	above	above	ADV
ejpam-5136	300	18	,	,	PUNCT
ejpam-5136	300	19	compute	compute	VERB
ejpam-5136	300	20	the	the	DET
ejpam-5136	300	21	maximum	maximum	ADJ
ejpam-5136	300	22	likelihood	likelihood	NOUN
ejpam-5136	300	23	estimate	estimate	NOUN
ejpam-5136	300	24	of	of	ADP
ejpam-5136	300	25	λ	λ	PROPN
ejpam-5136	300	26	.	.	PROPN
ejpam-5136	300	27	step	step	NOUN
ejpam-5136	300	28	3	3	NUM
ejpam-5136	300	29	.	.	PUNCT
ejpam-5136	301	1	*	*	PUNCT
ejpam-5136	301	2	*	*	PUNCT
ejpam-5136	301	3	*	*	PUNCT
ejpam-5136	301	4	repeat	repeat	VERB
ejpam-5136	301	5	the	the	DET
ejpam-5136	301	6	preceding	precede	VERB
ejpam-5136	301	7	steps	step	NOUN
ejpam-5136	301	8	1	1	NUM
ejpam-5136	301	9	-	-	SYM
ejpam-5136	301	10	2	2	NUM
ejpam-5136	301	11	n	n	NOUN
ejpam-5136	301	12	=	=	SYM
ejpam-5136	301	13	1000	1000	NUM
ejpam-5136	301	14	times	time	NOUN
ejpam-5136	301	15	to	to	PART
ejpam-5136	301	16	get	get	VERB
ejpam-5136	301	17	1000	1000	NUM
ejpam-5136	301	18	estimates	estimate	NOUN
ejpam-5136	301	19	of	of	ADP
ejpam-5136	301	20	λ	λ	PROPN
ejpam-5136	301	21	.	.	PROPN
ejpam-5136	301	22	step	step	NOUN
ejpam-5136	301	23	4	4	NUM
ejpam-5136	301	24	.	.	PUNCT
ejpam-5136	302	1	*	*	PUNCT
ejpam-5136	302	2	*	*	PUNCT
ejpam-5136	302	3	*	*	PUNCT
ejpam-5136	302	4	compute	compute	NOUN
ejpam-5136	302	5	the	the	DET
ejpam-5136	302	6	mean	mean	ADJ
ejpam-5136	302	7	,	,	PUNCT
ejpam-5136	302	8	bias	bias	NOUN
ejpam-5136	302	9	,	,	PUNCT
ejpam-5136	302	10	and	and	CCONJ
ejpam-5136	302	11	mean	mean	VERB
ejpam-5136	302	12	squared	square	VERB
ejpam-5136	302	13	error	error	NOUN
ejpam-5136	302	14	(	(	PUNCT
ejpam-5136	302	15	mse	mse	NOUN
ejpam-5136	302	16	)	)	PUNCT
ejpam-5136	302	17	of	of	ADP
ejpam-5136	302	18	the	the	DET
ejpam-5136	302	19	1000	1000	NUM
ejpam-5136	302	20	estimates	estimate	NOUN
ejpam-5136	302	21	obtained	obtain	VERB
ejpam-5136	302	22	in	in	ADP
ejpam-5136	302	23	step	step	NOUN
ejpam-5136	302	24	3	3	NUM
ejpam-5136	302	25	to	to	PART
ejpam-5136	302	26	get	get	VERB
ejpam-5136	302	27	the	the	DET
ejpam-5136	302	28	desired	desire	VERB
ejpam-5136	302	29	results	result	NOUN
ejpam-5136	302	30	.	.	PUNCT
ejpam-5136	303	1	the	the	DET
ejpam-5136	303	2	mean	mean	ADJ
ejpam-5136	303	3	(	(	PUNCT
ejpam-5136	303	4	ae	ae	PROPN
ejpam-5136	303	5	)	)	PUNCT
ejpam-5136	303	6	,	,	PUNCT
ejpam-5136	303	7	bias	bias	NOUN
ejpam-5136	303	8	,	,	PUNCT
ejpam-5136	303	9	and	and	CCONJ
ejpam-5136	303	10	mse	mse	PROPN
ejpam-5136	303	11	are	be	AUX
ejpam-5136	303	12	,	,	PUNCT
ejpam-5136	303	13	respectively	respectively	ADV
ejpam-5136	303	14	,	,	PUNCT
ejpam-5136	303	15	defined	define	VERB
ejpam-5136	303	16	by	by	ADP
ejpam-5136	303	17	ae	ae	PROPN
ejpam-5136	304	1	=	=	PROPN
ejpam-5136	304	2	n∑	n∑	PROPN
ejpam-5136	304	3	i=1	i=1	PROPN
ejpam-5136	305	1	λi	λi	ADP
ejpam-5136	305	2	n	n	NOUN
ejpam-5136	305	3	,	,	PUNCT
ejpam-5136	305	4	bias	bias	NOUN
ejpam-5136	305	5	=	=	SYM
ejpam-5136	305	6	ae	ae	PROPN
ejpam-5136	305	7	−	−	PROPN
ejpam-5136	305	8	λ	λ	PROPN
ejpam-5136	305	9	and	and	CCONJ
ejpam-5136	305	10	mse	mse	PROPN
ejpam-5136	305	11	=	=	SYM
ejpam-5136	305	12	n∑	n∑	PROPN
ejpam-5136	305	13	i=1	i=1	PROPN
ejpam-5136	306	1	(	(	PUNCT
ejpam-5136	306	2	λi	λi	ADP
ejpam-5136	306	3	−	−	NOUN
ejpam-5136	306	4	λ)2	λ)2	NOUN
ejpam-5136	306	5	n	n	NOUN
ejpam-5136	306	6	.	.	PUNCT
ejpam-5136	307	1	table	table	NOUN
ejpam-5136	307	2	2	2	NUM
ejpam-5136	307	3	:	:	PUNCT
ejpam-5136	307	4	results	result	NOUN
ejpam-5136	307	5	of	of	ADP
ejpam-5136	307	6	the	the	DET
ejpam-5136	307	7	simulation	simulation	NOUN
ejpam-5136	307	8	study	study	NOUN
ejpam-5136	307	9	for	for	ADP
ejpam-5136	307	10	λ	λ	X
ejpam-5136	307	11	=	=	SYM
ejpam-5136	307	12	−0.3	−0.3	PROPN
ejpam-5136	307	13	,	,	PUNCT
ejpam-5136	307	14	0	0	NUM
ejpam-5136	307	15	and	and	CCONJ
ejpam-5136	307	16	0.5	0.5	NUM
ejpam-5136	307	17	.	.	PUNCT
ejpam-5136	308	1	λ	λ	NOUN
ejpam-5136	308	2	=	=	SYM
ejpam-5136	308	3	−0.3	−0.3	PROPN
ejpam-5136	309	1	λ	λ	X
ejpam-5136	309	2	=	=	SYM
ejpam-5136	309	3	0	0	NUM
ejpam-5136	309	4	λ	λ	NOUN
ejpam-5136	309	5	=	=	SYM
ejpam-5136	309	6	0.5	0.5	NUM
ejpam-5136	309	7	n	n	NOUN
ejpam-5136	309	8	ae	ae	PROPN
ejpam-5136	309	9	bias	bias	PROPN
ejpam-5136	309	10	mse	mse	PROPN
ejpam-5136	309	11	ae	ae	PROPN
ejpam-5136	309	12	bias	bias	PROPN
ejpam-5136	309	13	mse	mse	PROPN
ejpam-5136	309	14	ae	ae	PROPN
ejpam-5136	309	15	bias	bias	PROPN
ejpam-5136	309	16	mse	mse	PROPN
ejpam-5136	309	17	50	50	NUM
ejpam-5136	309	18	−0.302	−0.302	NOUN
ejpam-5136	309	19	−0.002	−0.002	NOUN
ejpam-5136	309	20	0.016	0.016	NUM
ejpam-5136	309	21	−0.004	−0.004	NOUN
ejpam-5136	309	22	−0.004	−0.004	VERB
ejpam-5136	309	23	0.025	0.025	NUM
ejpam-5136	309	24	0.494	0.494	NUM
ejpam-5136	309	25	−0.006	−0.006	NUM
ejpam-5136	309	26	0.025	0.025	NUM
ejpam-5136	309	27	100	100	NUM
ejpam-5136	309	28	−0.297	−0.297	NOUN
ejpam-5136	309	29	0.003	0.003	NUM
ejpam-5136	309	30	0.008	0.008	NUM
ejpam-5136	309	31	0.002	0.002	NUM
ejpam-5136	309	32	0.002	0.002	NUM
ejpam-5136	309	33	0.011	0.011	NUM
ejpam-5136	309	34	0.498	0.498	NUM
ejpam-5136	309	35	−0.002	−0.002	NOUN
ejpam-5136	309	36	0.011	0.011	NUM
ejpam-5136	309	37	200	200	NUM
ejpam-5136	310	1	−0.299	−0.299	NOUN
ejpam-5136	310	2	0.001	0.001	NUM
ejpam-5136	310	3	0.004	0.004	NUM
ejpam-5136	310	4	0.001	0.001	NUM
ejpam-5136	310	5	0.001	0.001	NUM
ejpam-5136	310	6	0.006	0.006	NUM
ejpam-5136	310	7	0.498	0.498	NUM
ejpam-5136	310	8	−0.002	−0.002	NOUN
ejpam-5136	310	9	0.006	0.006	NUM
ejpam-5136	310	10	500	500	NUM
ejpam-5136	310	11	−0.300	−0.300	NUM
ejpam-5136	310	12	0.000	0.000	NUM
ejpam-5136	310	13	0.002	0.002	NUM
ejpam-5136	310	14	−0.001	−0.001	NOUN
ejpam-5136	310	15	−0.001	−0.001	NOUN
ejpam-5136	310	16	0.002	0.002	NUM
ejpam-5136	310	17	0.498	0.498	NUM
ejpam-5136	310	18	−0.002	−0.002	NOUN
ejpam-5136	310	19	0.002	0.002	NUM
ejpam-5136	310	20	1000	1000	NUM
ejpam-5136	310	21	−0.300	−0.300	VERB
ejpam-5136	310	22	0.000	0.000	NUM
ejpam-5136	310	23	0.001	0.001	NUM
ejpam-5136	310	24	−0.001	−0.001	NOUN
ejpam-5136	310	25	−0.001	−0.001	NOUN
ejpam-5136	310	26	0.001	0.001	NUM
ejpam-5136	310	27	0.499	0.499	NUM
ejpam-5136	310	28	−0.001	−0.001	NOUN
ejpam-5136	310	29	0.001	0.001	NUM
ejpam-5136	310	30	table	table	NOUN
ejpam-5136	310	31	3	3	NUM
ejpam-5136	310	32	:	:	PUNCT
ejpam-5136	310	33	results	result	NOUN
ejpam-5136	310	34	of	of	ADP
ejpam-5136	310	35	the	the	DET
ejpam-5136	310	36	simulation	simulation	NOUN
ejpam-5136	310	37	study	study	NOUN
ejpam-5136	310	38	for	for	ADP
ejpam-5136	310	39	λ	λ	PROPN
ejpam-5136	310	40	=	=	SYM
ejpam-5136	310	41	−0.5	−0.5	PROPN
ejpam-5136	310	42	,	,	PUNCT
ejpam-5136	310	43	0.2	0.2	NUM
ejpam-5136	310	44	and	and	CCONJ
ejpam-5136	310	45	0.8	0.8	NUM
ejpam-5136	310	46	.	.	PUNCT
ejpam-5136	311	1	λ	λ	X
ejpam-5136	311	2	=	=	PUNCT
ejpam-5136	311	3	−0.5	−0.5	PUNCT
ejpam-5136	312	1	λ	λ	X
ejpam-5136	312	2	=	=	NOUN
ejpam-5136	312	3	0.2	0.2	NUM
ejpam-5136	312	4	λ	λ	NOUN
ejpam-5136	312	5	=	=	NOUN
ejpam-5136	312	6	0.8	0.8	NUM
ejpam-5136	312	7	n	n	NUM
ejpam-5136	312	8	ae	ae	PROPN
ejpam-5136	312	9	bias	bias	PROPN
ejpam-5136	312	10	mse	mse	PROPN
ejpam-5136	312	11	ae	ae	PROPN
ejpam-5136	312	12	bias	bias	PROPN
ejpam-5136	312	13	mse	mse	PROPN
ejpam-5136	312	14	ae	ae	PROPN
ejpam-5136	312	15	bias	bias	PROPN
ejpam-5136	312	16	mse	mse	PROPN
ejpam-5136	312	17	50	50	NUM
ejpam-5136	312	18	−0.471	−0.471	PROPN
ejpam-5136	312	19	0.029	0.029	NUM
ejpam-5136	312	20	0.004	0.004	NUM
ejpam-5136	312	21	0.195	0.195	NUM
ejpam-5136	312	22	−0.005	−0.005	NUM
ejpam-5136	312	23	0.027	0.027	NUM
ejpam-5136	312	24	0.794	0.794	NUM
ejpam-5136	312	25	−0.006	−0.006	NOUN
ejpam-5136	312	26	0.015	0.015	NUM
ejpam-5136	312	27	100	100	NUM
ejpam-5136	312	28	−0.481	−0.481	NUM
ejpam-5136	312	29	0.019	0.019	NUM
ejpam-5136	312	30	0.001	0.001	NUM
ejpam-5136	312	31	0.200	0.200	NUM
ejpam-5136	312	32	0.000	0.000	NUM
ejpam-5136	312	33	0.012	0.012	NUM
ejpam-5136	312	34	0.797	0.797	NUM
ejpam-5136	312	35	−0.003	−0.003	NOUN
ejpam-5136	312	36	0.007	0.007	NUM
ejpam-5136	312	37	200	200	NUM
ejpam-5136	312	38	−0.485	−0.485	NOUN
ejpam-5136	312	39	0.015	0.015	NUM
ejpam-5136	312	40	0.001	0.001	NUM
ejpam-5136	312	41	0.200	0.200	NUM
ejpam-5136	312	42	0.000	0.000	NUM
ejpam-5136	312	43	0.007	0.007	NUM
ejpam-5136	312	44	0.797	0.797	NUM
ejpam-5136	312	45	−0.003	−0.003	NOUN
ejpam-5136	312	46	0.004	0.004	NUM
ejpam-5136	312	47	500	500	NUM
ejpam-5136	312	48	−0.492	−0.492	NOUN
ejpam-5136	312	49	0.008	0.008	NUM
ejpam-5136	312	50	0.000	0.000	NUM
ejpam-5136	312	51	0.198	0.198	NUM
ejpam-5136	312	52	−0.002	−0.002	NOUN
ejpam-5136	312	53	0.003	0.003	NUM
ejpam-5136	312	54	0.797	0.797	NUM
ejpam-5136	312	55	−0.003	−0.003	NOUN
ejpam-5136	312	56	0.001	0.001	NUM
ejpam-5136	312	57	1000	1000	NUM
ejpam-5136	312	58	−0.495	−0.495	ADJ
ejpam-5136	312	59	0.005	0.005	NUM
ejpam-5136	312	60	0.000	0.000	NUM
ejpam-5136	312	61	0.199	0.199	NUM
ejpam-5136	312	62	−0.001	−0.001	NOUN
ejpam-5136	312	63	0.001	0.001	NUM
ejpam-5136	312	64	0.799	0.799	NUM
ejpam-5136	312	65	−0.001	−0.001	NOUN
ejpam-5136	312	66	0.001	0.001	NUM
ejpam-5136	312	67	considering	consider	VERB
ejpam-5136	312	68	nine	nine	NUM
ejpam-5136	312	69	different	different	ADJ
ejpam-5136	312	70	values	value	NOUN
ejpam-5136	312	71	of	of	ADP
ejpam-5136	312	72	λ	λ	NOUN
ejpam-5136	312	73	,	,	PUNCT
ejpam-5136	312	74	tables	table	VERB
ejpam-5136	312	75	2	2	NUM
ejpam-5136	312	76	to	to	PART
ejpam-5136	312	77	4	4	NUM
ejpam-5136	312	78	show	show	VERB
ejpam-5136	312	79	that	that	SCONJ
ejpam-5136	312	80	as	as	SCONJ
ejpam-5136	312	81	n	n	PRON
ejpam-5136	312	82	becomes	become	VERB
ejpam-5136	312	83	large	large	ADJ
ejpam-5136	312	84	,	,	PUNCT
ejpam-5136	312	85	the	the	DET
ejpam-5136	312	86	average	average	ADJ
ejpam-5136	312	87	estimate	estimate	NOUN
ejpam-5136	312	88	(	(	PUNCT
ejpam-5136	312	89	ae	ae	PROPN
ejpam-5136	312	90	)	)	PUNCT
ejpam-5136	312	91	of	of	ADP
ejpam-5136	312	92	λ	λ	PROPN
ejpam-5136	312	93	goes	go	VERB
ejpam-5136	312	94	closer	close	ADV
ejpam-5136	312	95	to	to	ADP
ejpam-5136	312	96	the	the	DET
ejpam-5136	312	97	true	true	ADJ
ejpam-5136	312	98	value	value	NOUN
ejpam-5136	312	99	while	while	SCONJ
ejpam-5136	312	100	the	the	DET
ejpam-5136	312	101	bias	bias	NOUN
ejpam-5136	312	102	and	and	CCONJ
ejpam-5136	312	103	the	the	DET
ejpam-5136	312	104	mse	mse	PROPN
ejpam-5136	312	105	i.	i.	PROPN
ejpam-5136	312	106	a.	a.	PROPN
ejpam-5136	312	107	lakibul	lakibul	PROPN
ejpam-5136	312	108	,	,	PUNCT
ejpam-5136	312	109	d.	d.	PROPN
ejpam-5136	312	110	l.	l.	PROPN
ejpam-5136	312	111	polestico	polestico	PROPN
ejpam-5136	312	112	,	,	PUNCT
ejpam-5136	312	113	a.	a.	PROPN
ejpam-5136	312	114	p.	p.	NOUN
ejpam-5136	312	115	supe	supe	PROPN
ejpam-5136	312	116	/	/	SYM
ejpam-5136	312	117	eur	eur	PROPN
ejpam-5136	312	118	.	.	PUNCT
ejpam-5136	313	1	j.	j.	PROPN
ejpam-5136	313	2	pure	pure	PROPN
ejpam-5136	313	3	appl	appl	PROPN
ejpam-5136	313	4	.	.	PROPN
ejpam-5136	313	5	math	math	PROPN
ejpam-5136	313	6	,	,	PUNCT
ejpam-5136	313	7	17	17	NUM
ejpam-5136	313	8	(	(	PUNCT
ejpam-5136	313	9	2	2	NUM
ejpam-5136	313	10	)	)	PUNCT
ejpam-5136	313	11	(	(	PUNCT
ejpam-5136	313	12	2024	2024	NUM
ejpam-5136	313	13	)	)	PUNCT
ejpam-5136	313	14	,	,	PUNCT
ejpam-5136	313	15	790	790	NUM
ejpam-5136	313	16	-	-	SYM
ejpam-5136	313	17	809	809	NUM
ejpam-5136	313	18	804	804	NUM
ejpam-5136	313	19	table	table	NOUN
ejpam-5136	313	20	4	4	NUM
ejpam-5136	313	21	:	:	PUNCT
ejpam-5136	313	22	results	result	NOUN
ejpam-5136	313	23	of	of	ADP
ejpam-5136	313	24	the	the	DET
ejpam-5136	313	25	simulation	simulation	NOUN
ejpam-5136	313	26	study	study	NOUN
ejpam-5136	313	27	for	for	ADP
ejpam-5136	313	28	λ	λ	X
ejpam-5136	313	29	=	=	SYM
ejpam-5136	313	30	−0.1	−0.1	PROPN
ejpam-5136	313	31	,	,	PUNCT
ejpam-5136	313	32	0.3	0.3	NUM
ejpam-5136	313	33	and	and	CCONJ
ejpam-5136	313	34	1	1	NUM
ejpam-5136	313	35	.	.	PUNCT
ejpam-5136	314	1	λ	λ	X
ejpam-5136	314	2	=	=	SYM
ejpam-5136	315	1	−0.1	−0.1	PUNCT
ejpam-5136	315	2	λ	λ	X
ejpam-5136	315	3	=	=	SYM
ejpam-5136	315	4	0.3	0.3	NUM
ejpam-5136	315	5	λ	λ	NOUN
ejpam-5136	315	6	=	=	SYM
ejpam-5136	315	7	1	1	NUM
ejpam-5136	315	8	n	n	NUM
ejpam-5136	315	9	ae	ae	PROPN
ejpam-5136	315	10	bias	bias	PROPN
ejpam-5136	315	11	mse	mse	PROPN
ejpam-5136	315	12	ae	ae	PROPN
ejpam-5136	315	13	bias	bias	PROPN
ejpam-5136	315	14	mse	mse	PROPN
ejpam-5136	315	15	ae	ae	PROPN
ejpam-5136	315	16	bias	bias	PROPN
ejpam-5136	315	17	mse	mse	PROPN
ejpam-5136	315	18	50	50	NUM
ejpam-5136	315	19	−0.104	−0.104	NOUN
ejpam-5136	315	20	−0.004	−0.004	VERB
ejpam-5136	315	21	0.023	0.023	NUM
ejpam-5136	315	22	0.294	0.294	NUM
ejpam-5136	315	23	−0.006	−0.006	NOUN
ejpam-5136	315	24	0.027	0.027	NUM
ejpam-5136	315	25	0.979	0.979	NUM
ejpam-5136	315	26	−0.021	−0.021	NUM
ejpam-5136	315	27	0.002	0.002	NUM
ejpam-5136	315	28	100	100	NUM
ejpam-5136	315	29	−0.097	−0.097	NOUN
ejpam-5136	315	30	0.003	0.003	NUM
ejpam-5136	315	31	0.010	0.010	NUM
ejpam-5136	315	32	0.299	0.299	NUM
ejpam-5136	315	33	−0.001	−0.001	NOUN
ejpam-5136	315	34	0.012	0.012	NUM
ejpam-5136	315	35	0.987	0.987	NUM
ejpam-5136	315	36	−0.013	−0.013	NOUN
ejpam-5136	315	37	0.001	0.001	NUM
ejpam-5136	315	38	200	200	NUM
ejpam-5136	315	39	−0.099	−0.099	NOUN
ejpam-5136	315	40	0.001	0.001	NUM
ejpam-5136	315	41	0.006	0.006	NUM
ejpam-5136	315	42	0.299	0.299	NUM
ejpam-5136	315	43	−0.001	−0.001	NOUN
ejpam-5136	315	44	0.007	0.007	NUM
ejpam-5136	315	45	0.992	0.992	NUM
ejpam-5136	315	46	−0.008	−0.008	NOUN
ejpam-5136	315	47	0.000	0.000	NUM
ejpam-5136	315	48	500	500	NUM
ejpam-5136	315	49	−0.101	−0.101	PROPN
ejpam-5136	315	50	−0.001	−0.001	VERB
ejpam-5136	315	51	0.002	0.002	NUM
ejpam-5136	315	52	0.298	0.298	NUM
ejpam-5136	315	53	−0.002	−0.002	NOUN
ejpam-5136	315	54	0.003	0.003	NUM
ejpam-5136	315	55	0.996	0.996	NUM
ejpam-5136	315	56	−0.004	−0.004	VERB
ejpam-5136	315	57	0.000	0.000	NUM
ejpam-5136	315	58	1000	1000	NUM
ejpam-5136	315	59	−0.100	−0.100	NOUN
ejpam-5136	315	60	0.000	0.000	NUM
ejpam-5136	315	61	0.001	0.001	NUM
ejpam-5136	315	62	0.299	0.299	NUM
ejpam-5136	315	63	−0.001	−0.001	NOUN
ejpam-5136	315	64	0.001	0.001	NUM
ejpam-5136	315	65	0.997	0.997	NUM
ejpam-5136	315	66	−0.003	−0.003	NOUN
ejpam-5136	315	67	0.000	0.000	NUM
ejpam-5136	315	68	diminish	diminish	VERB
ejpam-5136	315	69	to	to	ADP
ejpam-5136	315	70	zero	zero	NUM
ejpam-5136	315	71	.	.	PUNCT
ejpam-5136	316	1	thus	thus	ADV
ejpam-5136	316	2	,	,	PUNCT
ejpam-5136	316	3	the	the	DET
ejpam-5136	316	4	maximum	maximum	ADJ
ejpam-5136	316	5	likelihood	likelihood	NOUN
ejpam-5136	316	6	estimate	estimate	NOUN
ejpam-5136	316	7	of	of	ADP
ejpam-5136	316	8	the	the	DET
ejpam-5136	316	9	proposed	propose	VERB
ejpam-5136	316	10	distribution	distribution	NOUN
ejpam-5136	316	11	parameter	parameter	NOUN
ejpam-5136	316	12	is	be	AUX
ejpam-5136	316	13	consistent	consistent	ADJ
ejpam-5136	316	14	.	.	PUNCT
ejpam-5136	317	1	7	7	X
ejpam-5136	317	2	.	.	X
ejpam-5136	317	3	application	application	NOUN
ejpam-5136	317	4	in	in	ADP
ejpam-5136	317	5	this	this	DET
ejpam-5136	317	6	section	section	NOUN
ejpam-5136	317	7	,	,	PUNCT
ejpam-5136	317	8	we	we	PRON
ejpam-5136	317	9	derive	derive	VERB
ejpam-5136	317	10	a	a	DET
ejpam-5136	317	11	bivariate	bivariate	ADJ
ejpam-5136	317	12	version	version	NOUN
ejpam-5136	317	13	of	of	ADP
ejpam-5136	317	14	the	the	DET
ejpam-5136	317	15	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	317	16	distribution	distribution	NOUN
ejpam-5136	317	17	and	and	CCONJ
ejpam-5136	317	18	use	use	VERB
ejpam-5136	317	19	it	it	PRON
ejpam-5136	317	20	to	to	PART
ejpam-5136	317	21	simulate	simulate	VERB
ejpam-5136	317	22	a	a	DET
ejpam-5136	317	23	bivariate	bivariate	ADJ
ejpam-5136	317	24	dataset	dataset	NOUN
ejpam-5136	317	25	.	.	PUNCT
ejpam-5136	318	1	since	since	SCONJ
ejpam-5136	318	2	there	there	PRON
ejpam-5136	318	3	is	be	VERB
ejpam-5136	318	4	a	a	DET
ejpam-5136	318	5	limited	limited	ADJ
ejpam-5136	318	6	to	to	ADP
ejpam-5136	318	7	none	none	NOUN
ejpam-5136	318	8	existing	exist	VERB
ejpam-5136	318	9	bivariate	bivariate	ADJ
ejpam-5136	318	10	distributions	distribution	NOUN
ejpam-5136	318	11	following	follow	VERB
ejpam-5136	318	12	a	a	DET
ejpam-5136	318	13	bathtub	bathtub	ADJ
ejpam-5136	318	14	shape	shape	NOUN
ejpam-5136	318	15	with	with	ADP
ejpam-5136	318	16	support	support	NOUN
ejpam-5136	318	17	particularly	particularly	ADV
ejpam-5136	318	18	on	on	ADP
ejpam-5136	318	19	(	(	PUNCT
ejpam-5136	318	20	0,1	0,1	NUM
ejpam-5136	318	21	)	)	PUNCT
ejpam-5136	318	22	,	,	PUNCT
ejpam-5136	318	23	we	we	PRON
ejpam-5136	318	24	derive	derive	VERB
ejpam-5136	318	25	a	a	DET
ejpam-5136	318	26	bivariate	bivariate	ADJ
ejpam-5136	318	27	extension	extension	NOUN
ejpam-5136	318	28	of	of	ADP
ejpam-5136	318	29	the	the	DET
ejpam-5136	318	30	cubic	cubic	ADJ
ejpam-5136	318	31	transmuted	transmuted	ADJ
ejpam-5136	318	32	uniform	uniform	NOUN
ejpam-5136	318	33	(	(	PUNCT
ejpam-5136	318	34	ctu	ctu	NOUN
ejpam-5136	318	35	)	)	PUNCT
ejpam-5136	318	36	distribution	distribution	NOUN
ejpam-5136	318	37	to	to	PART
ejpam-5136	318	38	compare	compare	VERB
ejpam-5136	318	39	it	it	PRON
ejpam-5136	318	40	with	with	ADP
ejpam-5136	318	41	the	the	DET
ejpam-5136	318	42	proposed	propose	VERB
ejpam-5136	318	43	bivariate	bivariate	ADJ
ejpam-5136	318	44	esu	esu	NOUN
ejpam-5136	318	45	distribution	distribution	NOUN
ejpam-5136	318	46	using	use	VERB
ejpam-5136	318	47	the	the	DET
ejpam-5136	318	48	simulated	simulated	ADJ
ejpam-5136	318	49	data	datum	NOUN
ejpam-5136	318	50	.	.	PUNCT
ejpam-5136	319	1	consider	consider	VERB
ejpam-5136	319	2	the	the	DET
ejpam-5136	319	3	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	319	4	(	(	PUNCT
ejpam-5136	319	5	km	km	NOUN
ejpam-5136	319	6	)	)	PUNCT
ejpam-5136	319	7	distribution	distribution	NOUN
ejpam-5136	319	8	of	of	ADP
ejpam-5136	319	9	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	319	10	[	[	X
ejpam-5136	319	11	2	2	NUM
ejpam-5136	319	12	]	]	PUNCT
ejpam-5136	319	13	,	,	PUNCT
ejpam-5136	319	14	that	that	ADV
ejpam-5136	319	15	is	is	ADV
ejpam-5136	319	16	,	,	PUNCT
ejpam-5136	319	17	for	for	ADP
ejpam-5136	319	18	a	a	DET
ejpam-5136	319	19	given	give	VERB
ejpam-5136	319	20	random	random	ADJ
ejpam-5136	319	21	variable	variable	NOUN
ejpam-5136	319	22	k	k	NOUN
ejpam-5136	319	23	,	,	PUNCT
ejpam-5136	319	24	the	the	DET
ejpam-5136	319	25	probability	probability	NOUN
ejpam-5136	319	26	density	density	NOUN
ejpam-5136	319	27	function	function	NOUN
ejpam-5136	319	28	(	(	PUNCT
ejpam-5136	319	29	pdf	pdf	NOUN
ejpam-5136	319	30	)	)	PUNCT
ejpam-5136	319	31	of	of	ADP
ejpam-5136	319	32	a	a	DET
ejpam-5136	319	33	km	km	NOUN
ejpam-5136	319	34	distribution	distribution	NOUN
ejpam-5136	319	35	is	be	AUX
ejpam-5136	319	36	given	give	VERB
ejpam-5136	319	37	by	by	ADP
ejpam-5136	319	38	f(k	f(k	NOUN
ejpam-5136	319	39	)	)	PUNCT
ejpam-5136	319	40	=	=	PUNCT
ejpam-5136	319	41	abka−1(1−	abka−1(1−	ADJ
ejpam-5136	319	42	ka)b−1	ka)b−1	NOUN
ejpam-5136	319	43	,	,	PUNCT
ejpam-5136	319	44	(	(	PUNCT
ejpam-5136	319	45	18	18	NUM
ejpam-5136	319	46	)	)	PUNCT
ejpam-5136	319	47	with	with	ADP
ejpam-5136	319	48	corresponding	correspond	VERB
ejpam-5136	319	49	cumulative	cumulative	ADJ
ejpam-5136	319	50	distribution	distribution	NOUN
ejpam-5136	319	51	function	function	NOUN
ejpam-5136	319	52	(	(	PUNCT
ejpam-5136	319	53	cdf	cdf	PROPN
ejpam-5136	319	54	)	)	PUNCT
ejpam-5136	319	55	f	f	PROPN
ejpam-5136	319	56	(	(	PUNCT
ejpam-5136	319	57	k	k	NOUN
ejpam-5136	319	58	)	)	PUNCT
ejpam-5136	319	59	=	=	SYM
ejpam-5136	319	60	1−	1−	NUM
ejpam-5136	320	1	(	(	PUNCT
ejpam-5136	320	2	1−	1−	NUM
ejpam-5136	320	3	ka)b	ka)b	PROPN
ejpam-5136	320	4	,	,	PUNCT
ejpam-5136	320	5	(	(	PUNCT
ejpam-5136	320	6	19	19	NUM
ejpam-5136	320	7	)	)	PUNCT
ejpam-5136	321	1	where	where	SCONJ
ejpam-5136	321	2	k	k	PROPN
ejpam-5136	321	3	∈	∈	PROPN
ejpam-5136	321	4	(	(	PUNCT
ejpam-5136	321	5	0	0	NUM
ejpam-5136	321	6	,	,	PUNCT
ejpam-5136	321	7	1	1	NUM
ejpam-5136	321	8	)	)	PUNCT
ejpam-5136	321	9	,	,	PUNCT
ejpam-5136	321	10	a	a	DET
ejpam-5136	321	11	>	>	X
ejpam-5136	321	12	0	0	NUM
ejpam-5136	321	13	and	and	CCONJ
ejpam-5136	321	14	b	b	X
ejpam-5136	321	15	>	>	X
ejpam-5136	321	16	0	0	X
ejpam-5136	321	17	.	.	PUNCT
ejpam-5136	322	1	it	it	PRON
ejpam-5136	322	2	was	be	AUX
ejpam-5136	322	3	observed	observe	VERB
ejpam-5136	322	4	that	that	SCONJ
ejpam-5136	322	5	the	the	DET
ejpam-5136	322	6	km	km	NOUN
ejpam-5136	322	7	distribution	distribution	NOUN
ejpam-5136	322	8	can	can	AUX
ejpam-5136	322	9	generate	generate	VERB
ejpam-5136	322	10	shapes	shape	NOUN
ejpam-5136	322	11	for	for	ADP
ejpam-5136	322	12	a	a	DET
ejpam-5136	322	13	bathtub	bathtub	NOUN
ejpam-5136	322	14	,	,	PUNCT
ejpam-5136	322	15	constant	constant	ADJ
ejpam-5136	322	16	,	,	PUNCT
ejpam-5136	322	17	inverted	inverted	ADJ
ejpam-5136	322	18	bathtub	bathtub	NOUN
ejpam-5136	322	19	,	,	PUNCT
ejpam-5136	322	20	increasing	increase	VERB
ejpam-5136	322	21	and	and	CCONJ
ejpam-5136	322	22	decreasing	decrease	VERB
ejpam-5136	322	23	distribution	distribution	NOUN
ejpam-5136	322	24	.	.	PUNCT
ejpam-5136	323	1	to	to	PART
ejpam-5136	323	2	generate	generate	VERB
ejpam-5136	323	3	a	a	DET
ejpam-5136	323	4	random	random	ADJ
ejpam-5136	323	5	sample	sample	NOUN
ejpam-5136	323	6	from	from	ADP
ejpam-5136	323	7	a	a	DET
ejpam-5136	323	8	km	km	NOUN
ejpam-5136	323	9	distribution	distribution	NOUN
ejpam-5136	323	10	,	,	PUNCT
ejpam-5136	323	11	we	we	PRON
ejpam-5136	323	12	consider	consider	VERB
ejpam-5136	323	13	k	k	X
ejpam-5136	323	14	=	=	PUNCT
ejpam-5136	324	1	[	[	PUNCT
ejpam-5136	324	2	1−	1−	NUM
ejpam-5136	324	3	(	(	PUNCT
ejpam-5136	324	4	1−	1−	NUM
ejpam-5136	324	5	u	u	NOUN
ejpam-5136	324	6	)	)	PUNCT
ejpam-5136	324	7	1	1	NUM
ejpam-5136	324	8	b	b	NOUN
ejpam-5136	324	9	]	]	PUNCT
ejpam-5136	324	10	1	1	NUM
ejpam-5136	324	11	a	a	PRON
ejpam-5136	324	12	,	,	PUNCT
ejpam-5136	324	13	(	(	PUNCT
ejpam-5136	324	14	20	20	NUM
ejpam-5136	324	15	)	)	PUNCT
ejpam-5136	324	16	where	where	SCONJ
ejpam-5136	324	17	u	u	NOUN
ejpam-5136	324	18	follows	follow	VERB
ejpam-5136	324	19	a	a	DET
ejpam-5136	324	20	uniform	uniform	ADJ
ejpam-5136	324	21	distribution	distribution	NOUN
ejpam-5136	324	22	defined	define	VERB
ejpam-5136	324	23	on	on	ADP
ejpam-5136	324	24	(	(	PUNCT
ejpam-5136	324	25	0	0	NUM
ejpam-5136	324	26	,	,	PUNCT
ejpam-5136	324	27	1	1	NUM
ejpam-5136	324	28	)	)	PUNCT
ejpam-5136	324	29	.	.	PUNCT
ejpam-5136	325	1	let	let	VERB
ejpam-5136	325	2	k1	k1	PROPN
ejpam-5136	325	3	be	be	AUX
ejpam-5136	325	4	a	a	DET
ejpam-5136	325	5	random	random	ADJ
ejpam-5136	325	6	variable	variable	NOUN
ejpam-5136	325	7	that	that	PRON
ejpam-5136	325	8	follows	follow	VERB
ejpam-5136	325	9	a	a	DET
ejpam-5136	325	10	km	km	NOUN
ejpam-5136	325	11	distribution	distribution	NOUN
ejpam-5136	325	12	with	with	ADP
ejpam-5136	325	13	parameters	parameter	NOUN
ejpam-5136	325	14	a	a	PRON
ejpam-5136	325	15	and	and	CCONJ
ejpam-5136	325	16	b.	b.	PROPN
ejpam-5136	325	17	let	let	VERB
ejpam-5136	325	18	k2	k2	PROPN
ejpam-5136	325	19	be	be	AUX
ejpam-5136	325	20	another	another	DET
ejpam-5136	325	21	random	random	ADJ
ejpam-5136	325	22	variable	variable	NOUN
ejpam-5136	325	23	such	such	ADJ
ejpam-5136	325	24	that	that	SCONJ
ejpam-5136	325	25	the	the	DET
ejpam-5136	325	26	conditional	conditional	ADJ
ejpam-5136	325	27	distribution	distribution	NOUN
ejpam-5136	325	28	of	of	ADP
ejpam-5136	325	29	k2	k2	NOUN
ejpam-5136	325	30	given	give	VERB
ejpam-5136	325	31	k1	k1	PROPN
ejpam-5136	325	32	follows	follow	VERB
ejpam-5136	325	33	a	a	DET
ejpam-5136	325	34	km	km	NOUN
ejpam-5136	325	35	distribution	distribution	NOUN
ejpam-5136	325	36	with	with	ADP
ejpam-5136	325	37	parameters	parameter	NOUN
ejpam-5136	325	38	h(k1	h(k1	ADV
ejpam-5136	325	39	)	)	PUNCT
ejpam-5136	325	40	>	>	X
ejpam-5136	325	41	0	0	PUNCT
ejpam-5136	326	1	and	and	CCONJ
ejpam-5136	326	2	b	b	X
ejpam-5136	326	3	>	>	X
ejpam-5136	326	4	0	0	NUM
ejpam-5136	326	5	.	.	PUNCT
ejpam-5136	327	1	from	from	ADP
ejpam-5136	327	2	the	the	DET
ejpam-5136	327	3	work	work	NOUN
ejpam-5136	327	4	of	of	ADP
ejpam-5136	327	5	shahbaz	shahbaz	PROPN
ejpam-5136	327	6	et	et	PROPN
ejpam-5136	327	7	al	al	PROPN
ejpam-5136	327	8	.	.	PUNCT
ejpam-5136	328	1	[	[	X
ejpam-5136	328	2	10	10	NUM
ejpam-5136	328	3	]	]	PUNCT
ejpam-5136	328	4	,	,	PUNCT
ejpam-5136	328	5	the	the	DET
ejpam-5136	328	6	joint	joint	ADJ
ejpam-5136	328	7	pdf	pdf	NOUN
ejpam-5136	328	8	of	of	ADP
ejpam-5136	328	9	k1	k1	PROPN
ejpam-5136	328	10	and	and	CCONJ
ejpam-5136	328	11	k2	k2	NOUN
ejpam-5136	328	12	is	be	AUX
ejpam-5136	328	13	given	give	VERB
ejpam-5136	328	14	by	by	ADP
ejpam-5136	328	15	f(k1	f(k1	NOUN
ejpam-5136	328	16	,	,	PUNCT
ejpam-5136	328	17	k2	k2	NOUN
ejpam-5136	328	18	)	)	PUNCT
ejpam-5136	328	19	=	=	PUNCT
ejpam-5136	329	1	ab2h(k1)k	ab2h(k1)k	ADV
ejpam-5136	329	2	a−1	a−1	PROPN
ejpam-5136	329	3	1	1	NUM
ejpam-5136	329	4	k	k	NOUN
ejpam-5136	329	5	h(k1)−1	h(k1)−1	SYM
ejpam-5136	329	6	2	2	NUM
ejpam-5136	329	7	[	[	PUNCT
ejpam-5136	329	8	(	(	PUNCT
ejpam-5136	329	9	1−	1−	NUM
ejpam-5136	329	10	ka1)(1−	ka1)(1−	NOUN
ejpam-5136	329	11	k	k	PROPN
ejpam-5136	329	12	h(k1	h(k1	PROPN
ejpam-5136	329	13	)	)	PUNCT
ejpam-5136	329	14	2	2	NUM
ejpam-5136	329	15	)	)	PUNCT
ejpam-5136	329	16	]	]	PUNCT
ejpam-5136	329	17	b−1	b−1	PROPN
ejpam-5136	329	18	.	.	PUNCT
ejpam-5136	329	19	i.	i.	PROPN
ejpam-5136	329	20	a.	a.	PROPN
ejpam-5136	329	21	lakibul	lakibul	PROPN
ejpam-5136	329	22	,	,	PUNCT
ejpam-5136	329	23	d.	d.	PROPN
ejpam-5136	329	24	l.	l.	PROPN
ejpam-5136	329	25	polestico	polestico	PROPN
ejpam-5136	329	26	,	,	PUNCT
ejpam-5136	329	27	a.	a.	PROPN
ejpam-5136	329	28	p.	p.	NOUN
ejpam-5136	329	29	supe	supe	PROPN
ejpam-5136	329	30	/	/	SYM
ejpam-5136	329	31	eur	eur	PROPN
ejpam-5136	329	32	.	.	PUNCT
ejpam-5136	330	1	j.	j.	PROPN
ejpam-5136	330	2	pure	pure	PROPN
ejpam-5136	330	3	appl	appl	PROPN
ejpam-5136	330	4	.	.	PROPN
ejpam-5136	330	5	math	math	PROPN
ejpam-5136	330	6	,	,	PUNCT
ejpam-5136	330	7	17	17	NUM
ejpam-5136	330	8	(	(	PUNCT
ejpam-5136	330	9	2	2	NUM
ejpam-5136	330	10	)	)	PUNCT
ejpam-5136	330	11	(	(	PUNCT
ejpam-5136	330	12	2024	2024	NUM
ejpam-5136	330	13	)	)	PUNCT
ejpam-5136	330	14	,	,	PUNCT
ejpam-5136	330	15	790	790	NUM
ejpam-5136	330	16	-	-	SYM
ejpam-5136	330	17	809	809	NUM
ejpam-5136	330	18	805	805	NUM
ejpam-5136	330	19	further	far	ADV
ejpam-5136	330	20	,	,	PUNCT
ejpam-5136	330	21	we	we	PRON
ejpam-5136	330	22	can	can	AUX
ejpam-5136	330	23	set	set	VERB
ejpam-5136	330	24	h(k1	h(k1	NOUN
ejpam-5136	330	25	)	)	PUNCT
ejpam-5136	330	26	=	=	SYM
ejpam-5136	331	1	−	−	PROPN
ejpam-5136	331	2	log(1−k1	log(1−k1	NOUN
ejpam-5136	331	3	)	)	PUNCT
ejpam-5136	331	4	since	since	SCONJ
ejpam-5136	331	5	0	0	NUM
ejpam-5136	331	6	<	<	X
ejpam-5136	331	7	−	−	PROPN
ejpam-5136	331	8	log(1−k1	log(1−k1	NOUN
ejpam-5136	331	9	)	)	PUNCT
ejpam-5136	331	10	<	<	X
ejpam-5136	331	11	∞.	∞.	PROPN
ejpam-5136	331	12	thus	thus	ADV
ejpam-5136	331	13	,	,	PUNCT
ejpam-5136	331	14	the	the	DET
ejpam-5136	331	15	joint	joint	ADJ
ejpam-5136	331	16	pdf	pdf	NOUN
ejpam-5136	331	17	of	of	ADP
ejpam-5136	331	18	k1	k1	PROPN
ejpam-5136	331	19	and	and	CCONJ
ejpam-5136	331	20	k2	k2	NOUN
ejpam-5136	331	21	reduces	reduce	VERB
ejpam-5136	331	22	to	to	PART
ejpam-5136	331	23	f(k1	f(k1	VERB
ejpam-5136	331	24	,	,	PUNCT
ejpam-5136	331	25	k2	k2	NOUN
ejpam-5136	331	26	)	)	PUNCT
ejpam-5136	331	27	=	=	SYM
ejpam-5136	331	28	ab2ka−1	ab2ka−1	PROPN
ejpam-5136	331	29	1	1	NUM
ejpam-5136	331	30	k	k	NOUN
ejpam-5136	332	1	−	−	NOUN
ejpam-5136	332	2	log(1−k1)−1	log(1−k1)−1	NOUN
ejpam-5136	332	3	2	2	NUM
ejpam-5136	332	4	[	[	PUNCT
ejpam-5136	332	5	(	(	PUNCT
ejpam-5136	332	6	1−	1−	NUM
ejpam-5136	332	7	ka1)(1−	ka1)(1−	NOUN
ejpam-5136	332	8	k	k	X
ejpam-5136	332	9	−	−	PROPN
ejpam-5136	332	10	log(1−k1	log(1−k1	NOUN
ejpam-5136	332	11	)	)	PUNCT
ejpam-5136	332	12	2	2	NUM
ejpam-5136	332	13	)	)	PUNCT
ejpam-5136	332	14	]	]	PUNCT
ejpam-5136	332	15	b−1	b−1	PROPN
ejpam-5136	332	16	log	log	NOUN
ejpam-5136	332	17	(	(	PUNCT
ejpam-5136	332	18	1	1	NUM
ejpam-5136	332	19	1−	1−	NUM
ejpam-5136	332	20	k1	k1	NOUN
ejpam-5136	332	21	)	)	PUNCT
ejpam-5136	332	22	.	.	PUNCT
ejpam-5136	333	1	(	(	PUNCT
ejpam-5136	333	2	21	21	NUM
ejpam-5136	333	3	)	)	PUNCT
ejpam-5136	333	4	equation	equation	NOUN
ejpam-5136	333	5	(	(	PUNCT
ejpam-5136	333	6	21	21	NUM
ejpam-5136	333	7	)	)	PUNCT
ejpam-5136	333	8	gives	give	VERB
ejpam-5136	333	9	the	the	DET
ejpam-5136	333	10	joint	joint	ADJ
ejpam-5136	333	11	pdf	pdf	NOUN
ejpam-5136	333	12	of	of	ADP
ejpam-5136	333	13	the	the	DET
ejpam-5136	333	14	bivariate	bivariate	ADJ
ejpam-5136	333	15	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	333	16	(	(	PUNCT
ejpam-5136	333	17	bkm	bkm	NOUN
ejpam-5136	333	18	)	)	PUNCT
ejpam-5136	333	19	distribution	distribution	NOUN
ejpam-5136	333	20	.	.	PUNCT
ejpam-5136	334	1	the	the	DET
ejpam-5136	334	2	following	follow	VERB
ejpam-5136	334	3	algorithm	algorithm	NOUN
ejpam-5136	334	4	presents	present	VERB
ejpam-5136	334	5	how	how	SCONJ
ejpam-5136	334	6	to	to	PART
ejpam-5136	334	7	generate	generate	VERB
ejpam-5136	334	8	a	a	DET
ejpam-5136	334	9	random	random	ADJ
ejpam-5136	334	10	sample	sample	NOUN
ejpam-5136	334	11	from	from	ADP
ejpam-5136	334	12	a	a	DET
ejpam-5136	334	13	bkm	bkm	PROPN
ejpam-5136	334	14	distribution	distribution	NOUN
ejpam-5136	334	15	:	:	PUNCT
ejpam-5136	334	16	step	step	NOUN
ejpam-5136	334	17	1.∗∗∗∗	1.∗∗∗∗	NUM
ejpam-5136	334	18	draw	draw	VERB
ejpam-5136	334	19	sample	sample	NOUN
ejpam-5136	334	20	of	of	ADP
ejpam-5136	334	21	size	size	NOUN
ejpam-5136	334	22	n	n	CCONJ
ejpam-5136	334	23	from	from	ADP
ejpam-5136	334	24	the	the	DET
ejpam-5136	334	25	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	334	26	distribution	distribution	NOUN
ejpam-5136	334	27	with	with	ADP
ejpam-5136	334	28	parameters	parameter	NOUN
ejpam-5136	334	29	a	a	PRON
ejpam-5136	334	30	and	and	CCONJ
ejpam-5136	334	31	b	b	NOUN
ejpam-5136	334	32	using	use	VERB
ejpam-5136	334	33	equation	equation	NOUN
ejpam-5136	334	34	(	(	PUNCT
ejpam-5136	334	35	20	20	NUM
ejpam-5136	334	36	)	)	PUNCT
ejpam-5136	334	37	.	.	PUNCT
ejpam-5136	335	1	denote	denote	VERB
ejpam-5136	335	2	this	this	DET
ejpam-5136	335	3	sample	sample	NOUN
ejpam-5136	335	4	as	as	ADP
ejpam-5136	335	5	x∗.	x∗.	PROPN
ejpam-5136	335	6	step	step	NOUN
ejpam-5136	335	7	2.∗∗∗∗	2.∗∗∗∗	PROPN
ejpam-5136	335	8	for	for	ADP
ejpam-5136	335	9	each	each	DET
ejpam-5136	335	10	observation	observation	NOUN
ejpam-5136	335	11	of	of	ADP
ejpam-5136	335	12	x∗	x∗	PROPN
ejpam-5136	335	13	,	,	PUNCT
ejpam-5136	335	14	draw	draw	VERB
ejpam-5136	335	15	a	a	DET
ejpam-5136	335	16	sample	sample	NOUN
ejpam-5136	335	17	of	of	ADP
ejpam-5136	335	18	size	size	NOUN
ejpam-5136	335	19	1	1	NUM
ejpam-5136	335	20	from	from	ADP
ejpam-5136	335	21	the	the	DET
ejpam-5136	335	22	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	335	23	distribution	distribution	NOUN
ejpam-5136	335	24	with	with	ADP
ejpam-5136	335	25	parameters	parameter	NOUN
ejpam-5136	336	1	−	−	NOUN
ejpam-5136	336	2	log(1	log(1	NOUN
ejpam-5136	336	3	−	−	NOUN
ejpam-5136	337	1	x	x	NOUN
ejpam-5136	337	2	)	)	PUNCT
ejpam-5136	338	1	and	and	CCONJ
ejpam-5136	338	2	b.	b.	PROPN
ejpam-5136	338	3	repeat	repeat	VERB
ejpam-5136	338	4	this	this	DET
ejpam-5136	338	5	process	process	NOUN
ejpam-5136	338	6	for	for	ADP
ejpam-5136	338	7	all	all	DET
ejpam-5136	338	8	observations	observation	NOUN
ejpam-5136	338	9	of	of	ADP
ejpam-5136	338	10	x∗.	x∗.	PROPN
ejpam-5136	338	11	denote	denote	VERB
ejpam-5136	338	12	this	this	DET
ejpam-5136	338	13	sample	sample	NOUN
ejpam-5136	338	14	as	as	SCONJ
ejpam-5136	338	15	y	y	PROPN
ejpam-5136	338	16	∗.	∗.	PROPN
ejpam-5136	338	17	step	step	NOUN
ejpam-5136	338	18	3.∗∗∗∗	3.∗∗∗∗	PROPN
ejpam-5136	338	19	finally	finally	ADV
ejpam-5136	338	20	,	,	PUNCT
ejpam-5136	338	21	the	the	DET
ejpam-5136	338	22	desired	desire	VERB
ejpam-5136	338	23	random	random	ADJ
ejpam-5136	338	24	sample	sample	NOUN
ejpam-5136	338	25	from	from	ADP
ejpam-5136	338	26	the	the	DET
ejpam-5136	338	27	bkm	bkm	PROPN
ejpam-5136	338	28	distribution	distribution	NOUN
ejpam-5136	338	29	is	be	AUX
ejpam-5136	338	30	(	(	PUNCT
ejpam-5136	338	31	x∗	x∗	PROPN
ejpam-5136	338	32	,	,	PUNCT
ejpam-5136	338	33	y∗	y∗	PROPN
ejpam-5136	338	34	)	)	PUNCT
ejpam-5136	338	35	.	.	PUNCT
ejpam-5136	339	1	here	here	ADV
ejpam-5136	339	2	,	,	PUNCT
ejpam-5136	339	3	we	we	PRON
ejpam-5136	339	4	generate	generate	VERB
ejpam-5136	339	5	a	a	DET
ejpam-5136	339	6	bivariate	bivariate	ADJ
ejpam-5136	339	7	set	set	NOUN
ejpam-5136	339	8	of	of	ADP
ejpam-5136	339	9	data	datum	NOUN
ejpam-5136	339	10	such	such	ADJ
ejpam-5136	339	11	that	that	SCONJ
ejpam-5136	339	12	x	x	PROPN
ejpam-5136	339	13	and	and	CCONJ
ejpam-5136	339	14	y	y	PROPN
ejpam-5136	339	15	have	have	AUX
ejpam-5136	339	16	bathtub	bathtub	VERB
ejpam-5136	339	17	shapes	shape	NOUN
ejpam-5136	339	18	from	from	ADP
ejpam-5136	339	19	the	the	DET
ejpam-5136	339	20	derived	derive	VERB
ejpam-5136	339	21	bivariate	bivariate	ADJ
ejpam-5136	339	22	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	339	23	distribution	distribution	NOUN
ejpam-5136	339	24	with	with	ADP
ejpam-5136	339	25	a	a	DET
ejpam-5136	339	26	=	=	SYM
ejpam-5136	339	27	0.5	0.5	NUM
ejpam-5136	339	28	and	and	CCONJ
ejpam-5136	339	29	b	b	NOUN
ejpam-5136	339	30	=	=	SYM
ejpam-5136	339	31	0.5	0.5	NUM
ejpam-5136	339	32	.	.	PUNCT
ejpam-5136	340	1	the	the	DET
ejpam-5136	340	2	following	follow	VERB
ejpam-5136	340	3	figures	figure	NOUN
ejpam-5136	340	4	show	show	VERB
ejpam-5136	340	5	the	the	DET
ejpam-5136	340	6	joint	joint	ADJ
ejpam-5136	340	7	and	and	CCONJ
ejpam-5136	340	8	marginal	marginal	ADJ
ejpam-5136	340	9	distributions	distribution	NOUN
ejpam-5136	340	10	of	of	ADP
ejpam-5136	340	11	x	x	X
ejpam-5136	340	12	and	and	CCONJ
ejpam-5136	340	13	y	y	PROPN
ejpam-5136	340	14	based	base	VERB
ejpam-5136	340	15	on	on	ADP
ejpam-5136	340	16	the	the	DET
ejpam-5136	340	17	simulated	simulate	VERB
ejpam-5136	340	18	dataset	dataset	NOUN
ejpam-5136	340	19	.	.	PUNCT
ejpam-5136	341	1	figure	figure	VERB
ejpam-5136	341	2	4	4	NUM
ejpam-5136	341	3	:	:	PUNCT
ejpam-5136	341	4	histogram	histogram	NOUN
ejpam-5136	341	5	plot	plot	NOUN
ejpam-5136	341	6	of	of	ADP
ejpam-5136	341	7	the	the	DET
ejpam-5136	341	8	simulated	simulate	VERB
ejpam-5136	341	9	data	datum	NOUN
ejpam-5136	341	10	for	for	ADP
ejpam-5136	341	11	variable	variable	ADJ
ejpam-5136	341	12	x.	x.	NOUN
ejpam-5136	341	13	next	next	ADV
ejpam-5136	341	14	,	,	PUNCT
ejpam-5136	341	15	consider	consider	VERB
ejpam-5136	341	16	the	the	DET
ejpam-5136	341	17	cubic	cubic	ADJ
ejpam-5136	341	18	transmuted	transmuted	ADJ
ejpam-5136	341	19	uniform	uniform	NOUN
ejpam-5136	341	20	(	(	PUNCT
ejpam-5136	341	21	ctu	ctu	NOUN
ejpam-5136	341	22	)	)	PUNCT
ejpam-5136	341	23	distribution	distribution	NOUN
ejpam-5136	341	24	of	of	ADP
ejpam-5136	341	25	rahman	rahman	PROPN
ejpam-5136	341	26	et	et	PROPN
ejpam-5136	341	27	al	al	PROPN
ejpam-5136	341	28	.	.	PUNCT
ejpam-5136	342	1	[	[	X
ejpam-5136	342	2	6	6	NUM
ejpam-5136	342	3	]	]	PUNCT
ejpam-5136	342	4	,	,	PUNCT
ejpam-5136	342	5	that	that	ADV
ejpam-5136	342	6	is	is	ADV
ejpam-5136	342	7	,	,	PUNCT
ejpam-5136	342	8	for	for	ADP
ejpam-5136	342	9	a	a	DET
ejpam-5136	342	10	given	give	VERB
ejpam-5136	342	11	random	random	ADJ
ejpam-5136	342	12	variable	variable	NOUN
ejpam-5136	342	13	c	c	NOUN
ejpam-5136	342	14	,	,	PUNCT
ejpam-5136	342	15	the	the	DET
ejpam-5136	342	16	probability	probability	NOUN
ejpam-5136	342	17	density	density	NOUN
ejpam-5136	342	18	function	function	NOUN
ejpam-5136	342	19	(	(	PUNCT
ejpam-5136	342	20	pdf	pdf	NOUN
ejpam-5136	342	21	)	)	PUNCT
ejpam-5136	342	22	of	of	ADP
ejpam-5136	342	23	a	a	DET
ejpam-5136	342	24	ctu	ctu	ADJ
ejpam-5136	342	25	distribution	distribution	NOUN
ejpam-5136	342	26	is	be	AUX
ejpam-5136	342	27	given	give	VERB
ejpam-5136	342	28	by	by	ADP
ejpam-5136	342	29	f(c	f(c	PROPN
ejpam-5136	342	30	)	)	PUNCT
ejpam-5136	342	31	=	=	SYM
ejpam-5136	342	32	1−	1−	NUM
ejpam-5136	342	33	δ	δ	NOUN
ejpam-5136	342	34	+	+	CCONJ
ejpam-5136	342	35	6δc−	6δc−	NUM
ejpam-5136	342	36	6δc2	6δc2	NUM
ejpam-5136	342	37	,	,	PUNCT
ejpam-5136	342	38	(	(	PUNCT
ejpam-5136	342	39	22	22	NUM
ejpam-5136	342	40	)	)	PUNCT
ejpam-5136	342	41	with	with	ADP
ejpam-5136	342	42	corresponding	correspond	VERB
ejpam-5136	342	43	cumulative	cumulative	ADJ
ejpam-5136	342	44	distribution	distribution	NOUN
ejpam-5136	342	45	function	function	NOUN
ejpam-5136	342	46	(	(	PUNCT
ejpam-5136	342	47	cdf	cdf	PROPN
ejpam-5136	342	48	)	)	PUNCT
ejpam-5136	342	49	f	f	PROPN
ejpam-5136	342	50	(	(	PUNCT
ejpam-5136	342	51	x	x	X
ejpam-5136	342	52	)	)	PUNCT
ejpam-5136	342	53	=	=	SYM
ejpam-5136	342	54	(	(	PUNCT
ejpam-5136	342	55	1−	1−	NUM
ejpam-5136	342	56	δ)c+	δ)c+	NUM
ejpam-5136	342	57	3δc2	3δc2	NUM
ejpam-5136	342	58	−	−	NOUN
ejpam-5136	342	59	2δc3	2δc3	NUM
ejpam-5136	342	60	,	,	PUNCT
ejpam-5136	342	61	(	(	PUNCT
ejpam-5136	342	62	23	23	NUM
ejpam-5136	342	63	)	)	PUNCT
ejpam-5136	342	64	i.	i.	PROPN
ejpam-5136	342	65	a.	a.	PROPN
ejpam-5136	342	66	lakibul	lakibul	PROPN
ejpam-5136	342	67	,	,	PUNCT
ejpam-5136	342	68	d.	d.	PROPN
ejpam-5136	342	69	l.	l.	PROPN
ejpam-5136	342	70	polestico	polestico	PROPN
ejpam-5136	342	71	,	,	PUNCT
ejpam-5136	342	72	a.	a.	PROPN
ejpam-5136	342	73	p.	p.	NOUN
ejpam-5136	342	74	supe	supe	PROPN
ejpam-5136	342	75	/	/	SYM
ejpam-5136	342	76	eur	eur	PROPN
ejpam-5136	342	77	.	.	PUNCT
ejpam-5136	343	1	j.	j.	PROPN
ejpam-5136	343	2	pure	pure	PROPN
ejpam-5136	343	3	appl	appl	PROPN
ejpam-5136	343	4	.	.	PROPN
ejpam-5136	343	5	math	math	PROPN
ejpam-5136	343	6	,	,	PUNCT
ejpam-5136	343	7	17	17	NUM
ejpam-5136	343	8	(	(	PUNCT
ejpam-5136	343	9	2	2	NUM
ejpam-5136	343	10	)	)	PUNCT
ejpam-5136	343	11	(	(	PUNCT
ejpam-5136	343	12	2024	2024	NUM
ejpam-5136	343	13	)	)	PUNCT
ejpam-5136	343	14	,	,	PUNCT
ejpam-5136	343	15	790	790	NUM
ejpam-5136	343	16	-	-	SYM
ejpam-5136	343	17	809	809	NUM
ejpam-5136	343	18	806	806	NUM
ejpam-5136	343	19	figure	figure	NOUN
ejpam-5136	343	20	5	5	NUM
ejpam-5136	343	21	:	:	PUNCT
ejpam-5136	343	22	histogram	histogram	NOUN
ejpam-5136	343	23	plot	plot	NOUN
ejpam-5136	343	24	of	of	ADP
ejpam-5136	343	25	the	the	DET
ejpam-5136	343	26	simulated	simulate	VERB
ejpam-5136	343	27	data	datum	NOUN
ejpam-5136	343	28	for	for	ADP
ejpam-5136	343	29	variable	variable	ADJ
ejpam-5136	343	30	y	y	PROPN
ejpam-5136	343	31	.	.	PUNCT
ejpam-5136	344	1	where	where	SCONJ
ejpam-5136	344	2	c	c	X
ejpam-5136	344	3	∈	∈	PROPN
ejpam-5136	344	4	[	[	X
ejpam-5136	344	5	0	0	NUM
ejpam-5136	344	6	,	,	PUNCT
ejpam-5136	344	7	1	1	NUM
ejpam-5136	344	8	]	]	PUNCT
ejpam-5136	344	9	and	and	CCONJ
ejpam-5136	344	10	δ	δ	PROPN
ejpam-5136	344	11	∈	∈	PROPN
ejpam-5136	345	1	[	[	X
ejpam-5136	345	2	−1	−1	NOUN
ejpam-5136	345	3	,	,	PUNCT
ejpam-5136	345	4	1	1	NUM
ejpam-5136	345	5	]	]	PUNCT
ejpam-5136	345	6	.	.	PUNCT
ejpam-5136	346	1	the	the	DET
ejpam-5136	346	2	ctu	ctu	ADJ
ejpam-5136	346	3	distribution	distribution	NOUN
ejpam-5136	346	4	can	can	AUX
ejpam-5136	346	5	generate	generate	VERB
ejpam-5136	346	6	the	the	DET
ejpam-5136	346	7	following	follow	VERB
ejpam-5136	346	8	shapes	shape	NOUN
ejpam-5136	346	9	:	:	PUNCT
ejpam-5136	346	10	(	(	PUNCT
ejpam-5136	346	11	i	i	NOUN
ejpam-5136	346	12	)	)	PUNCT
ejpam-5136	346	13	bathtub	bathtub	VERB
ejpam-5136	346	14	for	for	ADP
ejpam-5136	346	15	δ	δ	PROPN
ejpam-5136	346	16	∈	∈	PROPN
ejpam-5136	347	1	[	[	X
ejpam-5136	347	2	−1	−1	NOUN
ejpam-5136	347	3	,	,	PUNCT
ejpam-5136	347	4	0	0	NUM
ejpam-5136	347	5	)	)	PUNCT
ejpam-5136	347	6	;	;	PUNCT
ejpam-5136	347	7	(	(	PUNCT
ejpam-5136	347	8	ii	ii	NOUN
ejpam-5136	347	9	)	)	PUNCT
ejpam-5136	347	10	constant	constant	ADJ
ejpam-5136	347	11	for	for	ADP
ejpam-5136	347	12	δ	δ	PROPN
ejpam-5136	347	13	=	=	SYM
ejpam-5136	347	14	0	0	NUM
ejpam-5136	347	15	;	;	PUNCT
ejpam-5136	347	16	and	and	CCONJ
ejpam-5136	347	17	inverted	invert	VERB
ejpam-5136	347	18	bathtub	bathtub	NOUN
ejpam-5136	347	19	for	for	ADP
ejpam-5136	347	20	δ	δ	PROPN
ejpam-5136	347	21	∈	∈	PROPN
ejpam-5136	347	22	(	(	PUNCT
ejpam-5136	347	23	0	0	NUM
ejpam-5136	347	24	,	,	PUNCT
ejpam-5136	347	25	1	1	NUM
ejpam-5136	347	26	]	]	PUNCT
ejpam-5136	347	27	.	.	PUNCT
ejpam-5136	348	1	in	in	ADP
ejpam-5136	348	2	the	the	DET
ejpam-5136	348	3	work	work	NOUN
ejpam-5136	348	4	of	of	ADP
ejpam-5136	348	5	rahman	rahman	PROPN
ejpam-5136	348	6	et	et	PROPN
ejpam-5136	348	7	al	al	PROPN
ejpam-5136	348	8	.	.	PUNCT
ejpam-5136	349	1	[	[	X
ejpam-5136	349	2	6	6	NUM
ejpam-5136	349	3	]	]	PUNCT
ejpam-5136	349	4	,	,	PUNCT
ejpam-5136	349	5	the	the	DET
ejpam-5136	349	6	ctu	ctu	ADJ
ejpam-5136	349	7	distribution	distribution	NOUN
ejpam-5136	349	8	was	be	AUX
ejpam-5136	349	9	applied	apply	VERB
ejpam-5136	349	10	to	to	PART
ejpam-5136	349	11	model	model	VERB
ejpam-5136	349	12	the	the	DET
ejpam-5136	349	13	lifetimes	lifetime	NOUN
ejpam-5136	349	14	of	of	ADP
ejpam-5136	349	15	30	30	NUM
ejpam-5136	349	16	electronic	electronic	ADJ
ejpam-5136	349	17	devices	device	NOUN
ejpam-5136	349	18	where	where	SCONJ
ejpam-5136	349	19	the	the	DET
ejpam-5136	349	20	lifetimes	lifetime	NOUN
ejpam-5136	349	21	of	of	ADP
ejpam-5136	349	22	the	the	DET
ejpam-5136	349	23	devices	device	NOUN
ejpam-5136	349	24	follow	follow	VERB
ejpam-5136	349	25	a	a	DET
ejpam-5136	349	26	bathtub	bathtub	ADJ
ejpam-5136	349	27	shape	shape	NOUN
ejpam-5136	349	28	.	.	PUNCT
ejpam-5136	350	1	they	they	PRON
ejpam-5136	350	2	compared	compare	VERB
ejpam-5136	350	3	the	the	DET
ejpam-5136	350	4	ctu	ctu	ADJ
ejpam-5136	350	5	distribution	distribution	NOUN
ejpam-5136	350	6	with	with	ADP
ejpam-5136	350	7	the	the	DET
ejpam-5136	350	8	beta	beta	NOUN
ejpam-5136	350	9	,	,	PUNCT
ejpam-5136	350	10	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	350	11	and	and	CCONJ
ejpam-5136	350	12	skew	skew	ADJ
ejpam-5136	350	13	uniform	uniform	ADJ
ejpam-5136	350	14	distributions	distribution	NOUN
ejpam-5136	350	15	using	use	VERB
ejpam-5136	350	16	the	the	DET
ejpam-5136	350	17	said	say	VERB
ejpam-5136	350	18	data	datum	NOUN
ejpam-5136	350	19	.	.	PUNCT
ejpam-5136	351	1	they	they	PRON
ejpam-5136	351	2	found	find	VERB
ejpam-5136	351	3	out	out	ADP
ejpam-5136	351	4	that	that	SCONJ
ejpam-5136	351	5	the	the	DET
ejpam-5136	351	6	ctu	ctu	ADJ
ejpam-5136	351	7	distribution	distribution	NOUN
ejpam-5136	351	8	provided	provide	VERB
ejpam-5136	351	9	better	well	ADJ
ejpam-5136	351	10	fit	fit	ADJ
ejpam-5136	351	11	for	for	ADP
ejpam-5136	351	12	the	the	DET
ejpam-5136	351	13	said	say	VERB
ejpam-5136	351	14	dataset	dataset	NOUN
ejpam-5136	351	15	as	as	ADP
ejpam-5136	351	16	compared	compare	VERB
ejpam-5136	351	17	with	with	ADP
ejpam-5136	351	18	the	the	DET
ejpam-5136	351	19	said	say	VERB
ejpam-5136	351	20	competing	compete	VERB
ejpam-5136	351	21	distributions	distribution	NOUN
ejpam-5136	351	22	.	.	PUNCT
ejpam-5136	352	1	let	let	VERB
ejpam-5136	352	2	c1	c1	PROPN
ejpam-5136	352	3	be	be	AUX
ejpam-5136	352	4	a	a	DET
ejpam-5136	352	5	random	random	ADJ
ejpam-5136	352	6	variable	variable	NOUN
ejpam-5136	352	7	that	that	PRON
ejpam-5136	352	8	follows	follow	VERB
ejpam-5136	352	9	a	a	DET
ejpam-5136	352	10	ctu	ctu	ADJ
ejpam-5136	352	11	distribution	distribution	NOUN
ejpam-5136	352	12	with	with	ADP
ejpam-5136	352	13	parameter	parameter	PROPN
ejpam-5136	352	14	δ	δ	PROPN
ejpam-5136	352	15	.	.	PUNCT
ejpam-5136	353	1	let	let	VERB
ejpam-5136	353	2	c2	c2	PROPN
ejpam-5136	353	3	be	be	AUX
ejpam-5136	353	4	another	another	DET
ejpam-5136	353	5	random	random	ADJ
ejpam-5136	353	6	variable	variable	NOUN
ejpam-5136	353	7	such	such	ADJ
ejpam-5136	353	8	that	that	SCONJ
ejpam-5136	353	9	the	the	DET
ejpam-5136	353	10	conditional	conditional	ADJ
ejpam-5136	353	11	distribution	distribution	NOUN
ejpam-5136	353	12	of	of	ADP
ejpam-5136	353	13	c2	c2	PROPN
ejpam-5136	353	14	given	give	VERB
ejpam-5136	353	15	c1	c1	PROPN
ejpam-5136	353	16	follows	follow	VERB
ejpam-5136	353	17	a	a	DET
ejpam-5136	353	18	ctu	ctu	ADJ
ejpam-5136	353	19	distribution	distribution	NOUN
ejpam-5136	353	20	with	with	ADP
ejpam-5136	353	21	parameters	parameter	NOUN
ejpam-5136	353	22	q(c1	q(c1	PROPN
ejpam-5136	353	23	)	)	PUNCT
ejpam-5136	353	24	.	.	PUNCT
ejpam-5136	354	1	following	follow	VERB
ejpam-5136	354	2	the	the	DET
ejpam-5136	354	3	results	result	NOUN
ejpam-5136	354	4	of	of	ADP
ejpam-5136	354	5	shahbaz	shahbaz	PROPN
ejpam-5136	354	6	et	et	PROPN
ejpam-5136	354	7	al	al	PROPN
ejpam-5136	354	8	.	.	PUNCT
ejpam-5136	355	1	[	[	X
ejpam-5136	355	2	10	10	NUM
ejpam-5136	355	3	]	]	PUNCT
ejpam-5136	355	4	,	,	PUNCT
ejpam-5136	355	5	the	the	DET
ejpam-5136	355	6	joint	joint	ADJ
ejpam-5136	355	7	pdf	pdf	NOUN
ejpam-5136	355	8	of	of	ADP
ejpam-5136	355	9	c1	c1	PROPN
ejpam-5136	355	10	and	and	CCONJ
ejpam-5136	355	11	c2	c2	PROPN
ejpam-5136	355	12	is	be	AUX
ejpam-5136	355	13	given	give	VERB
ejpam-5136	355	14	by	by	ADP
ejpam-5136	355	15	f(c1	f(c1	NOUN
ejpam-5136	355	16	,	,	PUNCT
ejpam-5136	355	17	c2	c2	PROPN
ejpam-5136	355	18	)	)	PUNCT
ejpam-5136	355	19	=	=	PUNCT
ejpam-5136	356	1	[	[	PUNCT
ejpam-5136	356	2	1−	1−	NUM
ejpam-5136	356	3	δ	δ	NOUN
ejpam-5136	356	4	+	+	CCONJ
ejpam-5136	356	5	6δc1	6δc1	NUM
ejpam-5136	356	6	−	−	ADP
ejpam-5136	357	1	6δc21	6δc21	X
ejpam-5136	357	2	]	]	X
ejpam-5136	357	3	[	[	PUNCT
ejpam-5136	357	4	1−q(c1	1−q(c1	NUM
ejpam-5136	357	5	)	)	PUNCT
ejpam-5136	357	6	+	+	CCONJ
ejpam-5136	358	1	6q(c1)c2	6q(c1)c2	NUM
ejpam-5136	358	2	−	−	NUM
ejpam-5136	358	3	6q(c1)c	6q(c1)c	NUM
ejpam-5136	358	4	2	2	NUM
ejpam-5136	358	5	2	2	NUM
ejpam-5136	358	6	]	]	PUNCT
ejpam-5136	358	7	.	.	PUNCT
ejpam-5136	359	1	further	far	ADV
ejpam-5136	359	2	,	,	PUNCT
ejpam-5136	359	3	we	we	PRON
ejpam-5136	359	4	can	can	AUX
ejpam-5136	359	5	set	set	VERB
ejpam-5136	359	6	q(c1	q(c1	NOUN
ejpam-5136	359	7	)	)	PUNCT
ejpam-5136	360	1	=	=	SYM
ejpam-5136	361	1	2c1	2c1	NUM
ejpam-5136	362	1	−	−	NOUN
ejpam-5136	362	2	1	1	NUM
ejpam-5136	362	3	since	since	SCONJ
ejpam-5136	362	4	−1	−1	NOUN
ejpam-5136	362	5	≤	≤	NOUN
ejpam-5136	362	6	2c1	2c1	NUM
ejpam-5136	363	1	−	−	NUM
ejpam-5136	363	2	1	1	NUM
ejpam-5136	363	3	≤	≤	NUM
ejpam-5136	363	4	1	1	NUM
ejpam-5136	363	5	.	.	PUNCT
ejpam-5136	364	1	thus	thus	ADV
ejpam-5136	364	2	,	,	PUNCT
ejpam-5136	364	3	the	the	DET
ejpam-5136	364	4	joint	joint	ADJ
ejpam-5136	364	5	pdf	pdf	NOUN
ejpam-5136	364	6	of	of	ADP
ejpam-5136	364	7	c1	c1	PROPN
ejpam-5136	364	8	and	and	CCONJ
ejpam-5136	364	9	c2	c2	PROPN
ejpam-5136	364	10	reduces	reduce	VERB
ejpam-5136	364	11	to	to	ADP
ejpam-5136	364	12	f(c1	f(c1	NOUN
ejpam-5136	364	13	,	,	PUNCT
ejpam-5136	364	14	c2	c2	PROPN
ejpam-5136	364	15	)	)	PUNCT
ejpam-5136	364	16	=	=	PUNCT
ejpam-5136	365	1	[	[	PUNCT
ejpam-5136	365	2	1−	1−	NUM
ejpam-5136	365	3	δ	δ	NOUN
ejpam-5136	365	4	+	+	CCONJ
ejpam-5136	365	5	6δc1	6δc1	NUM
ejpam-5136	365	6	−	−	ADP
ejpam-5136	366	1	6δc21	6δc21	X
ejpam-5136	366	2	]	]	X
ejpam-5136	367	1	[	[	PUNCT
ejpam-5136	367	2	1−	1−	NUM
ejpam-5136	367	3	(	(	PUNCT
ejpam-5136	367	4	2c1	2c1	NUM
ejpam-5136	367	5	−	−	NOUN
ejpam-5136	367	6	1	1	NUM
ejpam-5136	367	7	)	)	PUNCT
ejpam-5136	367	8	+	+	CCONJ
ejpam-5136	367	9	6(2c1	6(2c1	ADJ
ejpam-5136	367	10	−	−	PROPN
ejpam-5136	368	1	1)c2	1)c2	NUM
ejpam-5136	368	2	−	−	NOUN
ejpam-5136	368	3	6(2c1	6(2c1	PUNCT
ejpam-5136	369	1	−	−	PROPN
ejpam-5136	369	2	1)c22	1)c22	PROPN
ejpam-5136	369	3	]	]	PUNCT
ejpam-5136	369	4	.	.	PUNCT
ejpam-5136	370	1	(	(	PUNCT
ejpam-5136	370	2	24	24	NUM
ejpam-5136	370	3	)	)	PUNCT
ejpam-5136	370	4	we	we	PRON
ejpam-5136	370	5	name	name	VERB
ejpam-5136	370	6	the	the	DET
ejpam-5136	370	7	joint	joint	ADJ
ejpam-5136	370	8	pdf	pdf	NOUN
ejpam-5136	370	9	in	in	ADP
ejpam-5136	370	10	(	(	PUNCT
ejpam-5136	370	11	24	24	NUM
ejpam-5136	370	12	)	)	PUNCT
ejpam-5136	370	13	as	as	ADP
ejpam-5136	370	14	the	the	DET
ejpam-5136	370	15	joint	joint	ADJ
ejpam-5136	370	16	pdf	pdf	NOUN
ejpam-5136	370	17	of	of	ADP
ejpam-5136	370	18	the	the	DET
ejpam-5136	370	19	bivariate	bivariate	ADJ
ejpam-5136	370	20	cubic	cubic	ADJ
ejpam-5136	370	21	transmuted	transmute	VERB
ejpam-5136	370	22	uniform	uniform	NOUN
ejpam-5136	370	23	(	(	PUNCT
ejpam-5136	370	24	bctu	bctu	ADJ
ejpam-5136	370	25	)	)	PUNCT
ejpam-5136	370	26	distribution	distribution	NOUN
ejpam-5136	370	27	.	.	PUNCT
ejpam-5136	371	1	in	in	ADP
ejpam-5136	371	2	the	the	DET
ejpam-5136	371	3	analysis	analysis	NOUN
ejpam-5136	371	4	,	,	PUNCT
ejpam-5136	371	5	we	we	PRON
ejpam-5136	371	6	use	use	VERB
ejpam-5136	371	7	the	the	DET
ejpam-5136	371	8	r	r	NOUN
ejpam-5136	371	9	-	-	PUNCT
ejpam-5136	371	10	package	package	NOUN
ejpam-5136	371	11	”	"	PUNCT
ejpam-5136	371	12	bbmle	bbmle	NOUN
ejpam-5136	371	13	”	"	PUNCT
ejpam-5136	371	14	to	to	PART
ejpam-5136	371	15	compute	compute	VERB
ejpam-5136	371	16	the	the	DET
ejpam-5136	371	17	maximum	maximum	ADJ
ejpam-5136	371	18	likelihood	likelihood	NOUN
ejpam-5136	371	19	estimates	estimate	NOUN
ejpam-5136	371	20	of	of	ADP
ejpam-5136	371	21	the	the	DET
ejpam-5136	371	22	parameters	parameter	NOUN
ejpam-5136	371	23	of	of	ADP
ejpam-5136	371	24	the	the	DET
ejpam-5136	371	25	proposed	propose	VERB
ejpam-5136	371	26	besu	besu	NOUN
ejpam-5136	371	27	and	and	CCONJ
ejpam-5136	371	28	bctu	bctu	ADJ
ejpam-5136	371	29	distributions	distribution	NOUN
ejpam-5136	371	30	.	.	PUNCT
ejpam-5136	372	1	in	in	ADP
ejpam-5136	372	2	addition	addition	NOUN
ejpam-5136	372	3	,	,	PUNCT
ejpam-5136	372	4	the	the	DET
ejpam-5136	372	5	akaike	akaike	ADJ
ejpam-5136	372	6	information	information	NOUN
ejpam-5136	372	7	criterion	criterion	NOUN
ejpam-5136	372	8	(	(	PUNCT
ejpam-5136	372	9	aic	aic	PROPN
ejpam-5136	372	10	)	)	PUNCT
ejpam-5136	372	11	and	and	CCONJ
ejpam-5136	372	12	bayesian	bayesian	NOUN
ejpam-5136	372	13	information	information	NOUN
ejpam-5136	372	14	criterion	criterion	NOUN
ejpam-5136	372	15	(	(	PUNCT
ejpam-5136	372	16	bic	bic	PROPN
ejpam-5136	372	17	)	)	PUNCT
ejpam-5136	372	18	are	be	AUX
ejpam-5136	372	19	used	use	VERB
ejpam-5136	372	20	to	to	PART
ejpam-5136	372	21	assess	assess	VERB
ejpam-5136	372	22	and	and	CCONJ
ejpam-5136	372	23	compare	compare	VERB
ejpam-5136	372	24	the	the	DET
ejpam-5136	372	25	performance	performance	NOUN
ejpam-5136	372	26	of	of	ADP
ejpam-5136	372	27	the	the	DET
ejpam-5136	372	28	proposed	propose	VERB
ejpam-5136	372	29	bivariate	bivariate	ADJ
ejpam-5136	372	30	distributions	distribution	NOUN
ejpam-5136	372	31	.	.	PUNCT
ejpam-5136	373	1	table	table	NOUN
ejpam-5136	373	2	5	5	NUM
ejpam-5136	373	3	:	:	PUNCT
ejpam-5136	373	4	estimates	estimate	NOUN
ejpam-5136	373	5	and	and	CCONJ
ejpam-5136	373	6	some	some	DET
ejpam-5136	373	7	diagnostic	diagnostic	ADJ
ejpam-5136	373	8	values	value	NOUN
ejpam-5136	373	9	of	of	ADP
ejpam-5136	373	10	the	the	DET
ejpam-5136	373	11	fitted	fit	VERB
ejpam-5136	373	12	models	model	NOUN
ejpam-5136	373	13	for	for	ADP
ejpam-5136	373	14	the	the	DET
ejpam-5136	373	15	simulated	simulate	VERB
ejpam-5136	373	16	dataset	dataset	NOUN
ejpam-5136	373	17	.	.	PUNCT
ejpam-5136	374	1	distribution	distribution	NOUN
ejpam-5136	374	2	estimate	estimate	VERB
ejpam-5136	374	3	std.error	std.error	NOUN
ejpam-5136	374	4	−2loglik	−2loglik	NOUN
ejpam-5136	374	5	aic	aic	PROPN
ejpam-5136	374	6	bic	bic	PROPN
ejpam-5136	374	7	besu	besu	NOUN
ejpam-5136	374	8	λ̂	λ̂	X
ejpam-5136	375	1	=	=	PUNCT
ejpam-5136	376	1	0.489109	0.489109	NUM
ejpam-5136	376	2	0.014249	0.014249	NUM
ejpam-5136	377	1	2243.733	2243.733	NUM
ejpam-5136	378	1	2245.733	2245.733	NUM
ejpam-5136	378	2	2252.25	2252.25	NUM
ejpam-5136	378	3	bctu	bctu	ADJ
ejpam-5136	378	4	δ̂	δ̂	NOUN
ejpam-5136	378	5	=	=	SYM
ejpam-5136	378	6	−0.978219	−0.978219	NUM
ejpam-5136	379	1	0.028498	0.028498	NUM
ejpam-5136	379	2	3127.089	3127.089	NUM
ejpam-5136	379	3	3129.089	3129.089	NUM
ejpam-5136	379	4	3135.606	3135.606	NUM
ejpam-5136	379	5	table	table	NOUN
ejpam-5136	379	6	5	5	NUM
ejpam-5136	379	7	shows	show	VERB
ejpam-5136	379	8	some	some	DET
ejpam-5136	379	9	diagnostic	diagnostic	ADJ
ejpam-5136	379	10	statistics	statistic	NOUN
ejpam-5136	379	11	and	and	CCONJ
ejpam-5136	379	12	maximum	maximum	ADJ
ejpam-5136	379	13	likelihood	likelihood	NOUN
ejpam-5136	379	14	estimates	estimate	NOUN
ejpam-5136	379	15	of	of	ADP
ejpam-5136	379	16	the	the	DET
ejpam-5136	379	17	fitted	fit	VERB
ejpam-5136	379	18	models	model	NOUN
ejpam-5136	379	19	for	for	ADP
ejpam-5136	379	20	the	the	DET
ejpam-5136	379	21	simulated	simulate	VERB
ejpam-5136	379	22	dataset	dataset	NOUN
ejpam-5136	379	23	.	.	PUNCT
ejpam-5136	380	1	it	it	PRON
ejpam-5136	380	2	is	be	AUX
ejpam-5136	380	3	observed	observe	VERB
ejpam-5136	380	4	that	that	SCONJ
ejpam-5136	380	5	the	the	DET
ejpam-5136	380	6	besu	besu	NOUN
ejpam-5136	380	7	distribution	distribution	NOUN
ejpam-5136	380	8	has	have	VERB
ejpam-5136	380	9	smaller	small	ADJ
ejpam-5136	380	10	i.	i.	PROPN
ejpam-5136	380	11	a.	a.	PROPN
ejpam-5136	380	12	lakibul	lakibul	PROPN
ejpam-5136	380	13	,	,	PUNCT
ejpam-5136	380	14	d.	d.	PROPN
ejpam-5136	380	15	l.	l.	PROPN
ejpam-5136	380	16	polestico	polestico	PROPN
ejpam-5136	380	17	,	,	PUNCT
ejpam-5136	380	18	a.	a.	PROPN
ejpam-5136	380	19	p.	p.	NOUN
ejpam-5136	380	20	supe	supe	PROPN
ejpam-5136	380	21	/	/	SYM
ejpam-5136	380	22	eur	eur	PROPN
ejpam-5136	380	23	.	.	PUNCT
ejpam-5136	381	1	j.	j.	PROPN
ejpam-5136	381	2	pure	pure	PROPN
ejpam-5136	381	3	appl	appl	PROPN
ejpam-5136	381	4	.	.	PROPN
ejpam-5136	381	5	math	math	PROPN
ejpam-5136	381	6	,	,	PUNCT
ejpam-5136	381	7	17	17	NUM
ejpam-5136	381	8	(	(	PUNCT
ejpam-5136	381	9	2	2	NUM
ejpam-5136	381	10	)	)	PUNCT
ejpam-5136	381	11	(	(	PUNCT
ejpam-5136	381	12	2024	2024	NUM
ejpam-5136	381	13	)	)	PUNCT
ejpam-5136	381	14	,	,	PUNCT
ejpam-5136	381	15	790	790	NUM
ejpam-5136	381	16	-	-	SYM
ejpam-5136	381	17	809	809	NUM
ejpam-5136	381	18	807	807	NUM
ejpam-5136	381	19	figure	figure	NOUN
ejpam-5136	381	20	6	6	NUM
ejpam-5136	381	21	:	:	PUNCT
ejpam-5136	381	22	bivariate	bivariate	ADJ
ejpam-5136	381	23	histogram	histogram	NOUN
ejpam-5136	381	24	of	of	ADP
ejpam-5136	381	25	the	the	DET
ejpam-5136	381	26	simulated	simulate	VERB
ejpam-5136	381	27	data	datum	NOUN
ejpam-5136	381	28	.	.	PUNCT
ejpam-5136	382	1	values	value	NOUN
ejpam-5136	382	2	of	of	ADP
ejpam-5136	382	3	the	the	DET
ejpam-5136	382	4	aic	aic	PROPN
ejpam-5136	382	5	and	and	CCONJ
ejpam-5136	382	6	bic	bic	PROPN
ejpam-5136	382	7	than	than	ADP
ejpam-5136	382	8	the	the	DET
ejpam-5136	382	9	bctu	bctu	ADJ
ejpam-5136	382	10	distribution	distribution	NOUN
ejpam-5136	382	11	.	.	PUNCT
ejpam-5136	383	1	thus	thus	ADV
ejpam-5136	383	2	,	,	PUNCT
ejpam-5136	383	3	the	the	DET
ejpam-5136	383	4	besu	besu	NOUN
ejpam-5136	383	5	distribution	distribution	NOUN
ejpam-5136	383	6	provides	provide	VERB
ejpam-5136	383	7	a	a	DET
ejpam-5136	383	8	better	well	ADJ
ejpam-5136	383	9	fit	fit	NOUN
ejpam-5136	383	10	for	for	ADP
ejpam-5136	383	11	this	this	DET
ejpam-5136	383	12	simulated	simulate	VERB
ejpam-5136	383	13	data	datum	NOUN
ejpam-5136	383	14	than	than	ADP
ejpam-5136	383	15	the	the	DET
ejpam-5136	383	16	bctu	bctu	ADJ
ejpam-5136	383	17	distribution	distribution	NOUN
ejpam-5136	383	18	.	.	PUNCT
ejpam-5136	384	1	8	8	X
ejpam-5136	384	2	.	.	X
ejpam-5136	384	3	conclusions	conclusion	NOUN
ejpam-5136	384	4	and	and	CCONJ
ejpam-5136	384	5	recommendations	recommendation	NOUN
ejpam-5136	384	6	in	in	ADP
ejpam-5136	384	7	this	this	DET
ejpam-5136	384	8	communication	communication	NOUN
ejpam-5136	384	9	,	,	PUNCT
ejpam-5136	384	10	the	the	DET
ejpam-5136	384	11	bivariate	bivariate	ADJ
ejpam-5136	384	12	extension	extension	NOUN
ejpam-5136	384	13	of	of	ADP
ejpam-5136	384	14	the	the	DET
ejpam-5136	384	15	extended	extended	ADJ
ejpam-5136	384	16	standard	standard	ADJ
ejpam-5136	384	17	u	u	ADJ
ejpam-5136	384	18	-	-	ADJ
ejpam-5136	384	19	quadratic	quadratic	ADJ
ejpam-5136	384	20	distribution	distribution	NOUN
ejpam-5136	384	21	called	call	VERB
ejpam-5136	384	22	the	the	DET
ejpam-5136	384	23	bivariate	bivariate	ADJ
ejpam-5136	384	24	extended	extend	VERB
ejpam-5136	384	25	standard	standard	ADJ
ejpam-5136	384	26	u	u	NOUN
ejpam-5136	384	27	-	-	ADJ
ejpam-5136	384	28	quadratic	quadratic	ADJ
ejpam-5136	384	29	(	(	PUNCT
ejpam-5136	384	30	besu	besu	NOUN
ejpam-5136	384	31	)	)	PUNCT
ejpam-5136	384	32	distribution	distribution	NOUN
ejpam-5136	384	33	has	have	AUX
ejpam-5136	384	34	been	be	AUX
ejpam-5136	384	35	derived	derive	VERB
ejpam-5136	384	36	.	.	PUNCT
ejpam-5136	385	1	some	some	DET
ejpam-5136	385	2	properties	property	NOUN
ejpam-5136	385	3	of	of	ADP
ejpam-5136	385	4	the	the	DET
ejpam-5136	385	5	proposed	propose	VERB
ejpam-5136	385	6	besu	besu	NOUN
ejpam-5136	385	7	distribution	distribution	NOUN
ejpam-5136	385	8	such	such	ADJ
ejpam-5136	385	9	as	as	ADP
ejpam-5136	385	10	the	the	DET
ejpam-5136	385	11	marginal	marginal	ADJ
ejpam-5136	385	12	distribution	distribution	NOUN
ejpam-5136	385	13	,	,	PUNCT
ejpam-5136	385	14	conditional	conditional	ADJ
ejpam-5136	385	15	distribution	distribution	NOUN
ejpam-5136	385	16	,	,	PUNCT
ejpam-5136	385	17	conditional	conditional	ADJ
ejpam-5136	385	18	moments	moment	NOUN
ejpam-5136	385	19	,	,	PUNCT
ejpam-5136	385	20	the	the	DET
ejpam-5136	385	21	product	product	NOUN
ejpam-5136	385	22	and	and	CCONJ
ejpam-5136	385	23	ratio	ratio	NOUN
ejpam-5136	385	24	moments	moment	NOUN
ejpam-5136	385	25	,	,	PUNCT
ejpam-5136	385	26	pearson	pearson	PROPN
ejpam-5136	385	27	correlation	correlation	NOUN
ejpam-5136	385	28	coefficient	coefficient	NOUN
ejpam-5136	385	29	,	,	PUNCT
ejpam-5136	385	30	joint	joint	ADJ
ejpam-5136	385	31	moment	moment	NOUN
ejpam-5136	385	32	generating	generate	VERB
ejpam-5136	385	33	function	function	NOUN
ejpam-5136	385	34	and	and	CCONJ
ejpam-5136	385	35	stress	stress	NOUN
ejpam-5136	385	36	strength	strength	NOUN
ejpam-5136	385	37	parameter	parameter	NOUN
ejpam-5136	385	38	were	be	AUX
ejpam-5136	385	39	computed	compute	VERB
ejpam-5136	385	40	.	.	PUNCT
ejpam-5136	386	1	maximum	maximum	ADJ
ejpam-5136	386	2	likelihood	likelihood	NOUN
ejpam-5136	386	3	estimation	estimation	NOUN
ejpam-5136	386	4	was	be	AUX
ejpam-5136	386	5	implemented	implement	VERB
ejpam-5136	386	6	to	to	PART
ejpam-5136	386	7	estimate	estimate	VERB
ejpam-5136	386	8	the	the	DET
ejpam-5136	386	9	parameters	parameter	NOUN
ejpam-5136	386	10	of	of	ADP
ejpam-5136	386	11	the	the	DET
ejpam-5136	386	12	besu	besu	NOUN
ejpam-5136	386	13	distribution	distribution	NOUN
ejpam-5136	386	14	and	and	CCONJ
ejpam-5136	386	15	a	a	DET
ejpam-5136	386	16	simulation	simulation	NOUN
ejpam-5136	386	17	study	study	NOUN
ejpam-5136	386	18	was	be	AUX
ejpam-5136	386	19	carried	carry	VERB
ejpam-5136	386	20	out	out	ADP
ejpam-5136	386	21	to	to	PART
ejpam-5136	386	22	assess	assess	VERB
ejpam-5136	386	23	the	the	DET
ejpam-5136	386	24	behavior	behavior	NOUN
ejpam-5136	386	25	of	of	ADP
ejpam-5136	386	26	the	the	DET
ejpam-5136	386	27	estimates	estimate	NOUN
ejpam-5136	386	28	of	of	ADP
ejpam-5136	386	29	the	the	DET
ejpam-5136	386	30	parameters	parameter	NOUN
ejpam-5136	386	31	of	of	ADP
ejpam-5136	386	32	this	this	DET
ejpam-5136	386	33	derived	derive	VERB
ejpam-5136	386	34	distribution	distribution	NOUN
ejpam-5136	386	35	.	.	PUNCT
ejpam-5136	387	1	it	it	PRON
ejpam-5136	387	2	was	be	AUX
ejpam-5136	387	3	observed	observe	VERB
ejpam-5136	387	4	that	that	SCONJ
ejpam-5136	387	5	the	the	DET
ejpam-5136	387	6	maximum	maximum	ADJ
ejpam-5136	387	7	likelihood	likelihood	NOUN
ejpam-5136	387	8	estimate	estimate	NOUN
ejpam-5136	387	9	of	of	ADP
ejpam-5136	387	10	the	the	DET
ejpam-5136	387	11	parameter	parameter	NOUN
ejpam-5136	387	12	of	of	ADP
ejpam-5136	387	13	the	the	DET
ejpam-5136	387	14	besu	besu	NOUN
ejpam-5136	387	15	distribution	distribution	NOUN
ejpam-5136	387	16	is	be	AUX
ejpam-5136	387	17	consistent	consistent	ADJ
ejpam-5136	387	18	.	.	PUNCT
ejpam-5136	388	1	moreover	moreover	ADV
ejpam-5136	388	2	,	,	PUNCT
ejpam-5136	388	3	bivariate	bivariate	ADJ
ejpam-5136	388	4	version	version	NOUN
ejpam-5136	388	5	of	of	ADP
ejpam-5136	388	6	the	the	DET
ejpam-5136	388	7	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	388	8	(	(	PUNCT
ejpam-5136	388	9	bkm	bkm	PROPN
ejpam-5136	388	10	)	)	PUNCT
ejpam-5136	388	11	distribution	distribution	NOUN
ejpam-5136	388	12	has	have	AUX
ejpam-5136	388	13	been	be	AUX
ejpam-5136	388	14	derived	derive	VERB
ejpam-5136	388	15	.	.	PUNCT
ejpam-5136	389	1	the	the	DET
ejpam-5136	389	2	new	new	ADJ
ejpam-5136	389	3	bivariate	bivariate	ADJ
ejpam-5136	389	4	version	version	NOUN
ejpam-5136	389	5	of	of	ADP
ejpam-5136	389	6	the	the	DET
ejpam-5136	389	7	cubic	cubic	ADJ
ejpam-5136	389	8	transmuted	transmute	VERB
ejpam-5136	389	9	uniform	uniform	ADJ
ejpam-5136	389	10	distribution	distribution	NOUN
ejpam-5136	389	11	is	be	AUX
ejpam-5136	389	12	also	also	ADV
ejpam-5136	389	13	obtained	obtain	VERB
ejpam-5136	389	14	and	and	CCONJ
ejpam-5136	389	15	compared	compare	VERB
ejpam-5136	389	16	with	with	ADP
ejpam-5136	389	17	the	the	DET
ejpam-5136	389	18	proposed	propose	VERB
ejpam-5136	389	19	besu	besu	NOUN
ejpam-5136	389	20	distribution	distribution	NOUN
ejpam-5136	389	21	using	use	VERB
ejpam-5136	389	22	simulated	simulated	ADJ
ejpam-5136	389	23	data	datum	NOUN
ejpam-5136	389	24	.	.	PUNCT
ejpam-5136	390	1	it	it	PRON
ejpam-5136	390	2	reveals	reveal	VERB
ejpam-5136	390	3	that	that	SCONJ
ejpam-5136	390	4	the	the	DET
ejpam-5136	390	5	proposed	propose	VERB
ejpam-5136	390	6	besu	besu	NOUN
ejpam-5136	390	7	distribution	distribution	NOUN
ejpam-5136	390	8	provides	provide	VERB
ejpam-5136	390	9	a	a	DET
ejpam-5136	390	10	better	well	ADJ
ejpam-5136	390	11	fit	fit	NOUN
ejpam-5136	390	12	for	for	ADP
ejpam-5136	390	13	the	the	DET
ejpam-5136	390	14	dataset	dataset	NOUN
ejpam-5136	390	15	generated	generate	VERB
ejpam-5136	390	16	from	from	ADP
ejpam-5136	390	17	the	the	DET
ejpam-5136	390	18	bkm	bkm	PROPN
ejpam-5136	390	19	distribution	distribution	NOUN
ejpam-5136	390	20	as	as	SCONJ
ejpam-5136	390	21	compared	compare	VERB
ejpam-5136	390	22	with	with	ADP
ejpam-5136	390	23	the	the	DET
ejpam-5136	390	24	derived	derive	VERB
ejpam-5136	390	25	bivariate	bivariate	ADJ
ejpam-5136	390	26	cubic	cubic	ADJ
ejpam-5136	390	27	transmuted	transmute	VERB
ejpam-5136	390	28	uniform	uniform	ADJ
ejpam-5136	390	29	distribution	distribution	NOUN
ejpam-5136	390	30	.	.	PUNCT
ejpam-5136	391	1	for	for	ADP
ejpam-5136	391	2	future	future	ADJ
ejpam-5136	391	3	studies	study	NOUN
ejpam-5136	391	4	in	in	ADP
ejpam-5136	391	5	this	this	DET
ejpam-5136	391	6	field	field	NOUN
ejpam-5136	391	7	,	,	PUNCT
ejpam-5136	391	8	it	it	PRON
ejpam-5136	391	9	is	be	AUX
ejpam-5136	391	10	recommended	recommend	VERB
ejpam-5136	391	11	to	to	PART
ejpam-5136	391	12	use	use	VERB
ejpam-5136	391	13	another	another	DET
ejpam-5136	391	14	bivariate	bivariate	ADJ
ejpam-5136	391	15	family	family	NOUN
ejpam-5136	391	16	of	of	ADP
ejpam-5136	391	17	distributions	distribution	NOUN
ejpam-5136	391	18	like	like	ADP
ejpam-5136	391	19	the	the	DET
ejpam-5136	391	20	bivariate	bivariate	ADJ
ejpam-5136	391	21	marshall	marshall	NOUN
ejpam-5136	391	22	-	-	PUNCT
ejpam-5136	391	23	olkin	olkin	PROPN
ejpam-5136	391	24	family	family	NOUN
ejpam-5136	391	25	and	and	CCONJ
ejpam-5136	391	26	farlie	farlie	ADJ
ejpam-5136	391	27	gumbel	gumbel	PROPN
ejpam-5136	391	28	morgenstern	morgenstern	PROPN
ejpam-5136	391	29	(	(	PUNCT
ejpam-5136	391	30	fgm	fgm	PROPN
ejpam-5136	391	31	)	)	PUNCT
ejpam-5136	391	32	family	family	NOUN
ejpam-5136	391	33	for	for	ADP
ejpam-5136	391	34	generalizing	generalize	VERB
ejpam-5136	391	35	the	the	DET
ejpam-5136	391	36	extended	extended	ADJ
ejpam-5136	391	37	standard	standard	ADJ
ejpam-5136	391	38	u	u	ADJ
ejpam-5136	391	39	-	-	ADJ
ejpam-5136	391	40	quadratic	quadratic	ADJ
ejpam-5136	391	41	distribureferences	distribureference	NOUN
ejpam-5136	391	42	808	808	NUM
ejpam-5136	391	43	tion	tion	NOUN
ejpam-5136	391	44	into	into	ADP
ejpam-5136	391	45	another	another	DET
ejpam-5136	391	46	form	form	NOUN
ejpam-5136	391	47	of	of	ADP
ejpam-5136	391	48	the	the	DET
ejpam-5136	391	49	bivariate	bivariate	ADJ
ejpam-5136	391	50	extended	extend	VERB
ejpam-5136	391	51	standard	standard	ADJ
ejpam-5136	391	52	u	u	ADJ
ejpam-5136	391	53	-	-	ADJ
ejpam-5136	391	54	quadratic	quadratic	ADJ
ejpam-5136	391	55	distributions	distribution	NOUN
ejpam-5136	391	56	and	and	CCONJ
ejpam-5136	391	57	to	to	PART
ejpam-5136	391	58	compare	compare	VERB
ejpam-5136	391	59	it	it	PRON
ejpam-5136	391	60	with	with	ADP
ejpam-5136	391	61	the	the	DET
ejpam-5136	391	62	proposed	propose	VERB
ejpam-5136	391	63	besu	besu	NOUN
ejpam-5136	391	64	distribution	distribution	NOUN
ejpam-5136	391	65	presented	present	VERB
ejpam-5136	391	66	in	in	ADP
ejpam-5136	391	67	this	this	DET
ejpam-5136	391	68	paper	paper	NOUN
ejpam-5136	391	69	.	.	PUNCT
ejpam-5136	392	1	in	in	ADP
ejpam-5136	392	2	addition	addition	NOUN
ejpam-5136	392	3	,	,	PUNCT
ejpam-5136	392	4	it	it	PRON
ejpam-5136	392	5	is	be	AUX
ejpam-5136	392	6	also	also	ADV
ejpam-5136	392	7	suggested	suggest	VERB
ejpam-5136	392	8	to	to	PART
ejpam-5136	392	9	use	use	VERB
ejpam-5136	392	10	the	the	DET
ejpam-5136	392	11	besu	besu	NOUN
ejpam-5136	392	12	distribution	distribution	NOUN
ejpam-5136	392	13	to	to	PART
ejpam-5136	392	14	model	model	VERB
ejpam-5136	392	15	the	the	DET
ejpam-5136	392	16	failure	failure	NOUN
ejpam-5136	392	17	rates	rate	NOUN
ejpam-5136	392	18	of	of	ADP
ejpam-5136	392	19	two	two	NUM
ejpam-5136	392	20	related	related	ADJ
ejpam-5136	392	21	components	component	NOUN
ejpam-5136	392	22	in	in	ADP
ejpam-5136	392	23	a	a	DET
ejpam-5136	392	24	system	system	NOUN
ejpam-5136	392	25	or	or	CCONJ
ejpam-5136	392	26	to	to	PART
ejpam-5136	392	27	model	model	VERB
ejpam-5136	392	28	the	the	DET
ejpam-5136	392	29	lifetimes	lifetime	NOUN
ejpam-5136	392	30	of	of	ADP
ejpam-5136	392	31	two	two	NUM
ejpam-5136	392	32	related	relate	VERB
ejpam-5136	392	33	electronic	electronic	ADJ
ejpam-5136	392	34	devices	device	NOUN
ejpam-5136	392	35	where	where	SCONJ
ejpam-5136	392	36	the	the	DET
ejpam-5136	392	37	failure	failure	NOUN
ejpam-5136	392	38	rates	rate	NOUN
ejpam-5136	392	39	or	or	CCONJ
ejpam-5136	392	40	lifetimes	lifetime	NOUN
ejpam-5136	392	41	follow	follow	VERB
ejpam-5136	392	42	the	the	DET
ejpam-5136	392	43	bathtub	bathtub	NOUN
ejpam-5136	392	44	shapes	shape	NOUN
ejpam-5136	392	45	on	on	ADP
ejpam-5136	392	46	the	the	DET
ejpam-5136	392	47	interval	interval	NOUN
ejpam-5136	392	48	[	[	X
ejpam-5136	392	49	0	0	NUM
ejpam-5136	392	50	,	,	PUNCT
ejpam-5136	392	51	1	1	NUM
ejpam-5136	392	52	]	]	PUNCT
ejpam-5136	392	53	.	.	PUNCT
ejpam-5136	393	1	acknowledgements	acknowledgement	NOUN
ejpam-5136	393	2	the	the	DET
ejpam-5136	393	3	authors	author	NOUN
ejpam-5136	393	4	are	be	AUX
ejpam-5136	393	5	grateful	grateful	ADJ
ejpam-5136	393	6	to	to	ADP
ejpam-5136	393	7	the	the	DET
ejpam-5136	393	8	anonymous	anonymous	ADJ
ejpam-5136	393	9	referees	referee	NOUN
ejpam-5136	393	10	for	for	ADP
ejpam-5136	393	11	their	their	PRON
ejpam-5136	393	12	valuable	valuable	ADJ
ejpam-5136	393	13	comments	comment	NOUN
ejpam-5136	393	14	and	and	CCONJ
ejpam-5136	393	15	suggestions	suggestion	NOUN
ejpam-5136	393	16	.	.	PUNCT
ejpam-5136	394	1	moreover	moreover	ADV
ejpam-5136	394	2	,	,	PUNCT
ejpam-5136	394	3	idzhar	idzhar	PROPN
ejpam-5136	394	4	a.	a.	NOUN
ejpam-5136	394	5	lakibul	lakibul	PROPN
ejpam-5136	394	6	is	be	AUX
ejpam-5136	394	7	also	also	ADV
ejpam-5136	394	8	grateful	grateful	ADJ
ejpam-5136	394	9	to	to	ADP
ejpam-5136	394	10	the	the	DET
ejpam-5136	394	11	department	department	NOUN
ejpam-5136	394	12	of	of	ADP
ejpam-5136	394	13	science	science	NOUN
ejpam-5136	394	14	and	and	CCONJ
ejpam-5136	394	15	technology	technology	NOUN
ejpam-5136	394	16	accelerated	accelerate	VERB
ejpam-5136	394	17	science	science	NOUN
ejpam-5136	394	18	and	and	CCONJ
ejpam-5136	394	19	technology	technology	NOUN
ejpam-5136	394	20	human	human	ADJ
ejpam-5136	394	21	resource	resource	NOUN
ejpam-5136	394	22	development	development	NOUN
ejpam-5136	394	23	program	program	NOUN
ejpam-5136	394	24	(	(	PUNCT
ejpam-5136	394	25	dost	dost	NOUN
ejpam-5136	394	26	-	-	PUNCT
ejpam-5136	394	27	asthrdp	asthrdp	NOUN
ejpam-5136	394	28	)	)	PUNCT
ejpam-5136	394	29	for	for	ADP
ejpam-5136	394	30	giving	give	VERB
ejpam-5136	394	31	him	he	PRON
ejpam-5136	394	32	financial	financial	ADJ
ejpam-5136	394	33	support	support	NOUN
ejpam-5136	394	34	to	to	PART
ejpam-5136	394	35	study	study	VERB
ejpam-5136	394	36	at	at	ADP
ejpam-5136	394	37	mindanao	mindanao	PROPN
ejpam-5136	394	38	state	state	PROPN
ejpam-5136	394	39	university	university	PROPN
ejpam-5136	394	40	iligan	iligan	PROPN
ejpam-5136	394	41	institute	institute	PROPN
ejpam-5136	394	42	of	of	ADP
ejpam-5136	394	43	technology	technology	PROPN
ejpam-5136	394	44	(	(	PUNCT
ejpam-5136	394	45	msu	msu	PROPN
ejpam-5136	394	46	-	-	PUNCT
ejpam-5136	394	47	iit	iit	NOUN
ejpam-5136	394	48	)	)	PUNCT
ejpam-5136	394	49	.	.	PUNCT
ejpam-5136	395	1	in	in	ADP
ejpam-5136	395	2	addition	addition	NOUN
ejpam-5136	395	3	,	,	PUNCT
ejpam-5136	395	4	this	this	DET
ejpam-5136	395	5	paper	paper	NOUN
ejpam-5136	395	6	is	be	AUX
ejpam-5136	395	7	also	also	ADV
ejpam-5136	395	8	supported	support	VERB
ejpam-5136	395	9	by	by	ADP
ejpam-5136	395	10	the	the	DET
ejpam-5136	395	11	dost	dost	NOUN
ejpam-5136	395	12	-	-	PUNCT
ejpam-5136	395	13	asthrdp	asthrdp	NOUN
ejpam-5136	395	14	and	and	CCONJ
ejpam-5136	395	15	the	the	DET
ejpam-5136	395	16	msu	msu	PROPN
ejpam-5136	395	17	-	-	PUNCT
ejpam-5136	395	18	iligan	iligan	PROPN
ejpam-5136	395	19	institute	institute	PROPN
ejpam-5136	395	20	of	of	ADP
ejpam-5136	395	21	technology	technology	PROPN
ejpam-5136	395	22	.	.	PUNCT
ejpam-5136	396	1	references	reference	NOUN
ejpam-5136	396	2	[	[	X
ejpam-5136	396	3	1	1	X
ejpam-5136	396	4	]	]	PUNCT
ejpam-5136	396	5	j.	j.	PROPN
ejpam-5136	396	6	k.	k.	PROPN
ejpam-5136	396	7	filus	filus	PROPN
ejpam-5136	396	8	and	and	CCONJ
ejpam-5136	396	9	l.	l.	PROPN
ejpam-5136	396	10	z.	z.	PROPN
ejpam-5136	396	11	filus	filus	PROPN
ejpam-5136	396	12	.	.	PUNCT
ejpam-5136	397	1	on	on	ADP
ejpam-5136	397	2	some	some	DET
ejpam-5136	397	3	new	new	ADJ
ejpam-5136	397	4	classes	class	NOUN
ejpam-5136	397	5	of	of	ADP
ejpam-5136	397	6	multivariate	multivariate	NOUN
ejpam-5136	397	7	probability	probability	NOUN
ejpam-5136	397	8	distributions	distribution	NOUN
ejpam-5136	397	9	.	.	PUNCT
ejpam-5136	398	1	pakistan	pakistan	PROPN
ejpam-5136	398	2	journal	journal	PROPN
ejpam-5136	398	3	of	of	ADP
ejpam-5136	398	4	statistics	statistic	NOUN
ejpam-5136	398	5	,	,	PUNCT
ejpam-5136	398	6	22:21–42	22:21–42	NUM
ejpam-5136	398	7	,	,	PUNCT
ejpam-5136	398	8	2006	2006	NUM
ejpam-5136	398	9	.	.	PUNCT
ejpam-5136	399	1	[	[	X
ejpam-5136	399	2	2	2	NUM
ejpam-5136	399	3	]	]	PUNCT
ejpam-5136	399	4	p.	p.	NOUN
ejpam-5136	399	5	kumaraswamy	kumaraswamy	NOUN
ejpam-5136	399	6	.	.	PUNCT
ejpam-5136	400	1	a	a	DET
ejpam-5136	400	2	generalized	generalize	VERB
ejpam-5136	400	3	probability	probability	NOUN
ejpam-5136	400	4	density	density	NOUN
ejpam-5136	400	5	function	function	NOUN
ejpam-5136	400	6	for	for	ADP
ejpam-5136	400	7	double	double	ADJ
ejpam-5136	400	8	-	-	PUNCT
ejpam-5136	400	9	bounded	bound	VERB
ejpam-5136	400	10	random	random	ADJ
ejpam-5136	400	11	processes	process	NOUN
ejpam-5136	400	12	.	.	PUNCT
ejpam-5136	401	1	journal	journal	NOUN
ejpam-5136	401	2	of	of	ADP
ejpam-5136	401	3	hydrology	hydrology	NOUN
ejpam-5136	401	4	,	,	PUNCT
ejpam-5136	401	5	46:79–88	46:79–88	NUM
ejpam-5136	401	6	,	,	PUNCT
ejpam-5136	401	7	1980	1980	NUM
ejpam-5136	401	8	.	.	PUNCT
ejpam-5136	402	1	[	[	X
ejpam-5136	402	2	3	3	X
ejpam-5136	402	3	]	]	X
ejpam-5136	402	4	i.	i.	PROPN
ejpam-5136	402	5	a.	a.	PROPN
ejpam-5136	402	6	lakibul	lakibul	PROPN
ejpam-5136	402	7	and	and	CCONJ
ejpam-5136	402	8	b.	b.	PROPN
ejpam-5136	402	9	f.	f.	PROPN
ejpam-5136	402	10	tubo	tubo	PROPN
ejpam-5136	402	11	.	.	PROPN
ejpam-5136	403	1	on	on	ADP
ejpam-5136	403	2	the	the	DET
ejpam-5136	403	3	four	four	NUM
ejpam-5136	403	4	-	-	PUNCT
ejpam-5136	403	5	parameter	parameter	NOUN
ejpam-5136	403	6	t	t	PROPN
ejpam-5136	403	7	-	-	PUNCT
ejpam-5136	403	8	extended	extend	VERB
ejpam-5136	403	9	standard	standard	ADJ
ejpam-5136	403	10	uquadratic	uquadratic	ADJ
ejpam-5136	403	11	exponentiated	exponentiate	VERB
ejpam-5136	403	12	weibull	weibull	NOUN
ejpam-5136	403	13	distribution	distribution	NOUN
ejpam-5136	403	14	.	.	PUNCT
ejpam-5136	404	1	the	the	DET
ejpam-5136	404	2	mindanawan	mindanawan	PROPN
ejpam-5136	404	3	journal	journal	PROPN
ejpam-5136	404	4	of	of	ADP
ejpam-5136	404	5	mathematics	mathematic	NOUN
ejpam-5136	404	6	,	,	PUNCT
ejpam-5136	404	7	5:17–33	5:17–33	NOUN
ejpam-5136	404	8	,	,	PUNCT
ejpam-5136	404	9	2023	2023	NUM
ejpam-5136	404	10	.	.	PUNCT
ejpam-5136	405	1	[	[	X
ejpam-5136	405	2	4	4	X
ejpam-5136	405	3	]	]	PUNCT
ejpam-5136	405	4	i.	i.	PROPN
ejpam-5136	405	5	a.	a.	PROPN
ejpam-5136	405	6	lakibul	lakibul	PROPN
ejpam-5136	405	7	and	and	CCONJ
ejpam-5136	405	8	b.	b.	PROPN
ejpam-5136	405	9	f.	f.	PROPN
ejpam-5136	405	10	tubo	tubo	PROPN
ejpam-5136	405	11	.	.	PROPN
ejpam-5136	406	1	on	on	ADP
ejpam-5136	406	2	the	the	DET
ejpam-5136	406	3	tesu	tesu	PROPN
ejpam-5136	406	4	-	-	PUNCT
ejpam-5136	406	5	g	g	NOUN
ejpam-5136	406	6	family	family	NOUN
ejpam-5136	406	7	of	of	ADP
ejpam-5136	406	8	distributions	distribution	NOUN
ejpam-5136	406	9	applied	apply	VERB
ejpam-5136	406	10	to	to	ADP
ejpam-5136	406	11	life	life	NOUN
ejpam-5136	406	12	data	datum	NOUN
ejpam-5136	406	13	analysis	analysis	NOUN
ejpam-5136	406	14	.	.	PUNCT
ejpam-5136	407	1	reliability	reliability	NOUN
ejpam-5136	407	2	:	:	PUNCT
ejpam-5136	407	3	theory	theory	NOUN
ejpam-5136	407	4	and	and	CCONJ
ejpam-5136	407	5	applications	application	NOUN
ejpam-5136	407	6	,	,	PUNCT
ejpam-5136	407	7	18:24–38	18:24–38	NUM
ejpam-5136	407	8	,	,	PUNCT
ejpam-5136	407	9	2023	2023	NUM
ejpam-5136	407	10	.	.	PUNCT
ejpam-5136	408	1	[	[	X
ejpam-5136	408	2	5	5	NUM
ejpam-5136	408	3	]	]	PUNCT
ejpam-5136	408	4	m.	m.	NOUN
ejpam-5136	408	5	mohsin	mohsin	PROPN
ejpam-5136	408	6	,	,	PUNCT
ejpam-5136	408	7	m.	m.	NOUN
ejpam-5136	408	8	ahmad	ahmad	PROPN
ejpam-5136	408	9	,	,	PUNCT
ejpam-5136	408	10	s.	s.	PROPN
ejpam-5136	408	11	shahbaz	shahbaz	PROPN
ejpam-5136	408	12	,	,	PUNCT
ejpam-5136	408	13	and	and	CCONJ
ejpam-5136	408	14	m.	m.	PROPN
ejpam-5136	408	15	q.	q.	PROPN
ejpam-5136	408	16	shahbaz	shahbaz	PROPN
ejpam-5136	408	17	.	.	PUNCT
ejpam-5136	409	1	concomitants	concomitant	NOUN
ejpam-5136	409	2	of	of	ADP
ejpam-5136	409	3	lower	low	ADJ
ejpam-5136	409	4	records	record	NOUN
ejpam-5136	409	5	for	for	ADP
ejpam-5136	409	6	bivariate	bivariate	ADJ
ejpam-5136	409	7	pseudo	pseudo	NOUN
ejpam-5136	409	8	–	–	PUNCT
ejpam-5136	409	9	inverse	inverse	ADJ
ejpam-5136	409	10	rayleigh	rayleigh	NOUN
ejpam-5136	409	11	distribution	distribution	NOUN
ejpam-5136	409	12	.	.	PUNCT
ejpam-5136	410	1	sci	sci	PROPN
ejpam-5136	410	2	.	.	PUNCT
ejpam-5136	410	3	int	int	PROPN
ejpam-5136	410	4	.	.	PUNCT
ejpam-5136	411	1	(	(	PUNCT
ejpam-5136	411	2	lahore	lahore	NOUN
ejpam-5136	411	3	)	)	PUNCT
ejpam-5136	411	4	,	,	PUNCT
ejpam-5136	411	5	21:21–23	21:21–23	PROPN
ejpam-5136	411	6	,	,	PUNCT
ejpam-5136	411	7	2009	2009	NUM
ejpam-5136	411	8	.	.	PUNCT
ejpam-5136	412	1	[	[	X
ejpam-5136	412	2	6	6	NUM
ejpam-5136	412	3	]	]	PUNCT
ejpam-5136	412	4	m.	m.	NOUN
ejpam-5136	412	5	m.	m.	PROPN
ejpam-5136	412	6	rahman	rahman	PROPN
ejpam-5136	412	7	,	,	PUNCT
ejpam-5136	412	8	b.	b.	PROPN
ejpam-5136	412	9	al	al	PROPN
ejpam-5136	412	10	-	-	PUNCT
ejpam-5136	412	11	zahrani	zahrani	PROPN
ejpam-5136	412	12	,	,	PUNCT
ejpam-5136	412	13	s.	s.	PROPN
ejpam-5136	412	14	h.	h.	PROPN
ejpam-5136	412	15	shahbaz	shahbaz	PROPN
ejpam-5136	412	16	,	,	PUNCT
ejpam-5136	412	17	and	and	CCONJ
ejpam-5136	412	18	m.	m.	PROPN
ejpam-5136	412	19	q.	q.	PROPN
ejpam-5136	412	20	shahbaz	shahbaz	PROPN
ejpam-5136	412	21	.	.	PUNCT
ejpam-5136	412	22	cubic	cubic	ADJ
ejpam-5136	412	23	transmuted	transmute	VERB
ejpam-5136	412	24	uniform	uniform	ADJ
ejpam-5136	412	25	distribution	distribution	NOUN
ejpam-5136	412	26	:	:	PUNCT
ejpam-5136	412	27	an	an	DET
ejpam-5136	412	28	alternative	alternative	NOUN
ejpam-5136	412	29	to	to	ADP
ejpam-5136	412	30	beta	beta	ADJ
ejpam-5136	412	31	and	and	CCONJ
ejpam-5136	412	32	kumaraswamy	kumaraswamy	ADJ
ejpam-5136	412	33	distributions	distribution	NOUN
ejpam-5136	412	34	.	.	PUNCT
ejpam-5136	413	1	european	european	ADJ
ejpam-5136	413	2	journal	journal	PROPN
ejpam-5136	413	3	of	of	ADP
ejpam-5136	413	4	pure	pure	ADJ
ejpam-5136	413	5	and	and	CCONJ
ejpam-5136	413	6	applied	applied	ADJ
ejpam-5136	413	7	mathematics	mathematic	NOUN
ejpam-5136	413	8	,	,	PUNCT
ejpam-5136	413	9	12:1106–1121	12:1106–1121	NUM
ejpam-5136	413	10	,	,	PUNCT
ejpam-5136	413	11	2019	2019	NUM
ejpam-5136	413	12	.	.	PUNCT
ejpam-5136	414	1	[	[	X
ejpam-5136	414	2	7	7	X
ejpam-5136	414	3	]	]	PUNCT
ejpam-5136	414	4	m.	m.	PROPN
ejpam-5136	414	5	q.	q.	PROPN
ejpam-5136	414	6	shahbaz	shahbaz	PROPN
ejpam-5136	414	7	and	and	CCONJ
ejpam-5136	414	8	s.	s.	PROPN
ejpam-5136	414	9	shahbaz	shahbaz	PROPN
ejpam-5136	414	10	.	.	PUNCT
ejpam-5136	415	1	order	order	NOUN
ejpam-5136	415	2	statistics	statistic	NOUN
ejpam-5136	415	3	and	and	CCONJ
ejpam-5136	415	4	concomitants	concomitant	NOUN
ejpam-5136	415	5	of	of	ADP
ejpam-5136	415	6	bivariate	bivariate	ADJ
ejpam-5136	415	7	pseudorayleigh	pseudorayleigh	ADJ
ejpam-5136	415	8	distribution	distribution	NOUN
ejpam-5136	415	9	.	.	PUNCT
ejpam-5136	416	1	world	world	NOUN
ejpam-5136	416	2	applied	apply	VERB
ejpam-5136	416	3	sciences	science	NOUN
ejpam-5136	416	4	journal	journal	NOUN
ejpam-5136	416	5	,	,	PUNCT
ejpam-5136	416	6	7:826–828	7:826–828	NOUN
ejpam-5136	416	7	,	,	PUNCT
ejpam-5136	416	8	2009	2009	NUM
ejpam-5136	416	9	.	.	PUNCT
ejpam-5136	417	1	[	[	X
ejpam-5136	417	2	8	8	NUM
ejpam-5136	417	3	]	]	PUNCT
ejpam-5136	417	4	m.	m.	PROPN
ejpam-5136	417	5	q.	q.	PROPN
ejpam-5136	417	6	shahbaz	shahbaz	PROPN
ejpam-5136	417	7	,	,	PUNCT
ejpam-5136	417	8	s.	s.	PROPN
ejpam-5136	417	9	shahbaz	shahbaz	PROPN
ejpam-5136	417	10	,	,	PUNCT
ejpam-5136	417	11	and	and	CCONJ
ejpam-5136	417	12	a.	a.	PROPN
ejpam-5136	417	13	rafiq	rafiq	PROPN
ejpam-5136	417	14	.	.	PUNCT
ejpam-5136	418	1	a	a	DET
ejpam-5136	418	2	new	new	ADJ
ejpam-5136	418	3	bivariate	bivariate	ADJ
ejpam-5136	418	4	gumbel	gumbel	NOUN
ejpam-5136	418	5	distribution	distribution	NOUN
ejpam-5136	418	6	.	.	PUNCT
ejpam-5136	419	1	nonlinear	nonlinear	ADJ
ejpam-5136	419	2	analysis	analysis	NOUN
ejpam-5136	419	3	forum	forum	PROPN
ejpam-5136	419	4	,	,	PUNCT
ejpam-5136	419	5	16:133–136	16:133–136	PROPN
ejpam-5136	419	6	,	,	PUNCT
ejpam-5136	419	7	2011	2011	NUM
ejpam-5136	419	8	.	.	PUNCT
ejpam-5136	420	1	[	[	X
ejpam-5136	420	2	9	9	NUM
ejpam-5136	420	3	]	]	PUNCT
ejpam-5136	420	4	s.	s.	PROPN
ejpam-5136	420	5	shahbaz	shahbaz	PROPN
ejpam-5136	420	6	and	and	CCONJ
ejpam-5136	420	7	m.	m.	PROPN
ejpam-5136	420	8	ahmad	ahmad	PROPN
ejpam-5136	420	9	.	.	PUNCT
ejpam-5136	421	1	concomitants	concomitant	NOUN
ejpam-5136	421	2	of	of	ADP
ejpam-5136	421	3	order	order	NOUN
ejpam-5136	421	4	statistics	statistic	NOUN
ejpam-5136	421	5	for	for	ADP
ejpam-5136	421	6	bivariate	bivariate	ADJ
ejpam-5136	421	7	pseudoweibull	pseudoweibull	ADJ
ejpam-5136	421	8	distribution	distribution	NOUN
ejpam-5136	421	9	.	.	PUNCT
ejpam-5136	422	1	world	world	NOUN
ejpam-5136	422	2	applied	apply	VERB
ejpam-5136	422	3	sciences	science	NOUN
ejpam-5136	422	4	journal	journal	NOUN
ejpam-5136	422	5	,	,	PUNCT
ejpam-5136	422	6	6:1409–1412	6:1409–1412	NUM
ejpam-5136	422	7	,	,	PUNCT
ejpam-5136	422	8	2009	2009	NUM
ejpam-5136	422	9	.	.	PUNCT
ejpam-5136	423	1	references	reference	NOUN
ejpam-5136	423	2	809	809	NUM
ejpam-5136	424	1	[	[	X
ejpam-5136	424	2	10	10	NUM
ejpam-5136	424	3	]	]	X
ejpam-5136	424	4	s.	s.	PROPN
ejpam-5136	424	5	shahbaz	shahbaz	PROPN
ejpam-5136	424	6	,	,	PUNCT
ejpam-5136	424	7	m.	m.	PROPN
ejpam-5136	424	8	q.	q.	PROPN
ejpam-5136	424	9	shahbaz	shahbaz	PROPN
ejpam-5136	424	10	,	,	PUNCT
ejpam-5136	424	11	and	and	CCONJ
ejpam-5136	424	12	m.	m.	PROPN
ejpam-5136	424	13	mohsin	mohsin	PROPN
ejpam-5136	424	14	.	.	PUNCT
ejpam-5136	425	1	on	on	ADP
ejpam-5136	425	2	concomitants	concomitant	NOUN
ejpam-5136	425	3	of	of	ADP
ejpam-5136	425	4	order	order	NOUN
ejpam-5136	425	5	statistics	statistic	NOUN
ejpam-5136	425	6	for	for	ADP
ejpam-5136	425	7	bivariate	bivariate	ADJ
ejpam-5136	425	8	pseudo	pseudo	NOUN
ejpam-5136	425	9	exponential	exponential	ADJ
ejpam-5136	425	10	distribution	distribution	NOUN
ejpam-5136	425	11	.	.	PUNCT
ejpam-5136	426	1	world	world	NOUN
ejpam-5136	426	2	applied	apply	VERB
ejpam-5136	426	3	sciences	science	NOUN
ejpam-5136	426	4	journal	journal	NOUN
ejpam-5136	426	5	,	,	PUNCT
ejpam-5136	426	6	6:1151	6:1151	NUM
ejpam-5136	426	7	–	–	PUNCT
ejpam-5136	426	8	1156	1156	NUM
ejpam-5136	426	9	,	,	PUNCT
ejpam-5136	426	10	2009	2009	NUM
ejpam-5136	426	11	.	.	PUNCT
ejpam-5136	427	1	[	[	X
ejpam-5136	427	2	11	11	NUM
ejpam-5136	427	3	]	]	PUNCT
ejpam-5136	427	4	s.	s.	PROPN
ejpam-5136	427	5	h.	h.	PROPN
ejpam-5136	427	6	shahbaz	shahbaz	PROPN
ejpam-5136	427	7	and	and	CCONJ
ejpam-5136	427	8	m.	m.	PROPN
ejpam-5136	427	9	q.	q.	PROPN
ejpam-5136	427	10	shahbaz	shahbaz	PROPN
ejpam-5136	427	11	.	.	PUNCT
ejpam-5136	428	1	on	on	ADP
ejpam-5136	428	2	concomitants	concomitant	NOUN
ejpam-5136	428	3	of	of	ADP
ejpam-5136	428	4	dual	dual	ADJ
ejpam-5136	428	5	generalized	generalize	VERB
ejpam-5136	428	6	order	order	NOUN
ejpam-5136	428	7	statistics	statistic	NOUN
ejpam-5136	428	8	for	for	ADP
ejpam-5136	428	9	a	a	DET
ejpam-5136	428	10	bivariate	bivariate	ADJ
ejpam-5136	428	11	inverse	inverse	ADJ
ejpam-5136	428	12	exponential	exponential	ADJ
ejpam-5136	428	13	distribution	distribution	NOUN
ejpam-5136	428	14	.	.	PUNCT
ejpam-5136	429	1	european	european	ADJ
ejpam-5136	429	2	journal	journal	PROPN
ejpam-5136	429	3	of	of	ADP
ejpam-5136	429	4	pure	pure	ADJ
ejpam-5136	429	5	and	and	CCONJ
ejpam-5136	429	6	applied	applied	ADJ
ejpam-5136	429	7	mathematics	mathematic	NOUN
ejpam-5136	429	8	,	,	PUNCT
ejpam-5136	429	9	11:929–936	11:929–936	NUM
ejpam-5136	429	10	,	,	PUNCT
ejpam-5136	429	11	2018	2018	NUM
ejpam-5136	429	12	.	.	PUNCT