id	sid	tid	token	lemma	pos
iajs-3044	1	1	ihjpas	ihjpas	PROPN
iajs-3044	1	2	.	.	PUNCT
iajs-3044	2	1	36(2)2023	36(2)2023	NUM
iajs-3044	2	2	390	390	NUM
iajs-3044	2	3	this	this	DET
iajs-3044	2	4	work	work	NOUN
iajs-3044	2	5	is	be	AUX
iajs-3044	2	6	licensed	license	VERB
iajs-3044	2	7	under	under	ADP
iajs-3044	2	8	a	a	DET
iajs-3044	2	9	creative	creative	ADJ
iajs-3044	2	10	commons	common	NOUN
iajs-3044	2	11	attribution	attribution	NOUN
iajs-3044	2	12	4.0	4.0	NUM
iajs-3044	2	13	international	international	ADJ
iajs-3044	2	14	license	license	NOUN
iajs-3044	2	15	.	.	PUNCT
iajs-3044	3	1	abstract	abstract	ADJ
iajs-3044	3	2	this	this	DET
iajs-3044	3	3	paper	paper	NOUN
iajs-3044	3	4	deals	deal	NOUN
iajs-3044	3	5	with	with	ADP
iajs-3044	3	6	the	the	DET
iajs-3044	3	7	mathematical	mathematical	ADJ
iajs-3044	3	8	method	method	NOUN
iajs-3044	3	9	for	for	ADP
iajs-3044	3	10	extracting	extract	VERB
iajs-3044	3	11	the	the	DET
iajs-3044	3	12	exponential	exponential	ADJ
iajs-3044	3	13	rayleighh	rayleighh	NOUN
iajs-3044	3	14	(	(	PUNCT
iajs-3044	3	15	er	er	INTJ
iajs-3044	3	16	)	)	PUNCT
iajs-3044	3	17	distribution	distribution	NOUN
iajs-3044	3	18	based	base	VERB
iajs-3044	3	19	on	on	ADP
iajs-3044	3	20	mixed	mix	VERB
iajs-3044	3	21	between	between	ADP
iajs-3044	3	22	the	the	DET
iajs-3044	3	23	cumulative	cumulative	ADJ
iajs-3044	3	24	distribution	distribution	NOUN
iajs-3044	3	25	function	function	NOUN
iajs-3044	3	26	of	of	ADP
iajs-3044	3	27	exponential	exponential	ADJ
iajs-3044	3	28	distribution	distribution	NOUN
iajs-3044	3	29	and	and	CCONJ
iajs-3044	3	30	the	the	DET
iajs-3044	3	31	cumulative	cumulative	ADJ
iajs-3044	3	32	distribution	distribution	NOUN
iajs-3044	3	33	function	function	NOUN
iajs-3044	3	34	of	of	ADP
iajs-3044	3	35	rayleigh	rayleigh	ADJ
iajs-3044	3	36	distribution	distribution	NOUN
iajs-3044	3	37	using	use	VERB
iajs-3044	3	38	an	an	DET
iajs-3044	3	39	application	application	NOUN
iajs-3044	3	40	(	(	PUNCT
iajs-3044	3	41	maximum	maximum	ADJ
iajs-3044	3	42	)	)	PUNCT
iajs-3044	3	43	,	,	PUNCT
iajs-3044	3	44	as	as	ADV
iajs-3044	3	45	well	well	ADV
iajs-3044	3	46	as	as	ADP
iajs-3044	3	47	derived	derive	VERB
iajs-3044	3	48	different	different	ADJ
iajs-3044	3	49	statistical	statistical	ADJ
iajs-3044	3	50	properties	property	NOUN
iajs-3044	3	51	for	for	ADP
iajs-3044	3	52	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	3	53	distribution	distribution	NOUN
iajs-3044	3	54	(	(	PUNCT
iajs-3044	3	55	mode	mode	NOUN
iajs-3044	3	56	,	,	PUNCT
iajs-3044	3	57	the	the	DET
iajs-3044	3	58	median	median	NOUN
iajs-3044	3	59	,	,	PUNCT
iajs-3044	3	60	𝑟𝑡ℎ	𝑟𝑡ℎ	NOUN
iajs-3044	3	61	moment	moment	NOUN
iajs-3044	3	62	,	,	PUNCT
iajs-3044	3	63	the	the	DET
iajs-3044	3	64	variance	variance	NOUN
iajs-3044	3	65	,	,	PUNCT
iajs-3044	3	66	coefficient	coefficient	NOUN
iajs-3044	3	67	of	of	ADP
iajs-3044	3	68	skewness	skewness	NOUN
iajs-3044	3	69	,	,	PUNCT
iajs-3044	3	70	coefficient	coefficient	NOUN
iajs-3044	3	71	of	of	ADP
iajs-3044	3	72	kurtosis	kurtosis	NOUN
iajs-3044	3	73	,	,	PUNCT
iajs-3044	3	74	moment	moment	NOUN
iajs-3044	3	75	generating	generate	VERB
iajs-3044	3	76	function	function	NOUN
iajs-3044	3	77	,	,	PUNCT
iajs-3044	3	78	factorial	factorial	ADJ
iajs-3044	3	79	moment	moment	NOUN
iajs-3044	3	80	generating	generate	VERB
iajs-3044	3	81	function	function	NOUN
iajs-3044	3	82	,	,	PUNCT
iajs-3044	3	83	quantile	quantile	ADJ
iajs-3044	3	84	function	function	NOUN
iajs-3044	3	85	,	,	PUNCT
iajs-3044	3	86	characteristic	characteristic	ADJ
iajs-3044	3	87	function	function	NOUN
iajs-3044	3	88	)	)	PUNCT
iajs-3044	3	89	.	.	PUNCT
iajs-3044	4	1	then	then	ADV
iajs-3044	4	2	,	,	PUNCT
iajs-3044	4	3	we	we	PRON
iajs-3044	4	4	present	present	VERB
iajs-3044	4	5	a	a	DET
iajs-3044	4	6	structure	structure	NOUN
iajs-3044	4	7	of	of	ADP
iajs-3044	4	8	a	a	DET
iajs-3044	4	9	new	new	ADJ
iajs-3044	4	10	distribution	distribution	NOUN
iajs-3044	4	11	based	base	VERB
iajs-3044	4	12	on	on	ADP
iajs-3044	4	13	a	a	DET
iajs-3044	4	14	modified	modify	VERB
iajs-3044	4	15	weighted	weight	VERB
iajs-3044	4	16	version	version	NOUN
iajs-3044	4	17	of	of	ADP
iajs-3044	4	18	azzalini	azzalini	PROPN
iajs-3044	4	19	’s	’s	PART
iajs-3044	4	20	named	name	VERB
iajs-3044	4	21	modified	modify	VERB
iajs-3044	4	22	weighted	weight	VERB
iajs-3044	4	23	exponential	exponential	ADJ
iajs-3044	4	24	rayleigh	rayleigh	PROPN
iajs-3044	4	25	(	(	PUNCT
iajs-3044	4	26	mwer	mwer	NOUN
iajs-3044	4	27	)	)	PUNCT
iajs-3044	4	28	distribution	distribution	NOUN
iajs-3044	4	29	such	such	ADJ
iajs-3044	4	30	that	that	SCONJ
iajs-3044	4	31	this	this	DET
iajs-3044	4	32	new	new	ADJ
iajs-3044	4	33	distribution	distribution	NOUN
iajs-3044	4	34	is	be	AUX
iajs-3044	4	35	generalization	generalization	NOUN
iajs-3044	4	36	of	of	ADP
iajs-3044	4	37	the	the	DET
iajs-3044	4	38	er	er	INTJ
iajs-3044	4	39	distribution	distribution	NOUN
iajs-3044	4	40	and	and	CCONJ
iajs-3044	4	41	provide	provide	VERB
iajs-3044	4	42	some	some	DET
iajs-3044	4	43	special	special	ADJ
iajs-3044	4	44	models	model	NOUN
iajs-3044	4	45	of	of	ADP
iajs-3044	4	46	the	the	DET
iajs-3044	4	47	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	4	48	distribution	distribution	NOUN
iajs-3044	4	49	,	,	PUNCT
iajs-3044	4	50	as	as	ADV
iajs-3044	4	51	well	well	ADV
iajs-3044	4	52	as	as	ADP
iajs-3044	4	53	derived	derive	VERB
iajs-3044	4	54	different	different	ADJ
iajs-3044	4	55	statistical	statistical	ADJ
iajs-3044	4	56	properties	property	NOUN
iajs-3044	4	57	for	for	ADP
iajs-3044	4	58	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	4	59	distribution	distribution	NOUN
iajs-3044	4	60	.	.	PUNCT
iajs-3044	5	1	keywords	keyword	NOUN
iajs-3044	5	2	:	:	PUNCT
iajs-3044	5	3	exponential	exponential	ADJ
iajs-3044	5	4	rayleigh	rayleigh	NOUN
iajs-3044	5	5	(	(	PUNCT
iajs-3044	5	6	er	er	INTJ
iajs-3044	5	7	)	)	PUNCT
iajs-3044	5	8	distribution	distribution	NOUN
iajs-3044	5	9	,	,	PUNCT
iajs-3044	5	10	modified	modify	VERB
iajs-3044	5	11	weighted	weight	VERB
iajs-3044	5	12	exponential	exponential	ADJ
iajs-3044	5	13	rayleigh	rayleigh	PROPN
iajs-3044	5	14	(	(	PUNCT
iajs-3044	5	15	mwer	mwer	NOUN
iajs-3044	5	16	)	)	PUNCT
iajs-3044	5	17	distribution	distribution	NOUN
iajs-3044	5	18	.	.	PUNCT
iajs-3044	6	1	1.introduction	1.introduction	NUM
iajs-3044	6	2	statistical	statistical	ADJ
iajs-3044	6	3	distributions	distribution	NOUN
iajs-3044	6	4	are	be	AUX
iajs-3044	6	5	very	very	ADV
iajs-3044	6	6	important	important	ADJ
iajs-3044	6	7	for	for	ADP
iajs-3044	6	8	parametric	parametric	ADJ
iajs-3044	6	9	inferences	inference	NOUN
iajs-3044	6	10	and	and	CCONJ
iajs-3044	6	11	are	be	AUX
iajs-3044	6	12	usually	usually	ADV
iajs-3044	6	13	applied	apply	VERB
iajs-3044	6	14	to	to	PART
iajs-3044	6	15	describe	describe	VERB
iajs-3044	6	16	real	real	ADJ
iajs-3044	6	17	world	world	NOUN
iajs-3044	6	18	phenomena	phenomenon	NOUN
iajs-3044	6	19	.	.	PUNCT
iajs-3044	7	1	although	although	SCONJ
iajs-3044	7	2	they	they	PRON
iajs-3044	7	3	are	be	AUX
iajs-3044	7	4	useful	useful	ADJ
iajs-3044	7	5	in	in	ADP
iajs-3044	7	6	several	several	ADJ
iajs-3044	7	7	scientific	scientific	ADJ
iajs-3044	7	8	fields	field	NOUN
iajs-3044	7	9	,	,	PUNCT
iajs-3044	7	10	it	it	PRON
iajs-3044	7	11	is	be	AUX
iajs-3044	7	12	observed	observe	VERB
iajs-3044	7	13	that	that	SCONJ
iajs-3044	7	14	most	most	ADJ
iajs-3044	7	15	common	common	ADJ
iajs-3044	7	16	distributions	distribution	NOUN
iajs-3044	7	17	,	,	PUNCT
iajs-3044	7	18	such	such	ADJ
iajs-3044	7	19	as	as	ADP
iajs-3044	7	20	exponential	exponential	NOUN
iajs-3044	7	21	,	,	PUNCT
iajs-3044	7	22	gamma	gamma	NOUN
iajs-3044	7	23	,	,	PUNCT
iajs-3044	7	24	weibull	weibull	PROPN
iajs-3044	7	25	,	,	PUNCT
iajs-3044	7	26	rayleigh	rayleigh	PROPN
iajs-3044	7	27	and	and	CCONJ
iajs-3044	7	28	lindley	lindley	NOUN
iajs-3044	7	29	are	be	AUX
iajs-3044	7	30	not	not	PART
iajs-3044	7	31	sufficiently	sufficiently	ADV
iajs-3044	7	32	flexible	flexible	ADJ
iajs-3044	7	33	to	to	PART
iajs-3044	7	34	accommodate	accommodate	VERB
iajs-3044	7	35	various	various	ADJ
iajs-3044	7	36	phenomena	phenomenon	NOUN
iajs-3044	7	37	of	of	ADP
iajs-3044	7	38	nature	nature	NOUN
iajs-3044	7	39	for	for	ADP
iajs-3044	7	40	example	example	NOUN
iajs-3044	7	41	,	,	PUNCT
iajs-3044	7	42	while	while	SCONJ
iajs-3044	7	43	exponential	exponential	ADJ
iajs-3044	7	44	distribution	distribution	NOUN
iajs-3044	7	45	is	be	AUX
iajs-3044	7	46	frequently	frequently	ADV
iajs-3044	7	47	defined	define	VERB
iajs-3044	7	48	as	as	ADP
iajs-3044	7	49	flexible	flexible	ADJ
iajs-3044	7	50	,	,	PUNCT
iajs-3044	7	51	its	its	PRON
iajs-3044	7	52	hazard	hazard	NOUN
iajs-3044	7	53	function	function	NOUN
iajs-3044	7	54	is	be	AUX
iajs-3044	7	55	constant	constant	ADJ
iajs-3044	7	56	.	.	PUNCT
iajs-3044	8	1	for	for	ADP
iajs-3044	8	2	this	this	DET
iajs-3044	8	3	cause	cause	NOUN
iajs-3044	8	4	,	,	PUNCT
iajs-3044	8	5	researchers	researcher	NOUN
iajs-3044	8	6	have	have	AUX
iajs-3044	8	7	focused	focus	VERB
iajs-3044	8	8	on	on	ADP
iajs-3044	8	9	the	the	DET
iajs-3044	8	10	expansion	expansion	NOUN
iajs-3044	8	11	of	of	ADP
iajs-3044	8	12	these	these	DET
iajs-3044	8	13	common	common	ADJ
iajs-3044	8	14	distributions	distribution	NOUN
iajs-3044	8	15	in	in	ADP
iajs-3044	8	16	order	order	NOUN
iajs-3044	8	17	to	to	ADP
iajs-3044	8	18	ibn	ibn	PROPN
iajs-3044	8	19	al	al	PROPN
iajs-3044	8	20	-	-	PUNCT
iajs-3044	8	21	haitham	haitham	PROPN
iajs-3044	8	22	journal	journal	PROPN
iajs-3044	8	23	for	for	ADP
iajs-3044	8	24	pure	pure	ADJ
iajs-3044	8	25	and	and	CCONJ
iajs-3044	8	26	applied	applied	ADJ
iajs-3044	8	27	sciences	sciences	PROPN
iajs-3044	8	28	journal	journal	PROPN
iajs-3044	8	29	homepage	homepage	NOUN
iajs-3044	8	30	:	:	PUNCT
iajs-3044	8	31	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3044	8	32	doi.org/10.30526/36.2.3044	doi.org/10.30526/36.2.3044	ADP
iajs-3044	8	33	article	article	NOUN
iajs-3044	8	34	history	history	NOUN
iajs-3044	8	35	:	:	PUNCT
iajs-3044	8	36	received	receive	VERB
iajs-3044	8	37	18	18	NUM
iajs-3044	8	38	september	september	PROPN
iajs-3044	8	39	2022	2022	NUM
iajs-3044	8	40	,	,	PUNCT
iajs-3044	8	41	accepted	accept	VERB
iajs-3044	8	42	12	12	NUM
iajs-3044	8	43	december	december	PROPN
iajs-3044	8	44	2022	2022	NUM
iajs-3044	8	45	,	,	PUNCT
iajs-3044	8	46	published	publish	VERB
iajs-3044	8	47	in	in	ADP
iajs-3044	8	48	april	april	PROPN
iajs-3044	8	49	2023	2023	NUM
iajs-3044	8	50	.	.	PUNCT
iajs-3044	9	1	a	a	DET
iajs-3044	9	2	class	class	NOUN
iajs-3044	9	3	of	of	ADP
iajs-3044	9	4	exponential	exponential	ADJ
iajs-3044	9	5	rayleigh	rayleigh	NOUN
iajs-3044	9	6	distribution	distribution	NOUN
iajs-3044	9	7	and	and	CCONJ
iajs-3044	9	8	new	new	ADJ
iajs-3044	9	9	modified	modify	VERB
iajs-3044	9	10	weighted	weight	VERB
iajs-3044	9	11	exponential	exponential	ADJ
iajs-3044	9	12	rayleigh	rayleigh	NOUN
iajs-3044	9	13	distribution	distribution	NOUN
iajs-3044	9	14	with	with	ADP
iajs-3044	9	15	statistical	statistical	ADJ
iajs-3044	9	16	properties	property	NOUN
iajs-3044	9	17	iden	iden	PROPN
iajs-3044	9	18	hasan	hasan	PROPN
iajs-3044	9	19	hussein	hussein	PROPN
iajs-3044	10	1	2department	2department	NUM
iajs-3044	10	2	of	of	ADP
iajs-3044	10	3	mathematic	mathematic	ADJ
iajs-3044	10	4	,	,	PUNCT
iajs-3044	10	5	college	college	NOUN
iajs-3044	10	6	of	of	ADP
iajs-3044	10	7	science	science	NOUN
iajs-3044	10	8	for	for	ADP
iajs-3044	10	9	women	woman	NOUN
iajs-3044	10	10	,	,	PUNCT
iajs-3044	10	11	university	university	NOUN
iajs-3044	10	12	of	of	ADP
iajs-3044	10	13	baghdad	baghdad	PROPN
iajs-3044	10	14	,	,	PUNCT
iajs-3044	10	15	baghdad	baghdad	PROPN
iajs-3044	10	16	,	,	PUNCT
iajs-3044	10	17	iraq	iraq	PROPN
iajs-3044	10	18	idenalkanani58@gmail.com	idenalkanani58@gmail.com	PROPN
iajs-3044	10	19	lamyaa	lamyaa	PROPN
iajs-3044	10	20	khalid	khalid	PROPN
iajs-3044	10	21	hussein	hussein	PROPN
iajs-3044	10	22	1department	1department	NUM
iajs-3044	10	23	of	of	ADP
iajs-3044	10	24	mathematics	mathematic	NOUN
iajs-3044	10	25	,	,	PUNCT
iajs-3044	10	26	college	college	NOUN
iajs-3044	10	27	of	of	ADP
iajs-3044	10	28	science	science	NOUN
iajs-3044	10	29	,	,	PUNCT
iajs-3044	10	30	mustansiriyah	mustansiriyah	NOUN
iajs-3044	10	31	university	university	NOUN
iajs-3044	10	32	,	,	PUNCT
iajs-3044	10	33	baghdad	baghdad	PROPN
iajs-3044	10	34	,	,	PUNCT
iajs-3044	10	35	iraq	iraq	PROPN
iajs-3044	10	36	lamyaakhalid8242@gmail.com	lamyaakhalid8242@gmail.com	X
iajs-3044	11	1	huda	huda	PROPN
iajs-3044	11	2	abdullah	abdullah	PROPN
iajs-3044	11	3	rasheed	rasheed	PROPN
iajs-3044	11	4	3department	3department	NUM
iajs-3044	11	5	of	of	ADP
iajs-3044	11	6	mathematics	mathematic	NOUN
iajs-3044	11	7	,	,	PUNCT
iajs-3044	11	8	college	college	NOUN
iajs-3044	11	9	of	of	ADP
iajs-3044	11	10	science	science	NOUN
iajs-3044	11	11	,	,	PUNCT
iajs-3044	11	12	mustansiriyah	mustansiriyah	NOUN
iajs-3044	11	13	university	university	NOUN
iajs-3044	11	14	,	,	PUNCT
iajs-3044	11	15	baghdad	baghdad	PROPN
iajs-3044	11	16	,	,	PUNCT
iajs-3044	11	17	iraq	iraq	PROPN
iajs-3044	11	18	iraqalnoor1@gmail.com	iraqalnoor1@gmail.com	X
iajs-3044	12	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3044	12	2	mailto:idenalkanani58@gmail.com	mailto:idenalkanani58@gmail.com	PROPN
iajs-3044	12	3	mailto:lamyaakhalid8242@gmail.com	mailto:lamyaakhalid8242@gmail.com	PROPN
iajs-3044	12	4	mailto:iraqalnoor1@gmail.com	mailto:iraqalnoor1@gmail.com	PROPN
iajs-3044	12	5	ihjpas	ihjpa	VERB
iajs-3044	12	6	.	.	PUNCT
iajs-3044	13	1	36(2)2023	36(2)2023	NUM
iajs-3044	13	2	391	391	NUM
iajs-3044	13	3	produce	produce	VERB
iajs-3044	13	4	a	a	DET
iajs-3044	13	5	more	more	ADJ
iajs-3044	13	6	and	and	CCONJ
iajs-3044	13	7	more	more	ADV
iajs-3044	13	8	realistic	realistic	ADJ
iajs-3044	13	9	and	and	CCONJ
iajs-3044	13	10	flexible	flexible	ADJ
iajs-3044	13	11	models	model	NOUN
iajs-3044	13	12	for	for	ADP
iajs-3044	13	13	data	datum	NOUN
iajs-3044	13	14	.	.	PUNCT
iajs-3044	14	1	in	in	ADP
iajs-3044	14	2	1880	1880	NUM
iajs-3044	14	3	,	,	PUNCT
iajs-3044	14	4	[	[	X
iajs-3044	14	5	1	1	X
iajs-3044	14	6	]	]	PUNCT
iajs-3044	14	7	introduced	introduce	VERB
iajs-3044	14	8	the	the	DET
iajs-3044	14	9	rayleigh	rayleigh	NOUN
iajs-3044	14	10	distribution	distribution	NOUN
iajs-3044	14	11	this	this	DET
iajs-3044	14	12	distribution	distribution	NOUN
iajs-3044	14	13	with	with	ADP
iajs-3044	14	14	one	one	NUM
iajs-3044	14	15	scale	scale	NOUN
iajs-3044	14	16	parameter	parameter	NOUN
iajs-3044	14	17	is	be	AUX
iajs-3044	14	18	one	one	NUM
iajs-3044	14	19	of	of	ADP
iajs-3044	14	20	the	the	DET
iajs-3044	14	21	most	most	ADV
iajs-3044	14	22	widely	widely	ADV
iajs-3044	14	23	used	use	VERB
iajs-3044	14	24	distributions	distribution	NOUN
iajs-3044	14	25	.	.	PUNCT
iajs-3044	15	1	exponential	exponential	NOUN
iajs-3044	15	2	and	and	CCONJ
iajs-3044	15	3	rayleigh	rayleigh	PROPN
iajs-3044	15	4	were	be	AUX
iajs-3044	15	5	an	an	DET
iajs-3044	15	6	important	important	ADJ
iajs-3044	15	7	distribution	distribution	NOUN
iajs-3044	15	8	in	in	ADP
iajs-3044	15	9	statistics	statistic	NOUN
iajs-3044	15	10	and	and	CCONJ
iajs-3044	15	11	operation	operation	NOUN
iajs-3044	15	12	research	research	NOUN
iajs-3044	15	13	[	[	X
iajs-3044	15	14	2	2	NUM
iajs-3044	15	15	]	]	PUNCT
iajs-3044	15	16	.	.	PUNCT
iajs-3044	16	1	[	[	X
iajs-3044	16	2	3	3	NUM
iajs-3044	16	3	]	]	X
iajs-3044	16	4	mixed	mixed	ADJ
iajs-3044	16	5	exponential	exponential	NOUN
iajs-3044	16	6	and	and	CCONJ
iajs-3044	16	7	rayleigh	rayleigh	NOUN
iajs-3044	16	8	distributions	distribution	NOUN
iajs-3044	16	9	based	base	VERB
iajs-3044	16	10	on	on	ADP
iajs-3044	16	11	t	t	PROPN
iajs-3044	16	12	-	-	PUNCT
iajs-3044	16	13	x	x	NOUN
iajs-3044	16	14	families	family	NOUN
iajs-3044	16	15	.	.	PUNCT
iajs-3044	17	1	[	[	X
iajs-3044	17	2	4	4	NUM
iajs-3044	17	3	]	]	PUNCT
iajs-3044	17	4	.	.	PUNCT
iajs-3044	17	5	presented	present	VERB
iajs-3044	17	6	the	the	DET
iajs-3044	17	7	finite	finite	ADJ
iajs-3044	17	8	mixture	mixture	NOUN
iajs-3044	17	9	of	of	ADP
iajs-3044	17	10	exponential	exponential	ADJ
iajs-3044	17	11	rayleigh	rayleigh	PROPN
iajs-3044	17	12	and	and	CCONJ
iajs-3044	17	13	burr	burr	PROPN
iajs-3044	17	14	type	type	NOUN
iajs-3044	17	15	-	-	PUNCT
iajs-3044	17	16	xii	xii	NOUN
iajs-3044	17	17	distribution	distribution	NOUN
iajs-3044	17	18	.	.	PUNCT
iajs-3044	18	1	[	[	X
iajs-3044	18	2	5	5	NUM
iajs-3044	18	3	]	]	X
iajs-3044	18	4	mixed	mixed	ADJ
iajs-3044	18	5	multivariate	multivariate	NOUN
iajs-3044	18	6	exponential	exponential	ADJ
iajs-3044	18	7	distribution	distribution	NOUN
iajs-3044	18	8	and	and	CCONJ
iajs-3044	18	9	the	the	DET
iajs-3044	18	10	multivariate	multivariate	NOUN
iajs-3044	18	11	rayleigh	rayleigh	NOUN
iajs-3044	18	12	distribution	distribution	NOUN
iajs-3044	18	13	to	to	PART
iajs-3044	18	14	obtained	obtain	VERB
iajs-3044	18	15	multivariate	multivariate	NOUN
iajs-3044	18	16	rayleigh	rayleigh	PROPN
iajs-3044	18	17	and	and	CCONJ
iajs-3044	18	18	exponential	exponential	ADJ
iajs-3044	18	19	distributions	distribution	NOUN
iajs-3044	18	20	.	.	PUNCT
iajs-3044	19	1	[	[	X
iajs-3044	19	2	6	6	NUM
iajs-3044	19	3	]	]	PUNCT
iajs-3044	19	4	introduced	introduce	VERB
iajs-3044	19	5	a	a	DET
iajs-3044	19	6	new	new	ADJ
iajs-3044	19	7	mixture	mixture	NOUN
iajs-3044	19	8	distribution	distribution	NOUN
iajs-3044	19	9	based	base	VERB
iajs-3044	19	10	on	on	ADP
iajs-3044	19	11	the	the	DET
iajs-3044	19	12	tail	tail	NOUN
iajs-3044	19	13	of	of	ADP
iajs-3044	19	14	mixed	mix	VERB
iajs-3044	19	15	between	between	ADP
iajs-3044	19	16	exponential	exponential	ADJ
iajs-3044	19	17	rayleigh	rayleigh	NOUN
iajs-3044	19	18	and	and	CCONJ
iajs-3044	19	19	exponential	exponential	ADJ
iajs-3044	19	20	weibull	weibull	PROPN
iajs-3044	19	21	distributions	distribution	NOUN
iajs-3044	19	22	using	use	VERB
iajs-3044	19	23	an	an	DET
iajs-3044	19	24	application	application	NOUN
iajs-3044	19	25	(	(	PUNCT
iajs-3044	19	26	minimum	minimum	NOUN
iajs-3044	19	27	)	)	PUNCT
iajs-3044	19	28	.	.	PUNCT
iajs-3044	20	1	there	there	PRON
iajs-3044	20	2	are	be	VERB
iajs-3044	20	3	various	various	ADJ
iajs-3044	20	4	methods	method	NOUN
iajs-3044	20	5	of	of	ADP
iajs-3044	20	6	inputting	inputte	VERB
iajs-3044	20	7	the	the	DET
iajs-3044	20	8	shape	shape	NOUN
iajs-3044	20	9	parameter	parameter	NOUN
iajs-3044	20	10	of	of	ADP
iajs-3044	20	11	a	a	DET
iajs-3044	20	12	probability	probability	NOUN
iajs-3044	20	13	distribution	distribution	NOUN
iajs-3044	20	14	model	model	NOUN
iajs-3044	20	15	and	and	CCONJ
iajs-3044	20	16	they	they	PRON
iajs-3044	20	17	may	may	AUX
iajs-3044	20	18	result	result	VERB
iajs-3044	20	19	in	in	ADP
iajs-3044	20	20	a	a	DET
iajs-3044	20	21	variety	variety	NOUN
iajs-3044	20	22	of	of	ADP
iajs-3044	20	23	weighted	weight	VERB
iajs-3044	20	24	distributions	distribution	NOUN
iajs-3044	20	25	.	.	PUNCT
iajs-3044	21	1	the	the	DET
iajs-3044	21	2	weighted	weight	VERB
iajs-3044	21	3	distributions	distribution	NOUN
iajs-3044	21	4	are	be	AUX
iajs-3044	21	5	widely	widely	ADV
iajs-3044	21	6	used	use	VERB
iajs-3044	21	7	in	in	ADP
iajs-3044	21	8	reliability	reliability	NOUN
iajs-3044	21	9	,	,	PUNCT
iajs-3044	21	10	survival	survival	NOUN
iajs-3044	21	11	,	,	PUNCT
iajs-3044	21	12	bio	bio	NOUN
iajs-3044	21	13	-	-	NOUN
iajs-3044	21	14	medicine	medicine	NOUN
iajs-3044	21	15	,	,	PUNCT
iajs-3044	21	16	environment	environment	NOUN
iajs-3044	21	17	,	,	PUNCT
iajs-3044	21	18	and	and	CCONJ
iajs-3044	21	19	many	many	ADJ
iajs-3044	21	20	other	other	ADJ
iajs-3044	21	21	fields	field	NOUN
iajs-3044	21	22	of	of	ADP
iajs-3044	21	23	immense	immense	ADJ
iajs-3044	21	24	practical	practical	ADJ
iajs-3044	21	25	interest	interest	NOUN
iajs-3044	21	26	in	in	ADP
iajs-3044	21	27	mathematics	mathematic	NOUN
iajs-3044	21	28	,	,	PUNCT
iajs-3044	21	29	probability	probability	NOUN
iajs-3044	21	30	,	,	PUNCT
iajs-3044	21	31	statistics	statistic	NOUN
iajs-3044	21	32	.	.	PUNCT
iajs-3044	22	1	these	these	DET
iajs-3044	22	2	distributions	distribution	NOUN
iajs-3044	22	3	naturally	naturally	ADV
iajs-3044	22	4	arise	arise	VERB
iajs-3044	22	5	as	as	ADP
iajs-3044	22	6	a	a	DET
iajs-3044	22	7	result	result	NOUN
iajs-3044	22	8	of	of	ADP
iajs-3044	22	9	observations	observation	NOUN
iajs-3044	22	10	created	create	VERB
iajs-3044	22	11	by	by	ADP
iajs-3044	22	12	a	a	DET
iajs-3044	22	13	random	random	ADJ
iajs-3044	22	14	process	process	NOUN
iajs-3044	22	15	and	and	CCONJ
iajs-3044	22	16	recorded	record	VERB
iajs-3044	22	17	with	with	ADP
iajs-3044	22	18	some	some	DET
iajs-3044	22	19	weight	weight	NOUN
iajs-3044	22	20	functions	function	NOUN
iajs-3044	22	21	[	[	X
iajs-3044	22	22	7	7	NUM
iajs-3044	22	23	]	]	PUNCT
iajs-3044	22	24	.	.	PUNCT
iajs-3044	23	1	the	the	DET
iajs-3044	23	2	aim	aim	NOUN
iajs-3044	23	3	of	of	ADP
iajs-3044	23	4	this	this	DET
iajs-3044	23	5	paper	paper	NOUN
iajs-3044	23	6	,	,	PUNCT
iajs-3044	23	7	two	two	NUM
iajs-3044	23	8	distributions	distribution	NOUN
iajs-3044	23	9	have	have	AUX
iajs-3044	23	10	been	be	AUX
iajs-3044	23	11	introduced	introduce	VERB
iajs-3044	23	12	exponential	exponential	ADJ
iajs-3044	23	13	rayleigh	rayleigh	NOUN
iajs-3044	23	14	distribution	distribution	NOUN
iajs-3044	23	15	this	this	DET
iajs-3044	23	16	distribution	distribution	NOUN
iajs-3044	23	17	can	can	AUX
iajs-3044	23	18	be	be	AUX
iajs-3044	23	19	obtained	obtain	VERB
iajs-3044	23	20	based	base	VERB
iajs-3044	23	21	on	on	ADP
iajs-3044	23	22	mixed	mix	VERB
iajs-3044	23	23	between	between	ADP
iajs-3044	23	24	cumulative	cumulative	ADJ
iajs-3044	23	25	distribution	distribution	NOUN
iajs-3044	23	26	function	function	NOUN
iajs-3044	23	27	of	of	ADP
iajs-3044	23	28	exponential	exponential	ADJ
iajs-3044	23	29	distribution	distribution	NOUN
iajs-3044	23	30	and	and	CCONJ
iajs-3044	23	31	the	the	DET
iajs-3044	23	32	cumulative	cumulative	ADJ
iajs-3044	23	33	distribution	distribution	NOUN
iajs-3044	23	34	function	function	NOUN
iajs-3044	23	35	of	of	ADP
iajs-3044	23	36	rayleigh	rayleigh	ADJ
iajs-3044	23	37	distribution	distribution	NOUN
iajs-3044	23	38	using	use	VERB
iajs-3044	23	39	an	an	DET
iajs-3044	23	40	application	application	NOUN
iajs-3044	23	41	(	(	PUNCT
iajs-3044	23	42	maximum	maximum	ADJ
iajs-3044	23	43	)	)	PUNCT
iajs-3044	23	44	and	and	CCONJ
iajs-3044	23	45	present	present	VERB
iajs-3044	23	46	a	a	DET
iajs-3044	23	47	new	new	ADJ
iajs-3044	23	48	distribution	distribution	NOUN
iajs-3044	23	49	named	name	VERB
iajs-3044	23	50	modified	modify	VERB
iajs-3044	23	51	weighted	weight	VERB
iajs-3044	23	52	exponential	exponential	ADJ
iajs-3044	23	53	rayleigh	rayleigh	NOUN
iajs-3044	23	54	distribution	distribution	NOUN
iajs-3044	23	55	built	build	VERB
iajs-3044	23	56	on	on	ADP
iajs-3044	23	57	a	a	DET
iajs-3044	23	58	modified	modify	VERB
iajs-3044	23	59	weighted	weight	VERB
iajs-3044	23	60	version	version	NOUN
iajs-3044	23	61	of	of	ADP
iajs-3044	23	62	azzalini	azzalini	PROPN
iajs-3044	23	63	’s	’s	PART
iajs-3044	23	64	(	(	PUNCT
iajs-3044	23	65	1985	1985	NUM
iajs-3044	23	66	)	)	PUNCT
iajs-3044	23	67	,	,	PUNCT
iajs-3044	23	68	this	this	DET
iajs-3044	23	69	new	new	ADJ
iajs-3044	23	70	distribution	distribution	NOUN
iajs-3044	23	71	is	be	AUX
iajs-3044	23	72	a	a	DET
iajs-3044	23	73	generalization	generalization	NOUN
iajs-3044	23	74	of	of	ADP
iajs-3044	23	75	the	the	DET
iajs-3044	23	76	exponential	exponential	ADJ
iajs-3044	23	77	rayleigh	rayleigh	NOUN
iajs-3044	23	78	distribution	distribution	NOUN
iajs-3044	23	79	,	,	PUNCT
iajs-3044	23	80	as	as	ADV
iajs-3044	23	81	well	well	ADV
iajs-3044	23	82	as	as	ADP
iajs-3044	23	83	present	present	VERB
iajs-3044	23	84	the	the	DET
iajs-3044	23	85	most	most	ADV
iajs-3044	23	86	important	important	ADJ
iajs-3044	23	87	statistical	statistical	ADJ
iajs-3044	23	88	properties	property	NOUN
iajs-3044	23	89	of	of	ADP
iajs-3044	23	90	these	these	DET
iajs-3044	23	91	two	two	NUM
iajs-3044	23	92	distributions	distribution	NOUN
iajs-3044	23	93	,	,	PUNCT
iajs-3044	23	94	finally	finally	ADV
iajs-3044	23	95	the	the	DET
iajs-3044	23	96	conclusion	conclusion	NOUN
iajs-3044	23	97	of	of	ADP
iajs-3044	23	98	this	this	DET
iajs-3044	23	99	paper	paper	NOUN
iajs-3044	23	100	is	be	AUX
iajs-3044	23	101	determined	determine	VERB
iajs-3044	23	102	.	.	PUNCT
iajs-3044	24	1	2	2	X
iajs-3044	24	2	.	.	X
iajs-3044	24	3	exponential	exponential	ADJ
iajs-3044	24	4	rayleigh	rayleigh	NOUN
iajs-3044	24	5	distribution	distribution	NOUN
iajs-3044	24	6	a	a	DET
iajs-3044	24	7	continuous	continuous	ADJ
iajs-3044	24	8	non	non	ADJ
iajs-3044	24	9	-	-	ADJ
iajs-3044	24	10	negative	negative	ADJ
iajs-3044	24	11	random	random	ADJ
iajs-3044	24	12	variable	variable	ADJ
iajs-3044	24	13	𝑍	𝑍	NOUN
iajs-3044	24	14	is	be	AUX
iajs-3044	24	15	called	call	VERB
iajs-3044	24	16	to	to	PART
iajs-3044	24	17	have	have	VERB
iajs-3044	24	18	an	an	DET
iajs-3044	24	19	exponential	exponential	ADJ
iajs-3044	24	20	distribution	distribution	NOUN
iajs-3044	24	21	with	with	ADP
iajs-3044	24	22	parameter	parameter	NOUN
iajs-3044	24	23	𝛼	𝛼	PROPN
iajs-3044	24	24	,	,	PUNCT
iajs-3044	24	25	if	if	SCONJ
iajs-3044	24	26	its	its	PRON
iajs-3044	24	27	probability	probability	NOUN
iajs-3044	24	28	density	density	NOUN
iajs-3044	24	29	function	function	NOUN
iajs-3044	24	30	is	be	AUX
iajs-3044	24	31	given	give	VERB
iajs-3044	24	32	by	by	ADP
iajs-3044	24	33	[	[	X
iajs-3044	24	34	8	8	NUM
iajs-3044	24	35	]	]	X
iajs-3044	24	36	:	:	PUNCT
iajs-3044	24	37	𝑓(𝑧	𝑓(𝑧	NUM
iajs-3044	24	38	;	;	PUNCT
iajs-3044	24	39	𝛼)𝐸	𝛼)𝐸	NOUN
iajs-3044	24	40	=	=	SYM
iajs-3044	24	41	𝛼	𝛼	NOUN
iajs-3044	24	42	𝑒−𝛼𝑧	𝑒−𝛼𝑧	NOUN
iajs-3044	24	43	;	;	PUNCT
iajs-3044	24	44	𝑧	𝑧	DET
iajs-3044	24	45	≥	≥	NOUN
iajs-3044	24	46	0	0	NUM
iajs-3044	24	47	;	;	PUNCT
iajs-3044	24	48	𝛼	𝛼	X
iajs-3044	24	49	>	>	X
iajs-3044	24	50	0	0	NUM
iajs-3044	24	51	…	…	PUNCT
iajs-3044	24	52	(	(	PUNCT
iajs-3044	24	53	1	1	NUM
iajs-3044	24	54	)	)	PUNCT
iajs-3044	24	55	zero	zero	NUM
iajs-3044	24	56	otherwise	otherwise	ADV
iajs-3044	24	57	.	.	PUNCT
iajs-3044	25	1	where	where	SCONJ
iajs-3044	25	2	𝛼	𝛼	NOUN
iajs-3044	25	3	is	be	AUX
iajs-3044	25	4	a	a	DET
iajs-3044	25	5	scale	scale	NOUN
iajs-3044	25	6	parameter	parameter	NOUN
iajs-3044	25	7	.	.	PUNCT
iajs-3044	26	1	the	the	DET
iajs-3044	26	2	cumulative	cumulative	ADJ
iajs-3044	26	3	distribution	distribution	NOUN
iajs-3044	26	4	function	function	NOUN
iajs-3044	26	5	is	be	AUX
iajs-3044	26	6	:	:	PUNCT
iajs-3044	26	7	𝐹(𝑧	𝐹(𝑧	X
iajs-3044	26	8	;	;	PUNCT
iajs-3044	26	9	𝛼)𝐸	𝛼)𝐸	NOUN
iajs-3044	26	10	=	=	SYM
iajs-3044	26	11	1	1	NUM
iajs-3044	26	12	−	−	NOUN
iajs-3044	26	13	𝑒−𝛼𝑧	𝑒−𝛼𝑧	NOUN
iajs-3044	26	14	;	;	PUNCT
iajs-3044	26	15	𝑧	𝑧	PRON
iajs-3044	26	16	≥	≥	NOUN
iajs-3044	26	17	0	0	NUM
iajs-3044	26	18	;	;	PUNCT
iajs-3044	26	19	𝛼	𝛼	X
iajs-3044	26	20	>	>	X
iajs-3044	26	21	0	0	NUM
iajs-3044	26	22	…	…	PUNCT
iajs-3044	26	23	(	(	PUNCT
iajs-3044	26	24	2	2	NUM
iajs-3044	26	25	)	)	PUNCT
iajs-3044	26	26	a	a	DET
iajs-3044	26	27	continuous	continuous	ADJ
iajs-3044	26	28	non	non	ADJ
iajs-3044	26	29	-	-	ADJ
iajs-3044	26	30	negative	negative	ADJ
iajs-3044	26	31	random	random	ADJ
iajs-3044	26	32	variable	variable	NOUN
iajs-3044	26	33	𝑌	𝑌	PROPN
iajs-3044	26	34	is	be	AUX
iajs-3044	26	35	called	call	VERB
iajs-3044	26	36	to	to	PART
iajs-3044	26	37	have	have	VERB
iajs-3044	26	38	a	a	DET
iajs-3044	26	39	rayleigh	rayleigh	ADJ
iajs-3044	26	40	distribution	distribution	NOUN
iajs-3044	26	41	with	with	ADP
iajs-3044	26	42	parameter	parameter	NOUN
iajs-3044	26	43	𝜆	𝜆	ADP
iajs-3044	26	44	,	,	PUNCT
iajs-3044	26	45	if	if	SCONJ
iajs-3044	26	46	its	its	PRON
iajs-3044	26	47	probability	probability	NOUN
iajs-3044	26	48	density	density	NOUN
iajs-3044	26	49	function	function	NOUN
iajs-3044	26	50	is	be	AUX
iajs-3044	26	51	given	give	VERB
iajs-3044	26	52	by	by	ADP
iajs-3044	26	53	[	[	PUNCT
iajs-3044	26	54	9	9	NUM
iajs-3044	26	55	]	]	PUNCT
iajs-3044	26	56	:	:	PUNCT
iajs-3044	26	57	𝑓(𝑦	𝑓(𝑦	PROPN
iajs-3044	26	58	;	;	PUNCT
iajs-3044	26	59	𝜆)𝑅	𝜆)𝑅	SYM
iajs-3044	26	60	=	=	PUNCT
iajs-3044	26	61	𝜆𝑦	𝜆𝑦	NOUN
iajs-3044	26	62	𝑒−	𝑒−	NOUN
iajs-3044	26	63	𝜆	𝜆	SYM
iajs-3044	26	64	2	2	NUM
iajs-3044	26	65	𝑦2	𝑦2	NOUN
iajs-3044	26	66	;	;	PUNCT
iajs-3044	26	67	𝑦	𝑦	PRON
iajs-3044	26	68	≥	≥	NOUN
iajs-3044	26	69	0	0	NUM
iajs-3044	26	70	;	;	PUNCT
iajs-3044	26	71	𝜆	𝜆	X
iajs-3044	26	72	>	>	X
iajs-3044	26	73	0	0	NUM
iajs-3044	26	74	…	…	PUNCT
iajs-3044	26	75	(	(	PUNCT
iajs-3044	26	76	3	3	NUM
iajs-3044	26	77	)	)	PUNCT
iajs-3044	26	78	zero	zero	NUM
iajs-3044	26	79	otherwise	otherwise	ADV
iajs-3044	26	80	.	.	PUNCT
iajs-3044	27	1	where	where	SCONJ
iajs-3044	27	2	𝜆	𝜆	NOUN
iajs-3044	27	3	is	be	AUX
iajs-3044	27	4	a	a	DET
iajs-3044	27	5	scale	scale	NOUN
iajs-3044	27	6	parameter	parameter	NOUN
iajs-3044	27	7	.	.	PUNCT
iajs-3044	28	1	the	the	DET
iajs-3044	28	2	cumulative	cumulative	ADJ
iajs-3044	28	3	distribution	distribution	NOUN
iajs-3044	28	4	function	function	NOUN
iajs-3044	28	5	is	be	AUX
iajs-3044	28	6	:	:	PUNCT
iajs-3044	28	7	𝐹(𝑦	𝐹(𝑦	NUM
iajs-3044	28	8	;	;	PUNCT
iajs-3044	28	9	𝜆)𝑅	𝜆)𝑅	SYM
iajs-3044	28	10	=	=	SYM
iajs-3044	29	1	1	1	NUM
iajs-3044	29	2	−	−	NOUN
iajs-3044	29	3	𝑒−	𝑒−	NOUN
iajs-3044	29	4	𝜆	𝜆	ADP
iajs-3044	29	5	2	2	NUM
iajs-3044	29	6	𝑦2	𝑦2	NOUN
iajs-3044	29	7	;	;	PUNCT
iajs-3044	29	8	𝑦	𝑦	PRON
iajs-3044	29	9	≥	≥	NOUN
iajs-3044	29	10	0	0	NUM
iajs-3044	29	11	;	;	PUNCT
iajs-3044	29	12	𝜆	𝜆	X
iajs-3044	29	13	>	>	X
iajs-3044	29	14	0	0	NUM
iajs-3044	29	15	…	…	PUNCT
iajs-3044	29	16	(	(	PUNCT
iajs-3044	29	17	4	4	NUM
iajs-3044	29	18	)	)	PUNCT
iajs-3044	29	19	the	the	DET
iajs-3044	29	20	exponential	exponential	ADJ
iajs-3044	29	21	rayleigh	rayleigh	NOUN
iajs-3044	29	22	distribution	distribution	NOUN
iajs-3044	29	23	introduced	introduce	VERB
iajs-3044	29	24	by	by	ADP
iajs-3044	29	25	mohammed	mohammed	PROPN
iajs-3044	29	26	and	and	CCONJ
iajs-3044	29	27	hussein	hussein	PROPN
iajs-3044	29	28	in	in	ADP
iajs-3044	29	29	(	(	PUNCT
iajs-3044	29	30	2019	2019	NUM
iajs-3044	29	31	)	)	PUNCT
iajs-3044	29	32	depends	depend	VERB
iajs-3044	29	33	on	on	ADP
iajs-3044	29	34	mixed	mixed	ADJ
iajs-3044	29	35	of	of	ADP
iajs-3044	29	36	the	the	DET
iajs-3044	29	37	tail	tail	NOUN
iajs-3044	29	38	(	(	PUNCT
iajs-3044	29	39	survival	survival	NOUN
iajs-3044	29	40	)	)	PUNCT
iajs-3044	29	41	function	function	NOUN
iajs-3044	29	42	of	of	ADP
iajs-3044	29	43	exponential	exponential	ADJ
iajs-3044	29	44	distribution	distribution	NOUN
iajs-3044	29	45	and	and	CCONJ
iajs-3044	29	46	the	the	DET
iajs-3044	29	47	tail	tail	NOUN
iajs-3044	29	48	(	(	PUNCT
iajs-3044	29	49	survival	survival	NOUN
iajs-3044	29	50	)	)	PUNCT
iajs-3044	29	51	function	function	NOUN
iajs-3044	29	52	of	of	ADP
iajs-3044	29	53	rayleigh	rayleigh	ADJ
iajs-3044	29	54	distribution	distribution	NOUN
iajs-3044	29	55	using	use	VERB
iajs-3044	29	56	an	an	DET
iajs-3044	29	57	application	application	NOUN
iajs-3044	29	58	(	(	PUNCT
iajs-3044	29	59	minimum	minimum	NOUN
iajs-3044	29	60	)	)	PUNCT
iajs-3044	30	1	[	[	X
iajs-3044	30	2	6	6	NUM
iajs-3044	30	3	]	]	PUNCT
iajs-3044	30	4	.	.	PUNCT
iajs-3044	31	1	this	this	DET
iajs-3044	31	2	distribution	distribution	NOUN
iajs-3044	31	3	can	can	AUX
iajs-3044	31	4	be	be	AUX
iajs-3044	31	5	also	also	ADV
iajs-3044	31	6	generated	generate	VERB
iajs-3044	31	7	in	in	ADP
iajs-3044	31	8	another	another	DET
iajs-3044	31	9	way	way	NOUN
iajs-3044	31	10	depending	depend	VERB
iajs-3044	31	11	on	on	ADP
iajs-3044	31	12	mixed	mix	VERB
iajs-3044	31	13	between	between	ADP
iajs-3044	31	14	the	the	DET
iajs-3044	31	15	cumulative	cumulative	ADJ
iajs-3044	31	16	distribution	distribution	NOUN
iajs-3044	31	17	function	function	NOUN
iajs-3044	31	18	of	of	ADP
iajs-3044	31	19	ihjpas	ihjpas	PROPN
iajs-3044	31	20	.	.	PUNCT
iajs-3044	32	1	36(2)2023	36(2)2023	NUM
iajs-3044	32	2	392	392	NUM
iajs-3044	32	3	exponential	exponential	ADJ
iajs-3044	32	4	distribution	distribution	NOUN
iajs-3044	32	5	as	as	ADP
iajs-3044	32	6	in	in	ADP
iajs-3044	32	7	equation	equation	NOUN
iajs-3044	32	8	(	(	PUNCT
iajs-3044	32	9	2	2	NUM
iajs-3044	32	10	)	)	PUNCT
iajs-3044	32	11	and	and	CCONJ
iajs-3044	32	12	cumulative	cumulative	ADJ
iajs-3044	32	13	distribution	distribution	NOUN
iajs-3044	32	14	function	function	NOUN
iajs-3044	32	15	of	of	ADP
iajs-3044	32	16	rayleigh	rayleigh	PROPN
iajs-3044	32	17	distributions	distribution	NOUN
iajs-3044	32	18	as	as	ADP
iajs-3044	32	19	in	in	ADP
iajs-3044	32	20	equation	equation	NOUN
iajs-3044	32	21	(	(	PUNCT
iajs-3044	32	22	4	4	X
iajs-3044	32	23	)	)	PUNCT
iajs-3044	32	24	using	use	VERB
iajs-3044	32	25	an	an	DET
iajs-3044	32	26	application	application	NOUN
iajs-3044	32	27	(	(	PUNCT
iajs-3044	32	28	maximum	maximum	ADJ
iajs-3044	32	29	)	)	PUNCT
iajs-3044	32	30	as	as	SCONJ
iajs-3044	32	31	follows	follow	VERB
iajs-3044	32	32	:	:	PUNCT
iajs-3044	32	33	let	let	VERB
iajs-3044	32	34	𝑋	𝑋	PROPN
iajs-3044	32	35	=	=	SYM
iajs-3044	32	36	𝑚𝑎𝑥(𝑍	𝑚𝑎𝑥(𝑍	PROPN
iajs-3044	32	37	,	,	PUNCT
iajs-3044	32	38	𝑌	𝑌	PROPN
iajs-3044	32	39	)	)	PUNCT
iajs-3044	32	40	where	where	SCONJ
iajs-3044	32	41	𝑍~𝐸(𝛼	𝑍~𝐸(𝛼	VERB
iajs-3044	32	42	)	)	PUNCT
iajs-3044	32	43	,	,	PUNCT
iajs-3044	32	44	𝑌~𝑅(𝜆	𝑌~𝑅(𝜆	NOUN
iajs-3044	32	45	)	)	PUNCT
iajs-3044	32	46	,	,	PUNCT
iajs-3044	32	47	𝑍	𝑍	NOUN
iajs-3044	32	48	and	and	CCONJ
iajs-3044	32	49	𝑌	𝑌	PROPN
iajs-3044	32	50	are	be	AUX
iajs-3044	32	51	two	two	NUM
iajs-3044	32	52	independent	independent	ADJ
iajs-3044	32	53	random	random	ADJ
iajs-3044	32	54	variables	variable	NOUN
iajs-3044	32	55	then	then	ADV
iajs-3044	32	56	:	:	PUNCT
iajs-3044	32	57	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3044	32	58	;	;	PUNCT
iajs-3044	32	59	𝛼	𝛼	X
iajs-3044	32	60	,	,	PUNCT
iajs-3044	32	61	𝜆	𝜆	X
iajs-3044	32	62	)	)	PUNCT
iajs-3044	33	1	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	33	2	=	=	SYM
iajs-3044	33	3	1	1	NUM
iajs-3044	33	4	−	−	NOUN
iajs-3044	33	5	𝑝𝑟(𝑚𝑎𝑥(𝑍	𝑝𝑟(𝑚𝑎𝑥(𝑍	NOUN
iajs-3044	33	6	,	,	PUNCT
iajs-3044	33	7	𝑌	𝑌	PROPN
iajs-3044	33	8	)	)	PUNCT
iajs-3044	33	9	>	>	X
iajs-3044	34	1	𝑥	𝑥	X
iajs-3044	34	2	)	)	PUNCT
iajs-3044	34	3	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3044	34	4	;	;	PUNCT
iajs-3044	34	5	𝛼	𝛼	X
iajs-3044	34	6	,	,	PUNCT
iajs-3044	34	7	𝜆	𝜆	X
iajs-3044	34	8	)	)	PUNCT
iajs-3044	34	9	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	34	10	=	=	NOUN
iajs-3044	34	11	1	1	NUM
iajs-3044	34	12	−	−	PROPN
iajs-3044	35	1	[	[	X
iajs-3044	35	2	𝑝𝑟(𝑍	𝑝𝑟(𝑍	PROPN
iajs-3044	35	3	>	>	X
iajs-3044	35	4	𝑥	𝑥	PROPN
iajs-3044	35	5	)	)	PUNCT
iajs-3044	35	6	.	.	PUNCT
iajs-3044	36	1	𝑝𝑟(𝑌	𝑝𝑟(𝑌	X
iajs-3044	36	2	>	>	PUNCT
iajs-3044	37	1	𝑥	𝑥	X
iajs-3044	37	2	)	)	PUNCT
iajs-3044	37	3	]	]	PUNCT
iajs-3044	37	4	𝐹(𝑥	𝐹(𝑥	X
iajs-3044	37	5	;	;	PUNCT
iajs-3044	37	6	𝛼	𝛼	X
iajs-3044	37	7	,	,	PUNCT
iajs-3044	37	8	𝜆	𝜆	X
iajs-3044	37	9	)	)	PUNCT
iajs-3044	37	10	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	37	11	=	=	NOUN
iajs-3044	37	12	1	1	NUM
iajs-3044	37	13	−	−	NOUN
iajs-3044	38	1	[	[	X
iajs-3044	38	2	(	(	PUNCT
iajs-3044	38	3	∫	∫	PROPN
iajs-3044	38	4	𝛼	𝛼	PROPN
iajs-3044	38	5	𝑒−𝛼𝑧	𝑒−𝛼𝑧	PROPN
iajs-3044	38	6	𝑑𝑧	𝑑𝑧	NOUN
iajs-3044	38	7	∞	∞	NUM
iajs-3044	38	8	𝑥	𝑥	NOUN
iajs-3044	38	9	)	)	PUNCT
iajs-3044	38	10	.	.	PUNCT
iajs-3044	39	1	(	(	PUNCT
iajs-3044	39	2	∫	∫	PROPN
iajs-3044	39	3	𝜆𝑦	𝜆𝑦	PROPN
iajs-3044	39	4	𝑒−	𝑒−	PROPN
iajs-3044	39	5	𝜆	𝜆	ADP
iajs-3044	39	6	2	2	NUM
iajs-3044	39	7	𝑦2	𝑦2	NOUN
iajs-3044	39	8	𝑑𝑦	𝑑𝑦	ADP
iajs-3044	39	9	∞	∞	PROPN
iajs-3044	39	10	𝑥	𝑥	PROPN
iajs-3044	39	11	)	)	PUNCT
iajs-3044	39	12	]	]	PUNCT
iajs-3044	39	13	𝐹(𝑥	𝐹(𝑥	X
iajs-3044	39	14	;	;	PUNCT
iajs-3044	39	15	𝛼	𝛼	X
iajs-3044	39	16	,	,	PUNCT
iajs-3044	39	17	𝜆	𝜆	X
iajs-3044	39	18	)	)	PUNCT
iajs-3044	39	19	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	39	20	=	=	SYM
iajs-3044	39	21	1	1	NUM
iajs-3044	39	22	−	−	NOUN
iajs-3044	39	23	𝑒−	𝑒−	NOUN
iajs-3044	39	24	(	(	PUNCT
iajs-3044	39	25	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	39	26	+	+	CCONJ
iajs-3044	39	27	𝜆	𝜆	X
iajs-3044	39	28	2	2	NUM
iajs-3044	39	29	𝑥2	𝑥2	NOUN
iajs-3044	39	30	)	)	PUNCT
iajs-3044	39	31	;	;	PUNCT
iajs-3044	39	32	𝑥	𝑥	PRON
iajs-3044	39	33	≥	≥	NOUN
iajs-3044	39	34	0	0	NUM
iajs-3044	39	35	;	;	PUNCT
iajs-3044	39	36	𝛼	𝛼	X
iajs-3044	39	37	,	,	PUNCT
iajs-3044	39	38	𝜆	𝜆	PROPN
iajs-3044	39	39	>	>	X
iajs-3044	39	40	0	0	NUM
iajs-3044	39	41	…	…	PUNCT
iajs-3044	39	42	(	(	PUNCT
iajs-3044	39	43	5	5	NUM
iajs-3044	39	44	)	)	PUNCT
iajs-3044	39	45	figure	figure	NOUN
iajs-3044	39	46	1	1	NUM
iajs-3044	39	47	.	.	PUNCT
iajs-3044	39	48	plot	plot	NOUN
iajs-3044	39	49	of	of	ADP
iajs-3044	39	50	the	the	DET
iajs-3044	39	51	cumulative	cumulative	ADJ
iajs-3044	39	52	distribution	distribution	NOUN
iajs-3044	39	53	function	function	NOUN
iajs-3044	39	54	of	of	ADP
iajs-3044	39	55	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	39	56	distribution	distribution	NOUN
iajs-3044	39	57	for	for	ADP
iajs-3044	39	58	𝜆	𝜆	NOUN
iajs-3044	39	59	=	=	SYM
iajs-3044	39	60	0.1	0.1	NUM
iajs-3044	39	61	and	and	CCONJ
iajs-3044	39	62	different	different	ADJ
iajs-3044	39	63	values	value	NOUN
iajs-3044	39	64	of	of	ADP
iajs-3044	39	65	(	(	PUNCT
iajs-3044	39	66	𝛼	𝛼	X
iajs-3044	39	67	=	=	SYM
iajs-3044	39	68	0.1,0.2,0.3,0.4,0.5	0.1,0.2,0.3,0.4,0.5	NUM
iajs-3044	39	69	,	,	PUNCT
iajs-3044	39	70	0.6	0.6	NUM
iajs-3044	39	71	,	,	PUNCT
iajs-3044	39	72	0.7	0.7	NUM
iajs-3044	39	73	)	)	PUNCT
iajs-3044	39	74	[	[	PUNCT
iajs-3044	39	75	matlab	matlab	PROPN
iajs-3044	39	76	r2013a	r2013a	X
iajs-3044	39	77	]	]	X
iajs-3044	39	78	.	.	PUNCT
iajs-3044	40	1	the	the	DET
iajs-3044	40	2	probability	probability	NOUN
iajs-3044	40	3	density	density	NOUN
iajs-3044	40	4	function	function	NOUN
iajs-3044	40	5	of	of	ADP
iajs-3044	40	6	exponential	exponential	ADJ
iajs-3044	40	7	rayleigh	rayleigh	PROPN
iajs-3044	40	8	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	40	9	distribution	distribution	NOUN
iajs-3044	40	10	is	be	AUX
iajs-3044	40	11	given	give	VERB
iajs-3044	40	12	by	by	ADP
iajs-3044	40	13	:	:	PUNCT
iajs-3044	40	14	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	40	15	;	;	PUNCT
iajs-3044	40	16	𝛼	𝛼	X
iajs-3044	40	17	,	,	PUNCT
iajs-3044	40	18	𝜆	𝜆	X
iajs-3044	40	19	)	)	PUNCT
iajs-3044	40	20	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	40	21	=	=	SYM
iajs-3044	40	22	(	(	PUNCT
iajs-3044	40	23	𝛼	𝛼	NOUN
iajs-3044	40	24	+	+	CCONJ
iajs-3044	40	25	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	40	26	)	)	PUNCT
iajs-3044	40	27	𝑒−	𝑒−	NOUN
iajs-3044	40	28	(	(	PUNCT
iajs-3044	40	29	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	40	30	+	+	CCONJ
iajs-3044	40	31	𝜆	𝜆	X
iajs-3044	40	32	2	2	NUM
iajs-3044	40	33	𝑥2	𝑥2	NOUN
iajs-3044	40	34	)	)	PUNCT
iajs-3044	40	35	;	;	PUNCT
iajs-3044	41	1	𝑥	𝑥	PRON
iajs-3044	41	2	≥	≥	NOUN
iajs-3044	41	3	0	0	NUM
iajs-3044	41	4	;	;	PUNCT
iajs-3044	41	5	𝛼	𝛼	X
iajs-3044	41	6	,	,	PUNCT
iajs-3044	41	7	𝜆	𝜆	PROPN
iajs-3044	41	8	>	>	X
iajs-3044	41	9	0	0	NUM
iajs-3044	41	10	…	…	PUNCT
iajs-3044	41	11	(	(	PUNCT
iajs-3044	41	12	6	6	NUM
iajs-3044	41	13	)	)	PUNCT
iajs-3044	41	14	zero	zero	NUM
iajs-3044	41	15	otherwise	otherwise	ADV
iajs-3044	41	16	.	.	PUNCT
iajs-3044	42	1	where	where	SCONJ
iajs-3044	42	2	𝛼	𝛼	PROPN
iajs-3044	42	3	𝑎nd	𝑎nd	PROPN
iajs-3044	42	4	𝜆	𝜆	NOUN
iajs-3044	42	5	are	be	AUX
iajs-3044	42	6	scale	scale	NOUN
iajs-3044	42	7	parameters	parameter	NOUN
iajs-3044	42	8	.	.	PUNCT
iajs-3044	43	1	such	such	ADJ
iajs-3044	43	2	that	that	DET
iajs-3044	43	3	,	,	PUNCT
iajs-3044	43	4	•	•	NUM
iajs-3044	43	5	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	43	6	;	;	PUNCT
iajs-3044	43	7	𝛼	𝛼	X
iajs-3044	43	8	,	,	PUNCT
iajs-3044	43	9	𝜆	𝜆	X
iajs-3044	43	10	)	)	PUNCT
iajs-3044	43	11	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	43	12	>	>	SYM
iajs-3044	43	13	0	0	NUM
iajs-3044	43	14	•	•	NUM
iajs-3044	43	15	∫	∫	NOUN
iajs-3044	43	16	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	43	17	;	;	PUNCT
iajs-3044	43	18	𝛼	𝛼	X
iajs-3044	43	19	,	,	PUNCT
iajs-3044	43	20	𝜆	𝜆	X
iajs-3044	43	21	)	)	PUNCT
iajs-3044	43	22	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	43	23	∞	∞	NOUN
iajs-3044	43	24	0	0	NUM
iajs-3044	43	25	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	43	26	=	=	SYM
iajs-3044	43	27	∫	∫	PROPN
iajs-3044	43	28	(	(	PUNCT
iajs-3044	43	29	𝛼	𝛼	PROPN
iajs-3044	43	30	+	+	CCONJ
iajs-3044	43	31	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	43	32	)	)	PUNCT
iajs-3044	43	33	𝑒−	𝑒−	NOUN
iajs-3044	43	34	(	(	PUNCT
iajs-3044	43	35	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	43	36	+	+	CCONJ
iajs-3044	43	37	𝜆	𝜆	X
iajs-3044	43	38	2	2	NUM
iajs-3044	43	39	𝑥2	𝑥2	NOUN
iajs-3044	43	40	)	)	PUNCT
iajs-3044	43	41	∞	∞	NOUN
iajs-3044	43	42	0	0	NUM
iajs-3044	43	43	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	43	44	=	=	SYM
iajs-3044	43	45	−	−	PROPN
iajs-3044	43	46	[	[	PUNCT
iajs-3044	43	47	𝑒−	𝑒−	NOUN
iajs-3044	43	48	(	(	PUNCT
iajs-3044	43	49	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	43	50	+	+	CCONJ
iajs-3044	43	51	𝜆	𝜆	X
iajs-3044	43	52	2	2	NUM
iajs-3044	43	53	𝑥2	𝑥2	NOUN
iajs-3044	43	54	)	)	PUNCT
iajs-3044	43	55	]	]	PUNCT
iajs-3044	43	56	0	0	NUM
iajs-3044	44	1	∞	∞	NUM
iajs-3044	44	2	=	=	SYM
iajs-3044	44	3	1	1	NUM
iajs-3044	44	4	figure	figure	NOUN
iajs-3044	44	5	2	2	NUM
iajs-3044	44	6	.	.	PUNCT
iajs-3044	44	7	plot	plot	NOUN
iajs-3044	44	8	of	of	ADP
iajs-3044	44	9	the	the	DET
iajs-3044	44	10	probability	probability	NOUN
iajs-3044	44	11	density	density	NOUN
iajs-3044	44	12	function	function	NOUN
iajs-3044	44	13	of	of	ADP
iajs-3044	44	14	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	44	15	distribution	distribution	NOUN
iajs-3044	44	16	for	for	ADP
iajs-3044	44	17	𝜆	𝜆	NOUN
iajs-3044	44	18	=	=	SYM
iajs-3044	44	19	0.1	0.1	NUM
iajs-3044	44	20	and	and	CCONJ
iajs-3044	44	21	different	different	ADJ
iajs-3044	44	22	values	value	NOUN
iajs-3044	44	23	of	of	ADP
iajs-3044	44	24	(	(	PUNCT
iajs-3044	44	25	𝛼	𝛼	X
iajs-3044	44	26	=	=	NOUN
iajs-3044	44	27	0.1	0.1	NUM
iajs-3044	44	28	,	,	PUNCT
iajs-3044	44	29	0.2	0.2	NUM
iajs-3044	44	30	,	,	PUNCT
iajs-3044	44	31	0.3	0.3	NUM
iajs-3044	44	32	,	,	PUNCT
iajs-3044	44	33	0.4,0.5	0.4,0.5	PROPN
iajs-3044	44	34	,	,	PUNCT
iajs-3044	44	35	0.6	0.6	NUM
iajs-3044	44	36	,	,	PUNCT
iajs-3044	44	37	0.7	0.7	NUM
iajs-3044	44	38	)	)	PUNCT
iajs-3044	45	1	[	[	X
iajs-3044	45	2	matlabr2013a	matlabr2013a	NOUN
iajs-3044	45	3	]	]	PUNCT
iajs-3044	45	4	.	.	PUNCT
iajs-3044	46	1	ihjpas	ihjpas	PROPN
iajs-3044	46	2	.	.	PUNCT
iajs-3044	47	1	36(2)2023	36(2)2023	NUM
iajs-3044	47	2	393	393	NUM
iajs-3044	47	3	•	•	NOUN
iajs-3044	47	4	the	the	DET
iajs-3044	47	5	survival	survival	NOUN
iajs-3044	47	6	function	function	NOUN
iajs-3044	47	7	is	be	AUX
iajs-3044	47	8	given	give	VERB
iajs-3044	47	9	by	by	ADP
iajs-3044	47	10	:	:	PUNCT
iajs-3044	47	11	𝑆(𝑡	𝑆(𝑡	ADJ
iajs-3044	47	12	;	;	PUNCT
iajs-3044	47	13	𝛼	𝛼	X
iajs-3044	47	14	,	,	PUNCT
iajs-3044	47	15	𝜆	𝜆	X
iajs-3044	47	16	)	)	PUNCT
iajs-3044	47	17	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	47	18	=	=	SYM
iajs-3044	47	19	𝑒−	𝑒−	NOUN
iajs-3044	47	20	(	(	PUNCT
iajs-3044	47	21	𝛼𝑡	𝛼𝑡	ADP
iajs-3044	47	22	+	+	NOUN
iajs-3044	47	23	𝜆	𝜆	DET
iajs-3044	47	24	2	2	NUM
iajs-3044	47	25	𝑡2	𝑡2	NOUN
iajs-3044	47	26	)	)	PUNCT
iajs-3044	47	27	;	;	PUNCT
iajs-3044	47	28	𝑡	𝑡	X
iajs-3044	47	29	≥	≥	NOUN
iajs-3044	47	30	0	0	NUM
iajs-3044	47	31	;	;	PUNCT
iajs-3044	47	32	𝛼	𝛼	X
iajs-3044	47	33	,	,	PUNCT
iajs-3044	47	34	𝜆	𝜆	PROPN
iajs-3044	47	35	>	>	X
iajs-3044	47	36	0	0	NUM
iajs-3044	47	37	…	…	PUNCT
iajs-3044	47	38	(	(	PUNCT
iajs-3044	47	39	7	7	X
iajs-3044	47	40	)	)	PUNCT
iajs-3044	47	41	figure	figure	NOUN
iajs-3044	47	42	3	3	NUM
iajs-3044	47	43	.	.	PUNCT
iajs-3044	47	44	plot	plot	NOUN
iajs-3044	47	45	of	of	ADP
iajs-3044	47	46	the	the	DET
iajs-3044	47	47	survival	survival	NOUN
iajs-3044	47	48	function	function	NOUN
iajs-3044	47	49	of	of	ADP
iajs-3044	47	50	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	47	51	distribution	distribution	NOUN
iajs-3044	47	52	for	for	ADP
iajs-3044	47	53	𝜆	𝜆	NOUN
iajs-3044	47	54	=	=	SYM
iajs-3044	47	55	0.1	0.1	NUM
iajs-3044	47	56	and	and	CCONJ
iajs-3044	47	57	different	different	ADJ
iajs-3044	47	58	values	value	NOUN
iajs-3044	47	59	of	of	ADP
iajs-3044	47	60	(	(	PUNCT
iajs-3044	47	61	𝛼	𝛼	X
iajs-3044	47	62	=	=	NOUN
iajs-3044	47	63	0.1	0.1	NUM
iajs-3044	47	64	,	,	PUNCT
iajs-3044	47	65	0.2	0.2	NUM
iajs-3044	47	66	,	,	PUNCT
iajs-3044	47	67	0.3	0.3	NUM
iajs-3044	47	68	,	,	PUNCT
iajs-3044	47	69	0.4	0.4	NUM
iajs-3044	47	70	,	,	PUNCT
iajs-3044	47	71	0.5	0.5	NUM
iajs-3044	47	72	,	,	PUNCT
iajs-3044	47	73	0.6	0.6	NUM
iajs-3044	47	74	,	,	PUNCT
iajs-3044	47	75	0.7	0.7	NUM
iajs-3044	47	76	)	)	PUNCT
iajs-3044	47	77	[	[	PUNCT
iajs-3044	47	78	matlab	matlab	X
iajs-3044	47	79	r2013a	r2013a	X
iajs-3044	47	80	]	]	X
iajs-3044	47	81	.	.	PUNCT
iajs-3044	48	1	the	the	DET
iajs-3044	48	2	hazard	hazard	NOUN
iajs-3044	48	3	rate	rate	NOUN
iajs-3044	48	4	function	function	NOUN
iajs-3044	48	5	is	be	AUX
iajs-3044	48	6	obtained	obtain	VERB
iajs-3044	48	7	by	by	ADP
iajs-3044	48	8	:	:	PUNCT
iajs-3044	48	9	ℎ(𝑡	ℎ(𝑡	PROPN
iajs-3044	48	10	;	;	PUNCT
iajs-3044	48	11	𝛼	𝛼	X
iajs-3044	48	12	,	,	PUNCT
iajs-3044	48	13	𝜆	𝜆	X
iajs-3044	48	14	)	)	PUNCT
iajs-3044	48	15	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	48	16	=	=	SYM
iajs-3044	48	17	𝛼	𝛼	PROPN
iajs-3044	49	1	+	+	NOUN
iajs-3044	49	2	𝜆𝑡	𝜆𝑡	NUM
iajs-3044	49	3	;	;	PUNCT
iajs-3044	49	4	𝑡	𝑡	X
iajs-3044	49	5	≥	≥	NOUN
iajs-3044	49	6	0	0	NUM
iajs-3044	49	7	;	;	PUNCT
iajs-3044	49	8	𝛼	𝛼	X
iajs-3044	49	9	,	,	PUNCT
iajs-3044	49	10	𝜆	𝜆	PROPN
iajs-3044	49	11	>	>	X
iajs-3044	49	12	0	0	NUM
iajs-3044	49	13	…	…	PUNCT
iajs-3044	49	14	(	(	PUNCT
iajs-3044	49	15	8)	8)	NUM
iajs-3044	49	16	figure	figure	NOUN
iajs-3044	49	17	4	4	NUM
iajs-3044	49	18	.	.	PUNCT
iajs-3044	49	19	plot	plot	NOUN
iajs-3044	49	20	of	of	ADP
iajs-3044	49	21	hazard	hazard	NOUN
iajs-3044	49	22	rate	rate	NOUN
iajs-3044	49	23	function	function	NOUN
iajs-3044	49	24	of	of	ADP
iajs-3044	49	25	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	49	26	distribution	distribution	NOUN
iajs-3044	49	27	for	for	ADP
iajs-3044	49	28	𝜆	𝜆	NOUN
iajs-3044	49	29	=	=	SYM
iajs-3044	49	30	0.1	0.1	NUM
iajs-3044	49	31	and	and	CCONJ
iajs-3044	49	32	different	different	ADJ
iajs-3044	49	33	values	value	NOUN
iajs-3044	49	34	of	of	ADP
iajs-3044	49	35	(	(	PUNCT
iajs-3044	49	36	𝛼	𝛼	X
iajs-3044	49	37	=	=	NOUN
iajs-3044	49	38	0.1	0.1	NUM
iajs-3044	49	39	,	,	PUNCT
iajs-3044	49	40	0.2	0.2	NUM
iajs-3044	49	41	,	,	PUNCT
iajs-3044	49	42	0.3	0.3	NUM
iajs-3044	49	43	,	,	PUNCT
iajs-3044	49	44	0.4	0.4	NUM
iajs-3044	49	45	,	,	PUNCT
iajs-3044	49	46	0.5	0.5	NUM
iajs-3044	49	47	,	,	PUNCT
iajs-3044	49	48	0.6	0.6	NUM
iajs-3044	49	49	,	,	PUNCT
iajs-3044	49	50	0.7	0.7	NUM
iajs-3044	49	51	)	)	PUNCT
iajs-3044	49	52	[	[	PUNCT
iajs-3044	49	53	matlab	matlab	X
iajs-3044	49	54	r2013a	r2013a	X
iajs-3044	49	55	]	]	X
iajs-3044	49	56	.	.	PUNCT
iajs-3044	50	1	the	the	DET
iajs-3044	50	2	reverse	reverse	ADJ
iajs-3044	50	3	hazard	hazard	NOUN
iajs-3044	50	4	rate	rate	NOUN
iajs-3044	50	5	function	function	NOUN
iajs-3044	50	6	is	be	AUX
iajs-3044	50	7	given	give	VERB
iajs-3044	50	8	by	by	ADP
iajs-3044	50	9	:	:	PUNCT
iajs-3044	50	10	∅(𝑡	∅(𝑡	NOUN
iajs-3044	50	11	;	;	PUNCT
iajs-3044	50	12	𝛼	𝛼	X
iajs-3044	50	13	,	,	PUNCT
iajs-3044	50	14	𝜆)𝐸𝑅	𝜆)𝐸𝑅	PUNCT
iajs-3044	50	15	=	=	PUNCT
iajs-3044	50	16	(	(	PUNCT
iajs-3044	50	17	𝛼+𝜆𝑡	𝛼+𝜆𝑡	NOUN
iajs-3044	50	18	)	)	PUNCT
iajs-3044	50	19	𝑒	𝑒	PROPN
iajs-3044	50	20	−	−	PROPN
iajs-3044	50	21	(	(	PUNCT
iajs-3044	50	22	𝛼𝑡	𝛼𝑡	PROPN
iajs-3044	50	23	+	+	NOUN
iajs-3044	50	24	𝜆	𝜆	DET
iajs-3044	50	25	2	2	NUM
iajs-3044	50	26	𝑡2	𝑡2	NOUN
iajs-3044	50	27	)	)	PUNCT
iajs-3044	50	28	1−	1−	NUM
iajs-3044	50	29	𝑒	𝑒	PROPN
iajs-3044	50	30	−	−	PROPN
iajs-3044	50	31	(	(	PUNCT
iajs-3044	50	32	𝛼𝑡	𝛼𝑡	PROPN
iajs-3044	50	33	+	+	NOUN
iajs-3044	50	34	𝜆	𝜆	DET
iajs-3044	50	35	2	2	NUM
iajs-3044	50	36	𝑡2	𝑡2	NOUN
iajs-3044	50	37	)	)	PUNCT
iajs-3044	50	38	;	;	PUNCT
iajs-3044	50	39	𝑡	𝑡	X
iajs-3044	50	40	≥	≥	NOUN
iajs-3044	50	41	0	0	NUM
iajs-3044	50	42	;	;	PUNCT
iajs-3044	50	43	𝛼	𝛼	X
iajs-3044	50	44	,	,	PUNCT
iajs-3044	50	45	𝜆	𝜆	PROPN
iajs-3044	50	46	>	>	X
iajs-3044	50	47	0	0	NUM
iajs-3044	50	48	…	…	PUNCT
iajs-3044	50	49	(	(	PUNCT
iajs-3044	50	50	9	9	X
iajs-3044	50	51	)	)	PUNCT
iajs-3044	50	52	figure	figure	NOUN
iajs-3044	50	53	5	5	NUM
iajs-3044	50	54	.	.	PUNCT
iajs-3044	50	55	plot	plot	NOUN
iajs-3044	50	56	of	of	ADP
iajs-3044	50	57	the	the	DET
iajs-3044	50	58	reverse	reverse	ADJ
iajs-3044	50	59	hazard	hazard	NOUN
iajs-3044	50	60	rate	rate	NOUN
iajs-3044	50	61	function	function	NOUN
iajs-3044	50	62	of	of	ADP
iajs-3044	50	63	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	50	64	distribution	distribution	NOUN
iajs-3044	50	65	for	for	ADP
iajs-3044	50	66	𝜆	𝜆	DET
iajs-3044	50	67	=	=	SYM
iajs-3044	50	68	0.1and	0.1and	NUM
iajs-3044	50	69	different	different	ADJ
iajs-3044	50	70	values	value	NOUN
iajs-3044	50	71	of	of	ADP
iajs-3044	50	72	(	(	PUNCT
iajs-3044	50	73	𝛼	𝛼	X
iajs-3044	50	74	=	=	NOUN
iajs-3044	50	75	0.1	0.1	NUM
iajs-3044	50	76	,	,	PUNCT
iajs-3044	50	77	0.2	0.2	NUM
iajs-3044	50	78	,	,	PUNCT
iajs-3044	50	79	0.3	0.3	NUM
iajs-3044	50	80	,	,	PUNCT
iajs-3044	50	81	0.4,0.5	0.4,0.5	PROPN
iajs-3044	50	82	,	,	PUNCT
iajs-3044	50	83	0.6	0.6	NUM
iajs-3044	50	84	,	,	PUNCT
iajs-3044	50	85	0.7	0.7	NUM
iajs-3044	50	86	)	)	PUNCT
iajs-3044	50	87	[	[	PUNCT
iajs-3044	50	88	matlab	matlab	X
iajs-3044	50	89	r2013a	r2013a	X
iajs-3044	50	90	]	]	X
iajs-3044	50	91	.	.	PUNCT
iajs-3044	51	1	2.1	2.1	NUM
iajs-3044	51	2	some	some	DET
iajs-3044	51	3	statistical	statistical	ADJ
iajs-3044	51	4	properties	property	NOUN
iajs-3044	51	5	of	of	ADP
iajs-3044	51	6	𝑬𝑹	𝑬𝑹	PROPN
iajs-3044	51	7	distribution	distribution	NOUN
iajs-3044	51	8	2.1.1	2.1.1	NOUN
iajs-3044	51	9	the	the	DET
iajs-3044	51	10	mode	mode	NOUN
iajs-3044	51	11	we	we	PRON
iajs-3044	51	12	can	can	AUX
iajs-3044	51	13	give	give	VERB
iajs-3044	51	14	the	the	DET
iajs-3044	51	15	mode	mode	NOUN
iajs-3044	51	16	of	of	ADP
iajs-3044	51	17	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	51	18	distribution	distribution	NOUN
iajs-3044	51	19	as	as	SCONJ
iajs-3044	51	20	follows	follow	VERB
iajs-3044	51	21	:	:	PUNCT
iajs-3044	51	22	t	t	PROPN
iajs-3044	51	23	t	t	PROPN
iajs-3044	51	24	t	t	NOUN
iajs-3044	51	25	h	h	NOUN
iajs-3044	52	1	e	e	X
iajs-3044	52	2	s	s	PROPN
iajs-3044	52	3	u	u	X
iajs-3044	52	4	rv	rv	NOUN
iajs-3044	52	5	iv	iv	NUM
iajs-3044	52	6	al	al	PROPN
iajs-3044	52	7	f	f	PROPN
iajs-3044	52	8	u	u	PROPN
iajs-3044	52	9	n	n	PROPN
iajs-3044	52	10	ct	ct	PROPN
iajs-3044	52	11	io	io	PROPN
iajs-3044	52	12	n	n	PRON
iajs-3044	52	13	ihjpas	ihjpa	VERB
iajs-3044	52	14	.	.	PUNCT
iajs-3044	53	1	36(2)2023	36(2)2023	NUM
iajs-3044	53	2	394	394	NUM
iajs-3044	53	3	𝜕𝑓(𝑥	𝜕𝑓(𝑥	NOUN
iajs-3044	53	4	;	;	PUNCT
iajs-3044	53	5	𝛼	𝛼	X
iajs-3044	53	6	,	,	PUNCT
iajs-3044	53	7	𝜆)𝐸𝑅	𝜆)𝐸𝑅	NUM
iajs-3044	53	8	𝜕𝑥	𝜕𝑥	X
iajs-3044	53	9	=	=	SYM
iajs-3044	53	10	−	−	PROPN
iajs-3044	53	11	(	(	PUNCT
iajs-3044	53	12	𝛼	𝛼	X
iajs-3044	53	13	+	+	X
iajs-3044	53	14	𝜆𝑥)2	𝜆𝑥)2	PROPN
iajs-3044	53	15	𝑒	𝑒	PROPN
iajs-3044	53	16	−	−	PROPN
iajs-3044	53	17	(	(	PUNCT
iajs-3044	53	18	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	53	19	+	+	CCONJ
iajs-3044	53	20	𝜆	𝜆	X
iajs-3044	53	21	2	2	NUM
iajs-3044	53	22	𝑥2	𝑥2	NOUN
iajs-3044	53	23	)	)	PUNCT
iajs-3044	54	1	+	+	CCONJ
iajs-3044	54	2	𝜆	𝜆	ADP
iajs-3044	54	3	𝑒	𝑒	PROPN
iajs-3044	54	4	−	−	PROPN
iajs-3044	54	5	(	(	PUNCT
iajs-3044	54	6	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	54	7	+	+	CCONJ
iajs-3044	54	8	𝜆	𝜆	X
iajs-3044	54	9	2	2	NUM
iajs-3044	54	10	𝑥2	𝑥2	NOUN
iajs-3044	54	11	)	)	PUNCT
iajs-3044	55	1	[	[	X
iajs-3044	55	2	−	−	X
iajs-3044	55	3	(	(	PUNCT
iajs-3044	55	4	𝛼	𝛼	X
iajs-3044	55	5	+	+	X
iajs-3044	55	6	𝜆𝑥)2	𝜆𝑥)2	PROPN
iajs-3044	55	7	+	+	CCONJ
iajs-3044	55	8	𝜆	𝜆	X
iajs-3044	55	9	]	]	X
iajs-3044	55	10	𝑒−	𝑒−	NOUN
iajs-3044	55	11	(	(	PUNCT
iajs-3044	55	12	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	55	13	+	+	CCONJ
iajs-3044	55	14	𝜆	𝜆	X
iajs-3044	55	15	2	2	NUM
iajs-3044	55	16	𝑥2	𝑥2	NOUN
iajs-3044	55	17	)	)	PUNCT
iajs-3044	55	18	=	=	SYM
iajs-3044	55	19	0	0	NUM
iajs-3044	55	20	…	…	PUNCT
iajs-3044	55	21	(	(	PUNCT
iajs-3044	55	22	10	10	NUM
iajs-3044	55	23	)	)	PUNCT
iajs-3044	55	24	it	it	PRON
iajs-3044	55	25	is	be	AUX
iajs-3044	55	26	clear	clear	ADJ
iajs-3044	55	27	that	that	SCONJ
iajs-3044	55	28	𝜕𝑓(𝑥;𝛼,𝜆)𝐸𝑅	𝜕𝑓(𝑥;𝛼,𝜆)𝐸𝑅	ADV
iajs-3044	55	29	𝜕𝑥	𝜕𝑥	X
iajs-3044	55	30	=	=	PUNCT
iajs-3044	56	1	[	[	PUNCT
iajs-3044	56	2	−	−	X
iajs-3044	56	3	{	{	PUNCT
iajs-3044	56	4	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3044	56	5	;	;	PUNCT
iajs-3044	56	6	𝛼	𝛼	X
iajs-3044	56	7	,	,	PUNCT
iajs-3044	56	8	𝜆)𝐸𝑅}2	𝜆)𝐸𝑅}2	X
iajs-3044	56	9	+	+	CCONJ
iajs-3044	56	10	ℎ′(𝑥	ℎ′(𝑥	X
iajs-3044	56	11	;	;	PUNCT
iajs-3044	56	12	𝛼	𝛼	X
iajs-3044	56	13	,	,	PUNCT
iajs-3044	56	14	𝜆)𝐸𝑅	𝜆)𝐸𝑅	SYM
iajs-3044	56	15	]	]	X
iajs-3044	56	16	𝑆(𝑥	𝑆(𝑥	X
iajs-3044	56	17	;	;	PUNCT
iajs-3044	56	18	𝛼	𝛼	X
iajs-3044	56	19	,	,	PUNCT
iajs-3044	56	20	𝜆)𝐸𝑅	𝜆)𝐸𝑅	PRON
iajs-3044	56	21	,	,	PUNCT
iajs-3044	56	22	where	where	SCONJ
iajs-3044	56	23	ℎ(𝑥	ℎ(𝑥	NOUN
iajs-3044	56	24	;	;	PUNCT
iajs-3044	56	25	𝛼	𝛼	X
iajs-3044	56	26	,	,	PUNCT
iajs-3044	56	27	𝜆)𝐸𝑅	𝜆)𝐸𝑅	NUM
iajs-3044	56	28	is	be	AUX
iajs-3044	56	29	the	the	DET
iajs-3044	56	30	hazard	hazard	NOUN
iajs-3044	56	31	rate	rate	NOUN
iajs-3044	56	32	function	function	NOUN
iajs-3044	56	33	given	give	VERB
iajs-3044	56	34	in	in	ADP
iajs-3044	56	35	equation	equation	NOUN
iajs-3044	56	36	(	(	PUNCT
iajs-3044	56	37	8)	8)	NUM
iajs-3044	56	38	,	,	PUNCT
iajs-3044	56	39	and	and	CCONJ
iajs-3044	56	40	𝑆(𝑥	𝑆(𝑥	NUM
iajs-3044	56	41	;	;	PUNCT
iajs-3044	56	42	𝛼	𝛼	X
iajs-3044	56	43	,	,	PUNCT
iajs-3044	56	44	𝜆)𝐸𝑅	𝜆)𝐸𝑅	PUNCT
iajs-3044	56	45	is	be	AUX
iajs-3044	56	46	the	the	DET
iajs-3044	56	47	survival	survival	NOUN
iajs-3044	56	48	function	function	NOUN
iajs-3044	56	49	was	be	AUX
iajs-3044	56	50	given	give	VERB
iajs-3044	56	51	in	in	ADP
iajs-3044	56	52	equation	equation	NOUN
iajs-3044	56	53	(	(	PUNCT
iajs-3044	56	54	7	7	NUM
iajs-3044	56	55	)	)	PUNCT
iajs-3044	56	56	.	.	PUNCT
iajs-3044	57	1	since	since	SCONJ
iajs-3044	57	2	𝑆(𝑥	𝑆(𝑥	NUM
iajs-3044	57	3	;	;	PUNCT
iajs-3044	57	4	𝛼	𝛼	X
iajs-3044	57	5	,	,	PUNCT
iajs-3044	57	6	𝜆)𝐸𝑅	𝜆)𝐸𝑅	PUNCT
iajs-3044	57	7	≠	≠	PROPN
iajs-3044	57	8	0	0	NUM
iajs-3044	57	9	.	.	PUNCT
iajs-3044	58	1	thus	thus	ADV
iajs-3044	58	2	dividing	divide	VERB
iajs-3044	58	3	the	the	DET
iajs-3044	58	4	equation	equation	NOUN
iajs-3044	58	5	(	(	PUNCT
iajs-3044	58	6	10	10	NUM
iajs-3044	58	7	)	)	PUNCT
iajs-3044	58	8	by	by	ADP
iajs-3044	58	9	𝑆(𝑥	𝑆(𝑥	SYM
iajs-3044	58	10	;	;	PUNCT
iajs-3044	58	11	𝛼	𝛼	X
iajs-3044	58	12	,	,	PUNCT
iajs-3044	58	13	𝜆)𝐸𝑅	𝜆)𝐸𝑅	NUM
iajs-3044	58	14	,	,	PUNCT
iajs-3044	58	15	we	we	PRON
iajs-3044	58	16	get	get	VERB
iajs-3044	58	17	:	:	PUNCT
iajs-3044	58	18	𝜆2𝑥2	𝜆2𝑥2	X
iajs-3044	58	19	+	+	CCONJ
iajs-3044	58	20	2	2	NUM
iajs-3044	58	21	𝜆𝛼𝑥	𝜆𝛼𝑥	NOUN
iajs-3044	58	22	+	+	CCONJ
iajs-3044	58	23	(	(	PUNCT
iajs-3044	58	24	𝛼2	𝛼2	VERB
iajs-3044	58	25	−	−	PROPN
iajs-3044	58	26	𝜆	𝜆	NOUN
iajs-3044	58	27	)	)	PUNCT
iajs-3044	58	28	=	=	SYM
iajs-3044	58	29	0	0	NUM
iajs-3044	58	30	based	base	VERB
iajs-3044	58	31	on	on	ADP
iajs-3044	58	32	the	the	DET
iajs-3044	58	33	law	law	NOUN
iajs-3044	58	34	of	of	ADP
iajs-3044	58	35	the	the	DET
iajs-3044	58	36	constitution	constitution	NOUN
iajs-3044	58	37	,	,	PUNCT
iajs-3044	58	38	we	we	PRON
iajs-3044	58	39	get	get	VERB
iajs-3044	58	40	:	:	PUNCT
iajs-3044	58	41	𝑥	𝑥	X
iajs-3044	58	42	=	=	SYM
iajs-3044	58	43	−(2	−(2	PROPN
iajs-3044	58	44	𝜆𝛼	𝜆𝛼	PROPN
iajs-3044	58	45	)	)	PUNCT
iajs-3044	58	46	∓	∓	PROPN
iajs-3044	59	1	√(2	√(2	PRON
iajs-3044	59	2	𝜆𝛼)2−	𝜆𝛼)2−	PROPN
iajs-3044	59	3	4	4	NUM
iajs-3044	59	4	𝜆2(𝛼2−𝜆	𝜆2(𝛼2−𝜆	ADJ
iajs-3044	59	5	)	)	PUNCT
iajs-3044	59	6	2𝜆2	2𝜆2	NUM
iajs-3044	59	7	…	…	PUNCT
iajs-3044	59	8	(	(	PUNCT
iajs-3044	59	9	11	11	NUM
iajs-3044	59	10	)	)	PUNCT
iajs-3044	59	11	since	since	SCONJ
iajs-3044	59	12	𝑥	𝑥	PROPN
iajs-3044	59	13	>	>	X
iajs-3044	59	14	0	0	PROPN
iajs-3044	59	15	,	,	PUNCT
iajs-3044	59	16	the	the	DET
iajs-3044	59	17	negative	negative	ADJ
iajs-3044	59	18	value	value	NOUN
iajs-3044	59	19	of	of	ADP
iajs-3044	59	20	𝑥	𝑥	PROPN
iajs-3044	59	21	is	be	AUX
iajs-3044	59	22	ignored	ignore	VERB
iajs-3044	59	23	.	.	PUNCT
iajs-3044	60	1	suppose	suppose	VERB
iajs-3044	60	2	that	that	SCONJ
iajs-3044	60	3	𝑥	𝑥	PROPN
iajs-3044	60	4	=	=	SYM
iajs-3044	60	5	𝑥0	𝑥0	NOUN
iajs-3044	60	6	that	that	PRON
iajs-3044	60	7	is	be	AUX
iajs-3044	60	8	a	a	DET
iajs-3044	60	9	root	root	NOUN
iajs-3044	60	10	of	of	ADP
iajs-3044	60	11	equation	equation	NOUN
iajs-3044	60	12	(	(	PUNCT
iajs-3044	60	13	11	11	NUM
iajs-3044	60	14	)	)	PUNCT
iajs-3044	60	15	.	.	PUNCT
iajs-3044	61	1	this	this	DET
iajs-3044	61	2	root	root	NOUN
iajs-3044	61	3	based	base	VERB
iajs-3044	61	4	on	on	ADP
iajs-3044	61	5	the	the	DET
iajs-3044	61	6	second	second	ADJ
iajs-3044	61	7	derivative	derivative	NOUN
iajs-3044	61	8	of	of	ADP
iajs-3044	61	9	the	the	DET
iajs-3044	61	10	equation	equation	NOUN
iajs-3044	61	11	:	:	PUNCT
iajs-3044	61	12	if	if	SCONJ
iajs-3044	61	13	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	VERB
iajs-3044	61	14	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	61	15	⃒𝑥=𝑥0	⃒𝑥=𝑥0	X
iajs-3044	61	16	<	<	X
iajs-3044	61	17	0	0	X
iajs-3044	62	1	the	the	DET
iajs-3044	62	2	root	root	NOUN
iajs-3044	62	3	is	be	AUX
iajs-3044	62	4	the	the	DET
iajs-3044	62	5	local	local	ADJ
iajs-3044	62	6	maximum	maximum	NOUN
iajs-3044	62	7	.	.	PUNCT
iajs-3044	63	1	if	if	SCONJ
iajs-3044	63	2	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	VERB
iajs-3044	63	3	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	63	4	⃒𝑥=𝑥0	⃒𝑥=𝑥0	X
iajs-3044	63	5	>	>	X
iajs-3044	63	6	0	0	NUM
iajs-3044	64	1	the	the	DET
iajs-3044	64	2	root	root	NOUN
iajs-3044	64	3	is	be	AUX
iajs-3044	64	4	the	the	DET
iajs-3044	64	5	local	local	ADJ
iajs-3044	64	6	minimum	minimum	NOUN
iajs-3044	64	7	.	.	PUNCT
iajs-3044	65	1	if	if	SCONJ
iajs-3044	65	2	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆)𝐸𝑅	VERB
iajs-3044	65	3	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	65	4	⃒𝑥=𝑥0	⃒𝑥=𝑥0	PROPN
iajs-3044	65	5	=	=	SYM
iajs-3044	65	6	0	0	PROPN
iajs-3044	65	7	the	the	DET
iajs-3044	65	8	point	point	NOUN
iajs-3044	65	9	is	be	AUX
iajs-3044	65	10	inflection	inflection	NOUN
iajs-3044	65	11	.	.	PUNCT
iajs-3044	66	1	2.1.2	2.1.2	NUM
iajs-3044	66	2	the	the	DET
iajs-3044	66	3	median	median	NOUN
iajs-3044	66	4	the	the	DET
iajs-3044	66	5	median	median	NOUN
iajs-3044	66	6	of	of	ADP
iajs-3044	66	7	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	66	8	distribution	distribution	NOUN
iajs-3044	66	9	is	be	AUX
iajs-3044	66	10	given	give	VERB
iajs-3044	66	11	by	by	ADP
iajs-3044	66	12	:	:	PUNCT
iajs-3044	66	13	1	1	NUM
iajs-3044	66	14	−	−	NOUN
iajs-3044	66	15	𝑒	𝑒	PROPN
iajs-3044	66	16	−	−	PROPN
iajs-3044	66	17	(	(	PUNCT
iajs-3044	66	18	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	66	19	+	+	CCONJ
iajs-3044	66	20	𝜆	𝜆	X
iajs-3044	66	21	2	2	NUM
iajs-3044	66	22	𝑥2	𝑥2	NOUN
iajs-3044	66	23	)	)	PUNCT
iajs-3044	66	24	=	=	SYM
iajs-3044	66	25	1	1	NUM
iajs-3044	66	26	2	2	NUM
iajs-3044	66	27	𝜆	𝜆	DET
iajs-3044	66	28	𝑥2	𝑥2	NOUN
iajs-3044	66	29	+	+	CCONJ
iajs-3044	66	30	2	2	NUM
iajs-3044	66	31	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	66	32	−	−	NUM
iajs-3044	66	33	2	2	NUM
iajs-3044	66	34	ln	ln	NOUN
iajs-3044	66	35	2	2	NUM
iajs-3044	66	36	=	=	SYM
iajs-3044	66	37	0	0	NUM
iajs-3044	66	38	based	base	VERB
iajs-3044	66	39	on	on	ADP
iajs-3044	66	40	the	the	DET
iajs-3044	66	41	law	law	NOUN
iajs-3044	66	42	of	of	ADP
iajs-3044	66	43	the	the	DET
iajs-3044	66	44	constitution	constitution	NOUN
iajs-3044	66	45	,	,	PUNCT
iajs-3044	66	46	we	we	PRON
iajs-3044	66	47	get	get	VERB
iajs-3044	66	48	:	:	PUNCT
iajs-3044	66	49	𝑥	𝑥	PROPN
iajs-3044	66	50	=	=	SYM
iajs-3044	66	51	−(2𝛼	−(2𝛼	PROPN
iajs-3044	66	52	)	)	PUNCT
iajs-3044	67	1	∓	∓	PROPN
iajs-3044	68	1	√4𝛼2	√4𝛼2	PROPN
iajs-3044	68	2	+	+	ADP
iajs-3044	68	3	8	8	NUM
iajs-3044	68	4	𝜆	𝜆	NOUN
iajs-3044	68	5	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	68	6	2	2	NUM
iajs-3044	68	7	2	2	NUM
iajs-3044	68	8	𝜆	𝜆	PRON
iajs-3044	68	9	…	…	PUNCT
iajs-3044	68	10	(	(	PUNCT
iajs-3044	68	11	12	12	NUM
iajs-3044	68	12	)	)	PUNCT
iajs-3044	68	13	since	since	SCONJ
iajs-3044	68	14	𝑥	𝑥	PROPN
iajs-3044	68	15	>	>	X
iajs-3044	68	16	0	0	PROPN
iajs-3044	68	17	,	,	PUNCT
iajs-3044	68	18	the	the	DET
iajs-3044	68	19	negative	negative	ADJ
iajs-3044	68	20	value	value	NOUN
iajs-3044	68	21	of	of	ADP
iajs-3044	68	22	𝑥	𝑥	NOUN
iajs-3044	68	23	will	will	AUX
iajs-3044	68	24	be	be	AUX
iajs-3044	68	25	ignored	ignore	VERB
iajs-3044	68	26	.	.	PUNCT
iajs-3044	69	1	2.1.3	2.1.3	NUM
iajs-3044	69	2	the	the	DET
iajs-3044	69	3	moment	moment	NOUN
iajs-3044	69	4	about	about	ADP
iajs-3044	69	5	the	the	DET
iajs-3044	69	6	origin	origin	NOUN
iajs-3044	69	7	the	the	DET
iajs-3044	69	8	𝑟𝑡ℎ	𝑟𝑡ℎ	NOUN
iajs-3044	69	9	moment	moment	NOUN
iajs-3044	69	10	about	about	ADP
iajs-3044	69	11	the	the	DET
iajs-3044	69	12	origin	origin	NOUN
iajs-3044	69	13	can	can	AUX
iajs-3044	69	14	be	be	AUX
iajs-3044	69	15	obtained	obtain	VERB
iajs-3044	69	16	by	by	ADP
iajs-3044	69	17	:	:	PUNCT
iajs-3044	69	18	𝐸(𝑋𝑟)𝐸𝑅	𝐸(𝑋𝑟)𝐸𝑅	PUNCT
iajs-3044	69	19	=	=	SYM
iajs-3044	69	20	∫	∫	X
iajs-3044	69	21	𝑥𝑟(𝛼	𝑥𝑟(𝛼	X
iajs-3044	69	22	+	+	SYM
iajs-3044	69	23	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	69	24	)	)	PUNCT
iajs-3044	69	25	𝑒−	𝑒−	NOUN
iajs-3044	69	26	(	(	PUNCT
iajs-3044	69	27	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	69	28	+	+	CCONJ
iajs-3044	69	29	𝜆	𝜆	X
iajs-3044	69	30	2	2	NUM
iajs-3044	69	31	𝑥2	𝑥2	NOUN
iajs-3044	69	32	)	)	PUNCT
iajs-3044	69	33	∞	∞	NOUN
iajs-3044	69	34	0	0	NUM
iajs-3044	69	35	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	69	36	…	…	PUNCT
iajs-3044	69	37	(	(	PUNCT
iajs-3044	69	38	13	13	NUM
iajs-3044	69	39	)	)	PUNCT
iajs-3044	69	40	let	let	VERB
iajs-3044	69	41	𝐾(𝑟	𝐾(𝑟	NUM
iajs-3044	69	42	,	,	PUNCT
iajs-3044	69	43	𝛼	𝛼	NOUN
iajs-3044	69	44	,	,	PUNCT
iajs-3044	69	45	𝜆	𝜆	X
iajs-3044	69	46	)	)	PUNCT
iajs-3044	70	1	=	=	SYM
iajs-3044	70	2	𝑥𝑟	𝑥𝑟	NOUN
iajs-3044	70	3	𝑒−	𝑒−	NOUN
iajs-3044	70	4	(	(	PUNCT
iajs-3044	70	5	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	70	6	+	+	CCONJ
iajs-3044	70	7	𝜆	𝜆	X
iajs-3044	70	8	2	2	NUM
iajs-3044	70	9	𝑥2	𝑥2	NOUN
iajs-3044	70	10	)	)	PUNCT
iajs-3044	70	11	…	…	PUNCT
iajs-3044	70	12	(	(	PUNCT
iajs-3044	70	13	14	14	NUM
iajs-3044	70	14	)	)	PUNCT
iajs-3044	70	15	by	by	ADP
iajs-3044	70	16	maclaurin	maclaurin	NOUN
iajs-3044	70	17	series	series	NOUN
iajs-3044	70	18	:	:	PUNCT
iajs-3044	70	19	𝑒−𝛼𝑥	𝑒−𝛼𝑥	PROPN
iajs-3044	70	20	=	=	SYM
iajs-3044	70	21	∑	∑	PROPN
iajs-3044	70	22	(	(	PUNCT
iajs-3044	70	23	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	70	24	𝑛	𝑛	PROPN
iajs-3044	70	25	!	!	PUNCT
iajs-3044	70	26	∞	∞	NUM
iajs-3044	71	1	𝑛=0	𝑛=0	PROPN
iajs-3044	71	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	71	3	…	…	PUNCT
iajs-3044	71	4	(	(	PUNCT
iajs-3044	71	5	15	15	NUM
iajs-3044	71	6	)	)	PUNCT
iajs-3044	71	7	substituting	substitute	VERB
iajs-3044	71	8	equation	equation	NOUN
iajs-3044	71	9	(	(	PUNCT
iajs-3044	71	10	15	15	NUM
iajs-3044	71	11	)	)	PUNCT
iajs-3044	71	12	in	in	ADP
iajs-3044	71	13	equation	equation	NOUN
iajs-3044	71	14	(	(	PUNCT
iajs-3044	71	15	14	14	NUM
iajs-3044	71	16	)	)	PUNCT
iajs-3044	71	17	,	,	PUNCT
iajs-3044	71	18	we	we	PRON
iajs-3044	71	19	get	get	VERB
iajs-3044	71	20	:	:	PUNCT
iajs-3044	71	21	𝐾(𝑟	𝐾(𝑟	NUM
iajs-3044	71	22	,	,	PUNCT
iajs-3044	71	23	𝛼	𝛼	NOUN
iajs-3044	71	24	,	,	PUNCT
iajs-3044	71	25	𝜆	𝜆	X
iajs-3044	71	26	)	)	PUNCT
iajs-3044	71	27	=	=	SYM
iajs-3044	71	28	∑	∑	PROPN
iajs-3044	71	29	(	(	PUNCT
iajs-3044	71	30	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	71	31	𝑛	𝑛	PROPN
iajs-3044	71	32	!	!	PUNCT
iajs-3044	71	33	∞	∞	NUM
iajs-3044	72	1	𝑛=0	𝑛=0	PROPN
iajs-3044	72	2	𝑥𝑟+𝑛	𝑥𝑟+𝑛	PROPN
iajs-3044	72	3	𝑒−	𝑒−	X
iajs-3044	72	4	𝜆	𝜆	DET
iajs-3044	72	5	2	2	NUM
iajs-3044	72	6	𝑥2	𝑥2	NOUN
iajs-3044	72	7	…	…	PUNCT
iajs-3044	72	8	(	(	PUNCT
iajs-3044	72	9	16	16	NUM
iajs-3044	72	10	)	)	PUNCT
iajs-3044	72	11	substituting	substitute	VERB
iajs-3044	72	12	equation	equation	NOUN
iajs-3044	72	13	(	(	PUNCT
iajs-3044	72	14	16	16	NUM
iajs-3044	72	15	)	)	PUNCT
iajs-3044	72	16	in	in	ADP
iajs-3044	72	17	equation	equation	NOUN
iajs-3044	72	18	(	(	PUNCT
iajs-3044	72	19	13	13	NUM
iajs-3044	72	20	)	)	PUNCT
iajs-3044	72	21	we	we	PRON
iajs-3044	72	22	get	get	VERB
iajs-3044	72	23	:	:	PUNCT
iajs-3044	72	24	𝐸(𝑋𝑟)𝐸𝑅	𝐸(𝑋𝑟)𝐸𝑅	X
iajs-3044	72	25	=	=	SYM
iajs-3044	72	26	∑	∑	PUNCT
iajs-3044	72	27	(	(	PUNCT
iajs-3044	72	28	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	72	29	𝑛	𝑛	PROPN
iajs-3044	72	30	!	!	PUNCT
iajs-3044	72	31	∞	∞	NUM
iajs-3044	73	1	𝑛=0	𝑛=0	PROPN
iajs-3044	74	1	[	[	X
iajs-3044	74	2	∫	∫	X
iajs-3044	74	3	𝛼	𝛼	VERB
iajs-3044	74	4	𝑥𝑟+𝑛	𝑥𝑟+𝑛	PROPN
iajs-3044	74	5	𝑒−	𝑒−	X
iajs-3044	74	6	𝜆	𝜆	ADP
iajs-3044	74	7	2	2	NUM
iajs-3044	74	8	𝑥2	𝑥2	NOUN
iajs-3044	74	9	∞	∞	NOUN
iajs-3044	74	10	0	0	NUM
iajs-3044	74	11	𝑑𝑥	𝑑𝑥	X
iajs-3044	74	12	+	+	NOUN
iajs-3044	74	13	∫	∫	PROPN
iajs-3044	74	14	𝜆	𝜆	DET
iajs-3044	74	15	𝑥𝑟+𝑛+1	𝑥𝑟+𝑛+1	ADJ
iajs-3044	74	16	𝑒−	𝑒−	NOUN
iajs-3044	74	17	𝜆	𝜆	NOUN
iajs-3044	74	18	2	2	NUM
iajs-3044	74	19	𝑥2	𝑥2	NOUN
iajs-3044	74	20	∞	∞	NOUN
iajs-3044	74	21	0	0	NUM
iajs-3044	74	22	𝑑𝑥	𝑑𝑥	X
iajs-3044	74	23	]	]	X
iajs-3044	74	24	…	…	PUNCT
iajs-3044	74	25	(	(	PUNCT
iajs-3044	74	26	17	17	NUM
iajs-3044	74	27	)	)	PUNCT
iajs-3044	74	28	now	now	ADV
iajs-3044	74	29	,	,	PUNCT
iajs-3044	74	30	solve	solve	VERB
iajs-3044	74	31	the	the	DET
iajs-3044	74	32	first	first	ADJ
iajs-3044	74	33	integral	integral	ADJ
iajs-3044	74	34	as	as	SCONJ
iajs-3044	74	35	follows	follow	VERB
iajs-3044	74	36	:	:	PUNCT
iajs-3044	74	37	𝐿1	𝐿1	PROPN
iajs-3044	75	1	=	=	SYM
iajs-3044	75	2	∫	∫	PROPN
iajs-3044	75	3	𝛼	𝛼	PROPN
iajs-3044	75	4	𝑥𝑟+𝑛	𝑥𝑟+𝑛	PROPN
iajs-3044	75	5	𝑒−	𝑒−	X
iajs-3044	75	6	𝜆	𝜆	ADP
iajs-3044	75	7	2	2	NUM
iajs-3044	75	8	𝑥2	𝑥2	NOUN
iajs-3044	75	9	∞	∞	NOUN
iajs-3044	75	10	0	0	NUM
iajs-3044	75	11	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	75	12	=	=	SYM
iajs-3044	75	13	𝛼	𝛼	PRON
iajs-3044	75	14	2	2	NUM
iajs-3044	75	15	𝑟+𝑛−1	𝑟+𝑛−1	PROPN
iajs-3044	75	16	2	2	NUM
iajs-3044	75	17	𝜆	𝜆	PRON
iajs-3044	75	18	𝑟+𝑛+1	𝑟+𝑛+1	ADJ
iajs-3044	75	19	2	2	NUM
iajs-3044	75	20	𝛤	𝛤	PROPN
iajs-3044	75	21	(	(	PUNCT
iajs-3044	75	22	𝑟+𝑛+1	𝑟+𝑛+1	NOUN
iajs-3044	75	23	2	2	NUM
iajs-3044	75	24	)	)	PUNCT
iajs-3044	75	25	…	…	PUNCT
iajs-3044	75	26	(	(	PUNCT
iajs-3044	75	27	18	18	NUM
iajs-3044	75	28	)	)	PUNCT
iajs-3044	75	29	now	now	ADV
iajs-3044	75	30	,	,	PUNCT
iajs-3044	75	31	solve	solve	VERB
iajs-3044	75	32	the	the	DET
iajs-3044	75	33	second	second	ADJ
iajs-3044	75	34	integral	integral	ADJ
iajs-3044	75	35	as	as	SCONJ
iajs-3044	75	36	follows	follow	VERB
iajs-3044	75	37	:	:	PUNCT
iajs-3044	75	38	ihjpas	ihjpas	PROPN
iajs-3044	75	39	.	.	PUNCT
iajs-3044	76	1	36(2)2023	36(2)2023	NUM
iajs-3044	76	2	395	395	NUM
iajs-3044	76	3	𝐿2	𝐿2	NOUN
iajs-3044	76	4	=	=	SYM
iajs-3044	76	5	∫	∫	PROPN
iajs-3044	77	1	𝜆	𝜆	DET
iajs-3044	77	2	𝑥𝑟+𝑛+1	𝑥𝑟+𝑛+1	ADJ
iajs-3044	77	3	𝑒−	𝑒−	NOUN
iajs-3044	77	4	𝜆	𝜆	NOUN
iajs-3044	77	5	2	2	NUM
iajs-3044	77	6	𝑥2	𝑥2	NOUN
iajs-3044	77	7	∞	∞	NOUN
iajs-3044	77	8	0	0	PUNCT
iajs-3044	77	9	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	77	10	=	=	SYM
iajs-3044	77	11	2	2	NUM
iajs-3044	77	12	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	77	13	2	2	NUM
iajs-3044	77	14	𝜆	𝜆	ADP
iajs-3044	77	15	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	77	16	2	2	NUM
iajs-3044	77	17	𝛤	𝛤	PROPN
iajs-3044	77	18	(	(	PUNCT
iajs-3044	77	19	𝑟+𝑛+2	𝑟+𝑛+2	NOUN
iajs-3044	77	20	2	2	NUM
iajs-3044	77	21	)	)	PUNCT
iajs-3044	77	22	…	…	PUNCT
iajs-3044	77	23	(	(	PUNCT
iajs-3044	77	24	19	19	NUM
iajs-3044	77	25	)	)	PUNCT
iajs-3044	77	26	substituting	substitute	VERB
iajs-3044	77	27	equations	equation	NOUN
iajs-3044	77	28	(	(	PUNCT
iajs-3044	77	29	18	18	NUM
iajs-3044	77	30	)	)	PUNCT
iajs-3044	77	31	and	and	CCONJ
iajs-3044	77	32	(	(	PUNCT
iajs-3044	77	33	19	19	NUM
iajs-3044	77	34	)	)	PUNCT
iajs-3044	77	35	in	in	ADP
iajs-3044	77	36	equation	equation	NOUN
iajs-3044	77	37	(	(	PUNCT
iajs-3044	77	38	17	17	NUM
iajs-3044	77	39	)	)	PUNCT
iajs-3044	77	40	we	we	PRON
iajs-3044	77	41	get	get	VERB
iajs-3044	77	42	:	:	PUNCT
iajs-3044	77	43	𝐸(𝑋𝑟)𝐸𝑅	𝐸(𝑋𝑟)𝐸𝑅	X
iajs-3044	77	44	=	=	SYM
iajs-3044	77	45	∑	∑	PUNCT
iajs-3044	77	46	(	(	PUNCT
iajs-3044	77	47	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	77	48	𝑛	𝑛	PROPN
iajs-3044	77	49	!	!	PUNCT
iajs-3044	78	1	∞	∞	NUM
iajs-3044	78	2	𝑛=0	𝑛=0	PROPN
iajs-3044	78	3	2	2	NUM
iajs-3044	78	4	𝑟+𝑛	𝑟+𝑛	PROPN
iajs-3044	78	5	2	2	NUM
iajs-3044	78	6	𝜆	𝜆	ADP
iajs-3044	78	7	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	78	8	2	2	NUM
iajs-3044	78	9	[	[	PUNCT
iajs-3044	78	10	𝛼	𝛼	NOUN
iajs-3044	78	11	√2𝜆	√2𝜆	NUM
iajs-3044	78	12	𝛤	𝛤	PROPN
iajs-3044	78	13	(	(	PUNCT
iajs-3044	78	14	𝑟+𝑛+1	𝑟+𝑛+1	NOUN
iajs-3044	78	15	2	2	NUM
iajs-3044	78	16	)	)	PUNCT
iajs-3044	79	1	+	+	CCONJ
iajs-3044	79	2	𝛤	𝛤	PROPN
iajs-3044	79	3	(	(	PUNCT
iajs-3044	79	4	𝑟+𝑛+2	𝑟+𝑛+2	NOUN
iajs-3044	79	5	2	2	NUM
iajs-3044	79	6	)	)	PUNCT
iajs-3044	79	7	]	]	PUNCT
iajs-3044	79	8	…	…	PUNCT
iajs-3044	79	9	(	(	PUNCT
iajs-3044	79	10	20	20	NUM
iajs-3044	79	11	)	)	PUNCT
iajs-3044	79	12	the	the	DET
iajs-3044	79	13	mean	mean	NOUN
iajs-3044	79	14	:	:	PUNCT
iajs-3044	79	15	let	let	VERB
iajs-3044	79	16	𝑟	𝑟	NOUN
iajs-3044	79	17	=	=	SYM
iajs-3044	79	18	1	1	NUM
iajs-3044	79	19	in	in	ADP
iajs-3044	79	20	equation	equation	NOUN
iajs-3044	79	21	(	(	PUNCT
iajs-3044	79	22	20	20	NUM
iajs-3044	79	23	)	)	PUNCT
iajs-3044	79	24	we	we	PRON
iajs-3044	79	25	get	get	VERB
iajs-3044	79	26	the	the	DET
iajs-3044	79	27	first	first	ADJ
iajs-3044	79	28	moment	moment	NOUN
iajs-3044	79	29	which	which	PRON
iajs-3044	79	30	is	be	AUX
iajs-3044	79	31	called	call	VERB
iajs-3044	79	32	the	the	DET
iajs-3044	79	33	mean	mean	ADJ
iajs-3044	79	34	,	,	PUNCT
iajs-3044	79	35	thus	thus	ADV
iajs-3044	79	36	:	:	PUNCT
iajs-3044	79	37	𝐸(𝑋)𝐸𝑅	𝐸(𝑋)𝐸𝑅	X
iajs-3044	80	1	=	=	SYM
iajs-3044	80	2	∑	∑	PUNCT
iajs-3044	80	3	(	(	PUNCT
iajs-3044	80	4	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	80	5	𝑛	𝑛	PROPN
iajs-3044	80	6	!	!	PUNCT
iajs-3044	80	7	∞	∞	NUM
iajs-3044	81	1	𝑛=0	𝑛=0	NOUN
iajs-3044	81	2	2	2	NUM
iajs-3044	81	3	1+𝑛	1+𝑛	NUM
iajs-3044	81	4	2	2	NUM
iajs-3044	81	5	𝜆	𝜆	PROPN
iajs-3044	81	6	1+𝑛	1+𝑛	NUM
iajs-3044	81	7	2	2	NUM
iajs-3044	81	8	[	[	PUNCT
iajs-3044	81	9	𝛼	𝛼	NOUN
iajs-3044	81	10	√2𝜆	√2𝜆	NUM
iajs-3044	81	11	𝛤	𝛤	PROPN
iajs-3044	81	12	(	(	PUNCT
iajs-3044	81	13	𝑛+2	𝑛+2	NUM
iajs-3044	81	14	2	2	NUM
iajs-3044	81	15	)	)	PUNCT
iajs-3044	81	16	+	+	CCONJ
iajs-3044	81	17	𝛤	𝛤	PROPN
iajs-3044	81	18	(	(	PUNCT
iajs-3044	81	19	𝑛+3	𝑛+3	NUM
iajs-3044	81	20	2	2	NUM
iajs-3044	81	21	)	)	PUNCT
iajs-3044	81	22	]	]	PUNCT
iajs-3044	81	23	…	…	PUNCT
iajs-3044	81	24	(	(	PUNCT
iajs-3044	81	25	21	21	NUM
iajs-3044	81	26	)	)	PUNCT
iajs-3044	81	27	the	the	DET
iajs-3044	81	28	variance	variance	NOUN
iajs-3044	81	29	:	:	PUNCT
iajs-3044	81	30	the	the	DET
iajs-3044	81	31	general	general	ADJ
iajs-3044	81	32	form	form	NOUN
iajs-3044	81	33	of	of	ADP
iajs-3044	81	34	𝑣(𝑋	𝑣(𝑋	NOUN
iajs-3044	81	35	)	)	PUNCT
iajs-3044	81	36	of	of	ADP
iajs-3044	81	37	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	81	38	distribution	distribution	NOUN
iajs-3044	81	39	is	be	AUX
iajs-3044	81	40	given	give	VERB
iajs-3044	81	41	by	by	ADP
iajs-3044	81	42	:	:	PUNCT
iajs-3044	81	43	𝑣(𝑋)𝐸𝑅	𝑣(𝑋)𝐸𝑅	NOUN
iajs-3044	81	44	=	=	SYM
iajs-3044	81	45	𝐸(𝑋2)𝐸𝑅	𝐸(𝑋2)𝐸𝑅	NOUN
iajs-3044	81	46	−	−	PROPN
iajs-3044	82	1	[	[	X
iajs-3044	82	2	𝐸(𝑋)𝐸𝑅]2	𝐸(𝑋)𝐸𝑅]2	NOUN
iajs-3044	82	3	𝑣(𝑋)𝐸𝑅	𝑣(𝑋)𝐸𝑅	NOUN
iajs-3044	83	1	=	=	SYM
iajs-3044	84	1	[	[	X
iajs-3044	84	2	∑	∑	INTJ
iajs-3044	84	3	(	(	PUNCT
iajs-3044	84	4	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	84	5	𝑛	𝑛	PROPN
iajs-3044	84	6	!	!	PUNCT
iajs-3044	84	7	∞	∞	NUM
iajs-3044	84	8	𝑛=0	𝑛=0	PROPN
iajs-3044	84	9	2	2	NUM
iajs-3044	84	10	2+𝑛	2+𝑛	NUM
iajs-3044	84	11	2	2	NUM
iajs-3044	84	12	𝜆	𝜆	DET
iajs-3044	84	13	2+𝑛	2+𝑛	NUM
iajs-3044	84	14	2	2	NUM
iajs-3044	84	15	[	[	PUNCT
iajs-3044	84	16	𝛼	𝛼	NOUN
iajs-3044	84	17	√2𝜆	√2𝜆	NUM
iajs-3044	84	18	𝛤	𝛤	PROPN
iajs-3044	84	19	(	(	PUNCT
iajs-3044	84	20	𝑛+3	𝑛+3	NUM
iajs-3044	84	21	2	2	NUM
iajs-3044	84	22	)	)	PUNCT
iajs-3044	84	23	+	+	CCONJ
iajs-3044	85	1	𝛤	𝛤	PROPN
iajs-3044	85	2	(	(	PUNCT
iajs-3044	85	3	𝑛+4	𝑛+4	PROPN
iajs-3044	85	4	2	2	NUM
iajs-3044	85	5	)	)	PUNCT
iajs-3044	85	6	]	]	PUNCT
iajs-3044	85	7	]	]	PUNCT
iajs-3044	85	8	–	–	PUNCT
iajs-3044	85	9	[	[	X
iajs-3044	85	10	∑	∑	INTJ
iajs-3044	85	11	(	(	PUNCT
iajs-3044	85	12	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	85	13	𝑛	𝑛	PROPN
iajs-3044	85	14	!	!	PUNCT
iajs-3044	85	15	∞	∞	NUM
iajs-3044	86	1	𝑛=0	𝑛=0	NOUN
iajs-3044	86	2	2	2	NUM
iajs-3044	86	3	1+𝑛	1+𝑛	NUM
iajs-3044	86	4	2	2	NUM
iajs-3044	86	5	𝜆	𝜆	PROPN
iajs-3044	86	6	1+𝑛	1+𝑛	NUM
iajs-3044	86	7	2	2	NUM
iajs-3044	86	8	[	[	PUNCT
iajs-3044	86	9	𝛼	𝛼	NOUN
iajs-3044	86	10	√2𝜆	√2𝜆	NUM
iajs-3044	86	11	𝛤	𝛤	PROPN
iajs-3044	86	12	(	(	PUNCT
iajs-3044	86	13	𝑛+2	𝑛+2	NUM
iajs-3044	86	14	2	2	NUM
iajs-3044	86	15	)	)	PUNCT
iajs-3044	86	16	+	+	CCONJ
iajs-3044	86	17	𝛤	𝛤	PROPN
iajs-3044	86	18	(	(	PUNCT
iajs-3044	86	19	𝑛+3	𝑛+3	NUM
iajs-3044	86	20	2	2	NUM
iajs-3044	86	21	)	)	PUNCT
iajs-3044	86	22	]	]	X
iajs-3044	86	23	]	]	X
iajs-3044	86	24	2	2	NUM
iajs-3044	86	25	…	…	PUNCT
iajs-3044	86	26	(	(	PUNCT
iajs-3044	86	27	22	22	NUM
iajs-3044	86	28	)	)	PUNCT
iajs-3044	86	29	2.1.4	2.1.4	NUM
iajs-3044	86	30	coefficient	coefficient	NOUN
iajs-3044	86	31	of	of	ADP
iajs-3044	86	32	skewness	skewness	NOUN
iajs-3044	86	33	the	the	DET
iajs-3044	86	34	general	general	ADJ
iajs-3044	86	35	form	form	NOUN
iajs-3044	86	36	of	of	ADP
iajs-3044	86	37	the	the	DET
iajs-3044	86	38	coefficient	coefficient	NOUN
iajs-3044	86	39	of	of	ADP
iajs-3044	86	40	skewness	skewness	NOUN
iajs-3044	86	41	(	(	PUNCT
iajs-3044	86	42	𝐶.	𝐶.	PROPN
iajs-3044	86	43	𝑆	𝑆	PROPN
iajs-3044	86	44	)	)	PUNCT
iajs-3044	86	45	of	of	ADP
iajs-3044	86	46	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	86	47	distribution	distribution	NOUN
iajs-3044	86	48	is	be	AUX
iajs-3044	86	49	given	give	VERB
iajs-3044	86	50	by	by	ADP
iajs-3044	86	51	:	:	PUNCT
iajs-3044	86	52	𝐶.	𝐶.	PROPN
iajs-3044	86	53	𝑆𝐸𝑅	𝑆𝐸𝑅	PROPN
iajs-3044	86	54	=	=	SYM
iajs-3044	86	55	𝐸(𝑋3	𝐸(𝑋3	ADJ
iajs-3044	86	56	)	)	PUNCT
iajs-3044	86	57	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	87	1	[	[	X
iajs-3044	87	2	𝐸(𝑋2)𝐸𝑅	𝐸(𝑋2)𝐸𝑅	NOUN
iajs-3044	87	3	]	]	X
iajs-3044	87	4	3	3	NUM
iajs-3044	87	5	2	2	NUM
iajs-3044	87	6	=	=	SYM
iajs-3044	87	7	∑	∑	PROPN
iajs-3044	87	8	(	(	PUNCT
iajs-3044	87	9	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	87	10	𝑛	𝑛	PROPN
iajs-3044	87	11	!	!	PUNCT
iajs-3044	87	12	∞	∞	NUM
iajs-3044	88	1	𝑛=0	𝑛=0	PROPN
iajs-3044	88	2	2	2	NUM
iajs-3044	88	3	3+𝑛	3+𝑛	NUM
iajs-3044	88	4	2	2	NUM
iajs-3044	88	5	𝜆	𝜆	SYM
iajs-3044	88	6	3+𝑛	3+𝑛	NUM
iajs-3044	88	7	2	2	NUM
iajs-3044	88	8	[	[	PUNCT
iajs-3044	88	9	𝛼	𝛼	NOUN
iajs-3044	88	10	√2𝜆	√2𝜆	NUM
iajs-3044	88	11	𝛤	𝛤	PROPN
iajs-3044	88	12	(	(	PUNCT
iajs-3044	88	13	𝑛+4	𝑛+4	PROPN
iajs-3044	88	14	2	2	NUM
iajs-3044	88	15	)	)	PUNCT
iajs-3044	88	16	+	+	X
iajs-3044	89	1	𝛤	𝛤	PROPN
iajs-3044	89	2	(	(	PUNCT
iajs-3044	89	3	𝑛+5	𝑛+5	ADP
iajs-3044	89	4	2	2	NUM
iajs-3044	89	5	)	)	PUNCT
iajs-3044	89	6	]	]	PUNCT
iajs-3044	90	1	[	[	X
iajs-3044	90	2	∑	∑	INTJ
iajs-3044	90	3	(	(	PUNCT
iajs-3044	90	4	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	90	5	𝑛	𝑛	PROPN
iajs-3044	90	6	!	!	PUNCT
iajs-3044	90	7	∞	∞	NUM
iajs-3044	90	8	𝑛=0	𝑛=0	PROPN
iajs-3044	90	9	2	2	NUM
iajs-3044	90	10	2+𝑛	2+𝑛	NUM
iajs-3044	90	11	2	2	NUM
iajs-3044	90	12	𝜆	𝜆	PRON
iajs-3044	90	13	2+𝑛	2+𝑛	NUM
iajs-3044	90	14	2	2	NUM
iajs-3044	90	15	[	[	PUNCT
iajs-3044	90	16	𝛼	𝛼	NOUN
iajs-3044	90	17	√2𝜆	√2𝜆	NUM
iajs-3044	90	18	𝛤	𝛤	PROPN
iajs-3044	90	19	(	(	PUNCT
iajs-3044	90	20	𝑛+3	𝑛+3	NUM
iajs-3044	90	21	2	2	NUM
iajs-3044	90	22	)	)	PUNCT
iajs-3044	90	23	+	+	X
iajs-3044	90	24	𝛤	𝛤	PROPN
iajs-3044	90	25	(	(	PUNCT
iajs-3044	90	26	𝑛+4	𝑛+4	PROPN
iajs-3044	90	27	2	2	NUM
iajs-3044	90	28	)	)	PUNCT
iajs-3044	90	29	]	]	PUNCT
iajs-3044	90	30	]	]	X
iajs-3044	90	31	3	3	NUM
iajs-3044	90	32	2	2	NUM
iajs-3044	90	33	…	…	PUNCT
iajs-3044	90	34	(	(	PUNCT
iajs-3044	90	35	23	23	NUM
iajs-3044	90	36	)	)	PUNCT
iajs-3044	90	37	2.1.5	2.1.5	NUM
iajs-3044	90	38	coefficient	coefficient	NOUN
iajs-3044	90	39	of	of	ADP
iajs-3044	90	40	kurtosis	kurtosis	NOUN
iajs-3044	90	41	the	the	DET
iajs-3044	90	42	general	general	ADJ
iajs-3044	90	43	form	form	NOUN
iajs-3044	90	44	of	of	ADP
iajs-3044	90	45	the	the	DET
iajs-3044	90	46	coefficient	coefficient	NOUN
iajs-3044	90	47	of	of	ADP
iajs-3044	90	48	kurtosis	kurtosis	NOUN
iajs-3044	90	49	(	(	PUNCT
iajs-3044	90	50	𝐶.	𝐶.	PROPN
iajs-3044	90	51	𝐾	𝐾	PROPN
iajs-3044	90	52	)	)	PUNCT
iajs-3044	90	53	of	of	ADP
iajs-3044	90	54	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	90	55	distribution	distribution	NOUN
iajs-3044	90	56	is	be	AUX
iajs-3044	90	57	given	give	VERB
iajs-3044	90	58	by	by	ADP
iajs-3044	90	59	:	:	PUNCT
iajs-3044	90	60	𝐶.	𝐶.	PROPN
iajs-3044	90	61	𝐾𝐸𝑅	𝐾𝐸𝑅	PROPN
iajs-3044	90	62	=	=	SYM
iajs-3044	90	63	𝐸(𝑋4	𝐸(𝑋4	NOUN
iajs-3044	90	64	)	)	PUNCT
iajs-3044	90	65	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	91	1	[	[	X
iajs-3044	91	2	𝐸(𝑋2)𝐸𝑅]2	𝐸(𝑋2)𝐸𝑅]2	ADJ
iajs-3044	91	3	−	−	PROPN
iajs-3044	91	4	3	3	NUM
iajs-3044	91	5	=	=	SYM
iajs-3044	91	6	∑	∑	PROPN
iajs-3044	91	7	(	(	PUNCT
iajs-3044	91	8	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	91	9	𝑛	𝑛	PROPN
iajs-3044	91	10	!	!	PUNCT
iajs-3044	91	11	∞	∞	NUM
iajs-3044	91	12	𝑛=0	𝑛=0	PROPN
iajs-3044	91	13	2	2	NUM
iajs-3044	91	14	4+𝑛	4+𝑛	NUM
iajs-3044	91	15	2	2	NUM
iajs-3044	91	16	𝜆	𝜆	NOUN
iajs-3044	91	17	4+𝑛	4+𝑛	NUM
iajs-3044	91	18	2	2	NUM
iajs-3044	91	19	[	[	PUNCT
iajs-3044	91	20	𝛼	𝛼	NOUN
iajs-3044	91	21	√2𝜆	√2𝜆	NUM
iajs-3044	91	22	𝛤	𝛤	PROPN
iajs-3044	91	23	(	(	PUNCT
iajs-3044	91	24	𝑛+5	𝑛+5	ADP
iajs-3044	91	25	2	2	NUM
iajs-3044	91	26	)	)	PUNCT
iajs-3044	91	27	+	+	CCONJ
iajs-3044	92	1	𝛤	𝛤	PROPN
iajs-3044	92	2	(	(	PUNCT
iajs-3044	92	3	𝑛+6	𝑛+6	PROPN
iajs-3044	92	4	2	2	NUM
iajs-3044	92	5	)	)	PUNCT
iajs-3044	92	6	]	]	PUNCT
iajs-3044	93	1	[	[	X
iajs-3044	93	2	∑	∑	INTJ
iajs-3044	93	3	(	(	PUNCT
iajs-3044	93	4	−𝛼)𝑛	−𝛼)𝑛	PROPN
iajs-3044	93	5	𝑛	𝑛	PROPN
iajs-3044	93	6	!	!	PUNCT
iajs-3044	93	7	∞	∞	NUM
iajs-3044	93	8	𝑛=0	𝑛=0	PROPN
iajs-3044	93	9	2	2	NUM
iajs-3044	93	10	2+𝑛	2+𝑛	NUM
iajs-3044	93	11	2	2	NUM
iajs-3044	93	12	𝜆	𝜆	PRON
iajs-3044	93	13	2+𝑛	2+𝑛	NUM
iajs-3044	93	14	2	2	NUM
iajs-3044	93	15	[	[	PUNCT
iajs-3044	93	16	𝛼	𝛼	NOUN
iajs-3044	93	17	√2𝜆	√2𝜆	NUM
iajs-3044	93	18	𝛤	𝛤	PROPN
iajs-3044	93	19	(	(	PUNCT
iajs-3044	93	20	𝑛+3	𝑛+3	NUM
iajs-3044	93	21	2	2	NUM
iajs-3044	93	22	)	)	PUNCT
iajs-3044	93	23	+	+	X
iajs-3044	93	24	𝛤	𝛤	PROPN
iajs-3044	93	25	(	(	PUNCT
iajs-3044	93	26	𝑛+4	𝑛+4	PROPN
iajs-3044	93	27	2	2	NUM
iajs-3044	93	28	)	)	PUNCT
iajs-3044	93	29	]	]	X
iajs-3044	93	30	]	]	X
iajs-3044	93	31	2	2	NUM
iajs-3044	93	32	−	−	PROPN
iajs-3044	93	33	3	3	NUM
iajs-3044	93	34	…	…	PUNCT
iajs-3044	93	35	(	(	PUNCT
iajs-3044	93	36	24	24	NUM
iajs-3044	93	37	)	)	PUNCT
iajs-3044	93	38	2.1.6	2.1.6	NUM
iajs-3044	93	39	moment	moment	NOUN
iajs-3044	93	40	generating	generate	VERB
iajs-3044	93	41	function	function	NOUN
iajs-3044	93	42	the	the	DET
iajs-3044	93	43	moment	moment	NOUN
iajs-3044	93	44	generating	generate	VERB
iajs-3044	93	45	function	function	NOUN
iajs-3044	93	46	of	of	ADP
iajs-3044	93	47	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	93	48	distribution	distribution	NOUN
iajs-3044	93	49	can	can	AUX
iajs-3044	93	50	be	be	AUX
iajs-3044	93	51	derived	derive	VERB
iajs-3044	93	52	as	as	SCONJ
iajs-3044	93	53	follows	follow	VERB
iajs-3044	93	54	:	:	PUNCT
iajs-3044	93	55	𝑀𝑋(𝑡)𝐸𝑅	𝑀𝑋(𝑡)𝐸𝑅	PUNCT
iajs-3044	93	56	=	=	PUNCT
iajs-3044	93	57	𝐸(𝑒𝑥𝑡	𝐸(𝑒𝑥𝑡	PROPN
iajs-3044	93	58	)	)	PUNCT
iajs-3044	94	1	=	=	SYM
iajs-3044	94	2	∫	∫	PROPN
iajs-3044	94	3	𝑒𝑥𝑡	𝑒𝑥𝑡	INTJ
iajs-3044	94	4	(	(	PUNCT
iajs-3044	94	5	𝛼	𝛼	NOUN
iajs-3044	94	6	+	+	CCONJ
iajs-3044	94	7	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	94	8	)	)	PUNCT
iajs-3044	94	9	𝑒	𝑒	NOUN
iajs-3044	94	10	−	−	PROPN
iajs-3044	94	11	(	(	PUNCT
iajs-3044	94	12	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	94	13	+	+	CCONJ
iajs-3044	94	14	𝜆	𝜆	X
iajs-3044	94	15	2	2	NUM
iajs-3044	94	16	𝑥2	𝑥2	NOUN
iajs-3044	94	17	)	)	PUNCT
iajs-3044	94	18	∞	∞	NOUN
iajs-3044	94	19	0	0	NUM
iajs-3044	94	20	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	94	21	𝑀𝑋(𝑡)𝐸𝑅	𝑀𝑋(𝑡)𝐸𝑅	X
iajs-3044	94	22	=	=	SYM
iajs-3044	94	23	∫	∫	PROPN
iajs-3044	94	24	(	(	PUNCT
iajs-3044	94	25	𝛼	𝛼	PROPN
iajs-3044	94	26	+	+	CCONJ
iajs-3044	94	27	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	94	28	)	)	PUNCT
iajs-3044	94	29	𝑒−	𝑒−	NOUN
iajs-3044	94	30	(	(	PUNCT
iajs-3044	94	31	(	(	PUNCT
iajs-3044	94	32	𝛼−𝑡	𝛼−𝑡	PROPN
iajs-3044	94	33	)	)	PUNCT
iajs-3044	94	34	𝑥	𝑥	PROPN
iajs-3044	95	1	+	+	CCONJ
iajs-3044	95	2	𝜆	𝜆	X
iajs-3044	95	3	2	2	NUM
iajs-3044	95	4	𝑥2	𝑥2	NOUN
iajs-3044	95	5	)	)	PUNCT
iajs-3044	95	6	∞	∞	NOUN
iajs-3044	95	7	0	0	NUM
iajs-3044	95	8	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	95	9	…	…	PUNCT
iajs-3044	95	10	(	(	PUNCT
iajs-3044	95	11	25	25	NUM
iajs-3044	95	12	)	)	PUNCT
iajs-3044	95	13	let	let	VERB
iajs-3044	95	14	𝑊((𝛼	𝑊((𝛼	PROPN
iajs-3044	95	15	−	−	PROPN
iajs-3044	95	16	𝑡	𝑡	NOUN
iajs-3044	95	17	)	)	PUNCT
iajs-3044	95	18	,	,	PUNCT
iajs-3044	95	19	𝜆	𝜆	X
iajs-3044	95	20	)	)	PUNCT
iajs-3044	95	21	=	=	SYM
iajs-3044	95	22	𝑒−	𝑒−	NOUN
iajs-3044	95	23	(	(	PUNCT
iajs-3044	95	24	(	(	PUNCT
iajs-3044	95	25	𝛼−𝑡	𝛼−𝑡	PROPN
iajs-3044	95	26	)	)	PUNCT
iajs-3044	95	27	𝑥	𝑥	PROPN
iajs-3044	96	1	+	+	CCONJ
iajs-3044	96	2	𝜆	𝜆	X
iajs-3044	96	3	2	2	NUM
iajs-3044	96	4	𝑥2	𝑥2	NOUN
iajs-3044	96	5	)	)	PUNCT
iajs-3044	96	6	…	…	PUNCT
iajs-3044	96	7	(	(	PUNCT
iajs-3044	96	8	26	26	NUM
iajs-3044	96	9	)	)	PUNCT
iajs-3044	96	10	by	by	ADP
iajs-3044	96	11	maclaurin	maclaurin	NOUN
iajs-3044	96	12	series	series	NOUN
iajs-3044	96	13	:	:	PUNCT
iajs-3044	96	14	𝑒−(𝛼−𝑡)𝑥	𝑒−(𝛼−𝑡)𝑥	NUM
iajs-3044	96	15	=	=	SYM
iajs-3044	96	16	∑	∑	PROPN
iajs-3044	96	17	(	(	PUNCT
iajs-3044	96	18	−(𝛼−𝑡))𝑛	−(𝛼−𝑡))𝑛	PROPN
iajs-3044	96	19	𝑛	𝑛	PROPN
iajs-3044	96	20	!	!	PUNCT
iajs-3044	96	21	∞	∞	NUM
iajs-3044	97	1	𝑛=0	𝑛=0	PROPN
iajs-3044	97	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	97	3	…	…	PUNCT
iajs-3044	97	4	(	(	PUNCT
iajs-3044	97	5	27	27	NUM
iajs-3044	97	6	)	)	PUNCT
iajs-3044	97	7	substituting	substitute	VERB
iajs-3044	97	8	equation	equation	NOUN
iajs-3044	97	9	(	(	PUNCT
iajs-3044	97	10	27	27	NUM
iajs-3044	97	11	)	)	PUNCT
iajs-3044	97	12	in	in	ADP
iajs-3044	97	13	equation	equation	NOUN
iajs-3044	97	14	(	(	PUNCT
iajs-3044	97	15	26	26	NUM
iajs-3044	97	16	)	)	PUNCT
iajs-3044	97	17	we	we	PRON
iajs-3044	97	18	get	get	VERB
iajs-3044	97	19	:	:	PUNCT
iajs-3044	97	20	ihjpas	ihjpas	PROPN
iajs-3044	97	21	.	.	PUNCT
iajs-3044	98	1	36(2)2023	36(2)2023	NUM
iajs-3044	98	2	396	396	NUM
iajs-3044	98	3	𝑊((𝛼	𝑊((𝛼	NOUN
iajs-3044	98	4	−	−	PROPN
iajs-3044	98	5	𝑡	𝑡	NOUN
iajs-3044	98	6	)	)	PUNCT
iajs-3044	98	7	,	,	PUNCT
iajs-3044	98	8	𝜆	𝜆	X
iajs-3044	98	9	)	)	PUNCT
iajs-3044	98	10	=	=	SYM
iajs-3044	98	11	∑	∑	PUNCT
iajs-3044	98	12	(	(	PUNCT
iajs-3044	98	13	−(𝛼−𝑡))𝑛	−(𝛼−𝑡))𝑛	PROPN
iajs-3044	98	14	𝑛	𝑛	PROPN
iajs-3044	98	15	!	!	PUNCT
iajs-3044	98	16	∞	∞	NUM
iajs-3044	99	1	𝑛=0	𝑛=0	PROPN
iajs-3044	99	2	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	99	3	𝑒−	𝑒−	NOUN
iajs-3044	99	4	𝜆	𝜆	DET
iajs-3044	99	5	2	2	NUM
iajs-3044	99	6	𝑥2	𝑥2	NOUN
iajs-3044	99	7	…	…	PUNCT
iajs-3044	99	8	(	(	PUNCT
iajs-3044	99	9	28	28	NUM
iajs-3044	99	10	)	)	PUNCT
iajs-3044	99	11	substituting	substitute	VERB
iajs-3044	99	12	equation	equation	NOUN
iajs-3044	99	13	(	(	PUNCT
iajs-3044	99	14	28	28	NUM
iajs-3044	99	15	)	)	PUNCT
iajs-3044	99	16	in	in	ADP
iajs-3044	99	17	equation	equation	NOUN
iajs-3044	99	18	(	(	PUNCT
iajs-3044	99	19	25	25	NUM
iajs-3044	99	20	)	)	PUNCT
iajs-3044	99	21	we	we	PRON
iajs-3044	99	22	get	get	VERB
iajs-3044	99	23	:	:	PUNCT
iajs-3044	99	24	𝑀𝑋(𝑡)𝐸𝑅	𝑀𝑋(𝑡)𝐸𝑅	X
iajs-3044	99	25	=	=	PUNCT
iajs-3044	99	26	∑	∑	PUNCT
iajs-3044	99	27	(	(	PUNCT
iajs-3044	99	28	−(𝛼−𝑡))𝑛	−(𝛼−𝑡))𝑛	PROPN
iajs-3044	99	29	𝑛	𝑛	PROPN
iajs-3044	99	30	!	!	PUNCT
iajs-3044	99	31	∞	∞	NUM
iajs-3044	100	1	𝑛=0	𝑛=0	PROPN
iajs-3044	101	1	[	[	X
iajs-3044	101	2	∫	∫	X
iajs-3044	101	3	𝛼	𝛼	VERB
iajs-3044	101	4	𝑥𝑛	𝑥𝑛	NOUN
iajs-3044	101	5	𝑒−	𝑒−	VERB
iajs-3044	101	6	𝜆	𝜆	DET
iajs-3044	101	7	2	2	NUM
iajs-3044	101	8	𝑥2	𝑥2	NOUN
iajs-3044	101	9	∞	∞	NOUN
iajs-3044	101	10	0	0	NUM
iajs-3044	101	11	𝑑𝑥	𝑑𝑥	X
iajs-3044	101	12	+	+	NOUN
iajs-3044	101	13	∫	∫	PROPN
iajs-3044	101	14	𝜆	𝜆	PRON
iajs-3044	101	15	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	101	16	𝑒−	𝑒−	NOUN
iajs-3044	101	17	𝜆	𝜆	DET
iajs-3044	101	18	2	2	NUM
iajs-3044	101	19	𝑥2	𝑥2	NOUN
iajs-3044	101	20	∞	∞	NOUN
iajs-3044	101	21	0	0	NUM
iajs-3044	101	22	𝑑𝑥	𝑑𝑥	X
iajs-3044	101	23	]	]	X
iajs-3044	101	24	…	…	PUNCT
iajs-3044	101	25	(	(	PUNCT
iajs-3044	101	26	29	29	NUM
iajs-3044	101	27	)	)	PUNCT
iajs-3044	101	28	now	now	ADV
iajs-3044	101	29	,	,	PUNCT
iajs-3044	101	30	solve	solve	VERB
iajs-3044	101	31	the	the	DET
iajs-3044	101	32	first	first	ADJ
iajs-3044	101	33	integral	integral	ADJ
iajs-3044	101	34	as	as	SCONJ
iajs-3044	101	35	follows	follow	VERB
iajs-3044	101	36	:	:	PUNCT
iajs-3044	101	37	𝐿1	𝐿1	PROPN
iajs-3044	102	1	=	=	PUNCT
iajs-3044	102	2	∫	∫	PROPN
iajs-3044	102	3	𝛼	𝛼	PRON
iajs-3044	102	4	𝑥𝑛	𝑥𝑛	NOUN
iajs-3044	102	5	𝑒−	𝑒−	VERB
iajs-3044	102	6	𝜆	𝜆	DET
iajs-3044	102	7	2	2	NUM
iajs-3044	102	8	𝑥2	𝑥2	NOUN
iajs-3044	102	9	∞	∞	NOUN
iajs-3044	102	10	0	0	NUM
iajs-3044	102	11	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	102	12	=	=	SYM
iajs-3044	102	13	𝛼	𝛼	NOUN
iajs-3044	102	14	2	2	NUM
iajs-3044	102	15	𝑛−1	𝑛−1	NUM
iajs-3044	102	16	2	2	NUM
iajs-3044	102	17	𝜆	𝜆	PRON
iajs-3044	102	18	𝑛+1	𝑛+1	PROPN
iajs-3044	102	19	2	2	NUM
iajs-3044	102	20	𝛤	𝛤	PROPN
iajs-3044	102	21	(	(	PUNCT
iajs-3044	102	22	𝑛+1	𝑛+1	PROPN
iajs-3044	102	23	2	2	NUM
iajs-3044	102	24	)	)	PUNCT
iajs-3044	102	25	…	…	PUNCT
iajs-3044	102	26	(	(	PUNCT
iajs-3044	102	27	30	30	NUM
iajs-3044	102	28	)	)	PUNCT
iajs-3044	102	29	now	now	ADV
iajs-3044	102	30	,	,	PUNCT
iajs-3044	102	31	solve	solve	VERB
iajs-3044	102	32	the	the	DET
iajs-3044	102	33	second	second	ADJ
iajs-3044	102	34	integral	integral	ADJ
iajs-3044	102	35	as	as	SCONJ
iajs-3044	102	36	follows	follow	VERB
iajs-3044	102	37	:	:	PUNCT
iajs-3044	102	38	𝐿2	𝐿2	PROPN
iajs-3044	102	39	=	=	PUNCT
iajs-3044	102	40	∫	∫	PROPN
iajs-3044	103	1	𝜆	𝜆	PRON
iajs-3044	103	2	𝑥𝑛+1	𝑥𝑛+1	PUNCT
iajs-3044	103	3	𝑒−	𝑒−	NOUN
iajs-3044	103	4	𝜆	𝜆	DET
iajs-3044	103	5	2	2	NUM
iajs-3044	103	6	𝑥2	𝑥2	NOUN
iajs-3044	103	7	∞	∞	NOUN
iajs-3044	103	8	0	0	PUNCT
iajs-3044	104	1	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	104	2	=	=	SYM
iajs-3044	104	3	2	2	NUM
iajs-3044	104	4	𝑛	𝑛	ADP
iajs-3044	104	5	2	2	NUM
iajs-3044	104	6	𝜆	𝜆	NOUN
iajs-3044	104	7	𝑛	𝑛	PRON
iajs-3044	104	8	2	2	NUM
iajs-3044	104	9	𝛤	𝛤	PROPN
iajs-3044	104	10	(	(	PUNCT
iajs-3044	104	11	𝑛+2	𝑛+2	NUM
iajs-3044	104	12	2	2	NUM
iajs-3044	104	13	)	)	PUNCT
iajs-3044	104	14	…	…	PUNCT
iajs-3044	104	15	(	(	PUNCT
iajs-3044	104	16	31	31	NUM
iajs-3044	104	17	)	)	PUNCT
iajs-3044	104	18	substituting	substitute	VERB
iajs-3044	104	19	equations	equation	NOUN
iajs-3044	104	20	(	(	PUNCT
iajs-3044	104	21	30	30	NUM
iajs-3044	104	22	)	)	PUNCT
iajs-3044	104	23	and	and	CCONJ
iajs-3044	104	24	(	(	PUNCT
iajs-3044	104	25	31	31	NUM
iajs-3044	104	26	)	)	PUNCT
iajs-3044	104	27	in	in	ADP
iajs-3044	104	28	equation	equation	NOUN
iajs-3044	104	29	(	(	PUNCT
iajs-3044	104	30	29	29	NUM
iajs-3044	104	31	)	)	PUNCT
iajs-3044	104	32	yields	yield	NOUN
iajs-3044	104	33	:	:	PUNCT
iajs-3044	104	34	𝑀𝑋(𝑡)𝐸𝑅	𝑀𝑋(𝑡)𝐸𝑅	X
iajs-3044	104	35	=	=	PUNCT
iajs-3044	104	36	∑	∑	PUNCT
iajs-3044	104	37	(	(	PUNCT
iajs-3044	104	38	−(𝛼−𝑡))𝑛	−(𝛼−𝑡))𝑛	PROPN
iajs-3044	104	39	𝑛	𝑛	PROPN
iajs-3044	104	40	!	!	PUNCT
iajs-3044	104	41	∞	∞	NUM
iajs-3044	105	1	𝑛=0	𝑛=0	NOUN
iajs-3044	105	2	2	2	NUM
iajs-3044	105	3	𝑛	𝑛	ADP
iajs-3044	105	4	2	2	NUM
iajs-3044	105	5	𝜆	𝜆	NOUN
iajs-3044	105	6	𝑛	𝑛	DET
iajs-3044	105	7	2	2	NUM
iajs-3044	105	8	[	[	PUNCT
iajs-3044	105	9	𝛼	𝛼	NOUN
iajs-3044	105	10	√2𝜆	√2𝜆	NUM
iajs-3044	105	11	𝛤	𝛤	PROPN
iajs-3044	105	12	(	(	PUNCT
iajs-3044	105	13	𝑛+1	𝑛+1	PROPN
iajs-3044	105	14	2	2	NUM
iajs-3044	105	15	)	)	PUNCT
iajs-3044	106	1	+	+	CCONJ
iajs-3044	106	2	𝛤	𝛤	PROPN
iajs-3044	106	3	(	(	PUNCT
iajs-3044	106	4	𝑛+2	𝑛+2	NUM
iajs-3044	106	5	2	2	NUM
iajs-3044	106	6	)	)	PUNCT
iajs-3044	106	7	]	]	PUNCT
iajs-3044	106	8	…	…	PUNCT
iajs-3044	106	9	(	(	PUNCT
iajs-3044	106	10	32	32	NUM
iajs-3044	106	11	)	)	PUNCT
iajs-3044	106	12	2.1.7	2.1.7	NUM
iajs-3044	106	13	factorial	factorial	ADJ
iajs-3044	106	14	moment	moment	NOUN
iajs-3044	106	15	generating	generate	VERB
iajs-3044	106	16	function	function	NOUN
iajs-3044	106	17	the	the	DET
iajs-3044	106	18	factorial	factorial	ADJ
iajs-3044	106	19	moment	moment	NOUN
iajs-3044	106	20	generating	generate	VERB
iajs-3044	106	21	function	function	NOUN
iajs-3044	106	22	of	of	ADP
iajs-3044	106	23	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	106	24	distribution	distribution	NOUN
iajs-3044	106	25	can	can	AUX
iajs-3044	106	26	be	be	AUX
iajs-3044	106	27	obtained	obtain	VERB
iajs-3044	106	28	as	as	SCONJ
iajs-3044	106	29	follows	follow	VERB
iajs-3044	106	30	:	:	PUNCT
iajs-3044	106	31	𝑀(𝑡)𝐸𝑅	𝑀(𝑡)𝐸𝑅	PUNCT
iajs-3044	106	32	=	=	PUNCT
iajs-3044	106	33	𝐸(𝑡𝑥	𝐸(𝑡𝑥	NOUN
iajs-3044	106	34	)	)	PUNCT
iajs-3044	106	35	=	=	SYM
iajs-3044	107	1	∫	∫	PROPN
iajs-3044	107	2	𝑡𝑥	𝑡𝑥	INTJ
iajs-3044	107	3	(	(	PUNCT
iajs-3044	107	4	𝛼	𝛼	PROPN
iajs-3044	107	5	+	+	CCONJ
iajs-3044	107	6	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	107	7	)	)	PUNCT
iajs-3044	107	8	𝑒	𝑒	NOUN
iajs-3044	107	9	−	−	PROPN
iajs-3044	107	10	(	(	PUNCT
iajs-3044	107	11	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	107	12	+	+	CCONJ
iajs-3044	107	13	𝜆	𝜆	X
iajs-3044	107	14	2	2	NUM
iajs-3044	107	15	𝑥2	𝑥2	NOUN
iajs-3044	107	16	)	)	PUNCT
iajs-3044	107	17	∞	∞	NOUN
iajs-3044	107	18	0	0	NUM
iajs-3044	107	19	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	107	20	𝑀(𝑡)𝐸𝑅	𝑀(𝑡)𝐸𝑅	VERB
iajs-3044	107	21	=	=	NOUN
iajs-3044	107	22	∫	∫	PROPN
iajs-3044	107	23	(	(	PUNCT
iajs-3044	107	24	𝛼	𝛼	PROPN
iajs-3044	107	25	+	+	CCONJ
iajs-3044	107	26	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	107	27	)	)	PUNCT
iajs-3044	107	28	𝑒−	𝑒−	NOUN
iajs-3044	107	29	(	(	PUNCT
iajs-3044	107	30	(	(	PUNCT
iajs-3044	107	31	𝛼−ln	𝛼−ln	NOUN
iajs-3044	107	32	(	(	PUNCT
iajs-3044	107	33	𝑡	𝑡	NOUN
iajs-3044	107	34	)	)	PUNCT
iajs-3044	107	35	)	)	PUNCT
iajs-3044	108	1	𝑥	𝑥	PROPN
iajs-3044	109	1	+	+	CCONJ
iajs-3044	109	2	𝜆	𝜆	X
iajs-3044	109	3	2	2	NUM
iajs-3044	109	4	𝑥2	𝑥2	NOUN
iajs-3044	109	5	)	)	PUNCT
iajs-3044	109	6	∞	∞	NOUN
iajs-3044	109	7	0	0	NUM
iajs-3044	109	8	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	109	9	…	…	PUNCT
iajs-3044	109	10	(	(	PUNCT
iajs-3044	109	11	33	33	NUM
iajs-3044	109	12	)	)	PUNCT
iajs-3044	109	13	let	let	VERB
iajs-3044	109	14	𝐴((𝛼	𝐴((𝛼	VERB
iajs-3044	109	15	−	−	PROPN
iajs-3044	109	16	ln(𝑡	ln(𝑡	PUNCT
iajs-3044	109	17	)	)	PUNCT
iajs-3044	109	18	)	)	PUNCT
iajs-3044	109	19	,	,	PUNCT
iajs-3044	109	20	𝜆	𝜆	X
iajs-3044	109	21	)	)	PUNCT
iajs-3044	109	22	=	=	SYM
iajs-3044	109	23	𝑒−	𝑒−	NOUN
iajs-3044	109	24	(	(	PUNCT
iajs-3044	109	25	(	(	PUNCT
iajs-3044	109	26	𝛼−𝑙𝑛(𝑡	𝛼−𝑙𝑛(𝑡	X
iajs-3044	109	27	)	)	PUNCT
iajs-3044	109	28	)	)	PUNCT
iajs-3044	110	1	𝑥	𝑥	PROPN
iajs-3044	111	1	+	+	CCONJ
iajs-3044	111	2	𝜆	𝜆	X
iajs-3044	111	3	2	2	NUM
iajs-3044	111	4	𝑥2	𝑥2	NOUN
iajs-3044	111	5	)	)	PUNCT
iajs-3044	111	6	…	…	PUNCT
iajs-3044	111	7	(	(	PUNCT
iajs-3044	111	8	34	34	NUM
iajs-3044	111	9	)	)	PUNCT
iajs-3044	111	10	by	by	ADP
iajs-3044	111	11	maclaurin	maclaurin	NOUN
iajs-3044	111	12	series	series	NOUN
iajs-3044	111	13	:	:	PUNCT
iajs-3044	111	14	𝑒−(𝛼−ln	𝑒−(𝛼−ln	X
iajs-3044	111	15	(	(	PUNCT
iajs-3044	111	16	𝑡))𝑥	𝑡))𝑥	PROPN
iajs-3044	111	17	=	=	SYM
iajs-3044	111	18	∑	∑	PROPN
iajs-3044	111	19	(	(	PUNCT
iajs-3044	111	20	−(𝛼−ln	−(𝛼−ln	X
iajs-3044	111	21	(	(	PUNCT
iajs-3044	111	22	𝑡)))𝑛	𝑡)))𝑛	NOUN
iajs-3044	111	23	𝑛	𝑛	NOUN
iajs-3044	111	24	!	!	PUNCT
iajs-3044	111	25	∞	∞	NUM
iajs-3044	112	1	𝑛=0	𝑛=0	PROPN
iajs-3044	112	2	𝑥𝑛	𝑥𝑛	X
iajs-3044	112	3	…	…	PUNCT
iajs-3044	112	4	(	(	PUNCT
iajs-3044	112	5	35	35	NUM
iajs-3044	112	6	)	)	PUNCT
iajs-3044	112	7	substituting	substitute	VERB
iajs-3044	112	8	equation	equation	NOUN
iajs-3044	112	9	(	(	PUNCT
iajs-3044	112	10	35	35	NUM
iajs-3044	112	11	)	)	PUNCT
iajs-3044	112	12	in	in	ADP
iajs-3044	112	13	equation	equation	NOUN
iajs-3044	112	14	(	(	PUNCT
iajs-3044	112	15	34	34	NUM
iajs-3044	112	16	)	)	PUNCT
iajs-3044	112	17	we	we	PRON
iajs-3044	112	18	get	get	VERB
iajs-3044	112	19	:	:	PUNCT
iajs-3044	112	20	𝐴((𝛼	𝐴((𝛼	ADP
iajs-3044	112	21	−	−	PROPN
iajs-3044	112	22	ln(𝑡	ln(𝑡	PUNCT
iajs-3044	112	23	)	)	PUNCT
iajs-3044	112	24	)	)	PUNCT
iajs-3044	112	25	,	,	PUNCT
iajs-3044	112	26	𝜆	𝜆	X
iajs-3044	112	27	)	)	PUNCT
iajs-3044	112	28	=	=	SYM
iajs-3044	112	29	∑	∑	PUNCT
iajs-3044	112	30	(	(	PUNCT
iajs-3044	112	31	−(𝛼−ln	−(𝛼−ln	X
iajs-3044	112	32	(	(	PUNCT
iajs-3044	112	33	𝑡)))𝑛	𝑡)))𝑛	NOUN
iajs-3044	112	34	𝑛	𝑛	NOUN
iajs-3044	112	35	!	!	PUNCT
iajs-3044	112	36	∞	∞	NUM
iajs-3044	113	1	𝑛=0	𝑛=0	PROPN
iajs-3044	113	2	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	113	3	𝑒−	𝑒−	NOUN
iajs-3044	113	4	𝜆	𝜆	PRON
iajs-3044	113	5	2	2	NUM
iajs-3044	113	6	𝑥2	𝑥2	NOUN
iajs-3044	113	7	…	…	PUNCT
iajs-3044	113	8	(	(	PUNCT
iajs-3044	113	9	36	36	NUM
iajs-3044	113	10	)	)	PUNCT
iajs-3044	113	11	substituting	substitute	VERB
iajs-3044	113	12	equation	equation	NOUN
iajs-3044	113	13	(	(	PUNCT
iajs-3044	113	14	36	36	NUM
iajs-3044	113	15	)	)	PUNCT
iajs-3044	113	16	in	in	ADP
iajs-3044	113	17	equation	equation	NOUN
iajs-3044	113	18	(	(	PUNCT
iajs-3044	113	19	33	33	NUM
iajs-3044	113	20	)	)	PUNCT
iajs-3044	113	21	we	we	PRON
iajs-3044	113	22	get	get	VERB
iajs-3044	113	23	:	:	PUNCT
iajs-3044	113	24	𝑀(𝑡)𝐸𝑅	𝑀(𝑡)𝐸𝑅	PROPN
iajs-3044	113	25	=	=	PUNCT
iajs-3044	113	26	∑	∑	PUNCT
iajs-3044	113	27	(	(	PUNCT
iajs-3044	113	28	−(𝛼−ln	−(𝛼−ln	X
iajs-3044	113	29	(	(	PUNCT
iajs-3044	113	30	𝑡)))𝑛	𝑡)))𝑛	NOUN
iajs-3044	113	31	𝑛	𝑛	NOUN
iajs-3044	113	32	!	!	PUNCT
iajs-3044	113	33	∞	∞	NUM
iajs-3044	114	1	𝑛=0	𝑛=0	PROPN
iajs-3044	115	1	[	[	X
iajs-3044	115	2	∫	∫	X
iajs-3044	115	3	𝛼	𝛼	VERB
iajs-3044	115	4	𝑥𝑛	𝑥𝑛	NOUN
iajs-3044	115	5	𝑒−	𝑒−	VERB
iajs-3044	115	6	𝜆	𝜆	DET
iajs-3044	115	7	2	2	NUM
iajs-3044	115	8	𝑥2	𝑥2	NOUN
iajs-3044	115	9	∞	∞	NOUN
iajs-3044	115	10	0	0	NUM
iajs-3044	115	11	𝑑𝑥	𝑑𝑥	X
iajs-3044	115	12	+	+	NOUN
iajs-3044	115	13	∫	∫	PROPN
iajs-3044	115	14	𝜆	𝜆	PRON
iajs-3044	115	15	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	115	16	𝑒−	𝑒−	NOUN
iajs-3044	115	17	𝜆	𝜆	DET
iajs-3044	115	18	2	2	NUM
iajs-3044	115	19	𝑥2	𝑥2	NOUN
iajs-3044	115	20	∞	∞	NOUN
iajs-3044	115	21	0	0	NUM
iajs-3044	115	22	𝑑𝑥	𝑑𝑥	X
iajs-3044	115	23	]	]	X
iajs-3044	115	24	…	…	PUNCT
iajs-3044	115	25	(	(	PUNCT
iajs-3044	115	26	37	37	NUM
iajs-3044	115	27	)	)	PUNCT
iajs-3044	115	28	now	now	ADV
iajs-3044	115	29	,	,	PUNCT
iajs-3044	115	30	based	base	VERB
iajs-3044	115	31	on	on	ADP
iajs-3044	115	32	equations	equation	NOUN
iajs-3044	115	33	(	(	PUNCT
iajs-3044	115	34	30	30	NUM
iajs-3044	115	35	)	)	PUNCT
iajs-3044	115	36	and	and	CCONJ
iajs-3044	115	37	(	(	PUNCT
iajs-3044	115	38	31	31	NUM
iajs-3044	115	39	)	)	PUNCT
iajs-3044	115	40	we	we	PRON
iajs-3044	115	41	get	get	VERB
iajs-3044	115	42	:	:	PUNCT
iajs-3044	115	43	𝑀(𝑡)𝐸𝑅	𝑀(𝑡)𝐸𝑅	PROPN
iajs-3044	115	44	=	=	PUNCT
iajs-3044	115	45	∑	∑	PUNCT
iajs-3044	115	46	(	(	PUNCT
iajs-3044	115	47	−(𝛼−ln(𝑡)))𝑛	−(𝛼−ln(𝑡)))𝑛	NOUN
iajs-3044	115	48	𝑛	𝑛	NOUN
iajs-3044	115	49	!	!	NOUN
iajs-3044	115	50	∞	∞	NUM
iajs-3044	116	1	𝑛=0	𝑛=0	NOUN
iajs-3044	116	2	2	2	NUM
iajs-3044	116	3	𝑛	𝑛	ADP
iajs-3044	116	4	2	2	NUM
iajs-3044	116	5	𝜆	𝜆	NOUN
iajs-3044	116	6	𝑛	𝑛	DET
iajs-3044	116	7	2	2	NUM
iajs-3044	116	8	[	[	PUNCT
iajs-3044	116	9	𝛼	𝛼	NOUN
iajs-3044	116	10	√2𝜆	√2𝜆	NUM
iajs-3044	116	11	𝛤	𝛤	PROPN
iajs-3044	116	12	(	(	PUNCT
iajs-3044	116	13	𝑛+1	𝑛+1	PROPN
iajs-3044	116	14	2	2	NUM
iajs-3044	116	15	)	)	PUNCT
iajs-3044	117	1	+	+	CCONJ
iajs-3044	117	2	𝛤	𝛤	PROPN
iajs-3044	117	3	(	(	PUNCT
iajs-3044	117	4	𝑛+2	𝑛+2	NUM
iajs-3044	117	5	2	2	NUM
iajs-3044	117	6	)	)	PUNCT
iajs-3044	117	7	]	]	PUNCT
iajs-3044	117	8	…	…	PUNCT
iajs-3044	117	9	(	(	PUNCT
iajs-3044	117	10	38	38	NUM
iajs-3044	117	11	)	)	PUNCT
iajs-3044	117	12	2.1.8	2.1.8	NUM
iajs-3044	117	13	characteristic	characteristic	ADJ
iajs-3044	117	14	function	function	NOUN
iajs-3044	117	15	the	the	DET
iajs-3044	117	16	characteristic	characteristic	ADJ
iajs-3044	117	17	function	function	NOUN
iajs-3044	117	18	of	of	ADP
iajs-3044	117	19	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	117	20	distribution	distribution	NOUN
iajs-3044	117	21	can	can	AUX
iajs-3044	117	22	be	be	AUX
iajs-3044	117	23	derived	derive	VERB
iajs-3044	117	24	as	as	SCONJ
iajs-3044	117	25	follows	follow	VERB
iajs-3044	117	26	:	:	PUNCT
iajs-3044	117	27	∅𝑋(𝑖𝑡)𝐸𝑅	∅𝑋(𝑖𝑡)𝐸𝑅	PROPN
iajs-3044	117	28	=	=	PUNCT
iajs-3044	117	29	𝐸(𝑒𝑖𝑡𝑥	𝐸(𝑒𝑖𝑡𝑥	PROPN
iajs-3044	117	30	)	)	PUNCT
iajs-3044	118	1	=	=	SYM
iajs-3044	118	2	∫	∫	PROPN
iajs-3044	118	3	𝑒𝑖𝑡𝑥	𝑒𝑖𝑡𝑥	PROPN
iajs-3044	118	4	(	(	PUNCT
iajs-3044	118	5	𝛼	𝛼	PROPN
iajs-3044	118	6	+	+	CCONJ
iajs-3044	118	7	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	118	8	)	)	PUNCT
iajs-3044	118	9	𝑒	𝑒	NOUN
iajs-3044	118	10	−	−	PROPN
iajs-3044	118	11	(	(	PUNCT
iajs-3044	118	12	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	118	13	+	+	CCONJ
iajs-3044	118	14	𝜆	𝜆	X
iajs-3044	118	15	2	2	NUM
iajs-3044	118	16	𝑥2	𝑥2	NOUN
iajs-3044	118	17	)	)	PUNCT
iajs-3044	118	18	∞	∞	NUM
iajs-3044	118	19	0	0	NUM
iajs-3044	118	20	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	118	21	∅𝑋(𝑖𝑡)𝐸𝑅	∅𝑋(𝑖𝑡)𝐸𝑅	NOUN
iajs-3044	118	22	=	=	SYM
iajs-3044	118	23	∫	∫	PROPN
iajs-3044	118	24	(	(	PUNCT
iajs-3044	118	25	𝛼	𝛼	PROPN
iajs-3044	118	26	+	+	CCONJ
iajs-3044	118	27	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	118	28	)	)	PUNCT
iajs-3044	118	29	𝑒−	𝑒−	NOUN
iajs-3044	118	30	(	(	PUNCT
iajs-3044	118	31	(	(	PUNCT
iajs-3044	118	32	𝛼−it	𝛼−it	X
iajs-3044	118	33	)	)	PUNCT
iajs-3044	118	34	𝑥	𝑥	PROPN
iajs-3044	119	1	+	+	CCONJ
iajs-3044	119	2	𝜆	𝜆	X
iajs-3044	119	3	2	2	NUM
iajs-3044	119	4	𝑥2	𝑥2	NOUN
iajs-3044	119	5	)	)	PUNCT
iajs-3044	119	6	∞	∞	NOUN
iajs-3044	119	7	0	0	NUM
iajs-3044	119	8	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	119	9	…	…	PUNCT
iajs-3044	119	10	(	(	PUNCT
iajs-3044	119	11	39	39	NUM
iajs-3044	119	12	)	)	PUNCT
iajs-3044	119	13	let	let	VERB
iajs-3044	119	14	𝑃((𝛼	𝑃((𝛼	NOUN
iajs-3044	119	15	−	−	VERB
iajs-3044	119	16	it	it	PRON
iajs-3044	119	17	)	)	PUNCT
iajs-3044	119	18	,	,	PUNCT
iajs-3044	119	19	𝜆	𝜆	X
iajs-3044	119	20	)	)	PUNCT
iajs-3044	119	21	=	=	SYM
iajs-3044	119	22	𝑒−	𝑒−	NOUN
iajs-3044	119	23	(	(	PUNCT
iajs-3044	119	24	(	(	PUNCT
iajs-3044	119	25	𝛼−𝑖𝑡	𝛼−𝑖𝑡	ADJ
iajs-3044	119	26	)	)	PUNCT
iajs-3044	119	27	𝑥	𝑥	PROPN
iajs-3044	120	1	+	+	CCONJ
iajs-3044	120	2	𝜆	𝜆	X
iajs-3044	120	3	2	2	NUM
iajs-3044	120	4	𝑥2	𝑥2	NOUN
iajs-3044	120	5	)	)	PUNCT
iajs-3044	120	6	…	…	PUNCT
iajs-3044	120	7	(	(	PUNCT
iajs-3044	120	8	40	40	NUM
iajs-3044	120	9	)	)	PUNCT
iajs-3044	120	10	by	by	ADP
iajs-3044	120	11	maclaurin	maclaurin	NOUN
iajs-3044	120	12	series	series	PROPN
iajs-3044	120	13	:	:	PUNCT
iajs-3044	120	14	ihjpas	ihjpas	PROPN
iajs-3044	120	15	.	.	PUNCT
iajs-3044	121	1	36(2)2023	36(2)2023	NUM
iajs-3044	121	2	397	397	NUM
iajs-3044	121	3	𝑒−(𝛼−it)𝑥	𝑒−(𝛼−it)𝑥	NOUN
iajs-3044	121	4	=	=	SYM
iajs-3044	121	5	∑	∑	PUNCT
iajs-3044	121	6	(	(	PUNCT
iajs-3044	121	7	−(𝛼−it))𝑛	−(𝛼−it))𝑛	NOUN
iajs-3044	121	8	𝑛	𝑛	NOUN
iajs-3044	121	9	!	!	NOUN
iajs-3044	121	10	∞	∞	NUM
iajs-3044	122	1	𝑛=0	𝑛=0	PROPN
iajs-3044	122	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	122	3	…	…	PUNCT
iajs-3044	122	4	(	(	PUNCT
iajs-3044	122	5	41	41	NUM
iajs-3044	122	6	)	)	PUNCT
iajs-3044	122	7	substituting	substitute	VERB
iajs-3044	122	8	equation	equation	NOUN
iajs-3044	122	9	(	(	PUNCT
iajs-3044	122	10	41	41	NUM
iajs-3044	122	11	)	)	PUNCT
iajs-3044	122	12	in	in	ADP
iajs-3044	122	13	equation	equation	NOUN
iajs-3044	122	14	(	(	PUNCT
iajs-3044	122	15	40	40	NUM
iajs-3044	122	16	)	)	PUNCT
iajs-3044	122	17	gives	give	VERB
iajs-3044	122	18	:	:	PUNCT
iajs-3044	122	19	𝑃((𝛼	𝑃((𝛼	NOUN
iajs-3044	122	20	−	−	PROPN
iajs-3044	122	21	it	it	PRON
iajs-3044	122	22	)	)	PUNCT
iajs-3044	122	23	,	,	PUNCT
iajs-3044	122	24	𝜆	𝜆	X
iajs-3044	122	25	)	)	PUNCT
iajs-3044	122	26	=	=	SYM
iajs-3044	122	27	∑	∑	PUNCT
iajs-3044	122	28	(	(	PUNCT
iajs-3044	122	29	−(𝛼−it))𝑛	−(𝛼−it))𝑛	NOUN
iajs-3044	122	30	𝑛	𝑛	NOUN
iajs-3044	122	31	!	!	PUNCT
iajs-3044	122	32	∞	∞	NUM
iajs-3044	123	1	𝑛=0	𝑛=0	PROPN
iajs-3044	123	2	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	123	3	𝑒−	𝑒−	NOUN
iajs-3044	123	4	𝜆	𝜆	PRON
iajs-3044	123	5	2	2	NUM
iajs-3044	123	6	𝑥2	𝑥2	NOUN
iajs-3044	123	7	…	…	PUNCT
iajs-3044	123	8	(	(	PUNCT
iajs-3044	123	9	42	42	NUM
iajs-3044	123	10	)	)	PUNCT
iajs-3044	123	11	substituting	substitute	VERB
iajs-3044	123	12	equation	equation	NOUN
iajs-3044	123	13	(	(	PUNCT
iajs-3044	123	14	42	42	NUM
iajs-3044	123	15	)	)	PUNCT
iajs-3044	123	16	in	in	ADP
iajs-3044	123	17	equation	equation	NOUN
iajs-3044	123	18	(	(	PUNCT
iajs-3044	123	19	39	39	NUM
iajs-3044	123	20	)	)	PUNCT
iajs-3044	123	21	gives	give	VERB
iajs-3044	123	22	:	:	PUNCT
iajs-3044	123	23	∅𝑋(𝑖𝑡)𝐸𝑅	∅𝑋(𝑖𝑡)𝐸𝑅	NOUN
iajs-3044	123	24	=	=	SYM
iajs-3044	123	25	∑	∑	PROPN
iajs-3044	123	26	(	(	PUNCT
iajs-3044	123	27	−(𝛼−it))𝑛	−(𝛼−it))𝑛	NOUN
iajs-3044	123	28	𝑛	𝑛	NOUN
iajs-3044	123	29	!	!	PUNCT
iajs-3044	123	30	∞	∞	NUM
iajs-3044	124	1	𝑛=0	𝑛=0	PROPN
iajs-3044	125	1	[	[	X
iajs-3044	125	2	∫	∫	X
iajs-3044	125	3	𝛼	𝛼	VERB
iajs-3044	125	4	𝑥𝑛	𝑥𝑛	NOUN
iajs-3044	125	5	𝑒−	𝑒−	VERB
iajs-3044	125	6	𝜆	𝜆	DET
iajs-3044	125	7	2	2	NUM
iajs-3044	125	8	𝑥2	𝑥2	NOUN
iajs-3044	125	9	∞	∞	NOUN
iajs-3044	125	10	0	0	NUM
iajs-3044	125	11	𝑑𝑥	𝑑𝑥	X
iajs-3044	125	12	+	+	NOUN
iajs-3044	125	13	∫	∫	PROPN
iajs-3044	125	14	𝜆	𝜆	PRON
iajs-3044	125	15	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	125	16	𝑒−	𝑒−	NOUN
iajs-3044	125	17	𝜆	𝜆	DET
iajs-3044	125	18	2	2	NUM
iajs-3044	125	19	𝑥2	𝑥2	NOUN
iajs-3044	125	20	∞	∞	NOUN
iajs-3044	125	21	0	0	NUM
iajs-3044	125	22	𝑑𝑥	𝑑𝑥	X
iajs-3044	125	23	]	]	X
iajs-3044	125	24	…	…	PUNCT
iajs-3044	125	25	(	(	PUNCT
iajs-3044	125	26	43	43	NUM
iajs-3044	125	27	)	)	PUNCT
iajs-3044	125	28	now	now	ADV
iajs-3044	125	29	,	,	PUNCT
iajs-3044	125	30	based	base	VERB
iajs-3044	125	31	on	on	ADP
iajs-3044	125	32	equations	equation	NOUN
iajs-3044	125	33	(	(	PUNCT
iajs-3044	125	34	30	30	NUM
iajs-3044	125	35	)	)	PUNCT
iajs-3044	125	36	and	and	CCONJ
iajs-3044	125	37	(	(	PUNCT
iajs-3044	125	38	31	31	NUM
iajs-3044	125	39	)	)	PUNCT
iajs-3044	125	40	we	we	PRON
iajs-3044	125	41	get	get	VERB
iajs-3044	125	42	:	:	PUNCT
iajs-3044	125	43	∅𝑋(𝑖𝑡)𝐸𝑅	∅𝑋(𝑖𝑡)𝐸𝑅	NOUN
iajs-3044	125	44	=	=	SYM
iajs-3044	125	45	∑	∑	PROPN
iajs-3044	125	46	(	(	PUNCT
iajs-3044	125	47	−(𝛼−it))𝑛	−(𝛼−it))𝑛	NOUN
iajs-3044	125	48	𝑛	𝑛	NOUN
iajs-3044	125	49	!	!	NOUN
iajs-3044	126	1	∞	∞	NUM
iajs-3044	127	1	𝑛=0	𝑛=0	NOUN
iajs-3044	127	2	2	2	NUM
iajs-3044	127	3	𝑛	𝑛	ADP
iajs-3044	127	4	2	2	NUM
iajs-3044	127	5	𝜆	𝜆	NOUN
iajs-3044	127	6	𝑛	𝑛	DET
iajs-3044	127	7	2	2	NUM
iajs-3044	127	8	[	[	PUNCT
iajs-3044	127	9	𝛼	𝛼	NOUN
iajs-3044	127	10	√2𝜆	√2𝜆	NUM
iajs-3044	127	11	𝛤	𝛤	PROPN
iajs-3044	127	12	(	(	PUNCT
iajs-3044	127	13	𝑛+1	𝑛+1	PROPN
iajs-3044	127	14	2	2	NUM
iajs-3044	127	15	)	)	PUNCT
iajs-3044	128	1	+	+	CCONJ
iajs-3044	128	2	𝛤	𝛤	PROPN
iajs-3044	128	3	(	(	PUNCT
iajs-3044	128	4	𝑛+2	𝑛+2	NUM
iajs-3044	128	5	2	2	NUM
iajs-3044	128	6	)	)	PUNCT
iajs-3044	128	7	]	]	PUNCT
iajs-3044	128	8	…	…	PUNCT
iajs-3044	128	9	(	(	PUNCT
iajs-3044	128	10	44	44	NUM
iajs-3044	128	11	)	)	PUNCT
iajs-3044	128	12	2.1.9	2.1.9	NUM
iajs-3044	128	13	quantile	quantile	ADJ
iajs-3044	128	14	function	function	NOUN
iajs-3044	128	15	the	the	DET
iajs-3044	128	16	quantile	quantile	ADJ
iajs-3044	128	17	function	function	NOUN
iajs-3044	128	18	of	of	ADP
iajs-3044	128	19	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	128	20	random	random	ADJ
iajs-3044	128	21	variable	variable	NOUN
iajs-3044	128	22	is	be	AUX
iajs-3044	128	23	defined	define	VERB
iajs-3044	128	24	as	as	ADP
iajs-3044	128	25	a	a	DET
iajs-3044	128	26	solution	solution	NOUN
iajs-3044	128	27	of	of	ADP
iajs-3044	128	28	𝑝(𝑥	𝑝(𝑥	PROPN
iajs-3044	128	29	≤	≤	NOUN
iajs-3044	128	30	𝑥(𝑞	𝑥(𝑞	NUM
iajs-3044	128	31	)	)	PUNCT
iajs-3044	128	32	)	)	PUNCT
iajs-3044	129	1	=	=	SYM
iajs-3044	129	2	𝐹(𝑥(𝑞))𝐸𝑅	𝐹(𝑥(𝑞))𝐸𝑅	NUM
iajs-3044	129	3	w.r.t	w.r.t	NOUN
iajs-3044	129	4	.	.	PUNCT
iajs-3044	130	1	𝑥(𝑞	𝑥(𝑞	X
iajs-3044	130	2	)	)	PUNCT
iajs-3044	130	3	,	,	PUNCT
iajs-3044	130	4	therefore	therefore	ADV
iajs-3044	130	5	,	,	PUNCT
iajs-3044	130	6	via	via	ADP
iajs-3044	130	7	using	use	VERB
iajs-3044	130	8	the	the	DET
iajs-3044	130	9	inverse	inverse	NOUN
iajs-3044	130	10	transformation	transformation	NOUN
iajs-3044	130	11	to	to	ADP
iajs-3044	130	12	equation	equation	NOUN
iajs-3044	130	13	(	(	PUNCT
iajs-3044	130	14	5	5	NUM
iajs-3044	130	15	)	)	PUNCT
iajs-3044	130	16	,	,	PUNCT
iajs-3044	130	17	it	it	PRON
iajs-3044	130	18	can	can	AUX
iajs-3044	130	19	be	be	AUX
iajs-3044	130	20	found	find	VERB
iajs-3044	130	21	as	as	ADP
iajs-3044	130	22	:	:	PUNCT
iajs-3044	130	23	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	130	24	)	)	PUNCT
iajs-3044	130	25	=	=	SYM
iajs-3044	130	26	𝐹−1(𝑞	𝐹−1(𝑞	NUM
iajs-3044	130	27	)	)	PUNCT
iajs-3044	130	28	;	;	PUNCT
iajs-3044	130	29	𝑥(𝑞	𝑥(𝑞	X
iajs-3044	130	30	)	)	PUNCT
iajs-3044	130	31	>	>	X
iajs-3044	130	32	0	0	NUM
iajs-3044	130	33	;	;	PUNCT
iajs-3044	130	34	0	0	NUM
iajs-3044	130	35	<	<	X
iajs-3044	130	36	𝑞	𝑞	X
iajs-3044	130	37	<	<	X
iajs-3044	130	38	1	1	NUM
iajs-3044	130	39	𝑞	𝑞	NOUN
iajs-3044	130	40	=	=	NOUN
iajs-3044	130	41	1	1	NUM
iajs-3044	130	42	−	−	NOUN
iajs-3044	130	43	𝑒−	𝑒−	NOUN
iajs-3044	130	44	(	(	PUNCT
iajs-3044	130	45	𝛼𝑥(𝑞	𝛼𝑥(𝑞	PUNCT
iajs-3044	130	46	)	)	PUNCT
iajs-3044	130	47	+	+	CCONJ
iajs-3044	130	48	𝜆	𝜆	DET
iajs-3044	130	49	2	2	NUM
iajs-3044	130	50	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	130	51	)	)	PUNCT
iajs-3044	130	52	2	2	NUM
iajs-3044	130	53	)	)	PUNCT
iajs-3044	130	54	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	130	55	(	(	PUNCT
iajs-3044	130	56	1	1	NUM
iajs-3044	130	57	−	−	PROPN
iajs-3044	130	58	𝑞	𝑞	PROPN
iajs-3044	130	59	)	)	PUNCT
iajs-3044	130	60	=	=	SYM
iajs-3044	130	61	−(𝛼𝑥(𝑞	−(𝛼𝑥(𝑞	VERB
iajs-3044	130	62	)	)	PUNCT
iajs-3044	131	1	+	+	CCONJ
iajs-3044	131	2	𝜆	𝜆	DET
iajs-3044	131	3	2	2	NUM
iajs-3044	131	4	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	131	5	)	)	PUNCT
iajs-3044	131	6	2	2	NUM
iajs-3044	131	7	)	)	PUNCT
iajs-3044	132	1	𝜆	𝜆	DET
iajs-3044	132	2	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	132	3	)	)	PUNCT
iajs-3044	132	4	2	2	NUM
iajs-3044	132	5	+	+	NUM
iajs-3044	132	6	2𝛼𝑥(𝑞	2𝛼𝑥(𝑞	NUM
iajs-3044	132	7	)	)	PUNCT
iajs-3044	133	1	+	+	CCONJ
iajs-3044	133	2	2	2	NUM
iajs-3044	133	3	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	133	4	(	(	PUNCT
iajs-3044	133	5	1	1	NUM
iajs-3044	133	6	−	−	PROPN
iajs-3044	133	7	𝑞	𝑞	NOUN
iajs-3044	133	8	)	)	PUNCT
iajs-3044	133	9	=	=	SYM
iajs-3044	133	10	0	0	NUM
iajs-3044	133	11	based	base	VERB
iajs-3044	133	12	on	on	ADP
iajs-3044	133	13	law	law	NOUN
iajs-3044	133	14	of	of	ADP
iajs-3044	133	15	the	the	DET
iajs-3044	133	16	constitution	constitution	NOUN
iajs-3044	133	17	,	,	PUNCT
iajs-3044	133	18	we	we	PRON
iajs-3044	133	19	get	get	VERB
iajs-3044	133	20	:	:	PUNCT
iajs-3044	133	21	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	133	22	)	)	PUNCT
iajs-3044	134	1	=	=	SYM
iajs-3044	134	2	−(2𝛼)∓√4𝛼2−8	−(2𝛼)∓√4𝛼2−8	NOUN
iajs-3044	134	3	𝜆	𝜆	PRON
iajs-3044	134	4	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	134	5	(	(	PUNCT
iajs-3044	134	6	1−𝑞	1−𝑞	NUM
iajs-3044	134	7	)	)	PUNCT
iajs-3044	134	8	2	2	NUM
iajs-3044	134	9	𝜆	𝜆	PRON
iajs-3044	134	10	…	…	PUNCT
iajs-3044	134	11	(	(	PUNCT
iajs-3044	134	12	45	45	NUM
iajs-3044	134	13	)	)	PUNCT
iajs-3044	134	14	since	since	SCONJ
iajs-3044	134	15	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	134	16	)	)	PUNCT
iajs-3044	134	17	>	>	X
iajs-3044	134	18	0	0	NUM
iajs-3044	134	19	,	,	PUNCT
iajs-3044	134	20	the	the	DET
iajs-3044	134	21	negative	negative	ADJ
iajs-3044	134	22	values	value	NOUN
iajs-3044	134	23	of	of	ADP
iajs-3044	134	24	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	134	25	)	)	PUNCT
iajs-3044	134	26	will	will	AUX
iajs-3044	134	27	be	be	AUX
iajs-3044	134	28	ignored	ignore	VERB
iajs-3044	134	29	.	.	PUNCT
iajs-3044	135	1	3	3	X
iajs-3044	135	2	.	.	X
iajs-3044	135	3	modified	modify	VERB
iajs-3044	135	4	weighted	weight	VERB
iajs-3044	135	5	exponential	exponential	ADJ
iajs-3044	135	6	rayleigh	rayleigh	NOUN
iajs-3044	135	7	distribution	distribution	NOUN
iajs-3044	135	8	this	this	DET
iajs-3044	135	9	section	section	NOUN
iajs-3044	135	10	discusses	discuss	VERB
iajs-3044	135	11	adding	add	VERB
iajs-3044	135	12	a	a	DET
iajs-3044	135	13	shape	shape	NOUN
iajs-3044	135	14	parameter	parameter	NOUN
iajs-3044	135	15	to	to	ADP
iajs-3044	135	16	exponential	exponential	ADJ
iajs-3044	135	17	rayleigh	rayleigh	PROPN
iajs-3044	135	18	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	135	19	distribution	distribution	NOUN
iajs-3044	135	20	and	and	CCONJ
iajs-3044	135	21	generating	generate	VERB
iajs-3044	135	22	a	a	DET
iajs-3044	135	23	modified	modify	VERB
iajs-3044	135	24	weighted	weight	VERB
iajs-3044	135	25	exponential	exponential	ADJ
iajs-3044	135	26	rayleigh	rayleigh	PROPN
iajs-3044	135	27	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	135	28	distribution	distribution	NOUN
iajs-3044	135	29	as	as	SCONJ
iajs-3044	135	30	follows	follow	VERB
iajs-3044	135	31	:	:	PUNCT
iajs-3044	135	32	the	the	DET
iajs-3044	135	33	general	general	ADJ
iajs-3044	135	34	definition	definition	NOUN
iajs-3044	135	35	for	for	ADP
iajs-3044	135	36	extracting	extract	VERB
iajs-3044	135	37	modified	modify	VERB
iajs-3044	135	38	weighted	weight	VERB
iajs-3044	135	39	non	non	ADJ
iajs-3044	135	40	-	-	ADJ
iajs-3044	135	41	negative	negative	ADJ
iajs-3044	135	42	models	model	NOUN
iajs-3044	135	43	depending	depend	VERB
iajs-3044	135	44	on	on	ADP
iajs-3044	135	45	a	a	DET
iajs-3044	135	46	modified	modify	VERB
iajs-3044	135	47	weighted	weight	VERB
iajs-3044	135	48	version	version	NOUN
iajs-3044	135	49	of	of	ADP
iajs-3044	135	50	azzalini	azzalini	PROPN
iajs-3044	135	51	’s	’s	PART
iajs-3044	135	52	(	(	PUNCT
iajs-3044	135	53	1985	1985	NUM
iajs-3044	135	54	)	)	PUNCT
iajs-3044	135	55	can	can	AUX
iajs-3044	135	56	be	be	AUX
iajs-3044	135	57	summarized	summarize	VERB
iajs-3044	135	58	by	by	ADP
iajs-3044	135	59	[	[	X
iajs-3044	135	60	10	10	NUM
iajs-3044	135	61	]	]	PUNCT
iajs-3044	135	62	:	:	PUNCT
iajs-3044	135	63	let	let	VERB
iajs-3044	135	64	𝑔(𝑥	𝑔(𝑥	NUM
iajs-3044	135	65	)	)	PUNCT
iajs-3044	135	66	be	be	AUX
iajs-3044	135	67	a	a	DET
iajs-3044	135	68	probability	probability	NOUN
iajs-3044	135	69	density	density	NOUN
iajs-3044	135	70	function	function	NOUN
iajs-3044	135	71	and	and	CCONJ
iajs-3044	135	72	�	�	NOUN
iajs-3044	135	73	̅	̅	NOUN
iajs-3044	135	74	�	�	NOUN
iajs-3044	135	75	(𝑥	(𝑥	VERB
iajs-3044	135	76	)	)	PUNCT
iajs-3044	135	77	be	be	AUX
iajs-3044	135	78	corresponding	correspond	VERB
iajs-3044	135	79	reliability	reliability	NOUN
iajs-3044	135	80	(	(	PUNCT
iajs-3044	135	81	survival	survival	NOUN
iajs-3044	135	82	)	)	PUNCT
iajs-3044	135	83	function	function	VERB
iajs-3044	135	84	such	such	ADJ
iajs-3044	135	85	that	that	SCONJ
iajs-3044	135	86	the	the	DET
iajs-3044	135	87	cumulative	cumulative	ADJ
iajs-3044	135	88	distribution	distribution	NOUN
iajs-3044	135	89	function	function	NOUN
iajs-3044	135	90	𝐺(𝑥	𝐺(𝑥	NOUN
iajs-3044	135	91	)	)	PUNCT
iajs-3044	135	92	exist	exist	VERB
iajs-3044	135	93	.	.	PUNCT
iajs-3044	136	1	then	then	ADV
iajs-3044	136	2	the	the	DET
iajs-3044	136	3	modified	modified	ADJ
iajs-3044	136	4	weighted	weight	VERB
iajs-3044	136	5	model	model	NOUN
iajs-3044	136	6	of	of	ADP
iajs-3044	136	7	distribution	distribution	NOUN
iajs-3044	136	8	is	be	AUX
iajs-3044	136	9	given	give	VERB
iajs-3044	136	10	by	by	ADP
iajs-3044	136	11	:	:	PUNCT
iajs-3044	136	12	𝑓(𝑥)𝑀𝑊	𝑓(𝑥)𝑀𝑊	X
iajs-3044	136	13	=	=	SYM
iajs-3044	136	14	𝑀	𝑀	PROPN
iajs-3044	136	15	𝑔(𝑥	𝑔(𝑥	NOUN
iajs-3044	136	16	)	)	PUNCT
iajs-3044	136	17	�	�	PROPN
iajs-3044	136	18	̅	̅	NOUN
iajs-3044	136	19	�	�	NOUN
iajs-3044	136	20	(𝜃𝑥	(𝜃𝑥	NOUN
iajs-3044	136	21	)	)	PUNCT
iajs-3044	136	22	where	where	SCONJ
iajs-3044	136	23	,	,	PUNCT
iajs-3044	136	24	𝑀	𝑀	PROPN
iajs-3044	136	25	is	be	AUX
iajs-3044	136	26	the	the	DET
iajs-3044	136	27	normalizing	normalize	VERB
iajs-3044	136	28	constant	constant	NOUN
iajs-3044	136	29	and	and	CCONJ
iajs-3044	136	30	𝜃	𝜃	X
iajs-3044	136	31	>	>	X
iajs-3044	136	32	0	0	PUNCT
iajs-3044	136	33	is	be	AUX
iajs-3044	136	34	the	the	DET
iajs-3044	136	35	shape	shape	NOUN
iajs-3044	136	36	parameter	parameter	NOUN
iajs-3044	136	37	.	.	PUNCT
iajs-3044	137	1	in	in	ADP
iajs-3044	137	2	our	our	PRON
iajs-3044	137	3	work	work	NOUN
iajs-3044	137	4	this	this	DET
iajs-3044	137	5	parameter	parameter	NOUN
iajs-3044	137	6	𝜃	𝜃	NOUN
iajs-3044	137	7	does	do	AUX
iajs-3044	137	8	not	not	PART
iajs-3044	137	9	depend	depend	VERB
iajs-3044	137	10	on	on	ADP
iajs-3044	137	11	the	the	DET
iajs-3044	137	12	degree	degree	NOUN
iajs-3044	137	13	of	of	ADP
iajs-3044	137	14	the	the	DET
iajs-3044	137	15	random	random	ADJ
iajs-3044	137	16	variable	variable	NOUN
iajs-3044	137	17	x.	x.	NOUN
iajs-3044	137	18	now	now	ADV
iajs-3044	137	19	,	,	PUNCT
iajs-3044	137	20	consider	consider	VERB
iajs-3044	137	21	a	a	DET
iajs-3044	137	22	probability	probability	NOUN
iajs-3044	137	23	density	density	NOUN
iajs-3044	137	24	function	function	NOUN
iajs-3044	137	25	of	of	ADP
iajs-3044	137	26	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	137	27	distribution	distribution	NOUN
iajs-3044	137	28	as	as	ADP
iajs-3044	137	29	in	in	ADP
iajs-3044	137	30	equation	equation	NOUN
iajs-3044	137	31	(	(	PUNCT
iajs-3044	137	32	6	6	NUM
iajs-3044	137	33	)	)	PUNCT
iajs-3044	137	34	and	and	CCONJ
iajs-3044	137	35	the	the	DET
iajs-3044	137	36	survival	survival	NOUN
iajs-3044	137	37	function	function	NOUN
iajs-3044	137	38	as	as	ADP
iajs-3044	137	39	in	in	ADP
iajs-3044	137	40	equation	equation	NOUN
iajs-3044	137	41	(	(	PUNCT
iajs-3044	137	42	7	7	NUM
iajs-3044	137	43	)	)	PUNCT
iajs-3044	137	44	,	,	PUNCT
iajs-3044	137	45	according	accord	VERB
iajs-3044	137	46	to	to	ADP
iajs-3044	137	47	the	the	DET
iajs-3044	137	48	previous	previous	ADJ
iajs-3044	137	49	definition	definition	NOUN
iajs-3044	137	50	for	for	ADP
iajs-3044	137	51	extracting	extract	VERB
iajs-3044	137	52	modified	modify	VERB
iajs-3044	137	53	weighted	weight	VERB
iajs-3044	137	54	non	non	ADJ
iajs-3044	137	55	-	-	ADJ
iajs-3044	137	56	negative	negative	ADJ
iajs-3044	137	57	models	model	NOUN
iajs-3044	137	58	,	,	PUNCT
iajs-3044	137	59	put	put	VERB
iajs-3044	137	60	𝑀	𝑀	PROPN
iajs-3044	137	61	=	=	PUNCT
iajs-3044	138	1	1	1	NUM
iajs-3044	138	2	+	+	NOUN
iajs-3044	138	3	𝜃	𝜃	PRON
iajs-3044	138	4	extract	extract	VERB
iajs-3044	138	5	the	the	DET
iajs-3044	138	6	probability	probability	NOUN
iajs-3044	138	7	density	density	NOUN
iajs-3044	138	8	function	function	NOUN
iajs-3044	138	9	of	of	ADP
iajs-3044	138	10	modified	modify	VERB
iajs-3044	138	11	weighted	weight	VERB
iajs-3044	138	12	exponential	exponential	ADJ
iajs-3044	138	13	rayleigh	rayleigh	PROPN
iajs-3044	138	14	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	138	15	distribution	distribution	NOUN
iajs-3044	138	16	as	as	SCONJ
iajs-3044	138	17	follows	follow	VERB
iajs-3044	138	18	:	:	PUNCT
iajs-3044	138	19	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	138	20	;	;	PUNCT
iajs-3044	138	21	𝛼	𝛼	X
iajs-3044	138	22	,	,	PUNCT
iajs-3044	138	23	𝜆	𝜆	X
iajs-3044	138	24	,	,	PUNCT
iajs-3044	138	25	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	138	26	=	=	SYM
iajs-3044	139	1	𝑀(𝛼	𝑀(𝛼	PROPN
iajs-3044	140	1	+	+	CCONJ
iajs-3044	140	2	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	140	3	)	)	PUNCT
iajs-3044	140	4	𝑒	𝑒	NOUN
iajs-3044	140	5	−	−	PROPN
iajs-3044	140	6	(	(	PUNCT
iajs-3044	140	7	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	140	8	+	+	CCONJ
iajs-3044	140	9	𝜆	𝜆	X
iajs-3044	140	10	2	2	NUM
iajs-3044	140	11	𝑥2	𝑥2	NOUN
iajs-3044	140	12	)	)	PUNCT
iajs-3044	140	13	𝑒	𝑒	ADP
iajs-3044	140	14	−	−	PROPN
iajs-3044	140	15	(	(	PUNCT
iajs-3044	140	16	𝛼𝜃𝑥	𝛼𝜃𝑥	NOUN
iajs-3044	140	17	+	+	CCONJ
iajs-3044	140	18	𝜆𝜃	𝜆𝜃	NUM
iajs-3044	140	19	2	2	NUM
iajs-3044	140	20	𝑥2	𝑥2	NOUN
iajs-3044	140	21	)	)	PUNCT
iajs-3044	140	22	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	140	23	;	;	PUNCT
iajs-3044	140	24	𝛼	𝛼	X
iajs-3044	140	25	,	,	PUNCT
iajs-3044	140	26	𝜆	𝜆	NOUN
iajs-3044	140	27	,	,	PUNCT
iajs-3044	140	28	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	140	29	=	=	SYM
iajs-3044	140	30	(	(	PUNCT
iajs-3044	140	31	1	1	NUM
iajs-3044	140	32	+	+	CCONJ
iajs-3044	140	33	𝜃)(𝛼	𝜃)(𝛼	PROPN
iajs-3044	140	34	+	+	CCONJ
iajs-3044	140	35	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	140	36	)	)	PUNCT
iajs-3044	140	37	𝑒	𝑒	NOUN
iajs-3044	140	38	−	−	PROPN
iajs-3044	140	39	(	(	PUNCT
iajs-3044	140	40	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	140	41	+	+	CCONJ
iajs-3044	140	42	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	140	43	)	)	PUNCT
iajs-3044	140	44	2	2	NUM
iajs-3044	140	45	𝑥2	𝑥2	NOUN
iajs-3044	140	46	)	)	PUNCT
iajs-3044	140	47	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	140	48	;	;	PUNCT
iajs-3044	140	49	𝛼	𝛼	X
iajs-3044	140	50	,	,	PUNCT
iajs-3044	140	51	𝜆	𝜆	NOUN
iajs-3044	140	52	,	,	PUNCT
iajs-3044	140	53	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	140	54	=	=	PUNCT
iajs-3044	140	55	(	(	PUNCT
iajs-3044	140	56	𝛼(1	𝛼(1	NOUN
iajs-3044	140	57	+	+	NUM
iajs-3044	140	58	𝜃	𝜃	X
iajs-3044	140	59	)	)	PUNCT
iajs-3044	141	1	+	+	CCONJ
iajs-3044	141	2	𝜆(1	𝜆(1	CCONJ
iajs-3044	141	3	+	+	NUM
iajs-3044	141	4	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	141	5	)	)	PUNCT
iajs-3044	141	6	𝑒−	𝑒−	NOUN
iajs-3044	141	7	(	(	PUNCT
iajs-3044	141	8	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	141	9	+	+	CCONJ
iajs-3044	141	10	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	141	11	)	)	PUNCT
iajs-3044	141	12	2	2	NUM
iajs-3044	141	13	𝑥2	𝑥2	NOUN
iajs-3044	141	14	)	)	PUNCT
iajs-3044	141	15	;	;	PUNCT
iajs-3044	142	1	𝑥	𝑥	PRON
iajs-3044	142	2	≥	≥	NOUN
iajs-3044	142	3	0	0	NUM
iajs-3044	142	4	…	…	PUNCT
iajs-3044	142	5	(	(	PUNCT
iajs-3044	142	6	46	46	NUM
iajs-3044	142	7	)	)	PUNCT
iajs-3044	142	8	zero	zero	NUM
iajs-3044	142	9	otherwise	otherwise	ADV
iajs-3044	142	10	.	.	PUNCT
iajs-3044	143	1	ihjpas	ihjpas	PROPN
iajs-3044	143	2	.	.	PUNCT
iajs-3044	144	1	36(2)2023	36(2)2023	NUM
iajs-3044	144	2	398	398	NUM
iajs-3044	144	3	where	where	SCONJ
iajs-3044	144	4	𝛼	𝛼	X
iajs-3044	144	5	,	,	PUNCT
iajs-3044	144	6	𝜆	𝜆	PROPN
iajs-3044	144	7	>	>	X
iajs-3044	144	8	0	0	NUM
iajs-3044	144	9	are	be	AUX
iajs-3044	144	10	scale	scale	NOUN
iajs-3044	144	11	parameters	parameter	NOUN
iajs-3044	144	12	and	and	CCONJ
iajs-3044	144	13	𝜃	𝜃	X
iajs-3044	144	14	>	>	X
iajs-3044	144	15	0	0	PUNCT
iajs-3044	144	16	is	be	AUX
iajs-3044	144	17	the	the	DET
iajs-3044	144	18	shape	shape	NOUN
iajs-3044	144	19	parameter	parameter	NOUN
iajs-3044	144	20	.	.	PUNCT
iajs-3044	145	1	such	such	ADJ
iajs-3044	145	2	that	that	DET
iajs-3044	145	3	,	,	PUNCT
iajs-3044	145	4	•	•	NUM
iajs-3044	145	5	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	145	6	;	;	PUNCT
iajs-3044	145	7	𝛼	𝛼	X
iajs-3044	145	8	,	,	PUNCT
iajs-3044	145	9	𝜆	𝜆	NOUN
iajs-3044	145	10	,	,	PUNCT
iajs-3044	145	11	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	145	12	>	>	X
iajs-3044	145	13	0	0	NUM
iajs-3044	145	14	•	•	NUM
iajs-3044	145	15	∫	∫	NOUN
iajs-3044	145	16	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	145	17	;	;	PUNCT
iajs-3044	145	18	𝛼	𝛼	X
iajs-3044	145	19	,	,	PUNCT
iajs-3044	145	20	𝜆	𝜆	X
iajs-3044	145	21	,	,	PUNCT
iajs-3044	145	22	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	145	23	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	145	24	∞	∞	NUM
iajs-3044	145	25	0	0	NUM
iajs-3044	145	26	=	=	SYM
iajs-3044	145	27	∫	∫	PROPN
iajs-3044	145	28	(	(	PUNCT
iajs-3044	145	29	𝛼(1	𝛼(1	NOUN
iajs-3044	145	30	+	+	NUM
iajs-3044	145	31	𝜃	𝜃	X
iajs-3044	145	32	)	)	PUNCT
iajs-3044	146	1	+	+	CCONJ
iajs-3044	146	2	𝜆(1	𝜆(1	CCONJ
iajs-3044	146	3	+	+	NUM
iajs-3044	146	4	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	146	5	)	)	PUNCT
iajs-3044	146	6	𝑒	𝑒	ADP
iajs-3044	146	7	−	−	PROPN
iajs-3044	146	8	(	(	PUNCT
iajs-3044	146	9	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	146	10	+	+	CCONJ
iajs-3044	146	11	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	146	12	)	)	PUNCT
iajs-3044	146	13	2	2	NUM
iajs-3044	146	14	𝑥2	𝑥2	NOUN
iajs-3044	146	15	)	)	PUNCT
iajs-3044	146	16	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	146	17	∞	∞	PROPN
iajs-3044	146	18	0	0	NUM
iajs-3044	146	19	=	=	SYM
iajs-3044	147	1	−	−	PROPN
iajs-3044	147	2	[	[	PUNCT
iajs-3044	147	3	𝑒	𝑒	PROPN
iajs-3044	147	4	−	−	PROPN
iajs-3044	147	5	(	(	PUNCT
iajs-3044	147	6	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	147	7	+	+	CCONJ
iajs-3044	147	8	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	147	9	)	)	PUNCT
iajs-3044	147	10	2	2	NUM
iajs-3044	147	11	𝑥2	𝑥2	NOUN
iajs-3044	147	12	)	)	PUNCT
iajs-3044	147	13	]	]	PUNCT
iajs-3044	148	1	0	0	NUM
iajs-3044	149	1	∞	∞	NUM
iajs-3044	149	2	=	=	SYM
iajs-3044	149	3	1	1	NUM
iajs-3044	149	4	figure	figure	NOUN
iajs-3044	149	5	6	6	NUM
iajs-3044	149	6	.	.	PUNCT
iajs-3044	149	7	plot	plot	NOUN
iajs-3044	149	8	of	of	ADP
iajs-3044	149	9	the	the	DET
iajs-3044	149	10	probability	probability	NOUN
iajs-3044	149	11	density	density	NOUN
iajs-3044	149	12	function	function	NOUN
iajs-3044	149	13	of	of	ADP
iajs-3044	149	14	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	149	15	distribution	distribution	NOUN
iajs-3044	149	16	for	for	ADP
iajs-3044	149	17	𝜆	𝜆	DET
iajs-3044	149	18	=	=	SYM
iajs-3044	149	19	𝜃	𝜃	PROPN
iajs-3044	149	20	=	=	SYM
iajs-3044	149	21	0.1	0.1	NUM
iajs-3044	149	22	and	and	CCONJ
iajs-3044	149	23	different	different	ADJ
iajs-3044	149	24	values	value	NOUN
iajs-3044	149	25	of	of	ADP
iajs-3044	149	26	(	(	PUNCT
iajs-3044	149	27	𝛼	𝛼	X
iajs-3044	149	28	=	=	NOUN
iajs-3044	149	29	0.1	0.1	NUM
iajs-3044	149	30	,	,	PUNCT
iajs-3044	149	31	0.2	0.2	NUM
iajs-3044	149	32	,	,	PUNCT
iajs-3044	149	33	0.3	0.3	NUM
iajs-3044	149	34	,	,	PUNCT
iajs-3044	149	35	0.4,0.5	0.4,0.5	PROPN
iajs-3044	149	36	,	,	PUNCT
iajs-3044	149	37	0.6	0.6	NUM
iajs-3044	149	38	,	,	PUNCT
iajs-3044	149	39	0.7	0.7	NUM
iajs-3044	149	40	)	)	PUNCT
iajs-3044	149	41	[	[	PUNCT
iajs-3044	149	42	matlab	matlab	X
iajs-3044	149	43	r2013a	r2013a	X
iajs-3044	149	44	]	]	X
iajs-3044	149	45	.	.	PUNCT
iajs-3044	150	1	the	the	DET
iajs-3044	150	2	cumulative	cumulative	ADJ
iajs-3044	150	3	distribution	distribution	NOUN
iajs-3044	150	4	function	function	NOUN
iajs-3044	150	5	of	of	ADP
iajs-3044	150	6	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	150	7	can	can	AUX
iajs-3044	150	8	be	be	AUX
iajs-3044	150	9	obtained	obtain	VERB
iajs-3044	150	10	by	by	ADP
iajs-3044	150	11	:	:	PUNCT
iajs-3044	150	12	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3044	150	13	;	;	PUNCT
iajs-3044	150	14	𝛼	𝛼	X
iajs-3044	150	15	,	,	PUNCT
iajs-3044	150	16	𝜆	𝜆	X
iajs-3044	150	17	,	,	PUNCT
iajs-3044	150	18	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	150	19	=	=	SYM
iajs-3044	150	20	1	1	NUM
iajs-3044	150	21	−	−	NOUN
iajs-3044	150	22	𝑒−	𝑒−	NOUN
iajs-3044	150	23	(	(	PUNCT
iajs-3044	150	24	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	150	25	+	+	CCONJ
iajs-3044	150	26	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	150	27	)	)	PUNCT
iajs-3044	150	28	2	2	NUM
iajs-3044	150	29	𝑥2	𝑥2	NOUN
iajs-3044	150	30	)	)	PUNCT
iajs-3044	150	31	;	;	PUNCT
iajs-3044	150	32	𝑥	𝑥	PRON
iajs-3044	150	33	≥	≥	NOUN
iajs-3044	150	34	0	0	NUM
iajs-3044	150	35	;	;	PUNCT
iajs-3044	150	36	𝛼	𝛼	X
iajs-3044	150	37	,	,	PUNCT
iajs-3044	150	38	𝜆	𝜆	X
iajs-3044	150	39	,	,	PUNCT
iajs-3044	150	40	𝜃	𝜃	X
iajs-3044	150	41	>	>	X
iajs-3044	150	42	0	0	NUM
iajs-3044	150	43	…	…	PUNCT
iajs-3044	150	44	(	(	PUNCT
iajs-3044	150	45	47	47	NUM
iajs-3044	150	46	)	)	PUNCT
iajs-3044	150	47	figure	figure	NOUN
iajs-3044	150	48	7	7	NUM
iajs-3044	150	49	.	.	PUNCT
iajs-3044	151	1	plot	plot	NOUN
iajs-3044	151	2	of	of	ADP
iajs-3044	151	3	the	the	DET
iajs-3044	151	4	cumulative	cumulative	ADJ
iajs-3044	151	5	distribution	distribution	NOUN
iajs-3044	151	6	function	function	NOUN
iajs-3044	151	7	of	of	ADP
iajs-3044	151	8	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	151	9	distribution	distribution	NOUN
iajs-3044	151	10	for	for	ADP
iajs-3044	151	11	𝜆	𝜆	PRON
iajs-3044	151	12	=	=	SYM
iajs-3044	151	13	𝜃	𝜃	PROPN
iajs-3044	151	14	=	=	SYM
iajs-3044	151	15	0.1	0.1	NUM
iajs-3044	151	16	and	and	CCONJ
iajs-3044	151	17	different	different	ADJ
iajs-3044	151	18	values	value	NOUN
iajs-3044	151	19	of	of	ADP
iajs-3044	151	20	(	(	PUNCT
iajs-3044	151	21	𝛼	𝛼	X
iajs-3044	151	22	=	=	NOUN
iajs-3044	151	23	0.1	0.1	NUM
iajs-3044	151	24	,	,	PUNCT
iajs-3044	151	25	0.2	0.2	NUM
iajs-3044	151	26	,	,	PUNCT
iajs-3044	151	27	0.3	0.3	NUM
iajs-3044	151	28	,	,	PUNCT
iajs-3044	151	29	0.4	0.4	NUM
iajs-3044	151	30	,	,	PUNCT
iajs-3044	151	31	0.5	0.5	NUM
iajs-3044	151	32	,	,	PUNCT
iajs-3044	151	33	0.6	0.6	NUM
iajs-3044	151	34	,	,	PUNCT
iajs-3044	151	35	0.7	0.7	NUM
iajs-3044	151	36	)	)	PUNCT
iajs-3044	151	37	[	[	PUNCT
iajs-3044	151	38	matlab	matlab	X
iajs-3044	151	39	r2013a	r2013a	X
iajs-3044	151	40	]	]	X
iajs-3044	151	41	.	.	PUNCT
iajs-3044	152	1	the	the	DET
iajs-3044	152	2	survival	survival	NOUN
iajs-3044	152	3	function	function	NOUN
iajs-3044	152	4	of	of	ADP
iajs-3044	152	5	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	152	6	is	be	AUX
iajs-3044	152	7	given	give	VERB
iajs-3044	152	8	by	by	ADP
iajs-3044	152	9	:	:	PUNCT
iajs-3044	152	10	𝑆(𝑡	𝑆(𝑡	ADJ
iajs-3044	152	11	;	;	PUNCT
iajs-3044	152	12	𝛼	𝛼	X
iajs-3044	152	13	,	,	PUNCT
iajs-3044	152	14	𝜆	𝜆	NOUN
iajs-3044	152	15	,	,	PUNCT
iajs-3044	152	16	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	152	17	=	=	PUNCT
iajs-3044	152	18	𝑒−	𝑒−	NOUN
iajs-3044	152	19	(	(	PUNCT
iajs-3044	152	20	𝛼(1+𝜃)𝑡	𝛼(1+𝜃)𝑡	NOUN
iajs-3044	152	21	+	+	NUM
iajs-3044	152	22	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	152	23	)	)	PUNCT
iajs-3044	152	24	2	2	NUM
iajs-3044	152	25	𝑡2	𝑡2	PROPN
iajs-3044	152	26	)	)	PUNCT
iajs-3044	152	27	;	;	PUNCT
iajs-3044	152	28	𝑡	𝑡	X
iajs-3044	152	29	≥	≥	NOUN
iajs-3044	152	30	0	0	NUM
iajs-3044	152	31	;	;	PUNCT
iajs-3044	152	32	𝛼	𝛼	X
iajs-3044	152	33	,	,	PUNCT
iajs-3044	152	34	𝜆	𝜆	X
iajs-3044	152	35	,	,	PUNCT
iajs-3044	152	36	𝜃	𝜃	X
iajs-3044	152	37	>	>	X
iajs-3044	152	38	0	0	NUM
iajs-3044	152	39	…	…	PUNCT
iajs-3044	152	40	(	(	PUNCT
iajs-3044	152	41	48	48	NUM
iajs-3044	152	42	)	)	PUNCT
iajs-3044	152	43	ihjpas	ihjpa	NOUN
iajs-3044	152	44	.	.	PUNCT
iajs-3044	153	1	36(2)2023	36(2)2023	NUM
iajs-3044	153	2	399	399	NUM
iajs-3044	153	3	figure	figure	NOUN
iajs-3044	153	4	8	8	NUM
iajs-3044	153	5	.	.	PUNCT
iajs-3044	154	1	plot	plot	NOUN
iajs-3044	154	2	of	of	ADP
iajs-3044	154	3	the	the	DET
iajs-3044	154	4	survival	survival	NOUN
iajs-3044	154	5	function	function	NOUN
iajs-3044	154	6	of	of	ADP
iajs-3044	154	7	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	154	8	distribution	distribution	NOUN
iajs-3044	154	9	for	for	ADP
iajs-3044	154	10	𝜆	𝜆	DET
iajs-3044	154	11	=	=	SYM
iajs-3044	154	12	𝜃	𝜃	PROPN
iajs-3044	154	13	=	=	SYM
iajs-3044	154	14	0.1	0.1	NUM
iajs-3044	154	15	and	and	CCONJ
iajs-3044	154	16	different	different	ADJ
iajs-3044	154	17	values	value	NOUN
iajs-3044	154	18	of	of	ADP
iajs-3044	154	19	(	(	PUNCT
iajs-3044	154	20	𝛼	𝛼	X
iajs-3044	154	21	=	=	NOUN
iajs-3044	154	22	0.1	0.1	NUM
iajs-3044	154	23	,	,	PUNCT
iajs-3044	154	24	0.2	0.2	NUM
iajs-3044	154	25	,	,	PUNCT
iajs-3044	154	26	0.3	0.3	NUM
iajs-3044	154	27	,	,	PUNCT
iajs-3044	154	28	0.4	0.4	NUM
iajs-3044	154	29	,	,	PUNCT
iajs-3044	154	30	0.5	0.5	NUM
iajs-3044	154	31	,	,	PUNCT
iajs-3044	154	32	0.6	0.6	NUM
iajs-3044	154	33	,	,	PUNCT
iajs-3044	154	34	0.7	0.7	NUM
iajs-3044	154	35	)	)	PUNCT
iajs-3044	154	36	[	[	PUNCT
iajs-3044	154	37	matlab	matlab	X
iajs-3044	154	38	r2013a	r2013a	X
iajs-3044	154	39	]	]	X
iajs-3044	154	40	.	.	PUNCT
iajs-3044	155	1	the	the	DET
iajs-3044	155	2	hazard	hazard	NOUN
iajs-3044	155	3	rate	rate	NOUN
iajs-3044	155	4	function	function	NOUN
iajs-3044	155	5	of	of	ADP
iajs-3044	155	6	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	155	7	is	be	AUX
iajs-3044	155	8	given	give	VERB
iajs-3044	155	9	by	by	ADP
iajs-3044	155	10	:	:	PUNCT
iajs-3044	155	11	ℎ(𝑡	ℎ(𝑡	PROPN
iajs-3044	155	12	;	;	PUNCT
iajs-3044	155	13	𝛼	𝛼	X
iajs-3044	155	14	,	,	PUNCT
iajs-3044	155	15	𝜆	𝜆	X
iajs-3044	155	16	,	,	PUNCT
iajs-3044	155	17	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	155	18	=	=	PUNCT
iajs-3044	156	1	𝛼(1	𝛼(1	NOUN
iajs-3044	156	2	+	+	NUM
iajs-3044	156	3	𝜃	𝜃	X
iajs-3044	156	4	)	)	PUNCT
iajs-3044	157	1	+	+	CCONJ
iajs-3044	158	1	𝜆(1	𝜆(1	NOUN
iajs-3044	158	2	+	+	PUNCT
iajs-3044	158	3	𝜃)𝑡	𝜃)𝑡	PUNCT
iajs-3044	158	4	;	;	PUNCT
iajs-3044	158	5	𝑡	𝑡	X
iajs-3044	158	6	>	>	X
iajs-3044	158	7	0	0	NUM
iajs-3044	158	8	;	;	PUNCT
iajs-3044	158	9	𝛼	𝛼	X
iajs-3044	158	10	,	,	PUNCT
iajs-3044	158	11	𝜆	𝜆	X
iajs-3044	158	12	,	,	PUNCT
iajs-3044	158	13	𝜃	𝜃	X
iajs-3044	158	14	>	>	X
iajs-3044	158	15	0	0	NUM
iajs-3044	158	16	…	…	PUNCT
iajs-3044	158	17	(	(	PUNCT
iajs-3044	158	18	49	49	NUM
iajs-3044	158	19	)	)	PUNCT
iajs-3044	158	20	figure	figure	NOUN
iajs-3044	158	21	9	9	NUM
iajs-3044	158	22	.	.	PUNCT
iajs-3044	159	1	plot	plot	NOUN
iajs-3044	159	2	of	of	ADP
iajs-3044	159	3	hazard	hazard	NOUN
iajs-3044	159	4	rate	rate	NOUN
iajs-3044	159	5	function	function	NOUN
iajs-3044	159	6	of	of	ADP
iajs-3044	159	7	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	159	8	distribution	distribution	NOUN
iajs-3044	159	9	for	for	ADP
iajs-3044	159	10	𝜆	𝜆	DET
iajs-3044	159	11	=	=	SYM
iajs-3044	159	12	𝜃	𝜃	PROPN
iajs-3044	159	13	=	=	SYM
iajs-3044	159	14	0.1	0.1	NUM
iajs-3044	159	15	and	and	CCONJ
iajs-3044	159	16	different	different	ADJ
iajs-3044	159	17	values	value	NOUN
iajs-3044	159	18	of	of	ADP
iajs-3044	159	19	(	(	PUNCT
iajs-3044	159	20	𝛼	𝛼	X
iajs-3044	159	21	=	=	NOUN
iajs-3044	159	22	0.1	0.1	NUM
iajs-3044	159	23	,	,	PUNCT
iajs-3044	159	24	0.2	0.2	NUM
iajs-3044	159	25	,	,	PUNCT
iajs-3044	159	26	0.3	0.3	NUM
iajs-3044	159	27	,	,	PUNCT
iajs-3044	159	28	0.4	0.4	NUM
iajs-3044	159	29	,	,	PUNCT
iajs-3044	159	30	0.5	0.5	NUM
iajs-3044	159	31	,	,	PUNCT
iajs-3044	159	32	0.6	0.6	NUM
iajs-3044	159	33	,	,	PUNCT
iajs-3044	159	34	0.7	0.7	NUM
iajs-3044	159	35	)	)	PUNCT
iajs-3044	159	36	[	[	PUNCT
iajs-3044	159	37	matlab	matlab	X
iajs-3044	159	38	r2013a	r2013a	X
iajs-3044	159	39	]	]	X
iajs-3044	159	40	.	.	PUNCT
iajs-3044	160	1	the	the	DET
iajs-3044	160	2	reverse	reverse	ADJ
iajs-3044	160	3	hazard	hazard	NOUN
iajs-3044	160	4	rate	rate	NOUN
iajs-3044	160	5	function	function	NOUN
iajs-3044	160	6	of	of	ADP
iajs-3044	160	7	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	160	8	is	be	AUX
iajs-3044	160	9	given	give	VERB
iajs-3044	160	10	by	by	ADP
iajs-3044	160	11	:	:	PUNCT
iajs-3044	160	12	∅(𝑡	∅(𝑡	NOUN
iajs-3044	160	13	;	;	PUNCT
iajs-3044	160	14	𝛼	𝛼	X
iajs-3044	160	15	,	,	PUNCT
iajs-3044	160	16	𝜆	𝜆	X
iajs-3044	160	17	,	,	PUNCT
iajs-3044	160	18	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	160	19	=	=	SYM
iajs-3044	160	20	(	(	PUNCT
iajs-3044	160	21	𝛼(1+𝜃)+𝜆(1+𝜃)𝑡	𝛼(1+𝜃)+𝜆(1+𝜃)𝑡	NOUN
iajs-3044	160	22	)	)	PUNCT
iajs-3044	160	23	𝑒	𝑒	ADP
iajs-3044	160	24	−	−	PROPN
iajs-3044	160	25	(	(	PUNCT
iajs-3044	160	26	𝛼(1+𝜃)𝑡	𝛼(1+𝜃)𝑡	PROPN
iajs-3044	160	27	+	+	NUM
iajs-3044	160	28	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	160	29	)	)	PUNCT
iajs-3044	160	30	2	2	NUM
iajs-3044	160	31	𝑡2	𝑡2	NOUN
iajs-3044	160	32	)	)	PUNCT
iajs-3044	160	33	1−	1−	NUM
iajs-3044	160	34	𝑒	𝑒	PROPN
iajs-3044	160	35	−	−	PROPN
iajs-3044	160	36	(	(	PUNCT
iajs-3044	160	37	𝛼(1+𝜃)𝑡	𝛼(1+𝜃)𝑡	PROPN
iajs-3044	160	38	+	+	NUM
iajs-3044	160	39	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	160	40	)	)	PUNCT
iajs-3044	160	41	2	2	NUM
iajs-3044	160	42	𝑡2	𝑡2	PROPN
iajs-3044	160	43	)	)	PUNCT
iajs-3044	160	44	;	;	PUNCT
iajs-3044	160	45	𝑡	𝑡	X
iajs-3044	160	46	≥	≥	NOUN
iajs-3044	160	47	0	0	NUM
iajs-3044	160	48	;	;	PUNCT
iajs-3044	160	49	𝛼	𝛼	X
iajs-3044	160	50	,	,	PUNCT
iajs-3044	160	51	𝜆	𝜆	X
iajs-3044	160	52	,	,	PUNCT
iajs-3044	160	53	𝜃	𝜃	X
iajs-3044	160	54	>	>	X
iajs-3044	160	55	0	0	NUM
iajs-3044	160	56	…	…	PUNCT
iajs-3044	160	57	(	(	PUNCT
iajs-3044	160	58	50	50	NUM
iajs-3044	160	59	)	)	PUNCT
iajs-3044	160	60	figure	figure	NOUN
iajs-3044	160	61	10	10	NUM
iajs-3044	160	62	.	.	PUNCT
iajs-3044	161	1	plot	plot	NOUN
iajs-3044	161	2	of	of	ADP
iajs-3044	161	3	the	the	DET
iajs-3044	161	4	reverse	reverse	ADJ
iajs-3044	161	5	hazard	hazard	NOUN
iajs-3044	161	6	rate	rate	NOUN
iajs-3044	161	7	function	function	NOUN
iajs-3044	161	8	of	of	ADP
iajs-3044	161	9	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	161	10	distribution	distribution	NOUN
iajs-3044	161	11	for	for	ADP
iajs-3044	161	12	𝜆	𝜆	DET
iajs-3044	161	13	=	=	SYM
iajs-3044	161	14	𝜃	𝜃	PROPN
iajs-3044	161	15	=	=	SYM
iajs-3044	161	16	0.1	0.1	NUM
iajs-3044	161	17	and	and	CCONJ
iajs-3044	161	18	different	different	ADJ
iajs-3044	161	19	values	value	NOUN
iajs-3044	161	20	of	of	ADP
iajs-3044	161	21	(	(	PUNCT
iajs-3044	161	22	𝛼	𝛼	X
iajs-3044	161	23	=	=	NOUN
iajs-3044	161	24	0.1	0.1	NUM
iajs-3044	161	25	,	,	PUNCT
iajs-3044	161	26	0.2	0.2	NUM
iajs-3044	161	27	,	,	PUNCT
iajs-3044	161	28	0.3	0.3	NUM
iajs-3044	161	29	,	,	PUNCT
iajs-3044	161	30	0.4	0.4	NUM
iajs-3044	161	31	,	,	PUNCT
iajs-3044	161	32	0.5	0.5	NUM
iajs-3044	161	33	,	,	PUNCT
iajs-3044	161	34	0.6	0.6	NUM
iajs-3044	161	35	,	,	PUNCT
iajs-3044	161	36	0.7	0.7	NUM
iajs-3044	161	37	)	)	PUNCT
iajs-3044	161	38	[	[	PUNCT
iajs-3044	161	39	matlab	matlab	X
iajs-3044	161	40	r2013a	r2013a	X
iajs-3044	161	41	]	]	PUNCT
iajs-3044	161	42	.	.	PUNCT
iajs-3044	162	1	ihjpas	ihjpas	PROPN
iajs-3044	162	2	.	.	PUNCT
iajs-3044	163	1	36(2)2023	36(2)2023	NUM
iajs-3044	163	2	400	400	NUM
iajs-3044	163	3	3.1	3.1	NUM
iajs-3044	163	4	special	special	ADJ
iajs-3044	163	5	models	model	NOUN
iajs-3044	163	6	in	in	ADP
iajs-3044	163	7	this	this	DET
iajs-3044	163	8	section	section	NOUN
iajs-3044	163	9	,	,	PUNCT
iajs-3044	163	10	we	we	PRON
iajs-3044	163	11	provide	provide	VERB
iajs-3044	163	12	special	special	ADJ
iajs-3044	163	13	models	model	NOUN
iajs-3044	163	14	of	of	ADP
iajs-3044	163	15	the	the	DET
iajs-3044	163	16	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	163	17	distribution	distribution	NOUN
iajs-3044	163	18	:	:	PUNCT
iajs-3044	164	1	1	1	X
iajs-3044	164	2	.	.	X
iajs-3044	164	3	when	when	SCONJ
iajs-3044	164	4	𝛼	𝛼	X
iajs-3044	164	5	=	=	X
iajs-3044	164	6	𝜃	𝜃	X
iajs-3044	164	7	=	=	PUNCT
iajs-3044	164	8	0	0	NUM
iajs-3044	165	1	the	the	DET
iajs-3044	165	2	probability	probability	NOUN
iajs-3044	165	3	density	density	NOUN
iajs-3044	165	4	function	function	NOUN
iajs-3044	165	5	of	of	ADP
iajs-3044	165	6	modified	modify	VERB
iajs-3044	165	7	weighted	weight	VERB
iajs-3044	165	8	exponential	exponential	ADJ
iajs-3044	165	9	rayleigh	rayleigh	PROPN
iajs-3044	165	10	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	165	11	distribution	distribution	NOUN
iajs-3044	165	12	reduces	reduce	VERB
iajs-3044	165	13	to	to	PART
iajs-3044	165	14	give	give	VERB
iajs-3044	165	15	the	the	DET
iajs-3044	165	16	probability	probability	NOUN
iajs-3044	165	17	density	density	NOUN
iajs-3044	165	18	function	function	NOUN
iajs-3044	165	19	of	of	ADP
iajs-3044	165	20	rayleigh	rayleigh	ADJ
iajs-3044	165	21	distribution	distribution	NOUN
iajs-3044	166	1	[	[	X
iajs-3044	166	2	11	11	NUM
iajs-3044	166	3	]	]	SYM
iajs-3044	166	4	:	:	PUNCT
iajs-3044	166	5	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	166	6	;	;	PUNCT
iajs-3044	166	7	𝜆)𝑅	𝜆)𝑅	SYM
iajs-3044	166	8	=	=	PUNCT
iajs-3044	167	1	𝜆𝑥	𝜆𝑥	NUM
iajs-3044	167	2	𝑒−	𝑒−	NOUN
iajs-3044	167	3	𝜆	𝜆	DET
iajs-3044	167	4	2	2	NUM
iajs-3044	167	5	𝑥2	𝑥2	NOUN
iajs-3044	167	6	;	;	PUNCT
iajs-3044	167	7	𝑥	𝑥	PRON
iajs-3044	167	8	≥	≥	NOUN
iajs-3044	167	9	0	0	NUM
iajs-3044	167	10	;	;	PUNCT
iajs-3044	167	11	𝜆	𝜆	X
iajs-3044	167	12	>	>	SYM
iajs-3044	167	13	0	0	NUM
iajs-3044	167	14	zero	zero	NUM
iajs-3044	167	15	otherwise	otherwise	ADV
iajs-3044	167	16	.	.	PUNCT
iajs-3044	168	1	where	where	SCONJ
iajs-3044	168	2	𝜆	𝜆	NOUN
iajs-3044	168	3	is	be	AUX
iajs-3044	168	4	scale	scale	NOUN
iajs-3044	168	5	parameter	parameter	NOUN
iajs-3044	168	6	.	.	PUNCT
iajs-3044	169	1	2	2	NUM
iajs-3044	169	2	.	.	X
iajs-3044	169	3	when	when	SCONJ
iajs-3044	169	4	𝜆	𝜆	ADP
iajs-3044	169	5	=	=	SYM
iajs-3044	169	6	𝜃	𝜃	SYM
iajs-3044	169	7	=	=	PUNCT
iajs-3044	169	8	0	0	NUM
iajs-3044	169	9	the	the	DET
iajs-3044	169	10	probability	probability	NOUN
iajs-3044	169	11	density	density	NOUN
iajs-3044	169	12	function	function	NOUN
iajs-3044	169	13	of	of	ADP
iajs-3044	169	14	modified	modify	VERB
iajs-3044	169	15	weighted	weight	VERB
iajs-3044	169	16	exponential	exponential	ADJ
iajs-3044	169	17	rayleigh	rayleigh	PROPN
iajs-3044	169	18	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	169	19	distribution	distribution	NOUN
iajs-3044	169	20	reduces	reduce	VERB
iajs-3044	169	21	to	to	PART
iajs-3044	169	22	give	give	VERB
iajs-3044	169	23	the	the	DET
iajs-3044	169	24	probability	probability	NOUN
iajs-3044	169	25	density	density	NOUN
iajs-3044	169	26	function	function	NOUN
iajs-3044	169	27	of	of	ADP
iajs-3044	169	28	exponential	exponential	ADJ
iajs-3044	169	29	distribution	distribution	NOUN
iajs-3044	169	30	[	[	X
iajs-3044	169	31	7	7	NUM
iajs-3044	169	32	]	]	NUM
iajs-3044	169	33	:	:	PUNCT
iajs-3044	169	34	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	169	35	;	;	PUNCT
iajs-3044	169	36	𝛼)𝐸	𝛼)𝐸	NUM
iajs-3044	169	37	=	=	SYM
iajs-3044	169	38	𝛼	𝛼	X
iajs-3044	169	39	𝑒−𝛼𝑥	𝑒−𝛼𝑥	NOUN
iajs-3044	169	40	;	;	PUNCT
iajs-3044	169	41	𝑥	𝑥	PRON
iajs-3044	169	42	≥	≥	NOUN
iajs-3044	169	43	0	0	NUM
iajs-3044	169	44	;	;	PUNCT
iajs-3044	169	45	𝛼	𝛼	X
iajs-3044	169	46	>	>	X
iajs-3044	169	47	0	0	NUM
iajs-3044	169	48	zero	zero	NUM
iajs-3044	169	49	otherwise	otherwise	ADV
iajs-3044	169	50	.	.	PUNCT
iajs-3044	170	1	where	where	SCONJ
iajs-3044	170	2	𝛼	𝛼	NOUN
iajs-3044	170	3	is	be	AUX
iajs-3044	170	4	scale	scale	NOUN
iajs-3044	170	5	parameter	parameter	NOUN
iajs-3044	170	6	.	.	PUNCT
iajs-3044	171	1	3	3	X
iajs-3044	171	2	.	.	X
iajs-3044	172	1	when	when	SCONJ
iajs-3044	172	2	𝜃	𝜃	X
iajs-3044	172	3	=	=	PUNCT
iajs-3044	172	4	0	0	PUNCT
iajs-3044	173	1	the	the	DET
iajs-3044	173	2	probability	probability	NOUN
iajs-3044	173	3	density	density	NOUN
iajs-3044	173	4	function	function	NOUN
iajs-3044	173	5	of	of	ADP
iajs-3044	173	6	modified	modify	VERB
iajs-3044	173	7	weighted	weight	VERB
iajs-3044	173	8	exponential	exponential	ADJ
iajs-3044	173	9	rayleigh	rayleigh	PROPN
iajs-3044	173	10	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	173	11	distribution	distribution	NOUN
iajs-3044	173	12	reduces	reduce	VERB
iajs-3044	173	13	to	to	PART
iajs-3044	173	14	give	give	VERB
iajs-3044	173	15	the	the	DET
iajs-3044	173	16	probability	probability	NOUN
iajs-3044	173	17	density	density	NOUN
iajs-3044	173	18	function	function	NOUN
iajs-3044	173	19	of	of	ADP
iajs-3044	173	20	exponential	exponential	ADJ
iajs-3044	173	21	rayleigh	rayleigh	PROPN
iajs-3044	173	22	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	173	23	distribution	distribution	NOUN
iajs-3044	173	24	:	:	PUNCT
iajs-3044	173	25	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	173	26	;	;	PUNCT
iajs-3044	173	27	𝛼	𝛼	X
iajs-3044	173	28	,	,	PUNCT
iajs-3044	173	29	𝜆	𝜆	X
iajs-3044	173	30	)	)	PUNCT
iajs-3044	173	31	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	173	32	=	=	SYM
iajs-3044	173	33	(	(	PUNCT
iajs-3044	173	34	𝛼	𝛼	NOUN
iajs-3044	173	35	+	+	CCONJ
iajs-3044	173	36	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	173	37	)	)	PUNCT
iajs-3044	173	38	𝑒−	𝑒−	NOUN
iajs-3044	173	39	(	(	PUNCT
iajs-3044	173	40	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	173	41	+	+	CCONJ
iajs-3044	173	42	𝜆	𝜆	X
iajs-3044	173	43	2	2	NUM
iajs-3044	173	44	𝑥2	𝑥2	NOUN
iajs-3044	173	45	)	)	PUNCT
iajs-3044	173	46	;	;	PUNCT
iajs-3044	174	1	𝑥	𝑥	PRON
iajs-3044	174	2	≥	≥	NOUN
iajs-3044	174	3	0	0	NUM
iajs-3044	174	4	;	;	PUNCT
iajs-3044	174	5	𝛼	𝛼	X
iajs-3044	174	6	,	,	PUNCT
iajs-3044	174	7	𝜆	𝜆	PROPN
iajs-3044	174	8	>	>	X
iajs-3044	174	9	0	0	NUM
iajs-3044	174	10	zero	zero	NUM
iajs-3044	174	11	otherwise	otherwise	ADV
iajs-3044	174	12	.	.	PUNCT
iajs-3044	175	1	where	where	SCONJ
iajs-3044	175	2	𝛼	𝛼	PROPN
iajs-3044	175	3	𝑎nd	𝑎nd	PROPN
iajs-3044	175	4	𝜆	𝜆	NOUN
iajs-3044	175	5	are	be	AUX
iajs-3044	175	6	scale	scale	NOUN
iajs-3044	175	7	parameters	parameter	NOUN
iajs-3044	175	8	.	.	PUNCT
iajs-3044	176	1	4	4	X
iajs-3044	176	2	.	.	X
iajs-3044	176	3	when	when	SCONJ
iajs-3044	176	4	𝜆	𝜆	ADP
iajs-3044	176	5	=	=	SYM
iajs-3044	176	6	0	0	PROPN
iajs-3044	177	1	the	the	DET
iajs-3044	177	2	probability	probability	NOUN
iajs-3044	177	3	density	density	NOUN
iajs-3044	177	4	function	function	NOUN
iajs-3044	177	5	of	of	ADP
iajs-3044	177	6	modified	modify	VERB
iajs-3044	177	7	weighted	weight	VERB
iajs-3044	177	8	exponential	exponential	ADJ
iajs-3044	177	9	rayleigh	rayleigh	PROPN
iajs-3044	177	10	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	177	11	distribution	distribution	NOUN
iajs-3044	177	12	reduces	reduce	VERB
iajs-3044	177	13	to	to	PART
iajs-3044	177	14	give	give	VERB
iajs-3044	177	15	the	the	DET
iajs-3044	177	16	probability	probability	NOUN
iajs-3044	177	17	density	density	NOUN
iajs-3044	177	18	function	function	NOUN
iajs-3044	177	19	of	of	ADP
iajs-3044	177	20	new	new	ADJ
iajs-3044	177	21	weighted	weight	VERB
iajs-3044	177	22	exponential	exponential	ADJ
iajs-3044	177	23	distribution	distribution	NOUN
iajs-3044	177	24	[	[	X
iajs-3044	177	25	12	12	NUM
iajs-3044	177	26	]	]	NUM
iajs-3044	177	27	:	:	PUNCT
iajs-3044	177	28	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	177	29	;	;	PUNCT
iajs-3044	177	30	𝛼	𝛼	X
iajs-3044	177	31	,	,	PUNCT
iajs-3044	177	32	𝜃)𝑁𝑊𝐸	𝜃)𝑁𝑊𝐸	PUNCT
iajs-3044	177	33	=	=	PUNCT
iajs-3044	178	1	𝛼(1	𝛼(1	NOUN
iajs-3044	178	2	+	+	NUM
iajs-3044	178	3	𝜃	𝜃	X
iajs-3044	178	4	)	)	PUNCT
iajs-3044	178	5	𝑒−	𝑒−	NOUN
iajs-3044	178	6	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	NOUN
iajs-3044	178	7	;	;	PUNCT
iajs-3044	178	8	𝑥	𝑥	PRON
iajs-3044	178	9	≥	≥	NOUN
iajs-3044	178	10	0	0	NUM
iajs-3044	178	11	;	;	PUNCT
iajs-3044	178	12	𝛼	𝛼	X
iajs-3044	178	13	,	,	PUNCT
iajs-3044	178	14	𝜃	𝜃	X
iajs-3044	178	15	>	>	X
iajs-3044	178	16	0	0	NUM
iajs-3044	178	17	zero	zero	NUM
iajs-3044	178	18	otherwise	otherwise	ADV
iajs-3044	178	19	.	.	PUNCT
iajs-3044	179	1	where	where	SCONJ
iajs-3044	179	2	𝛼	𝛼	NOUN
iajs-3044	179	3	is	be	AUX
iajs-3044	179	4	scale	scale	NOUN
iajs-3044	179	5	parameter	parameter	NOUN
iajs-3044	179	6	and	and	CCONJ
iajs-3044	179	7	𝜃	𝜃	NOUN
iajs-3044	179	8	is	be	AUX
iajs-3044	179	9	shape	shape	NOUN
iajs-3044	179	10	parameter	parameter	NOUN
iajs-3044	179	11	.	.	PUNCT
iajs-3044	180	1	5	5	NUM
iajs-3044	180	2	.	.	X
iajs-3044	180	3	when	when	SCONJ
iajs-3044	180	4	𝛼	𝛼	X
iajs-3044	181	1	=	=	VERB
iajs-3044	181	2	0	0	PUNCT
iajs-3044	182	1	the	the	DET
iajs-3044	182	2	probability	probability	NOUN
iajs-3044	182	3	density	density	NOUN
iajs-3044	182	4	function	function	NOUN
iajs-3044	182	5	of	of	ADP
iajs-3044	182	6	modified	modify	VERB
iajs-3044	182	7	weighted	weight	VERB
iajs-3044	182	8	exponential	exponential	ADJ
iajs-3044	182	9	rayleigh	rayleigh	PROPN
iajs-3044	182	10	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	182	11	distribution	distribution	NOUN
iajs-3044	182	12	reduces	reduce	VERB
iajs-3044	182	13	to	to	PART
iajs-3044	182	14	give	give	VERB
iajs-3044	182	15	the	the	DET
iajs-3044	182	16	probability	probability	NOUN
iajs-3044	182	17	density	density	NOUN
iajs-3044	182	18	function	function	NOUN
iajs-3044	182	19	of	of	ADP
iajs-3044	182	20	new	new	ADJ
iajs-3044	182	21	distribution	distribution	NOUN
iajs-3044	182	22	named	name	VERB
iajs-3044	182	23	modified	modify	VERB
iajs-3044	182	24	weighted	weight	VERB
iajs-3044	182	25	rayleigh	rayleigh	NOUN
iajs-3044	182	26	distribution	distribution	NOUN
iajs-3044	182	27	,	,	PUNCT
iajs-3044	182	28	this	this	DET
iajs-3044	182	29	distribution	distribution	NOUN
iajs-3044	182	30	is	be	AUX
iajs-3044	182	31	obtain	obtain	VERB
iajs-3044	182	32	depending	depend	VERB
iajs-3044	182	33	on	on	ADP
iajs-3044	182	34	definition	definition	NOUN
iajs-3044	182	35	of	of	ADP
iajs-3044	182	36	modified	modify	VERB
iajs-3044	182	37	weighted	weight	VERB
iajs-3044	182	38	version	version	NOUN
iajs-3044	182	39	of	of	ADP
iajs-3044	182	40	azzalini	azzalini	PROPN
iajs-3044	182	41	’s	’s	PART
iajs-3044	182	42	(	(	PUNCT
iajs-3044	182	43	1985	1985	NUM
iajs-3044	182	44	)	)	PUNCT
iajs-3044	182	45	as	as	SCONJ
iajs-3044	182	46	follows	follow	VERB
iajs-3044	182	47	:	:	PUNCT
iajs-3044	182	48	consider	consider	VERB
iajs-3044	182	49	a	a	DET
iajs-3044	182	50	probability	probability	NOUN
iajs-3044	182	51	density	density	NOUN
iajs-3044	182	52	function	function	NOUN
iajs-3044	182	53	of	of	ADP
iajs-3044	182	54	rayleigh	rayleigh	ADJ
iajs-3044	182	55	distribution	distribution	NOUN
iajs-3044	182	56	as	as	ADP
iajs-3044	182	57	in	in	ADP
iajs-3044	182	58	equation	equation	NOUN
iajs-3044	182	59	(	(	PUNCT
iajs-3044	182	60	3	3	NUM
iajs-3044	182	61	)	)	PUNCT
iajs-3044	182	62	and	and	CCONJ
iajs-3044	182	63	the	the	DET
iajs-3044	182	64	survival	survival	NOUN
iajs-3044	182	65	function	function	NOUN
iajs-3044	182	66	:	:	PUNCT
iajs-3044	182	67	𝑆(𝑥	𝑆(𝑥	X
iajs-3044	182	68	;	;	PUNCT
iajs-3044	182	69	𝜆)𝑅	𝜆)𝑅	SYM
iajs-3044	182	70	=	=	PUNCT
iajs-3044	182	71	𝑒−	𝑒−	X
iajs-3044	182	72	𝜆	𝜆	DET
iajs-3044	182	73	2	2	NUM
iajs-3044	182	74	𝑥2	𝑥2	NOUN
iajs-3044	182	75	depending	depend	VERB
iajs-3044	182	76	on	on	ADP
iajs-3044	182	77	definition	definition	NOUN
iajs-3044	182	78	of	of	ADP
iajs-3044	182	79	modified	modify	VERB
iajs-3044	182	80	weighted	weight	VERB
iajs-3044	182	81	version	version	NOUN
iajs-3044	182	82	of	of	ADP
iajs-3044	182	83	azzalini	azzalini	PROPN
iajs-3044	182	84	’s	’s	PART
iajs-3044	182	85	(	(	PUNCT
iajs-3044	182	86	1985	1985	NUM
iajs-3044	182	87	)	)	PUNCT
iajs-3044	182	88	and	and	CCONJ
iajs-3044	182	89	put	put	VERB
iajs-3044	182	90	𝑀	𝑀	PROPN
iajs-3044	182	91	=	=	PUNCT
iajs-3044	182	92	1	1	NUM
iajs-3044	182	93	+	+	NUM
iajs-3044	182	94	𝜃	𝜃	NOUN
iajs-3044	182	95	,	,	PUNCT
iajs-3044	182	96	define	define	VERB
iajs-3044	182	97	the	the	DET
iajs-3044	182	98	probability	probability	NOUN
iajs-3044	182	99	density	density	NOUN
iajs-3044	182	100	function	function	NOUN
iajs-3044	182	101	of	of	ADP
iajs-3044	182	102	modified	modified	PROPN
iajs-3044	182	103	weighted	weight	VERB
iajs-3044	182	104	rayleigh	rayleigh	ADJ
iajs-3044	182	105	𝑀𝑊𝑅	𝑀𝑊𝑅	NOUN
iajs-3044	182	106	distribution	distribution	NOUN
iajs-3044	182	107	as	as	SCONJ
iajs-3044	182	108	follows	follow	VERB
iajs-3044	182	109	:	:	PUNCT
iajs-3044	182	110	ihjpas	ihjpas	PROPN
iajs-3044	182	111	.	.	PUNCT
iajs-3044	183	1	36(2)2023	36(2)2023	NUM
iajs-3044	183	2	401	401	NUM
iajs-3044	183	3	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	183	4	;	;	PUNCT
iajs-3044	183	5	𝜆	𝜆	X
iajs-3044	183	6	,	,	PUNCT
iajs-3044	183	7	𝜃)𝑀𝑊𝑅	𝜃)𝑀𝑊𝑅	NUM
iajs-3044	183	8	=	=	PUNCT
iajs-3044	183	9	𝑀𝜆𝑥	𝑀𝜆𝑥	PROPN
iajs-3044	183	10	𝑒−	𝑒−	VERB
iajs-3044	183	11	𝜆	𝜆	ADP
iajs-3044	183	12	2	2	NUM
iajs-3044	183	13	𝑥2	𝑥2	NOUN
iajs-3044	183	14	𝑒−	𝑒−	NOUN
iajs-3044	183	15	𝜆𝜃	𝜆𝜃	ADP
iajs-3044	183	16	2	2	NUM
iajs-3044	183	17	𝑥2	𝑥2	NOUN
iajs-3044	183	18	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	183	19	;	;	PUNCT
iajs-3044	183	20	𝜆	𝜆	X
iajs-3044	183	21	,	,	PUNCT
iajs-3044	183	22	𝜃)𝑀𝑊𝑅	𝜃)𝑀𝑊𝑅	NUM
iajs-3044	183	23	=	=	PUNCT
iajs-3044	184	1	𝜆(1	𝜆(1	VERB
iajs-3044	184	2	+	+	CCONJ
iajs-3044	184	3	𝜃)𝑥	𝜃)𝑥	ADJ
iajs-3044	184	4	𝑒−	𝑒−	NOUN
iajs-3044	184	5	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	184	6	)	)	PUNCT
iajs-3044	184	7	2	2	NUM
iajs-3044	184	8	𝑥2	𝑥2	NOUN
iajs-3044	184	9	;	;	PUNCT
iajs-3044	184	10	𝑥	𝑥	PRON
iajs-3044	184	11	≥	≥	NOUN
iajs-3044	184	12	0	0	NUM
iajs-3044	184	13	;	;	PUNCT
iajs-3044	184	14	𝜆	𝜆	X
iajs-3044	184	15	,	,	PUNCT
iajs-3044	184	16	𝜃	𝜃	X
iajs-3044	184	17	>	>	X
iajs-3044	184	18	0	0	NUM
iajs-3044	184	19	zero	zero	NUM
iajs-3044	184	20	otherwise	otherwise	ADV
iajs-3044	184	21	.	.	PUNCT
iajs-3044	185	1	where	where	SCONJ
iajs-3044	185	2	𝜆	𝜆	NOUN
iajs-3044	185	3	is	be	AUX
iajs-3044	185	4	a	a	DET
iajs-3044	185	5	scale	scale	NOUN
iajs-3044	185	6	parameter	parameter	NOUN
iajs-3044	185	7	and	and	CCONJ
iajs-3044	185	8	𝜃	𝜃	NOUN
iajs-3044	185	9	is	be	AUX
iajs-3044	185	10	the	the	DET
iajs-3044	185	11	shape	shape	NOUN
iajs-3044	185	12	parameter	parameter	NOUN
iajs-3044	185	13	.	.	PUNCT
iajs-3044	186	1	such	such	ADJ
iajs-3044	186	2	that	that	PRON
iajs-3044	186	3	;	;	PUNCT
iajs-3044	186	4	•	•	NUM
iajs-3044	186	5	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	186	6	;	;	PUNCT
iajs-3044	186	7	𝜆	𝜆	X
iajs-3044	186	8	,	,	PUNCT
iajs-3044	186	9	𝜃)𝑀𝑊𝑅	𝜃)𝑀𝑊𝑅	NUM
iajs-3044	186	10	>	>	X
iajs-3044	186	11	0	0	NUM
iajs-3044	186	12	•	•	NUM
iajs-3044	186	13	∫	∫	NOUN
iajs-3044	186	14	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	186	15	;	;	PUNCT
iajs-3044	186	16	𝜆	𝜆	X
iajs-3044	186	17	,	,	PUNCT
iajs-3044	186	18	𝜃)𝑀𝑊𝑅	𝜃)𝑀𝑊𝑅	NUM
iajs-3044	186	19	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	186	20	=	=	SYM
iajs-3044	186	21	∫	∫	PROPN
iajs-3044	186	22	𝜆(1	𝜆(1	NOUN
iajs-3044	187	1	+	+	CCONJ
iajs-3044	187	2	𝜃)𝑥	𝜃)𝑥	ADJ
iajs-3044	187	3	𝑒−	𝑒−	NOUN
iajs-3044	187	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	187	5	)	)	PUNCT
iajs-3044	187	6	2	2	NUM
iajs-3044	187	7	𝑥2	𝑥2	NOUN
iajs-3044	187	8	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	187	9	∞	∞	NUM
iajs-3044	187	10	0	0	NUM
iajs-3044	188	1	∞	∞	NUM
iajs-3044	188	2	0	0	NUM
iajs-3044	188	3	=	=	SYM
iajs-3044	189	1	−	−	PROPN
iajs-3044	189	2	[	[	PUNCT
iajs-3044	189	3	𝑒−	𝑒−	NOUN
iajs-3044	189	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	189	5	)	)	PUNCT
iajs-3044	189	6	2	2	NUM
iajs-3044	189	7	𝑥2	𝑥2	NOUN
iajs-3044	189	8	]	]	PUNCT
iajs-3044	189	9	0	0	NUM
iajs-3044	190	1	∞	∞	NUM
iajs-3044	190	2	=	=	SYM
iajs-3044	190	3	1	1	NUM
iajs-3044	190	4	table	table	NOUN
iajs-3044	190	5	1	1	NUM
iajs-3044	190	6	.	.	PUNCT
iajs-3044	190	7	special	special	ADJ
iajs-3044	190	8	models	model	NOUN
iajs-3044	190	9	of	of	ADP
iajs-3044	190	10	the	the	DET
iajs-3044	190	11	modified	modify	VERB
iajs-3044	190	12	weighted	weight	VERB
iajs-3044	190	13	exponential	exponential	ADJ
iajs-3044	190	14	rayleigh	rayleigh	PROPN
iajs-3044	190	15	mwer	mwer	NOUN
iajs-3044	190	16	distribution	distribution	NOUN
iajs-3044	190	17	distribution	distribution	NOUN
iajs-3044	190	18	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3044	190	19	)	)	PUNCT
iajs-3044	190	20	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3044	190	21	)	)	PUNCT
iajs-3044	190	22	𝑆(𝑡	𝑆(𝑡	ADJ
iajs-3044	190	23	)	)	PUNCT
iajs-3044	190	24	ℎ(𝑡	ℎ(𝑡	PROPN
iajs-3044	190	25	)	)	PUNCT
iajs-3044	190	26	𝑅	𝑅	PROPN
iajs-3044	190	27	𝜆𝑥𝑒−	𝜆𝑥𝑒−	PROPN
iajs-3044	190	28	𝜆	𝜆	ADP
iajs-3044	190	29	2	2	NUM
iajs-3044	190	30	𝑥2	𝑥2	NOUN
iajs-3044	190	31	1	1	NUM
iajs-3044	190	32	−	−	NOUN
iajs-3044	190	33	𝑒−	𝑒−	NOUN
iajs-3044	190	34	𝜆	𝜆	NOUN
iajs-3044	190	35	2	2	NUM
iajs-3044	190	36	𝑥2	𝑥2	NOUN
iajs-3044	190	37	𝑒−	𝑒−	VERB
iajs-3044	190	38	𝜆	𝜆	ADP
iajs-3044	190	39	2	2	NUM
iajs-3044	190	40	𝑡2	𝑡2	NOUN
iajs-3044	190	41	𝜆𝑡	𝜆𝑡	ADP
iajs-3044	190	42	𝐸	𝐸	PROPN
iajs-3044	190	43	𝛼	𝛼	NOUN
iajs-3044	190	44	𝑒−𝛼𝑥	𝑒−𝛼𝑥	ADJ
iajs-3044	190	45	1	1	NUM
iajs-3044	190	46	−	−	PROPN
iajs-3044	190	47	𝑒−𝛼𝑥	𝑒−𝛼𝑥	PROPN
iajs-3044	190	48	𝑒−𝛼𝑡	𝑒−𝛼𝑡	PROPN
iajs-3044	190	49	𝛼	𝛼	PRON
iajs-3044	190	50	𝐸𝑅	𝐸𝑅	NOUN
iajs-3044	190	51	(	(	PUNCT
iajs-3044	190	52	𝛼	𝛼	NOUN
iajs-3044	190	53	+	+	CCONJ
iajs-3044	190	54	𝜆𝑥	𝜆𝑥	NOUN
iajs-3044	190	55	)	)	PUNCT
iajs-3044	190	56	𝑒	𝑒	NOUN
iajs-3044	190	57	−	−	PROPN
iajs-3044	190	58	(	(	PUNCT
iajs-3044	190	59	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	190	60	+	+	CCONJ
iajs-3044	190	61	𝜆	𝜆	X
iajs-3044	190	62	2	2	NUM
iajs-3044	190	63	𝑥2	𝑥2	NOUN
iajs-3044	190	64	)	)	PUNCT
iajs-3044	190	65	1	1	NUM
iajs-3044	190	66	−	−	NOUN
iajs-3044	190	67	𝑒−	𝑒−	NOUN
iajs-3044	190	68	(	(	PUNCT
iajs-3044	190	69	𝛼𝑥	𝛼𝑥	ADV
iajs-3044	190	70	+	+	CCONJ
iajs-3044	190	71	𝜆	𝜆	X
iajs-3044	190	72	2	2	NUM
iajs-3044	190	73	𝑥2	𝑥2	NOUN
iajs-3044	190	74	)	)	PUNCT
iajs-3044	190	75	𝑒−	𝑒−	NOUN
iajs-3044	190	76	(	(	PUNCT
iajs-3044	190	77	𝛼𝑡	𝛼𝑡	ADP
iajs-3044	190	78	+	+	NOUN
iajs-3044	190	79	𝜆	𝜆	DET
iajs-3044	190	80	2	2	NUM
iajs-3044	190	81	𝑡2	𝑡2	NOUN
iajs-3044	190	82	)	)	PUNCT
iajs-3044	190	83	𝛼	𝛼	PROPN
iajs-3044	191	1	+	+	X
iajs-3044	191	2	𝜆𝑡	𝜆𝑡	X
iajs-3044	191	3	𝑁𝑊𝐸	𝑁𝑊𝐸	PROPN
iajs-3044	191	4	𝛼(1	𝛼(1	PROPN
iajs-3044	191	5	+	+	NUM
iajs-3044	191	6	𝜃	𝜃	X
iajs-3044	191	7	)	)	PUNCT
iajs-3044	191	8	𝑒−	𝑒−	NOUN
iajs-3044	191	9	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	NOUN
iajs-3044	191	10	1	1	NUM
iajs-3044	191	11	−	−	NOUN
iajs-3044	191	12	𝑒−	𝑒−	NOUN
iajs-3044	191	13	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	191	14	𝑒−	𝑒−	NOUN
iajs-3044	191	15	𝛼(1+𝜃)𝑡	𝛼(1+𝜃)𝑡	ADJ
iajs-3044	191	16	𝛼(1	𝛼(1	NOUN
iajs-3044	191	17	+	+	NUM
iajs-3044	191	18	𝜃	𝜃	NOUN
iajs-3044	191	19	)	)	PUNCT
iajs-3044	191	20	𝑀𝑊𝑅	𝑀𝑊𝑅	NOUN
iajs-3044	191	21	𝜆(1	𝜆(1	PUNCT
iajs-3044	192	1	+	+	CCONJ
iajs-3044	193	1	𝜃)𝑥	𝜃)𝑥	ADJ
iajs-3044	193	2	𝑒−	𝑒−	VERB
iajs-3044	193	3	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	193	4	)	)	PUNCT
iajs-3044	193	5	2	2	NUM
iajs-3044	193	6	𝑥2	𝑥2	NOUN
iajs-3044	193	7	1	1	NUM
iajs-3044	193	8	−	−	NOUN
iajs-3044	193	9	𝑒−	𝑒−	NOUN
iajs-3044	193	10	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	193	11	)	)	PUNCT
iajs-3044	193	12	2	2	NUM
iajs-3044	193	13	𝑥2	𝑥2	NOUN
iajs-3044	193	14	𝑒−	𝑒−	NOUN
iajs-3044	193	15	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	193	16	)	)	PUNCT
iajs-3044	193	17	2	2	NUM
iajs-3044	193	18	𝑡2	𝑡2	NOUN
iajs-3044	193	19	𝜆(1	𝜆(1	PROPN
iajs-3044	194	1	+	+	CCONJ
iajs-3044	194	2	𝜃)𝑡	𝜃)𝑡	X
iajs-3044	194	3	3.2	3.2	NUM
iajs-3044	194	4	some	some	DET
iajs-3044	194	5	statistical	statistical	ADJ
iajs-3044	194	6	properties	property	NOUN
iajs-3044	194	7	of	of	ADP
iajs-3044	194	8	𝑴𝑾𝑬𝑹	𝑴𝑾𝑬𝑹	PROPN
iajs-3044	194	9	distribution	distribution	NOUN
iajs-3044	194	10	3.2.1	3.2.1	NUM
iajs-3044	194	11	the	the	DET
iajs-3044	194	12	mode	mode	NOUN
iajs-3044	194	13	the	the	DET
iajs-3044	194	14	mode	mode	NOUN
iajs-3044	194	15	of	of	ADP
iajs-3044	194	16	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	194	17	distribution	distribution	NOUN
iajs-3044	194	18	can	can	AUX
iajs-3044	194	19	be	be	AUX
iajs-3044	194	20	derived	derive	VERB
iajs-3044	194	21	as	as	SCONJ
iajs-3044	194	22	follows	follow	VERB
iajs-3044	194	23	:	:	PUNCT
iajs-3044	194	24	𝜕𝑓(𝑥	𝜕𝑓(𝑥	NOUN
iajs-3044	194	25	;	;	PUNCT
iajs-3044	194	26	𝛼	𝛼	X
iajs-3044	194	27	,	,	PUNCT
iajs-3044	194	28	𝜆	𝜆	NOUN
iajs-3044	194	29	,	,	PUNCT
iajs-3044	194	30	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	194	31	𝜕𝑥	𝜕𝑥	NOUN
iajs-3044	194	32	=	=	PUNCT
iajs-3044	194	33	−	−	PROPN
iajs-3044	194	34	(	(	PUNCT
iajs-3044	194	35	𝛼(1	𝛼(1	NOUN
iajs-3044	194	36	+	+	NUM
iajs-3044	194	37	𝜃	𝜃	X
iajs-3044	194	38	)	)	PUNCT
iajs-3044	195	1	+	+	CCONJ
iajs-3044	196	1	𝜆(1	𝜆(1	X
iajs-3044	197	1	+	+	CCONJ
iajs-3044	197	2	𝜃)𝑥)2	𝜃)𝑥)2	ADJ
iajs-3044	197	3	𝑒	𝑒	PRON
iajs-3044	197	4	−	−	NOUN
iajs-3044	197	5	(	(	PUNCT
iajs-3044	197	6	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	197	7	+	+	CCONJ
iajs-3044	197	8	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	197	9	)	)	PUNCT
iajs-3044	197	10	2	2	NUM
iajs-3044	197	11	𝑥2	𝑥2	NOUN
iajs-3044	197	12	)	)	PUNCT
iajs-3044	198	1	+	+	CCONJ
iajs-3044	198	2	𝜆	𝜆	X
iajs-3044	198	3	(	(	PUNCT
iajs-3044	198	4	1	1	NUM
iajs-3044	198	5	+	+	NUM
iajs-3044	198	6	𝜃	𝜃	X
iajs-3044	198	7	)	)	PUNCT
iajs-3044	198	8	𝑒	𝑒	PROPN
iajs-3044	198	9	−	−	PROPN
iajs-3044	198	10	(	(	PUNCT
iajs-3044	198	11	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	198	12	+	+	CCONJ
iajs-3044	198	13	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	198	14	)	)	PUNCT
iajs-3044	198	15	2	2	NUM
iajs-3044	198	16	𝑥2	𝑥2	NOUN
iajs-3044	198	17	)	)	PUNCT
iajs-3044	199	1	[	[	X
iajs-3044	199	2	−	−	X
iajs-3044	199	3	(	(	PUNCT
iajs-3044	199	4	𝛼(1	𝛼(1	NOUN
iajs-3044	199	5	+	+	NUM
iajs-3044	199	6	𝜃	𝜃	X
iajs-3044	199	7	)	)	PUNCT
iajs-3044	200	1	+	+	CCONJ
iajs-3044	201	1	𝜆(1	𝜆(1	X
iajs-3044	202	1	+	+	CCONJ
iajs-3044	202	2	𝜃)𝑥)2	𝜃)𝑥)2	ADJ
iajs-3044	202	3	+	+	PUNCT
iajs-3044	202	4	𝜆(1	𝜆(1	NUM
iajs-3044	202	5	+	+	NUM
iajs-3044	202	6	𝜃	𝜃	X
iajs-3044	202	7	)	)	PUNCT
iajs-3044	202	8	]	]	PUNCT
iajs-3044	202	9	𝑒−	𝑒−	NOUN
iajs-3044	202	10	(	(	PUNCT
iajs-3044	202	11	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	202	12	+	+	CCONJ
iajs-3044	202	13	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	202	14	)	)	PUNCT
iajs-3044	202	15	2	2	NUM
iajs-3044	202	16	𝑥2	𝑥2	NOUN
iajs-3044	202	17	)	)	PUNCT
iajs-3044	202	18	=	=	SYM
iajs-3044	202	19	0	0	NUM
iajs-3044	202	20	…	…	PUNCT
iajs-3044	202	21	(	(	PUNCT
iajs-3044	202	22	51	51	NUM
iajs-3044	202	23	)	)	PUNCT
iajs-3044	202	24	it	it	PRON
iajs-3044	202	25	is	be	AUX
iajs-3044	202	26	clear	clear	ADJ
iajs-3044	202	27	that	that	SCONJ
iajs-3044	202	28	𝜕𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	𝜕𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	ADP
iajs-3044	202	29	𝜕𝑥	𝜕𝑥	NOUN
iajs-3044	202	30	=	=	PUNCT
iajs-3044	202	31	[	[	PUNCT
iajs-3044	202	32	−	−	X
iajs-3044	202	33	{	{	PUNCT
iajs-3044	202	34	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3044	202	35	;	;	PUNCT
iajs-3044	202	36	𝛼	𝛼	X
iajs-3044	202	37	,	,	PUNCT
iajs-3044	202	38	𝜆	𝜆	PRON
iajs-3044	202	39	,	,	PUNCT
iajs-3044	202	40	𝜃)𝑀𝑊𝐸𝑅}2	𝜃)𝑀𝑊𝐸𝑅}2	ADJ
iajs-3044	202	41	+	+	CCONJ
iajs-3044	202	42	ℎ′(𝑥	ℎ′(𝑥	X
iajs-3044	202	43	;	;	PUNCT
iajs-3044	202	44	𝛼	𝛼	X
iajs-3044	202	45	,	,	PUNCT
iajs-3044	202	46	𝜆	𝜆	NOUN
iajs-3044	202	47	,	,	PUNCT
iajs-3044	202	48	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	202	49	]	]	X
iajs-3044	202	50	𝑆(𝑥	𝑆(𝑥	X
iajs-3044	202	51	;	;	PUNCT
iajs-3044	202	52	𝛼	𝛼	X
iajs-3044	202	53	,	,	PUNCT
iajs-3044	202	54	𝜆	𝜆	NOUN
iajs-3044	202	55	,	,	PUNCT
iajs-3044	202	56	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	202	57	where	where	SCONJ
iajs-3044	202	58	ℎ(𝑥	ℎ(𝑥	VERB
iajs-3044	202	59	;	;	PUNCT
iajs-3044	202	60	𝛼	𝛼	X
iajs-3044	202	61	,	,	PUNCT
iajs-3044	202	62	𝜆	𝜆	X
iajs-3044	202	63	,	,	PUNCT
iajs-3044	202	64	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	202	65	is	be	AUX
iajs-3044	202	66	the	the	DET
iajs-3044	202	67	hazard	hazard	NOUN
iajs-3044	202	68	rate	rate	NOUN
iajs-3044	202	69	function	function	NOUN
iajs-3044	202	70	was	be	AUX
iajs-3044	202	71	given	give	VERB
iajs-3044	202	72	in	in	ADP
iajs-3044	202	73	equation	equation	NOUN
iajs-3044	202	74	(	(	PUNCT
iajs-3044	202	75	49	49	NUM
iajs-3044	202	76	)	)	PUNCT
iajs-3044	202	77	,	,	PUNCT
iajs-3044	202	78	and	and	CCONJ
iajs-3044	202	79	𝑆(𝑥	𝑆(𝑥	NUM
iajs-3044	202	80	;	;	PUNCT
iajs-3044	202	81	𝛼	𝛼	X
iajs-3044	202	82	,	,	PUNCT
iajs-3044	202	83	𝜆	𝜆	X
iajs-3044	202	84	,	,	PUNCT
iajs-3044	202	85	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	202	86	is	be	AUX
iajs-3044	202	87	the	the	DET
iajs-3044	202	88	survival	survival	NOUN
iajs-3044	202	89	function	function	NOUN
iajs-3044	202	90	was	be	AUX
iajs-3044	202	91	given	give	VERB
iajs-3044	202	92	in	in	ADP
iajs-3044	202	93	equation	equation	NOUN
iajs-3044	202	94	(	(	PUNCT
iajs-3044	202	95	48	48	NUM
iajs-3044	202	96	)	)	PUNCT
iajs-3044	202	97	.	.	PUNCT
iajs-3044	203	1	since	since	SCONJ
iajs-3044	203	2	𝑆(𝑥	𝑆(𝑥	NUM
iajs-3044	203	3	;	;	PUNCT
iajs-3044	203	4	𝛼	𝛼	X
iajs-3044	203	5	,	,	PUNCT
iajs-3044	203	6	𝜆	𝜆	X
iajs-3044	203	7	,	,	PUNCT
iajs-3044	203	8	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	203	9	≠	≠	PROPN
iajs-3044	203	10	0	0	NUM
iajs-3044	203	11	thus	thus	ADV
iajs-3044	203	12	dividing	divide	VERB
iajs-3044	203	13	the	the	DET
iajs-3044	203	14	equation	equation	NOUN
iajs-3044	203	15	(	(	PUNCT
iajs-3044	203	16	51	51	NUM
iajs-3044	203	17	)	)	PUNCT
iajs-3044	203	18	by	by	ADP
iajs-3044	203	19	𝑆(𝑥	𝑆(𝑥	SYM
iajs-3044	203	20	;	;	PUNCT
iajs-3044	203	21	𝛼	𝛼	X
iajs-3044	203	22	,	,	PUNCT
iajs-3044	203	23	𝜆	𝜆	X
iajs-3044	203	24	,	,	PUNCT
iajs-3044	203	25	𝜃)𝑀𝑊𝐸𝑅	𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	203	26	yeilds	yeild	VERB
iajs-3044	203	27	:	:	PUNCT
iajs-3044	203	28	𝜆2(1	𝜆2(1	NOUN
iajs-3044	203	29	+	+	CCONJ
iajs-3044	203	30	𝜃)2𝑥2	𝜃)2𝑥2	X
iajs-3044	203	31	+	+	NUM
iajs-3044	203	32	2	2	NUM
iajs-3044	203	33	𝜆	𝜆	NOUN
iajs-3044	203	34	𝛼(1	𝛼(1	NOUN
iajs-3044	203	35	+	+	NUM
iajs-3044	203	36	𝜃)2𝑥	𝜃)2𝑥	NOUN
iajs-3044	203	37	+	+	CCONJ
iajs-3044	203	38	𝛼2(1	𝛼2(1	NOUN
iajs-3044	203	39	+	+	CCONJ
iajs-3044	203	40	𝜃)2	𝜃)2	VERB
iajs-3044	203	41	−	−	PROPN
iajs-3044	204	1	𝜆(1	𝜆(1	NOUN
iajs-3044	205	1	+	+	NUM
iajs-3044	205	2	𝜃	𝜃	X
iajs-3044	205	3	)	)	PUNCT
iajs-3044	205	4	=	=	SYM
iajs-3044	205	5	0	0	NUM
iajs-3044	205	6	ihjpas	ihjpas	PROPN
iajs-3044	205	7	.	.	PUNCT
iajs-3044	206	1	36(2)2023	36(2)2023	NUM
iajs-3044	206	2	402	402	NUM
iajs-3044	206	3	based	base	VERB
iajs-3044	206	4	on	on	ADP
iajs-3044	206	5	the	the	DET
iajs-3044	206	6	law	law	NOUN
iajs-3044	206	7	of	of	ADP
iajs-3044	206	8	the	the	DET
iajs-3044	206	9	constitution	constitution	NOUN
iajs-3044	206	10	,	,	PUNCT
iajs-3044	206	11	we	we	PRON
iajs-3044	206	12	get	get	VERB
iajs-3044	206	13	:	:	PUNCT
iajs-3044	206	14	𝑥	𝑥	NOUN
iajs-3044	206	15	=	=	PUNCT
iajs-3044	206	16	−2	−2	NOUN
iajs-3044	206	17	𝜆	𝜆	PRON
iajs-3044	206	18	𝛼(1+𝜃)2	𝛼(1+𝜃)2	PROPN
iajs-3044	206	19	∓	∓	NOUN
iajs-3044	206	20	√4𝛼2𝜆2(1+𝜃)4−	√4𝛼2𝜆2(1+𝜃)4−	NOUN
iajs-3044	206	21	4	4	NUM
iajs-3044	206	22	𝜆2(1+𝜃)2(𝛼2(1+𝜃)2−𝜆(1+𝜃	𝜆2(1+𝜃)2(𝛼2(1+𝜃)2−𝜆(1+𝜃	NUM
iajs-3044	206	23	)	)	PUNCT
iajs-3044	206	24	)	)	PUNCT
iajs-3044	207	1	2𝜆2	2𝜆2	NUM
iajs-3044	207	2	(	(	PUNCT
iajs-3044	207	3	1+𝜃)2	1+𝜃)2	NUM
iajs-3044	207	4	…	…	PUNCT
iajs-3044	207	5	(	(	PUNCT
iajs-3044	207	6	52	52	NUM
iajs-3044	207	7	)	)	PUNCT
iajs-3044	207	8	the	the	DET
iajs-3044	207	9	value	value	NOUN
iajs-3044	207	10	of	of	ADP
iajs-3044	207	11	𝑥	𝑥	PROPN
iajs-3044	207	12	is	be	AUX
iajs-3044	207	13	ignor	ignor	ADJ
iajs-3044	207	14	when	when	SCONJ
iajs-3044	207	15	𝑥	𝑥	X
iajs-3044	207	16	<	<	X
iajs-3044	207	17	0	0	NUM
iajs-3044	207	18	,	,	PUNCT
iajs-3044	207	19	suppose	suppose	VERB
iajs-3044	207	20	that	that	SCONJ
iajs-3044	207	21	𝑥	𝑥	PROPN
iajs-3044	207	22	=	=	SYM
iajs-3044	207	23	𝑥0	𝑥0	NOUN
iajs-3044	207	24	that	that	PRON
iajs-3044	207	25	is	be	AUX
iajs-3044	207	26	a	a	DET
iajs-3044	207	27	root	root	NOUN
iajs-3044	207	28	of	of	ADP
iajs-3044	207	29	equation	equation	NOUN
iajs-3044	207	30	(	(	PUNCT
iajs-3044	207	31	52	52	NUM
iajs-3044	207	32	)	)	PUNCT
iajs-3044	207	33	,	,	PUNCT
iajs-3044	207	34	if	if	SCONJ
iajs-3044	207	35	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	207	36	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	208	1	⃒𝑥=𝑥0	⃒𝑥=𝑥0	X
iajs-3044	208	2	<	<	X
iajs-3044	208	3	0	0	X
iajs-3044	209	1	the	the	DET
iajs-3044	209	2	root	root	NOUN
iajs-3044	209	3	is	be	AUX
iajs-3044	209	4	the	the	DET
iajs-3044	209	5	local	local	ADJ
iajs-3044	209	6	maximum	maximum	NOUN
iajs-3044	209	7	.	.	PUNCT
iajs-3044	210	1	if	if	SCONJ
iajs-3044	210	2	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	210	3	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	211	1	⃒𝑥=𝑥0	⃒𝑥=𝑥0	X
iajs-3044	211	2	>	>	X
iajs-3044	211	3	0	0	NUM
iajs-3044	212	1	the	the	DET
iajs-3044	212	2	root	root	NOUN
iajs-3044	212	3	is	be	AUX
iajs-3044	212	4	the	the	DET
iajs-3044	212	5	local	local	ADJ
iajs-3044	212	6	minimum	minimum	NOUN
iajs-3044	212	7	.	.	PUNCT
iajs-3044	213	1	if	if	SCONJ
iajs-3044	213	2	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	𝜕2𝑓(𝑥;𝛼,𝜆,𝜃)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	213	3	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3044	213	4	⃒𝑥=𝑥0	⃒𝑥=𝑥0	PROPN
iajs-3044	213	5	=	=	SYM
iajs-3044	213	6	0	0	PROPN
iajs-3044	214	1	the	the	DET
iajs-3044	214	2	point	point	NOUN
iajs-3044	214	3	is	be	AUX
iajs-3044	214	4	inflection	inflection	NOUN
iajs-3044	214	5	.	.	PUNCT
iajs-3044	215	1	3.2.2	3.2.2	NUM
iajs-3044	215	2	the	the	DET
iajs-3044	215	3	median	median	NOUN
iajs-3044	215	4	the	the	DET
iajs-3044	215	5	median	median	NOUN
iajs-3044	215	6	of	of	ADP
iajs-3044	215	7	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	215	8	distribution	distribution	NOUN
iajs-3044	215	9	can	can	AUX
iajs-3044	215	10	be	be	AUX
iajs-3044	215	11	obtained	obtain	VERB
iajs-3044	215	12	as	as	ADP
iajs-3044	215	13	follows	follow	VERB
iajs-3044	215	14	:	:	PUNCT
iajs-3044	215	15	1	1	NUM
iajs-3044	215	16	−	−	NOUN
iajs-3044	215	17	𝑒	𝑒	PROPN
iajs-3044	215	18	−	−	NOUN
iajs-3044	215	19	(	(	PUNCT
iajs-3044	215	20	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	215	21	+	+	CCONJ
iajs-3044	215	22	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	215	23	)	)	PUNCT
iajs-3044	215	24	2	2	NUM
iajs-3044	215	25	𝑥2	𝑥2	NOUN
iajs-3044	215	26	)	)	PUNCT
iajs-3044	215	27	=	=	SYM
iajs-3044	215	28	1	1	NUM
iajs-3044	215	29	2	2	NUM
iajs-3044	215	30	𝜆(1	𝜆(1	NUM
iajs-3044	215	31	+	+	NUM
iajs-3044	215	32	𝜃	𝜃	NOUN
iajs-3044	215	33	)	)	PUNCT
iajs-3044	215	34	𝑥2	𝑥2	NOUN
iajs-3044	215	35	+	+	CCONJ
iajs-3044	215	36	2	2	X
iajs-3044	215	37	𝛼(1	𝛼(1	NOUN
iajs-3044	215	38	+	+	CCONJ
iajs-3044	215	39	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	215	40	−	−	PROPN
iajs-3044	215	41	2	2	NUM
iajs-3044	215	42	ln	ln	NOUN
iajs-3044	215	43	2	2	NUM
iajs-3044	215	44	=	=	SYM
iajs-3044	215	45	0	0	NUM
iajs-3044	215	46	based	base	VERB
iajs-3044	215	47	on	on	ADP
iajs-3044	215	48	law	law	NOUN
iajs-3044	215	49	of	of	ADP
iajs-3044	215	50	the	the	DET
iajs-3044	215	51	constitution	constitution	NOUN
iajs-3044	215	52	,	,	PUNCT
iajs-3044	215	53	we	we	PRON
iajs-3044	215	54	get	get	VERB
iajs-3044	215	55	:	:	PUNCT
iajs-3044	215	56	𝑥	𝑥	PROPN
iajs-3044	215	57	=	=	SYM
iajs-3044	215	58	−2𝛼(1+𝜃	−2𝛼(1+𝜃	NUM
iajs-3044	215	59	)	)	PUNCT
iajs-3044	215	60	∓	∓	PROPN
iajs-3044	216	1	√4𝛼2(1+𝜃)2	√4𝛼2(1+𝜃)2	PROPN
iajs-3044	216	2	+	+	PROPN
iajs-3044	216	3	8	8	NUM
iajs-3044	216	4	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	216	5	)	)	PUNCT
iajs-3044	216	6	𝑙𝑛	𝑙𝑛	VERB
iajs-3044	216	7	2	2	NUM
iajs-3044	216	8	2	2	NUM
iajs-3044	216	9	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	216	10	)	)	PUNCT
iajs-3044	216	11	…	…	PUNCT
iajs-3044	216	12	(	(	PUNCT
iajs-3044	216	13	53	53	NUM
iajs-3044	216	14	)	)	PUNCT
iajs-3044	216	15	the	the	DET
iajs-3044	216	16	value	value	NOUN
iajs-3044	216	17	of	of	ADP
iajs-3044	216	18	𝑥	𝑥	PROPN
iajs-3044	216	19	is	be	AUX
iajs-3044	216	20	ignor	ignor	ADJ
iajs-3044	216	21	when	when	SCONJ
iajs-3044	216	22	𝑥	𝑥	X
iajs-3044	216	23	<	<	X
iajs-3044	216	24	0	0	NUM
iajs-3044	216	25	.	.	PUNCT
iajs-3044	217	1	3.2.3	3.2.3	NUM
iajs-3044	217	2	the	the	DET
iajs-3044	217	3	moment	moment	NOUN
iajs-3044	217	4	about	about	ADP
iajs-3044	217	5	the	the	DET
iajs-3044	217	6	origin	origin	NOUN
iajs-3044	217	7	the	the	DET
iajs-3044	217	8	𝑟𝑡ℎ	𝑟𝑡ℎ	NOUN
iajs-3044	217	9	moment	moment	NOUN
iajs-3044	217	10	about	about	ADP
iajs-3044	217	11	the	the	DET
iajs-3044	217	12	origin	origin	NOUN
iajs-3044	217	13	can	can	AUX
iajs-3044	217	14	be	be	AUX
iajs-3044	217	15	defined	define	VERB
iajs-3044	217	16	as	as	ADP
iajs-3044	217	17	:	:	PUNCT
iajs-3044	217	18	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	217	19	=	=	SYM
iajs-3044	217	20	∫	∫	PROPN
iajs-3044	217	21	𝑥𝑟(𝛼(1	𝑥𝑟(𝛼(1	PUNCT
iajs-3044	217	22	+	+	PUNCT
iajs-3044	217	23	𝜃	𝜃	X
iajs-3044	217	24	)	)	PUNCT
iajs-3044	217	25	+	+	CCONJ
iajs-3044	218	1	𝜆(1	𝜆(1	CCONJ
iajs-3044	219	1	+	+	NUM
iajs-3044	219	2	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	219	3	)	)	PUNCT
iajs-3044	219	4	𝑒−	𝑒−	NOUN
iajs-3044	219	5	(	(	PUNCT
iajs-3044	219	6	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	219	7	+	+	CCONJ
iajs-3044	219	8	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	219	9	)	)	PUNCT
iajs-3044	219	10	2	2	NUM
iajs-3044	219	11	𝑥2	𝑥2	NOUN
iajs-3044	219	12	)	)	PUNCT
iajs-3044	219	13	∞	∞	NOUN
iajs-3044	219	14	0	0	NUM
iajs-3044	219	15	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	219	16	…	…	PUNCT
iajs-3044	219	17	(	(	PUNCT
iajs-3044	219	18	54	54	NUM
iajs-3044	219	19	)	)	PUNCT
iajs-3044	219	20	let	let	VERB
iajs-3044	219	21	𝐷(𝑟	𝐷(𝑟	NOUN
iajs-3044	219	22	,	,	PUNCT
iajs-3044	219	23	𝛼	𝛼	NOUN
iajs-3044	219	24	,	,	PUNCT
iajs-3044	219	25	𝜆	𝜆	NOUN
iajs-3044	219	26	,	,	PUNCT
iajs-3044	219	27	𝜃	𝜃	NOUN
iajs-3044	219	28	)	)	PUNCT
iajs-3044	219	29	=	=	SYM
iajs-3044	219	30	𝑥𝑟	𝑥𝑟	NOUN
iajs-3044	219	31	𝑒−	𝑒−	NOUN
iajs-3044	219	32	(	(	PUNCT
iajs-3044	219	33	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	219	34	+	+	CCONJ
iajs-3044	219	35	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	219	36	)	)	PUNCT
iajs-3044	219	37	2	2	NUM
iajs-3044	219	38	𝑥2	𝑥2	NOUN
iajs-3044	219	39	)	)	PUNCT
iajs-3044	219	40	…	…	PUNCT
iajs-3044	219	41	(	(	PUNCT
iajs-3044	219	42	55	55	NUM
iajs-3044	219	43	)	)	PUNCT
iajs-3044	219	44	by	by	ADP
iajs-3044	219	45	maclaurin	maclaurin	NOUN
iajs-3044	219	46	series	series	NOUN
iajs-3044	219	47	:	:	PUNCT
iajs-3044	219	48	𝑒−𝛼(1+𝜃)𝑥	𝑒−𝛼(1+𝜃)𝑥	PUNCT
iajs-3044	219	49	=	=	SYM
iajs-3044	219	50	∑	∑	PUNCT
iajs-3044	219	51	(	(	PUNCT
iajs-3044	219	52	−𝛼(1+𝜃))𝑛	−𝛼(1+𝜃))𝑛	PRON
iajs-3044	219	53	𝑛	𝑛	PROPN
iajs-3044	219	54	!	!	NOUN
iajs-3044	219	55	∞	∞	NUM
iajs-3044	220	1	𝑛=0	𝑛=0	PROPN
iajs-3044	220	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	220	3	…	…	PUNCT
iajs-3044	220	4	(	(	PUNCT
iajs-3044	220	5	56	56	NUM
iajs-3044	220	6	)	)	PUNCT
iajs-3044	220	7	substituting	substitute	VERB
iajs-3044	220	8	equation	equation	NOUN
iajs-3044	220	9	(	(	PUNCT
iajs-3044	220	10	56	56	NUM
iajs-3044	220	11	)	)	PUNCT
iajs-3044	220	12	in	in	ADP
iajs-3044	220	13	equation	equation	NOUN
iajs-3044	220	14	(	(	PUNCT
iajs-3044	220	15	55	55	NUM
iajs-3044	220	16	)	)	PUNCT
iajs-3044	220	17	we	we	PRON
iajs-3044	220	18	get	get	VERB
iajs-3044	220	19	:	:	PUNCT
iajs-3044	220	20	𝐷(𝑟	𝐷(𝑟	NUM
iajs-3044	220	21	,	,	PUNCT
iajs-3044	220	22	𝛼	𝛼	NOUN
iajs-3044	220	23	,	,	PUNCT
iajs-3044	220	24	𝜆	𝜆	NOUN
iajs-3044	220	25	,	,	PUNCT
iajs-3044	220	26	𝜃	𝜃	NOUN
iajs-3044	220	27	)	)	PUNCT
iajs-3044	220	28	=	=	SYM
iajs-3044	221	1	∑	∑	PUNCT
iajs-3044	221	2	(	(	PUNCT
iajs-3044	221	3	−𝛼(1+𝜃))𝑛	−𝛼(1+𝜃))𝑛	PRON
iajs-3044	221	4	𝑛	𝑛	PROPN
iajs-3044	221	5	!	!	NOUN
iajs-3044	221	6	∞	∞	NUM
iajs-3044	222	1	𝑛=0	𝑛=0	PROPN
iajs-3044	222	2	𝑥𝑟+𝑛	𝑥𝑟+𝑛	PROPN
iajs-3044	222	3	𝑒−	𝑒−	NOUN
iajs-3044	222	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	222	5	)	)	PUNCT
iajs-3044	222	6	2	2	NUM
iajs-3044	222	7	𝑥2	𝑥2	NOUN
iajs-3044	222	8	…	…	PUNCT
iajs-3044	222	9	(	(	PUNCT
iajs-3044	222	10	57	57	NUM
iajs-3044	222	11	)	)	PUNCT
iajs-3044	222	12	substituting	substitute	VERB
iajs-3044	222	13	equation	equation	NOUN
iajs-3044	222	14	(	(	PUNCT
iajs-3044	222	15	57	57	NUM
iajs-3044	222	16	)	)	PUNCT
iajs-3044	222	17	in	in	ADP
iajs-3044	222	18	equation	equation	NOUN
iajs-3044	222	19	(	(	PUNCT
iajs-3044	222	20	54	54	NUM
iajs-3044	222	21	)	)	PUNCT
iajs-3044	222	22	we	we	PRON
iajs-3044	222	23	get	get	VERB
iajs-3044	222	24	:	:	PUNCT
iajs-3044	222	25	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	222	26	=	=	PUNCT
iajs-3044	222	27	∑	∑	PROPN
iajs-3044	222	28	(	(	PUNCT
iajs-3044	222	29	−𝛼(1+𝜃	−𝛼(1+𝜃	PROPN
iajs-3044	222	30	)	)	PUNCT
iajs-3044	222	31	)	)	PUNCT
iajs-3044	222	32	𝑛	𝑛	DET
iajs-3044	222	33	𝑛	𝑛	PROPN
iajs-3044	222	34	!	!	NOUN
iajs-3044	222	35	∞	∞	NUM
iajs-3044	223	1	𝑛=0	𝑛=0	PROPN
iajs-3044	223	2	[	[	PUNCT
iajs-3044	223	3	∫	∫	NOUN
iajs-3044	223	4	𝛼(1	𝛼(1	NOUN
iajs-3044	223	5	+	+	NUM
iajs-3044	223	6	𝜃)𝑥𝑟+𝑛	𝜃)𝑥𝑟+𝑛	PROPN
iajs-3044	223	7	𝑒−	𝑒−	NOUN
iajs-3044	223	8	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	223	9	)	)	PUNCT
iajs-3044	223	10	2	2	NUM
iajs-3044	223	11	𝑥2	𝑥2	NOUN
iajs-3044	223	12	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	223	13	∞	∞	PROPN
iajs-3044	223	14	0	0	NUM
iajs-3044	224	1	+	+	CCONJ
iajs-3044	225	1	∫	∫	X
iajs-3044	225	2	𝜆(1	𝜆(1	NOUN
iajs-3044	226	1	+	+	CCONJ
iajs-3044	226	2	∞	∞	NUM
iajs-3044	226	3	0	0	NUM
iajs-3044	226	4	𝜃)𝑥𝑟+𝑛+1	𝜃)𝑥𝑟+𝑛+1	ADJ
iajs-3044	226	5	𝑒−	𝑒−	NOUN
iajs-3044	226	6	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	226	7	)	)	PUNCT
iajs-3044	226	8	2	2	NUM
iajs-3044	226	9	𝑥2	𝑥2	NOUN
iajs-3044	226	10	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	226	11	]	]	X
iajs-3044	226	12	…	…	PUNCT
iajs-3044	226	13	(	(	PUNCT
iajs-3044	226	14	58	58	NUM
iajs-3044	226	15	)	)	PUNCT
iajs-3044	226	16	now	now	ADV
iajs-3044	226	17	,	,	PUNCT
iajs-3044	226	18	solve	solve	VERB
iajs-3044	226	19	the	the	DET
iajs-3044	226	20	first	first	ADJ
iajs-3044	226	21	integral	integral	ADJ
iajs-3044	226	22	as	as	SCONJ
iajs-3044	226	23	follows	follow	VERB
iajs-3044	226	24	:	:	PUNCT
iajs-3044	226	25	𝐿1	𝐿1	PROPN
iajs-3044	227	1	=	=	SYM
iajs-3044	227	2	∫	∫	PROPN
iajs-3044	228	1	𝛼(1	𝛼(1	NOUN
iajs-3044	228	2	+	+	NUM
iajs-3044	228	3	𝜃)𝑥𝑟+𝑛	𝜃)𝑥𝑟+𝑛	PROPN
iajs-3044	228	4	𝑒−	𝑒−	NOUN
iajs-3044	228	5	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	228	6	)	)	PUNCT
iajs-3044	228	7	2	2	NUM
iajs-3044	228	8	𝑥2	𝑥2	NOUN
iajs-3044	228	9	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	228	10	∞	∞	NUM
iajs-3044	228	11	0	0	NUM
iajs-3044	229	1	=	=	SYM
iajs-3044	229	2	𝛼	𝛼	X
iajs-3044	229	3	2	2	NUM
iajs-3044	229	4	𝑟+𝑛−1	𝑟+𝑛−1	PROPN
iajs-3044	229	5	2	2	NUM
iajs-3044	229	6	𝜆	𝜆	ADV
iajs-3044	229	7	𝑟+𝑛+1	𝑟+𝑛+1	ADJ
iajs-3044	229	8	2	2	NUM
iajs-3044	229	9	(	(	PUNCT
iajs-3044	229	10	1+𝜃	1+𝜃	NUM
iajs-3044	229	11	)	)	PUNCT
iajs-3044	229	12	𝑟+𝑛−1	𝑟+𝑛−1	PROPN
iajs-3044	229	13	2	2	NUM
iajs-3044	229	14	𝛤	𝛤	PROPN
iajs-3044	229	15	(	(	PUNCT
iajs-3044	229	16	𝑟+𝑛+1	𝑟+𝑛+1	NOUN
iajs-3044	229	17	2	2	NUM
iajs-3044	229	18	)	)	PUNCT
iajs-3044	229	19	…	…	PUNCT
iajs-3044	229	20	(	(	PUNCT
iajs-3044	229	21	59	59	NUM
iajs-3044	229	22	)	)	PUNCT
iajs-3044	229	23	now	now	ADV
iajs-3044	229	24	,	,	PUNCT
iajs-3044	229	25	solve	solve	VERB
iajs-3044	229	26	the	the	DET
iajs-3044	229	27	second	second	ADJ
iajs-3044	229	28	integral	integral	ADJ
iajs-3044	229	29	as	as	SCONJ
iajs-3044	229	30	follows	follow	VERB
iajs-3044	229	31	:	:	PUNCT
iajs-3044	229	32	𝐿2	𝐿2	PROPN
iajs-3044	229	33	=	=	SYM
iajs-3044	229	34	∫	∫	PROPN
iajs-3044	230	1	𝜆(1	𝜆(1	NUM
iajs-3044	231	1	+	+	NUM
iajs-3044	231	2	𝜃	𝜃	X
iajs-3044	231	3	)	)	PUNCT
iajs-3044	231	4	𝑥𝑟+𝑛+1	𝑥𝑟+𝑛+1	ADJ
iajs-3044	231	5	𝑒−	𝑒−	NOUN
iajs-3044	231	6	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	231	7	)	)	PUNCT
iajs-3044	231	8	2	2	NUM
iajs-3044	231	9	𝑥2	𝑥2	NOUN
iajs-3044	231	10	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	231	11	∞	∞	NUM
iajs-3044	231	12	0	0	NUM
iajs-3044	232	1	=	=	SYM
iajs-3044	232	2	2	2	NUM
iajs-3044	232	3	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	232	4	2	2	NUM
iajs-3044	232	5	𝜆	𝜆	ADP
iajs-3044	232	6	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	232	7	2	2	NUM
iajs-3044	232	8	(	(	PUNCT
iajs-3044	232	9	1	1	NUM
iajs-3044	232	10	+	+	NUM
iajs-3044	232	11	𝜃	𝜃	X
iajs-3044	232	12	)	)	PUNCT
iajs-3044	232	13	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	232	14	2	2	NUM
iajs-3044	232	15	𝛤	𝛤	PROPN
iajs-3044	232	16	(	(	PUNCT
iajs-3044	232	17	𝑟+𝑛+2	𝑟+𝑛+2	NOUN
iajs-3044	232	18	2	2	NUM
iajs-3044	232	19	)	)	PUNCT
iajs-3044	232	20	…	…	PUNCT
iajs-3044	232	21	(	(	PUNCT
iajs-3044	232	22	60	60	NUM
iajs-3044	232	23	)	)	PUNCT
iajs-3044	232	24	ihjpas	ihjpa	NOUN
iajs-3044	232	25	.	.	PUNCT
iajs-3044	233	1	36(2)2023	36(2)2023	NUM
iajs-3044	233	2	403	403	NUM
iajs-3044	233	3	substituting	substitute	VERB
iajs-3044	233	4	equations	equation	NOUN
iajs-3044	233	5	(	(	PUNCT
iajs-3044	233	6	59	59	NUM
iajs-3044	233	7	)	)	PUNCT
iajs-3044	233	8	and	and	CCONJ
iajs-3044	233	9	(	(	PUNCT
iajs-3044	233	10	60	60	NUM
iajs-3044	233	11	)	)	PUNCT
iajs-3044	233	12	in	in	ADP
iajs-3044	233	13	equation	equation	NOUN
iajs-3044	233	14	(	(	PUNCT
iajs-3044	233	15	58	58	NUM
iajs-3044	233	16	)	)	PUNCT
iajs-3044	233	17	we	we	PRON
iajs-3044	233	18	get	get	VERB
iajs-3044	233	19	:	:	PUNCT
iajs-3044	233	20	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	𝐸(𝑋𝑟)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	233	21	=	=	PUNCT
iajs-3044	233	22	∑	∑	PROPN
iajs-3044	233	23	(	(	PUNCT
iajs-3044	233	24	−𝛼(1	−𝛼(1	PROPN
iajs-3044	233	25	+	+	CCONJ
iajs-3044	233	26	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	233	27	𝑛	𝑛	PROPN
iajs-3044	233	28	!	!	NOUN
iajs-3044	233	29	∞	∞	NUM
iajs-3044	234	1	𝑛=0	𝑛=0	PROPN
iajs-3044	234	2	2	2	NUM
iajs-3044	234	3	𝑟+𝑛	𝑟+𝑛	PROPN
iajs-3044	234	4	2	2	NUM
iajs-3044	234	5	𝜆	𝜆	ADP
iajs-3044	234	6	𝑟+𝑛	𝑟+𝑛	NUM
iajs-3044	234	7	2	2	NUM
iajs-3044	234	8	(	(	PUNCT
iajs-3044	234	9	1	1	NUM
iajs-3044	234	10	+	+	NUM
iajs-3044	234	11	𝜃	𝜃	NOUN
iajs-3044	234	12	)	)	PUNCT
iajs-3044	234	13	𝑟+𝑛	𝑟+𝑛	VERB
iajs-3044	234	14	2	2	NUM
iajs-3044	234	15	[	[	PUNCT
iajs-3044	234	16	𝛼	𝛼	NOUN
iajs-3044	234	17	√𝜃	√𝜃	NUM
iajs-3044	234	18	√2𝜆	√2𝜆	NUM
iajs-3044	234	19	𝛤	𝛤	PROPN
iajs-3044	234	20	(	(	PUNCT
iajs-3044	234	21	𝑟+𝑛+1	𝑟+𝑛+1	NOUN
iajs-3044	234	22	2	2	NUM
iajs-3044	234	23	)	)	PUNCT
iajs-3044	235	1	+	+	CCONJ
iajs-3044	235	2	𝛤	𝛤	PROPN
iajs-3044	235	3	(	(	PUNCT
iajs-3044	235	4	𝑟+𝑛+2	𝑟+𝑛+2	NOUN
iajs-3044	235	5	2	2	NUM
iajs-3044	235	6	)	)	PUNCT
iajs-3044	235	7	]	]	PUNCT
iajs-3044	235	8	…	…	PUNCT
iajs-3044	235	9	(	(	PUNCT
iajs-3044	235	10	61	61	NUM
iajs-3044	235	11	)	)	PUNCT
iajs-3044	235	12	the	the	DET
iajs-3044	235	13	mean	mean	NOUN
iajs-3044	235	14	:	:	PUNCT
iajs-3044	235	15	let	let	VERB
iajs-3044	235	16	𝑟	𝑟	NOUN
iajs-3044	235	17	=	=	SYM
iajs-3044	235	18	1	1	NUM
iajs-3044	235	19	in	in	ADP
iajs-3044	235	20	equation	equation	NOUN
iajs-3044	235	21	(	(	PUNCT
iajs-3044	235	22	61	61	NUM
iajs-3044	235	23	)	)	PUNCT
iajs-3044	235	24	we	we	PRON
iajs-3044	235	25	get	get	VERB
iajs-3044	235	26	the	the	DET
iajs-3044	235	27	first	first	ADJ
iajs-3044	235	28	moment	moment	NOUN
iajs-3044	235	29	which	which	PRON
iajs-3044	235	30	is	be	AUX
iajs-3044	235	31	called	call	VERB
iajs-3044	235	32	the	the	DET
iajs-3044	235	33	mean	mean	NOUN
iajs-3044	235	34	,	,	PUNCT
iajs-3044	235	35	thus	thus	ADV
iajs-3044	235	36	:	:	PUNCT
iajs-3044	236	1	𝐸(𝑋)𝑀𝑊𝐸𝑅	𝐸(𝑋)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	236	2	=	=	PUNCT
iajs-3044	236	3	∑	∑	PROPN
iajs-3044	236	4	(	(	PUNCT
iajs-3044	236	5	−𝛼(1	−𝛼(1	PROPN
iajs-3044	236	6	+	+	CCONJ
iajs-3044	236	7	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	236	8	𝑛	𝑛	PROPN
iajs-3044	236	9	!	!	NOUN
iajs-3044	236	10	∞	∞	NUM
iajs-3044	237	1	𝑛=0	𝑛=0	NOUN
iajs-3044	237	2	2	2	NUM
iajs-3044	237	3	1+𝑛	1+𝑛	NUM
iajs-3044	237	4	2	2	NUM
iajs-3044	237	5	𝜆	𝜆	PROPN
iajs-3044	237	6	1+𝑛	1+𝑛	NUM
iajs-3044	237	7	2	2	NUM
iajs-3044	237	8	(	(	PUNCT
iajs-3044	237	9	1	1	NUM
iajs-3044	237	10	+	+	NUM
iajs-3044	237	11	𝜃	𝜃	X
iajs-3044	237	12	)	)	PUNCT
iajs-3044	237	13	1+𝑛	1+𝑛	NUM
iajs-3044	237	14	2	2	NUM
iajs-3044	237	15	[	[	PUNCT
iajs-3044	237	16	𝛼	𝛼	NOUN
iajs-3044	237	17	√𝜃	√𝜃	NUM
iajs-3044	237	18	√2𝜆	√2𝜆	NUM
iajs-3044	237	19	𝛤	𝛤	PROPN
iajs-3044	237	20	(	(	PUNCT
iajs-3044	237	21	𝑛+2	𝑛+2	NUM
iajs-3044	237	22	2	2	NUM
iajs-3044	237	23	)	)	PUNCT
iajs-3044	237	24	+	+	CCONJ
iajs-3044	237	25	𝛤	𝛤	PROPN
iajs-3044	237	26	(	(	PUNCT
iajs-3044	237	27	𝑛+3	𝑛+3	NUM
iajs-3044	237	28	2	2	NUM
iajs-3044	237	29	)	)	PUNCT
iajs-3044	237	30	]	]	PUNCT
iajs-3044	237	31	…	…	PUNCT
iajs-3044	237	32	(	(	PUNCT
iajs-3044	237	33	62	62	NUM
iajs-3044	237	34	)	)	PUNCT
iajs-3044	237	35	the	the	DET
iajs-3044	237	36	variance	variance	NOUN
iajs-3044	237	37	:	:	PUNCT
iajs-3044	237	38	the	the	DET
iajs-3044	237	39	general	general	ADJ
iajs-3044	237	40	form	form	NOUN
iajs-3044	237	41	of	of	ADP
iajs-3044	237	42	𝑣(𝑋	𝑣(𝑋	NOUN
iajs-3044	237	43	)	)	PUNCT
iajs-3044	237	44	of	of	ADP
iajs-3044	237	45	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	NOUN
iajs-3044	237	46	distribution	distribution	NOUN
iajs-3044	237	47	is	be	AUX
iajs-3044	237	48	defined	define	VERB
iajs-3044	237	49	as	as	ADP
iajs-3044	237	50	:	:	PUNCT
iajs-3044	237	51	𝑣(𝑋)𝑀𝑊𝐸𝑅	𝑣(𝑋)𝑀𝑊𝐸𝑅	NUM
iajs-3044	237	52	=	=	PUNCT
iajs-3044	238	1	[	[	X
iajs-3044	238	2	∑	∑	INTJ
iajs-3044	238	3	(	(	PUNCT
iajs-3044	238	4	−𝛼(1	−𝛼(1	PROPN
iajs-3044	238	5	+	+	CCONJ
iajs-3044	238	6	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	238	7	𝑛	𝑛	PROPN
iajs-3044	238	8	!	!	NOUN
iajs-3044	238	9	∞	∞	NUM
iajs-3044	239	1	𝑛=0	𝑛=0	PROPN
iajs-3044	239	2	2	2	NUM
iajs-3044	239	3	2+𝑛	2+𝑛	NUM
iajs-3044	239	4	2	2	NUM
iajs-3044	239	5	𝜆	𝜆	PRON
iajs-3044	239	6	2+𝑛	2+𝑛	NUM
iajs-3044	239	7	2	2	NUM
iajs-3044	239	8	(	(	PUNCT
iajs-3044	239	9	1	1	NUM
iajs-3044	239	10	+	+	NUM
iajs-3044	239	11	𝜃	𝜃	X
iajs-3044	239	12	)	)	PUNCT
iajs-3044	239	13	2+𝑛	2+𝑛	NUM
iajs-3044	239	14	2	2	NUM
iajs-3044	239	15	[	[	PUNCT
iajs-3044	239	16	𝛼	𝛼	NOUN
iajs-3044	239	17	√𝜃	√𝜃	NUM
iajs-3044	239	18	√2𝜆	√2𝜆	NUM
iajs-3044	239	19	𝛤	𝛤	PROPN
iajs-3044	239	20	(	(	PUNCT
iajs-3044	239	21	𝑛+3	𝑛+3	NUM
iajs-3044	239	22	2	2	NUM
iajs-3044	239	23	)	)	PUNCT
iajs-3044	240	1	+	+	CCONJ
iajs-3044	240	2	𝛤	𝛤	PROPN
iajs-3044	240	3	(	(	PUNCT
iajs-3044	240	4	𝑛+4	𝑛+4	PROPN
iajs-3044	240	5	2	2	NUM
iajs-3044	240	6	)	)	PUNCT
iajs-3044	240	7	]	]	PUNCT
iajs-3044	240	8	]	]	PUNCT
iajs-3044	240	9	−	−	PUNCT
iajs-3044	241	1	[	[	X
iajs-3044	241	2	∑	∑	INTJ
iajs-3044	241	3	(	(	PUNCT
iajs-3044	241	4	−𝛼(1	−𝛼(1	PROPN
iajs-3044	241	5	+	+	CCONJ
iajs-3044	241	6	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	241	7	𝑛	𝑛	PROPN
iajs-3044	241	8	!	!	NOUN
iajs-3044	241	9	∞	∞	NUM
iajs-3044	242	1	𝑛=0	𝑛=0	NOUN
iajs-3044	242	2	2	2	NUM
iajs-3044	242	3	1+𝑛	1+𝑛	NUM
iajs-3044	242	4	2	2	NUM
iajs-3044	242	5	𝜆	𝜆	PROPN
iajs-3044	242	6	1+𝑛	1+𝑛	NUM
iajs-3044	242	7	2	2	NUM
iajs-3044	242	8	(	(	PUNCT
iajs-3044	242	9	1	1	NUM
iajs-3044	242	10	+	+	NUM
iajs-3044	242	11	𝜃	𝜃	X
iajs-3044	242	12	)	)	PUNCT
iajs-3044	242	13	1+𝑛	1+𝑛	NUM
iajs-3044	242	14	2	2	NUM
iajs-3044	242	15	[	[	PUNCT
iajs-3044	242	16	𝛼	𝛼	NOUN
iajs-3044	242	17	√𝜃	√𝜃	NUM
iajs-3044	242	18	√2𝜆	√2𝜆	NUM
iajs-3044	242	19	𝛤	𝛤	PROPN
iajs-3044	242	20	(	(	PUNCT
iajs-3044	242	21	𝑛+2	𝑛+2	NUM
iajs-3044	242	22	2	2	NUM
iajs-3044	242	23	)	)	PUNCT
iajs-3044	242	24	+	+	CCONJ
iajs-3044	242	25	𝛤	𝛤	PROPN
iajs-3044	242	26	(	(	PUNCT
iajs-3044	242	27	𝑛+3	𝑛+3	NUM
iajs-3044	242	28	2	2	NUM
iajs-3044	242	29	)	)	PUNCT
iajs-3044	242	30	]	]	PUNCT
iajs-3044	242	31	]	]	PUNCT
iajs-3044	242	32	2	2	NUM
iajs-3044	242	33	…	…	PUNCT
iajs-3044	242	34	(	(	PUNCT
iajs-3044	242	35	63	63	NUM
iajs-3044	242	36	)	)	SYM
iajs-3044	242	37	3.2.4	3.2.4	NUM
iajs-3044	242	38	coefficient	coefficient	NOUN
iajs-3044	242	39	of	of	ADP
iajs-3044	242	40	skewness	skewness	NOUN
iajs-3044	242	41	the	the	DET
iajs-3044	242	42	general	general	ADJ
iajs-3044	242	43	form	form	NOUN
iajs-3044	242	44	of	of	ADP
iajs-3044	242	45	the	the	DET
iajs-3044	242	46	coefficient	coefficient	NOUN
iajs-3044	242	47	of	of	ADP
iajs-3044	242	48	skewness	skewness	NOUN
iajs-3044	242	49	(	(	PUNCT
iajs-3044	242	50	𝐶.	𝐶.	PROPN
iajs-3044	242	51	𝑆	𝑆	PROPN
iajs-3044	242	52	)	)	PUNCT
iajs-3044	242	53	of	of	ADP
iajs-3044	242	54	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	NOUN
iajs-3044	242	55	distribution	distribution	NOUN
iajs-3044	242	56	can	can	AUX
iajs-3044	242	57	be	be	AUX
iajs-3044	242	58	obtained	obtain	VERB
iajs-3044	242	59	by	by	ADP
iajs-3044	242	60	:	:	PUNCT
iajs-3044	242	61	𝐶.	𝐶.	PROPN
iajs-3044	242	62	𝑆𝑀𝑊𝐸𝑅	𝑆𝑀𝑊𝐸𝑅	PROPN
iajs-3044	242	63	=	=	PUNCT
iajs-3044	242	64	∑	∑	PROPN
iajs-3044	242	65	(	(	PUNCT
iajs-3044	242	66	−𝛼(1	−𝛼(1	PROPN
iajs-3044	242	67	+	+	CCONJ
iajs-3044	242	68	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	242	69	𝑛	𝑛	PROPN
iajs-3044	242	70	!	!	NOUN
iajs-3044	243	1	∞	∞	NUM
iajs-3044	243	2	𝑛=0	𝑛=0	PROPN
iajs-3044	243	3	2	2	NUM
iajs-3044	243	4	3+𝑛	3+𝑛	NUM
iajs-3044	243	5	2	2	NUM
iajs-3044	243	6	𝜆	𝜆	SYM
iajs-3044	243	7	3+𝑛	3+𝑛	NUM
iajs-3044	243	8	2	2	NUM
iajs-3044	243	9	(	(	PUNCT
iajs-3044	243	10	1	1	NUM
iajs-3044	243	11	+	+	NUM
iajs-3044	243	12	𝜃	𝜃	NOUN
iajs-3044	243	13	)	)	PUNCT
iajs-3044	243	14	3+𝑛	3+𝑛	NUM
iajs-3044	243	15	2	2	NUM
iajs-3044	243	16	[	[	PUNCT
iajs-3044	243	17	𝛼	𝛼	NOUN
iajs-3044	243	18	√𝜃	√𝜃	NUM
iajs-3044	243	19	√2𝜆	√2𝜆	NUM
iajs-3044	243	20	𝛤	𝛤	PROPN
iajs-3044	243	21	(	(	PUNCT
iajs-3044	243	22	𝑛+4	𝑛+4	PROPN
iajs-3044	243	23	2	2	NUM
iajs-3044	243	24	)	)	PUNCT
iajs-3044	243	25	+	+	X
iajs-3044	244	1	𝛤	𝛤	PROPN
iajs-3044	244	2	(	(	PUNCT
iajs-3044	244	3	𝑛+5	𝑛+5	ADP
iajs-3044	244	4	2	2	NUM
iajs-3044	244	5	)	)	PUNCT
iajs-3044	244	6	]	]	PUNCT
iajs-3044	245	1	[	[	X
iajs-3044	245	2	∑	∑	INTJ
iajs-3044	245	3	(	(	PUNCT
iajs-3044	245	4	−𝛼(1	−𝛼(1	PROPN
iajs-3044	245	5	+	+	CCONJ
iajs-3044	245	6	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	245	7	𝑛	𝑛	PROPN
iajs-3044	245	8	!	!	NOUN
iajs-3044	245	9	∞	∞	NUM
iajs-3044	245	10	𝑛=0	𝑛=0	PROPN
iajs-3044	245	11	2	2	NUM
iajs-3044	245	12	2+𝑛	2+𝑛	NUM
iajs-3044	245	13	2	2	NUM
iajs-3044	245	14	𝜆	𝜆	DET
iajs-3044	245	15	2+𝑛	2+𝑛	NUM
iajs-3044	245	16	2	2	NUM
iajs-3044	245	17	(	(	PUNCT
iajs-3044	245	18	1	1	NUM
iajs-3044	245	19	+	+	NUM
iajs-3044	245	20	𝜃	𝜃	X
iajs-3044	245	21	)	)	PUNCT
iajs-3044	245	22	2+𝑛	2+𝑛	NUM
iajs-3044	245	23	2	2	NUM
iajs-3044	245	24	[	[	PUNCT
iajs-3044	245	25	𝛼	𝛼	NOUN
iajs-3044	245	26	√𝜃	√𝜃	NUM
iajs-3044	245	27	√2𝜆	√2𝜆	NUM
iajs-3044	245	28	𝛤	𝛤	PROPN
iajs-3044	245	29	(	(	PUNCT
iajs-3044	245	30	𝑛+3	𝑛+3	NUM
iajs-3044	245	31	2	2	NUM
iajs-3044	245	32	)	)	PUNCT
iajs-3044	245	33	+	+	X
iajs-3044	246	1	𝛤	𝛤	PROPN
iajs-3044	246	2	(	(	PUNCT
iajs-3044	246	3	𝑛+4	𝑛+4	PROPN
iajs-3044	246	4	2	2	NUM
iajs-3044	246	5	)	)	PUNCT
iajs-3044	246	6	]	]	PUNCT
iajs-3044	246	7	]	]	X
iajs-3044	246	8	3	3	NUM
iajs-3044	246	9	2	2	NUM
iajs-3044	246	10	…	…	PUNCT
iajs-3044	246	11	(	(	PUNCT
iajs-3044	246	12	64	64	NUM
iajs-3044	246	13	)	)	PUNCT
iajs-3044	246	14	3.2.5	3.2.5	NUM
iajs-3044	246	15	coefficient	coefficient	NOUN
iajs-3044	246	16	of	of	ADP
iajs-3044	246	17	kurtosis	kurtosis	NOUN
iajs-3044	246	18	the	the	DET
iajs-3044	246	19	general	general	ADJ
iajs-3044	246	20	form	form	NOUN
iajs-3044	246	21	of	of	ADP
iajs-3044	246	22	the	the	DET
iajs-3044	246	23	coefficient	coefficient	NOUN
iajs-3044	246	24	of	of	ADP
iajs-3044	246	25	kurtosis	kurtosis	NOUN
iajs-3044	246	26	(	(	PUNCT
iajs-3044	246	27	𝐶.	𝐶.	PROPN
iajs-3044	246	28	𝐾	𝐾	PROPN
iajs-3044	246	29	)	)	PUNCT
iajs-3044	246	30	of	of	ADP
iajs-3044	246	31	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	246	32	distribution	distribution	NOUN
iajs-3044	246	33	is	be	AUX
iajs-3044	246	34	given	give	VERB
iajs-3044	246	35	by	by	ADP
iajs-3044	246	36	:	:	PUNCT
iajs-3044	246	37	𝐶.	𝐶.	PROPN
iajs-3044	246	38	𝐾𝑀𝑊𝐸𝑅	𝐾𝑀𝑊𝐸𝑅	PROPN
iajs-3044	246	39	=	=	PUNCT
iajs-3044	246	40	∑	∑	PUNCT
iajs-3044	246	41	(	(	PUNCT
iajs-3044	246	42	−𝛼(1	−𝛼(1	PROPN
iajs-3044	246	43	+	+	CCONJ
iajs-3044	246	44	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	246	45	𝑛	𝑛	PROPN
iajs-3044	246	46	!	!	NOUN
iajs-3044	246	47	∞	∞	NUM
iajs-3044	247	1	𝑛=0	𝑛=0	PROPN
iajs-3044	247	2	2	2	NUM
iajs-3044	247	3	4+𝑛	4+𝑛	NUM
iajs-3044	247	4	2	2	NUM
iajs-3044	247	5	𝜆	𝜆	PRON
iajs-3044	247	6	4+𝑛	4+𝑛	NUM
iajs-3044	247	7	2	2	NUM
iajs-3044	247	8	(	(	PUNCT
iajs-3044	247	9	1	1	NUM
iajs-3044	247	10	+	+	NUM
iajs-3044	247	11	𝜃	𝜃	X
iajs-3044	247	12	)	)	PUNCT
iajs-3044	247	13	4+𝑛	4+𝑛	NUM
iajs-3044	247	14	2	2	NUM
iajs-3044	247	15	[	[	PUNCT
iajs-3044	247	16	𝛼	𝛼	NOUN
iajs-3044	247	17	√𝜃	√𝜃	NUM
iajs-3044	247	18	√2𝜆	√2𝜆	NUM
iajs-3044	247	19	𝛤	𝛤	PROPN
iajs-3044	247	20	(	(	PUNCT
iajs-3044	247	21	𝑛+5	𝑛+5	ADP
iajs-3044	247	22	2	2	NUM
iajs-3044	247	23	)	)	PUNCT
iajs-3044	247	24	+	+	CCONJ
iajs-3044	248	1	𝛤	𝛤	PROPN
iajs-3044	248	2	(	(	PUNCT
iajs-3044	248	3	𝑛+6	𝑛+6	PROPN
iajs-3044	248	4	2	2	NUM
iajs-3044	248	5	)	)	PUNCT
iajs-3044	248	6	]	]	PUNCT
iajs-3044	249	1	[	[	X
iajs-3044	249	2	∑	∑	INTJ
iajs-3044	249	3	(	(	PUNCT
iajs-3044	249	4	−𝛼(1	−𝛼(1	PROPN
iajs-3044	249	5	+	+	CCONJ
iajs-3044	249	6	𝜃))𝑛	𝜃))𝑛	ADJ
iajs-3044	249	7	𝑛	𝑛	PROPN
iajs-3044	249	8	!	!	NOUN
iajs-3044	249	9	∞	∞	NUM
iajs-3044	249	10	𝑛=0	𝑛=0	PROPN
iajs-3044	249	11	2	2	NUM
iajs-3044	249	12	2+𝑛	2+𝑛	NUM
iajs-3044	249	13	2	2	NUM
iajs-3044	249	14	𝜆	𝜆	DET
iajs-3044	249	15	2+𝑛	2+𝑛	NUM
iajs-3044	249	16	2	2	NUM
iajs-3044	249	17	(	(	PUNCT
iajs-3044	249	18	1	1	NUM
iajs-3044	249	19	+	+	NUM
iajs-3044	249	20	𝜃	𝜃	X
iajs-3044	249	21	)	)	PUNCT
iajs-3044	249	22	2+𝑛	2+𝑛	NUM
iajs-3044	249	23	2	2	NUM
iajs-3044	249	24	[	[	PUNCT
iajs-3044	249	25	𝛼	𝛼	NOUN
iajs-3044	249	26	√𝜃	√𝜃	NUM
iajs-3044	249	27	√2𝜆	√2𝜆	NUM
iajs-3044	249	28	𝛤	𝛤	PROPN
iajs-3044	249	29	(	(	PUNCT
iajs-3044	249	30	𝑛+3	𝑛+3	NUM
iajs-3044	249	31	2	2	NUM
iajs-3044	249	32	)	)	PUNCT
iajs-3044	249	33	+	+	X
iajs-3044	250	1	𝛤	𝛤	PROPN
iajs-3044	250	2	(	(	PUNCT
iajs-3044	250	3	𝑛+4	𝑛+4	PROPN
iajs-3044	250	4	2	2	NUM
iajs-3044	250	5	)	)	PUNCT
iajs-3044	250	6	]	]	X
iajs-3044	250	7	]	]	X
iajs-3044	250	8	2	2	NUM
iajs-3044	250	9	−	−	PROPN
iajs-3044	250	10	3	3	NUM
iajs-3044	250	11	…	…	PUNCT
iajs-3044	250	12	(	(	PUNCT
iajs-3044	250	13	65	65	NUM
iajs-3044	250	14	)	)	PUNCT
iajs-3044	250	15	3.2.6	3.2.6	NUM
iajs-3044	250	16	moment	moment	NOUN
iajs-3044	250	17	generating	generate	VERB
iajs-3044	250	18	function	function	NOUN
iajs-3044	250	19	the	the	DET
iajs-3044	250	20	moment	moment	NOUN
iajs-3044	250	21	generating	generate	VERB
iajs-3044	250	22	function	function	NOUN
iajs-3044	250	23	of	of	ADP
iajs-3044	250	24	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	NOUN
iajs-3044	250	25	distribution	distribution	NOUN
iajs-3044	250	26	can	can	AUX
iajs-3044	250	27	be	be	AUX
iajs-3044	250	28	found	find	VERB
iajs-3044	250	29	as	as	SCONJ
iajs-3044	250	30	follows	follow	VERB
iajs-3044	250	31	:	:	PUNCT
iajs-3044	250	32	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	250	33	=	=	SYM
iajs-3044	250	34	∫	∫	PROPN
iajs-3044	250	35	𝑒𝑥𝑡	𝑒𝑥𝑡	NOUN
iajs-3044	250	36	(	(	PUNCT
iajs-3044	250	37	𝛼(1	𝛼(1	NOUN
iajs-3044	250	38	+	+	NUM
iajs-3044	250	39	𝜃	𝜃	X
iajs-3044	250	40	)	)	PUNCT
iajs-3044	251	1	+	+	CCONJ
iajs-3044	251	2	𝜆(1	𝜆(1	CCONJ
iajs-3044	251	3	+	+	NUM
iajs-3044	251	4	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	251	5	)	)	PUNCT
iajs-3044	251	6	𝑒−	𝑒−	NOUN
iajs-3044	251	7	(	(	PUNCT
iajs-3044	251	8	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	251	9	+	+	CCONJ
iajs-3044	251	10	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	251	11	)	)	PUNCT
iajs-3044	251	12	2	2	NUM
iajs-3044	251	13	𝑥2)∞	𝑥2)∞	NOUN
iajs-3044	251	14	0	0	NUM
iajs-3044	251	15	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	251	16	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	251	17	=	=	SYM
iajs-3044	251	18	∫	∫	PROPN
iajs-3044	251	19	(	(	PUNCT
iajs-3044	252	1	𝛼(1	𝛼(1	NOUN
iajs-3044	252	2	+	+	NUM
iajs-3044	252	3	𝜃	𝜃	X
iajs-3044	252	4	)	)	PUNCT
iajs-3044	253	1	+	+	CCONJ
iajs-3044	253	2	𝜆(1	𝜆(1	CCONJ
iajs-3044	253	3	+	+	NUM
iajs-3044	253	4	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	253	5	)	)	PUNCT
iajs-3044	253	6	𝑒−	𝑒−	NOUN
iajs-3044	253	7	(	(	PUNCT
iajs-3044	253	8	(	(	PUNCT
iajs-3044	253	9	𝛼(1+𝜃)−𝑡	𝛼(1+𝜃)−𝑡	PROPN
iajs-3044	253	10	)	)	PUNCT
iajs-3044	253	11	𝑥	𝑥	PROPN
iajs-3044	254	1	+	+	NUM
iajs-3044	254	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	254	3	)	)	PUNCT
iajs-3044	254	4	2	2	NUM
iajs-3044	254	5	𝑥2	𝑥2	NOUN
iajs-3044	254	6	)	)	PUNCT
iajs-3044	254	7	∞	∞	NOUN
iajs-3044	254	8	0	0	NUM
iajs-3044	254	9	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	254	10	…	…	PUNCT
iajs-3044	254	11	(	(	PUNCT
iajs-3044	254	12	66	66	NUM
iajs-3044	254	13	)	)	PUNCT
iajs-3044	254	14	let	let	VERB
iajs-3044	254	15	𝑇((𝛼(1	𝑇((𝛼(1	PUNCT
iajs-3044	255	1	+	+	SYM
iajs-3044	255	2	𝜃	𝜃	X
iajs-3044	255	3	)	)	PUNCT
iajs-3044	255	4	−	−	PRON
iajs-3044	256	1	𝑡	𝑡	NOUN
iajs-3044	256	2	)	)	PUNCT
iajs-3044	256	3	,	,	PUNCT
iajs-3044	256	4	𝜆	𝜆	X
iajs-3044	256	5	)	)	PUNCT
iajs-3044	256	6	=	=	SYM
iajs-3044	256	7	𝑒−	𝑒−	NOUN
iajs-3044	256	8	(	(	PUNCT
iajs-3044	256	9	(	(	PUNCT
iajs-3044	256	10	𝛼(1+𝜃)−𝑡	𝛼(1+𝜃)−𝑡	PROPN
iajs-3044	256	11	)	)	PUNCT
iajs-3044	256	12	𝑥	𝑥	PROPN
iajs-3044	257	1	+	+	NUM
iajs-3044	257	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	257	3	)	)	PUNCT
iajs-3044	257	4	2	2	NUM
iajs-3044	257	5	𝑥2	𝑥2	NOUN
iajs-3044	257	6	)	)	PUNCT
iajs-3044	257	7	…	…	PUNCT
iajs-3044	257	8	(	(	PUNCT
iajs-3044	257	9	67	67	NUM
iajs-3044	257	10	)	)	PUNCT
iajs-3044	257	11	by	by	ADP
iajs-3044	257	12	maclaurin	maclaurin	NOUN
iajs-3044	257	13	series	series	NOUN
iajs-3044	257	14	:	:	PUNCT
iajs-3044	257	15	𝑒−(𝛼(1+𝜃)−𝑡)𝑥	𝑒−(𝛼(1+𝜃)−𝑡)𝑥	NOUN
iajs-3044	257	16	=	=	SYM
iajs-3044	257	17	∑	∑	PROPN
iajs-3044	257	18	(	(	PUNCT
iajs-3044	257	19	−(𝛼(1+𝜃)−𝑡))𝑛	−(𝛼(1+𝜃)−𝑡))𝑛	NOUN
iajs-3044	257	20	𝑛	𝑛	NOUN
iajs-3044	257	21	!	!	PUNCT
iajs-3044	257	22	∞	∞	NUM
iajs-3044	258	1	𝑛=0	𝑛=0	PROPN
iajs-3044	258	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	258	3	…	…	PUNCT
iajs-3044	258	4	(	(	PUNCT
iajs-3044	258	5	68	68	NUM
iajs-3044	258	6	)	)	PUNCT
iajs-3044	258	7	substituting	substitute	VERB
iajs-3044	258	8	equation	equation	NOUN
iajs-3044	258	9	(	(	PUNCT
iajs-3044	258	10	68	68	NUM
iajs-3044	258	11	)	)	PUNCT
iajs-3044	258	12	in	in	ADP
iajs-3044	258	13	equation	equation	NOUN
iajs-3044	258	14	(	(	PUNCT
iajs-3044	258	15	67	67	NUM
iajs-3044	258	16	)	)	PUNCT
iajs-3044	258	17	we	we	PRON
iajs-3044	258	18	get	get	VERB
iajs-3044	258	19	:	:	PUNCT
iajs-3044	258	20	𝑇((𝛼(1	𝑇((𝛼(1	X
iajs-3044	258	21	+	+	CCONJ
iajs-3044	258	22	𝜃	𝜃	X
iajs-3044	258	23	)	)	PUNCT
iajs-3044	258	24	−	−	PRON
iajs-3044	258	25	𝑡	𝑡	NOUN
iajs-3044	258	26	)	)	PUNCT
iajs-3044	258	27	,	,	PUNCT
iajs-3044	258	28	𝜆	𝜆	X
iajs-3044	258	29	)	)	PUNCT
iajs-3044	258	30	=	=	SYM
iajs-3044	258	31	∑	∑	PROPN
iajs-3044	258	32	(	(	PUNCT
iajs-3044	258	33	−(𝛼(1+𝜃)−𝑡))𝑛	−(𝛼(1+𝜃)−𝑡))𝑛	NOUN
iajs-3044	258	34	𝑛	𝑛	NOUN
iajs-3044	258	35	!	!	PUNCT
iajs-3044	258	36	∞	∞	NUM
iajs-3044	259	1	𝑛=0	𝑛=0	PROPN
iajs-3044	259	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	259	3	𝑒−	𝑒−	NOUN
iajs-3044	259	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	259	5	)	)	PUNCT
iajs-3044	259	6	2	2	NUM
iajs-3044	259	7	𝑥2	𝑥2	NOUN
iajs-3044	259	8	…	…	PUNCT
iajs-3044	259	9	(	(	PUNCT
iajs-3044	259	10	69	69	NUM
iajs-3044	259	11	)	)	PUNCT
iajs-3044	259	12	substituting	substitute	VERB
iajs-3044	259	13	equation	equation	NOUN
iajs-3044	259	14	(	(	PUNCT
iajs-3044	259	15	69	69	NUM
iajs-3044	259	16	)	)	PUNCT
iajs-3044	259	17	in	in	ADP
iajs-3044	259	18	equation	equation	NOUN
iajs-3044	259	19	(	(	PUNCT
iajs-3044	259	20	66	66	NUM
iajs-3044	259	21	)	)	PUNCT
iajs-3044	259	22	we	we	PRON
iajs-3044	259	23	get	get	VERB
iajs-3044	259	24	:	:	PUNCT
iajs-3044	259	25	ihjpas	ihjpas	PROPN
iajs-3044	259	26	.	.	PUNCT
iajs-3044	260	1	36(2)2023	36(2)2023	NUM
iajs-3044	260	2	404	404	NUM
iajs-3044	260	3	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	260	4	=	=	PUNCT
iajs-3044	260	5	∑	∑	PROPN
iajs-3044	260	6	(	(	PUNCT
iajs-3044	260	7	−(𝛼(1+𝜃)−𝑡))𝑛	−(𝛼(1+𝜃)−𝑡))𝑛	NOUN
iajs-3044	260	8	𝑛	𝑛	NOUN
iajs-3044	260	9	!	!	PUNCT
iajs-3044	260	10	∞	∞	NUM
iajs-3044	260	11	𝑛=0	𝑛=0	PROPN
iajs-3044	261	1	[	[	X
iajs-3044	261	2	∫	∫	X
iajs-3044	261	3	𝛼(1	𝛼(1	NOUN
iajs-3044	261	4	+	+	NUM
iajs-3044	261	5	𝜃	𝜃	X
iajs-3044	261	6	)	)	PUNCT
iajs-3044	261	7	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	261	8	𝑒−	𝑒−	NOUN
iajs-3044	261	9	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	261	10	)	)	PUNCT
iajs-3044	261	11	2	2	NUM
iajs-3044	261	12	𝑥2	𝑥2	NOUN
iajs-3044	261	13	∞	∞	NOUN
iajs-3044	261	14	0	0	NUM
iajs-3044	261	15	𝑑𝑥	𝑑𝑥	X
iajs-3044	261	16	+	+	NOUN
iajs-3044	261	17	∫	∫	X
iajs-3044	262	1	𝜆(1	𝜆(1	NOUN
iajs-3044	263	1	+	+	CCONJ
iajs-3044	263	2	∞	∞	NUM
iajs-3044	263	3	0	0	NUM
iajs-3044	263	4	𝜃	𝜃	X
iajs-3044	263	5	)	)	PUNCT
iajs-3044	263	6	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	263	7	𝑒−	𝑒−	NOUN
iajs-3044	263	8	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	263	9	)	)	PUNCT
iajs-3044	263	10	2	2	NUM
iajs-3044	263	11	𝑥2	𝑥2	NOUN
iajs-3044	263	12	𝑑𝑥	𝑑𝑥	AUX
iajs-3044	263	13	]	]	X
iajs-3044	263	14	…	…	PUNCT
iajs-3044	263	15	(	(	PUNCT
iajs-3044	263	16	70	70	NUM
iajs-3044	263	17	)	)	PUNCT
iajs-3044	263	18	now	now	ADV
iajs-3044	263	19	,	,	PUNCT
iajs-3044	263	20	solve	solve	VERB
iajs-3044	263	21	the	the	DET
iajs-3044	263	22	first	first	ADJ
iajs-3044	263	23	integral	integral	ADJ
iajs-3044	263	24	as	as	SCONJ
iajs-3044	263	25	follows	follow	VERB
iajs-3044	263	26	:	:	PUNCT
iajs-3044	263	27	𝐿1	𝐿1	PROPN
iajs-3044	264	1	=	=	SYM
iajs-3044	264	2	∫	∫	PROPN
iajs-3044	265	1	𝛼(1	𝛼(1	NOUN
iajs-3044	265	2	+	+	NUM
iajs-3044	265	3	𝜃	𝜃	X
iajs-3044	265	4	)	)	PUNCT
iajs-3044	265	5	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	265	6	𝑒−	𝑒−	NOUN
iajs-3044	265	7	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	265	8	)	)	PUNCT
iajs-3044	265	9	2	2	NUM
iajs-3044	265	10	𝑥2	𝑥2	NOUN
iajs-3044	265	11	∞	∞	NOUN
iajs-3044	265	12	0	0	NUM
iajs-3044	266	1	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	266	2	=	=	SYM
iajs-3044	266	3	𝛼	𝛼	NOUN
iajs-3044	266	4	2	2	NUM
iajs-3044	266	5	𝑛−1	𝑛−1	NUM
iajs-3044	266	6	2	2	NUM
iajs-3044	266	7	𝜆	𝜆	PRON
iajs-3044	266	8	𝑛+1	𝑛+1	PROPN
iajs-3044	266	9	2	2	NUM
iajs-3044	266	10	(	(	PUNCT
iajs-3044	266	11	1+𝜃	1+𝜃	NUM
iajs-3044	266	12	)	)	PUNCT
iajs-3044	266	13	𝑛−1	𝑛−1	PROPN
iajs-3044	266	14	2	2	NUM
iajs-3044	266	15	𝛤	𝛤	PROPN
iajs-3044	266	16	(	(	PUNCT
iajs-3044	266	17	𝑛+1	𝑛+1	PROPN
iajs-3044	266	18	2	2	NUM
iajs-3044	266	19	)	)	PUNCT
iajs-3044	266	20	…	…	PUNCT
iajs-3044	266	21	(	(	PUNCT
iajs-3044	266	22	71	71	NUM
iajs-3044	266	23	)	)	PUNCT
iajs-3044	266	24	now	now	ADV
iajs-3044	266	25	,	,	PUNCT
iajs-3044	266	26	solve	solve	VERB
iajs-3044	266	27	the	the	DET
iajs-3044	266	28	second	second	ADJ
iajs-3044	266	29	integral	integral	ADJ
iajs-3044	266	30	as	as	SCONJ
iajs-3044	266	31	follows	follow	VERB
iajs-3044	266	32	:	:	PUNCT
iajs-3044	266	33	𝐿2	𝐿2	PROPN
iajs-3044	266	34	=	=	SYM
iajs-3044	266	35	∫	∫	PROPN
iajs-3044	267	1	𝜆(1	𝜆(1	NUM
iajs-3044	268	1	+	+	NUM
iajs-3044	268	2	𝜃	𝜃	X
iajs-3044	268	3	)	)	PUNCT
iajs-3044	268	4	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	268	5	𝑒−	𝑒−	NOUN
iajs-3044	268	6	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	268	7	)	)	PUNCT
iajs-3044	268	8	2	2	NUM
iajs-3044	268	9	𝑥2	𝑥2	NOUN
iajs-3044	268	10	∞	∞	NOUN
iajs-3044	268	11	0	0	PUNCT
iajs-3044	268	12	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	268	13	=	=	SYM
iajs-3044	268	14	2	2	NUM
iajs-3044	268	15	𝑛	𝑛	ADP
iajs-3044	268	16	2	2	NUM
iajs-3044	268	17	𝜆	𝜆	NOUN
iajs-3044	268	18	𝑛	𝑛	PRON
iajs-3044	268	19	2	2	NUM
iajs-3044	268	20	(	(	PUNCT
iajs-3044	268	21	1+𝜃	1+𝜃	NUM
iajs-3044	268	22	)	)	PUNCT
iajs-3044	268	23	𝑛	𝑛	DET
iajs-3044	268	24	2	2	NUM
iajs-3044	268	25	𝛤	𝛤	PROPN
iajs-3044	268	26	(	(	PUNCT
iajs-3044	268	27	𝑛+2	𝑛+2	NUM
iajs-3044	268	28	2	2	NUM
iajs-3044	268	29	)	)	PUNCT
iajs-3044	268	30	…	…	PUNCT
iajs-3044	268	31	(	(	PUNCT
iajs-3044	268	32	72	72	NUM
iajs-3044	268	33	)	)	PUNCT
iajs-3044	268	34	substituting	substitute	VERB
iajs-3044	268	35	equations	equation	NOUN
iajs-3044	268	36	(	(	PUNCT
iajs-3044	268	37	71	71	NUM
iajs-3044	268	38	)	)	PUNCT
iajs-3044	268	39	and	and	CCONJ
iajs-3044	268	40	(	(	PUNCT
iajs-3044	268	41	72	72	NUM
iajs-3044	268	42	)	)	PUNCT
iajs-3044	268	43	in	in	ADP
iajs-3044	268	44	equation	equation	NOUN
iajs-3044	268	45	(	(	PUNCT
iajs-3044	268	46	70	70	NUM
iajs-3044	268	47	)	)	PUNCT
iajs-3044	268	48	yields	yield	NOUN
iajs-3044	268	49	:	:	PUNCT
iajs-3044	268	50	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	𝑀𝑋(𝑡)𝑀𝑊𝐸𝑅	PART
iajs-3044	268	51	=	=	SYM
iajs-3044	268	52	∑	∑	PROPN
iajs-3044	268	53	(	(	PUNCT
iajs-3044	268	54	−(𝛼(1+𝜃)−𝑡))𝑛	−(𝛼(1+𝜃)−𝑡))𝑛	NOUN
iajs-3044	268	55	𝑛	𝑛	NOUN
iajs-3044	268	56	!	!	PUNCT
iajs-3044	268	57	∞	∞	NUM
iajs-3044	269	1	𝑛=0	𝑛=0	NOUN
iajs-3044	269	2	2	2	NUM
iajs-3044	269	3	𝑛	𝑛	ADP
iajs-3044	269	4	2	2	NUM
iajs-3044	269	5	𝜆	𝜆	NOUN
iajs-3044	269	6	𝑛	𝑛	PRON
iajs-3044	269	7	2	2	NUM
iajs-3044	269	8	(	(	PUNCT
iajs-3044	269	9	1+𝜃	1+𝜃	NUM
iajs-3044	269	10	)	)	PUNCT
iajs-3044	269	11	𝑛	𝑛	DET
iajs-3044	269	12	2	2	NUM
iajs-3044	269	13	[	[	PUNCT
iajs-3044	269	14	𝛼	𝛼	NOUN
iajs-3044	269	15	√𝜃	√𝜃	NUM
iajs-3044	269	16	√2𝜆	√2𝜆	NUM
iajs-3044	269	17	𝛤	𝛤	PROPN
iajs-3044	269	18	(	(	PUNCT
iajs-3044	269	19	𝑛+1	𝑛+1	PROPN
iajs-3044	269	20	2	2	NUM
iajs-3044	269	21	)	)	PUNCT
iajs-3044	270	1	+	+	CCONJ
iajs-3044	270	2	𝛤	𝛤	PROPN
iajs-3044	270	3	(	(	PUNCT
iajs-3044	270	4	𝑛+2	𝑛+2	NUM
iajs-3044	270	5	2	2	NUM
iajs-3044	270	6	)	)	PUNCT
iajs-3044	270	7	]	]	PUNCT
iajs-3044	270	8	…	…	PUNCT
iajs-3044	270	9	(	(	PUNCT
iajs-3044	270	10	73	73	NUM
iajs-3044	270	11	)	)	PUNCT
iajs-3044	270	12	3.2.7	3.2.7	NUM
iajs-3044	270	13	factorial	factorial	ADJ
iajs-3044	270	14	moment	moment	NOUN
iajs-3044	270	15	generating	generate	VERB
iajs-3044	270	16	function	function	NOUN
iajs-3044	270	17	the	the	DET
iajs-3044	270	18	factorial	factorial	ADJ
iajs-3044	270	19	moment	moment	NOUN
iajs-3044	270	20	generating	generate	VERB
iajs-3044	270	21	function	function	NOUN
iajs-3044	270	22	of	of	ADP
iajs-3044	270	23	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	NOUN
iajs-3044	270	24	distribution	distribution	NOUN
iajs-3044	270	25	can	can	AUX
iajs-3044	270	26	be	be	AUX
iajs-3044	270	27	obtained	obtain	VERB
iajs-3044	270	28	as	as	ADP
iajs-3044	270	29	follows	follow	VERB
iajs-3044	270	30	:	:	PUNCT
iajs-3044	270	31	𝑀(𝑡)𝑀𝑊𝐸𝑅	𝑀(𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	270	32	=	=	SYM
iajs-3044	270	33	𝐸(𝑡𝑥	𝐸(𝑡𝑥	NOUN
iajs-3044	270	34	)	)	PUNCT
iajs-3044	270	35	=	=	SYM
iajs-3044	271	1	∫	∫	PROPN
iajs-3044	271	2	𝑡𝑥	𝑡𝑥	INTJ
iajs-3044	271	3	(	(	PUNCT
iajs-3044	271	4	𝛼(1	𝛼(1	NOUN
iajs-3044	271	5	+	+	NUM
iajs-3044	271	6	𝜃	𝜃	X
iajs-3044	271	7	)	)	PUNCT
iajs-3044	271	8	+	+	CCONJ
iajs-3044	271	9	𝜆(1	𝜆(1	CCONJ
iajs-3044	271	10	+	+	NUM
iajs-3044	271	11	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	271	12	)	)	PUNCT
iajs-3044	271	13	𝑒−	𝑒−	NOUN
iajs-3044	271	14	(	(	PUNCT
iajs-3044	271	15	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	271	16	+	+	CCONJ
iajs-3044	271	17	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	271	18	)	)	PUNCT
iajs-3044	271	19	2	2	NUM
iajs-3044	271	20	𝑥2	𝑥2	NOUN
iajs-3044	271	21	)	)	PUNCT
iajs-3044	271	22	∞	∞	NOUN
iajs-3044	271	23	0	0	NUM
iajs-3044	271	24	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	271	25	𝑀(𝑡)𝑀𝑊𝐸𝑅	𝑀(𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	271	26	=	=	SYM
iajs-3044	271	27	∫	∫	PROPN
iajs-3044	271	28	(	(	PUNCT
iajs-3044	271	29	𝛼(1	𝛼(1	NOUN
iajs-3044	271	30	+	+	NUM
iajs-3044	271	31	𝜃	𝜃	X
iajs-3044	271	32	)	)	PUNCT
iajs-3044	271	33	+	+	CCONJ
iajs-3044	271	34	𝜆(1	𝜆(1	CCONJ
iajs-3044	272	1	+	+	NUM
iajs-3044	272	2	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	272	3	)	)	PUNCT
iajs-3044	272	4	𝑒−	𝑒−	NOUN
iajs-3044	272	5	(	(	PUNCT
iajs-3044	272	6	(	(	PUNCT
iajs-3044	272	7	𝛼(1+𝜃)−ln	𝛼(1+𝜃)−ln	PROPN
iajs-3044	272	8	(	(	PUNCT
iajs-3044	272	9	𝑡	𝑡	NOUN
iajs-3044	272	10	)	)	PUNCT
iajs-3044	272	11	)	)	PUNCT
iajs-3044	273	1	𝑥	𝑥	PROPN
iajs-3044	274	1	+	+	NUM
iajs-3044	274	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	274	3	)	)	PUNCT
iajs-3044	274	4	2	2	NUM
iajs-3044	274	5	𝑥2	𝑥2	NOUN
iajs-3044	274	6	)	)	PUNCT
iajs-3044	274	7	∞	∞	NOUN
iajs-3044	274	8	0	0	NUM
iajs-3044	274	9	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	274	10	…	…	PUNCT
iajs-3044	274	11	(	(	PUNCT
iajs-3044	274	12	74	74	NUM
iajs-3044	274	13	)	)	PUNCT
iajs-3044	274	14	let	let	VERB
iajs-3044	274	15	𝑈((𝛼(1	𝑈((𝛼(1	PUNCT
iajs-3044	275	1	+	+	CCONJ
iajs-3044	275	2	𝜃	𝜃	X
iajs-3044	275	3	)	)	PUNCT
iajs-3044	275	4	−	−	NOUN
iajs-3044	275	5	ln(𝑡	ln(𝑡	X
iajs-3044	275	6	)	)	PUNCT
iajs-3044	275	7	)	)	PUNCT
iajs-3044	275	8	,	,	PUNCT
iajs-3044	275	9	𝜆	𝜆	X
iajs-3044	275	10	)	)	PUNCT
iajs-3044	275	11	=	=	SYM
iajs-3044	275	12	𝑒−	𝑒−	NOUN
iajs-3044	275	13	(	(	PUNCT
iajs-3044	275	14	(	(	PUNCT
iajs-3044	275	15	𝛼(1+𝜃)−𝑙𝑛(𝑡	𝛼(1+𝜃)−𝑙𝑛(𝑡	NOUN
iajs-3044	275	16	)	)	PUNCT
iajs-3044	275	17	)	)	PUNCT
iajs-3044	276	1	𝑥	𝑥	PROPN
iajs-3044	277	1	+	+	NUM
iajs-3044	277	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	277	3	)	)	PUNCT
iajs-3044	277	4	2	2	NUM
iajs-3044	277	5	𝑥2	𝑥2	NOUN
iajs-3044	277	6	)	)	PUNCT
iajs-3044	277	7	…	…	PUNCT
iajs-3044	277	8	(	(	PUNCT
iajs-3044	277	9	75	75	NUM
iajs-3044	277	10	)	)	PUNCT
iajs-3044	277	11	by	by	ADP
iajs-3044	277	12	maclaurin	maclaurin	NOUN
iajs-3044	277	13	series	series	NOUN
iajs-3044	277	14	:	:	PUNCT
iajs-3044	277	15	𝑒−(𝛼(1+𝜃)−ln	𝑒−(𝛼(1+𝜃)−ln	PROPN
iajs-3044	277	16	(	(	PUNCT
iajs-3044	277	17	𝑡))𝑥	𝑡))𝑥	PROPN
iajs-3044	277	18	=	=	PUNCT
iajs-3044	277	19	∑	∑	PUNCT
iajs-3044	277	20	(	(	PUNCT
iajs-3044	277	21	−(𝛼(1+𝜃)−ln	−(𝛼(1+𝜃)−ln	X
iajs-3044	277	22	(	(	PUNCT
iajs-3044	277	23	𝑡)))𝑛	𝑡)))𝑛	PROPN
iajs-3044	277	24	𝑛	𝑛	PROPN
iajs-3044	277	25	!	!	PUNCT
iajs-3044	277	26	∞	∞	NUM
iajs-3044	278	1	𝑛=0	𝑛=0	PROPN
iajs-3044	278	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	278	3	…	…	PUNCT
iajs-3044	278	4	(	(	PUNCT
iajs-3044	278	5	76	76	NUM
iajs-3044	278	6	)	)	PUNCT
iajs-3044	278	7	substituting	substitute	VERB
iajs-3044	278	8	equation	equation	NOUN
iajs-3044	278	9	(	(	PUNCT
iajs-3044	278	10	76	76	NUM
iajs-3044	278	11	)	)	PUNCT
iajs-3044	278	12	in	in	ADP
iajs-3044	278	13	equation	equation	NOUN
iajs-3044	278	14	(	(	PUNCT
iajs-3044	278	15	75	75	NUM
iajs-3044	278	16	)	)	PUNCT
iajs-3044	278	17	we	we	PRON
iajs-3044	278	18	get	get	VERB
iajs-3044	278	19	:	:	PUNCT
iajs-3044	278	20	𝑈((𝛼(1	𝑈((𝛼(1	NUM
iajs-3044	279	1	+	+	X
iajs-3044	279	2	𝜃	𝜃	X
iajs-3044	279	3	)	)	PUNCT
iajs-3044	279	4	−	−	NOUN
iajs-3044	279	5	ln(𝑡	ln(𝑡	X
iajs-3044	279	6	)	)	PUNCT
iajs-3044	279	7	)	)	PUNCT
iajs-3044	280	1	,	,	PUNCT
iajs-3044	280	2	𝜆	𝜆	X
iajs-3044	280	3	)	)	PUNCT
iajs-3044	280	4	=	=	SYM
iajs-3044	280	5	∑	∑	PUNCT
iajs-3044	280	6	(	(	PUNCT
iajs-3044	280	7	−(𝛼(1+𝜃)−ln	−(𝛼(1+𝜃)−ln	X
iajs-3044	280	8	(	(	PUNCT
iajs-3044	280	9	𝑡)))𝑛	𝑡)))𝑛	PROPN
iajs-3044	280	10	𝑛	𝑛	PROPN
iajs-3044	280	11	!	!	PUNCT
iajs-3044	280	12	∞	∞	NUM
iajs-3044	281	1	𝑛=0	𝑛=0	PROPN
iajs-3044	281	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	281	3	𝑒−	𝑒−	NOUN
iajs-3044	281	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	281	5	)	)	PUNCT
iajs-3044	281	6	2	2	NUM
iajs-3044	281	7	𝑥2	𝑥2	NOUN
iajs-3044	281	8	…	…	PUNCT
iajs-3044	281	9	(	(	PUNCT
iajs-3044	281	10	77	77	NUM
iajs-3044	281	11	)	)	PUNCT
iajs-3044	281	12	substituting	substitute	VERB
iajs-3044	281	13	equation	equation	NOUN
iajs-3044	281	14	(	(	PUNCT
iajs-3044	281	15	77	77	NUM
iajs-3044	281	16	)	)	PUNCT
iajs-3044	281	17	in	in	ADP
iajs-3044	281	18	equation	equation	NOUN
iajs-3044	281	19	(	(	PUNCT
iajs-3044	281	20	74	74	NUM
iajs-3044	281	21	)	)	PUNCT
iajs-3044	281	22	we	we	PRON
iajs-3044	281	23	get	get	VERB
iajs-3044	281	24	:	:	PUNCT
iajs-3044	281	25	𝑀(𝑡)𝑀𝑊𝐸𝑅	𝑀(𝑡)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	281	26	=	=	PUNCT
iajs-3044	281	27	∑	∑	PUNCT
iajs-3044	281	28	(	(	PUNCT
iajs-3044	281	29	−(𝛼(1+𝜃)−ln	−(𝛼(1+𝜃)−ln	X
iajs-3044	281	30	(	(	PUNCT
iajs-3044	281	31	𝑡)))𝑛	𝑡)))𝑛	PROPN
iajs-3044	281	32	𝑛	𝑛	PROPN
iajs-3044	281	33	!	!	PUNCT
iajs-3044	281	34	∞	∞	NUM
iajs-3044	282	1	𝑛=0	𝑛=0	PROPN
iajs-3044	283	1	[	[	X
iajs-3044	283	2	∫	∫	X
iajs-3044	283	3	𝛼(1	𝛼(1	NOUN
iajs-3044	283	4	+	+	NUM
iajs-3044	283	5	𝜃	𝜃	X
iajs-3044	283	6	)	)	PUNCT
iajs-3044	283	7	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	283	8	𝑒−	𝑒−	NOUN
iajs-3044	283	9	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	283	10	)	)	PUNCT
iajs-3044	283	11	2	2	NUM
iajs-3044	283	12	𝑥2	𝑥2	NOUN
iajs-3044	283	13	∞	∞	NOUN
iajs-3044	283	14	0	0	NUM
iajs-3044	283	15	𝑑𝑥	𝑑𝑥	X
iajs-3044	283	16	+	+	NOUN
iajs-3044	283	17	∫	∫	X
iajs-3044	284	1	𝜆(1	𝜆(1	NOUN
iajs-3044	285	1	+	+	CCONJ
iajs-3044	285	2	∞	∞	NUM
iajs-3044	285	3	0	0	NUM
iajs-3044	285	4	𝜃	𝜃	X
iajs-3044	285	5	)	)	PUNCT
iajs-3044	285	6	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	285	7	𝑒−	𝑒−	NOUN
iajs-3044	285	8	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	285	9	)	)	PUNCT
iajs-3044	285	10	2	2	NUM
iajs-3044	285	11	𝑥2	𝑥2	NOUN
iajs-3044	285	12	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	285	13	]	]	X
iajs-3044	285	14	…	…	PUNCT
iajs-3044	285	15	(	(	PUNCT
iajs-3044	285	16	78	78	NUM
iajs-3044	285	17	)	)	PUNCT
iajs-3044	285	18	now	now	ADV
iajs-3044	285	19	,	,	PUNCT
iajs-3044	285	20	based	base	VERB
iajs-3044	285	21	on	on	ADP
iajs-3044	285	22	equations	equation	NOUN
iajs-3044	285	23	(	(	PUNCT
iajs-3044	285	24	71	71	NUM
iajs-3044	285	25	)	)	PUNCT
iajs-3044	285	26	and	and	CCONJ
iajs-3044	285	27	(	(	PUNCT
iajs-3044	285	28	72	72	X
iajs-3044	285	29	)	)	PUNCT
iajs-3044	285	30	we	we	PRON
iajs-3044	285	31	get	get	VERB
iajs-3044	285	32	:	:	PUNCT
iajs-3044	285	33	𝑀(𝑡)𝑀𝑊𝐸𝑅	𝑀(𝑡)𝑀𝑊𝐸𝑅	PROPN
iajs-3044	285	34	=	=	PUNCT
iajs-3044	285	35	∑	∑	PUNCT
iajs-3044	285	36	(	(	PUNCT
iajs-3044	285	37	−(𝛼(1+𝜃)−ln(𝑡)))𝑛	−(𝛼(1+𝜃)−ln(𝑡)))𝑛	PROPN
iajs-3044	285	38	𝑛	𝑛	PROPN
iajs-3044	285	39	!	!	NOUN
iajs-3044	286	1	∞	∞	NUM
iajs-3044	286	2	𝑛=0	𝑛=0	NOUN
iajs-3044	286	3	2	2	NUM
iajs-3044	286	4	𝑛	𝑛	ADP
iajs-3044	286	5	2	2	NUM
iajs-3044	286	6	𝜆	𝜆	NOUN
iajs-3044	286	7	𝑛	𝑛	PRON
iajs-3044	286	8	2	2	NUM
iajs-3044	286	9	(	(	PUNCT
iajs-3044	286	10	1+𝜃	1+𝜃	NUM
iajs-3044	286	11	)	)	PUNCT
iajs-3044	286	12	𝑛	𝑛	DET
iajs-3044	286	13	2	2	NUM
iajs-3044	286	14	[	[	PUNCT
iajs-3044	286	15	𝛼	𝛼	NOUN
iajs-3044	286	16	√𝜃	√𝜃	NUM
iajs-3044	286	17	√2𝜆	√2𝜆	NUM
iajs-3044	286	18	𝛤	𝛤	PROPN
iajs-3044	286	19	(	(	PUNCT
iajs-3044	286	20	𝑛+1	𝑛+1	PROPN
iajs-3044	286	21	2	2	NUM
iajs-3044	286	22	)	)	PUNCT
iajs-3044	287	1	+	+	CCONJ
iajs-3044	287	2	𝛤	𝛤	PROPN
iajs-3044	287	3	(	(	PUNCT
iajs-3044	287	4	𝑛+2	𝑛+2	NUM
iajs-3044	287	5	2	2	NUM
iajs-3044	287	6	)	)	PUNCT
iajs-3044	287	7	]	]	PUNCT
iajs-3044	287	8	…	…	PUNCT
iajs-3044	287	9	(	(	PUNCT
iajs-3044	287	10	79	79	NUM
iajs-3044	287	11	)	)	PUNCT
iajs-3044	287	12	3.2.8	3.2.8	NUM
iajs-3044	287	13	characteristic	characteristic	ADJ
iajs-3044	287	14	function	function	NOUN
iajs-3044	287	15	the	the	DET
iajs-3044	287	16	characteristic	characteristic	ADJ
iajs-3044	287	17	function	function	NOUN
iajs-3044	287	18	of	of	ADP
iajs-3044	287	19	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	NOUN
iajs-3044	287	20	distribution	distribution	NOUN
iajs-3044	287	21	can	can	AUX
iajs-3044	287	22	be	be	AUX
iajs-3044	287	23	found	find	VERB
iajs-3044	287	24	as	as	SCONJ
iajs-3044	287	25	follows	follow	VERB
iajs-3044	287	26	:	:	PUNCT
iajs-3044	287	27	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	287	28	=	=	SYM
iajs-3044	287	29	𝐸(𝑒𝑖𝑡𝑥	𝐸(𝑒𝑖𝑡𝑥	PROPN
iajs-3044	287	30	)	)	PUNCT
iajs-3044	288	1	=	=	SYM
iajs-3044	288	2	∫	∫	PROPN
iajs-3044	288	3	𝑒𝑖𝑡𝑥	𝑒𝑖𝑡𝑥	PROPN
iajs-3044	288	4	(	(	PUNCT
iajs-3044	288	5	𝛼(1	𝛼(1	NOUN
iajs-3044	288	6	+	+	NUM
iajs-3044	288	7	𝜃	𝜃	X
iajs-3044	288	8	)	)	PUNCT
iajs-3044	288	9	+	+	CCONJ
iajs-3044	289	1	𝜆(1	𝜆(1	CCONJ
iajs-3044	289	2	+	+	NUM
iajs-3044	289	3	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	289	4	)	)	PUNCT
iajs-3044	289	5	𝑒	𝑒	ADP
iajs-3044	289	6	−	−	PROPN
iajs-3044	289	7	(	(	PUNCT
iajs-3044	289	8	𝛼(1+𝜃)𝑥	𝛼(1+𝜃)𝑥	VERB
iajs-3044	289	9	+	+	CCONJ
iajs-3044	289	10	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	289	11	)	)	PUNCT
iajs-3044	289	12	2	2	NUM
iajs-3044	289	13	𝑥2	𝑥2	NOUN
iajs-3044	289	14	)	)	PUNCT
iajs-3044	289	15	∞	∞	NOUN
iajs-3044	289	16	0	0	NUM
iajs-3044	290	1	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	290	2	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	290	3	=	=	SYM
iajs-3044	290	4	∫	∫	PROPN
iajs-3044	290	5	(	(	PUNCT
iajs-3044	290	6	𝛼(1	𝛼(1	NOUN
iajs-3044	290	7	+	+	NUM
iajs-3044	290	8	𝜃	𝜃	X
iajs-3044	290	9	)	)	PUNCT
iajs-3044	291	1	+	+	CCONJ
iajs-3044	291	2	𝜆(1	𝜆(1	CCONJ
iajs-3044	291	3	+	+	NUM
iajs-3044	291	4	𝜃)𝑥	𝜃)𝑥	ADV
iajs-3044	291	5	)	)	PUNCT
iajs-3044	291	6	𝑒−	𝑒−	NOUN
iajs-3044	291	7	(	(	PUNCT
iajs-3044	291	8	(	(	PUNCT
iajs-3044	291	9	𝛼(1+𝜃)−it	𝛼(1+𝜃)−it	NOUN
iajs-3044	291	10	)	)	PUNCT
iajs-3044	291	11	𝑥	𝑥	PROPN
iajs-3044	292	1	+	+	NUM
iajs-3044	292	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	292	3	)	)	PUNCT
iajs-3044	292	4	2	2	NUM
iajs-3044	292	5	𝑥2	𝑥2	NOUN
iajs-3044	292	6	)	)	PUNCT
iajs-3044	292	7	∞	∞	NOUN
iajs-3044	292	8	0	0	NUM
iajs-3044	292	9	𝑑𝑥	𝑑𝑥	NOUN
iajs-3044	292	10	…	…	PUNCT
iajs-3044	292	11	(	(	PUNCT
iajs-3044	292	12	80	80	NUM
iajs-3044	292	13	)	)	PUNCT
iajs-3044	292	14	let	let	VERB
iajs-3044	292	15	𝐶((𝛼(1	𝐶((𝛼(1	PUNCT
iajs-3044	293	1	+	+	CCONJ
iajs-3044	293	2	𝜃	𝜃	X
iajs-3044	293	3	)	)	PUNCT
iajs-3044	293	4	−	−	PROPN
iajs-3044	294	1	it	it	PRON
iajs-3044	294	2	)	)	PUNCT
iajs-3044	294	3	,	,	PUNCT
iajs-3044	294	4	𝜆	𝜆	X
iajs-3044	294	5	)	)	PUNCT
iajs-3044	294	6	=	=	SYM
iajs-3044	294	7	𝑒−	𝑒−	NOUN
iajs-3044	294	8	(	(	PUNCT
iajs-3044	294	9	(	(	PUNCT
iajs-3044	294	10	𝛼(1+𝜃)−𝑖𝑡	𝛼(1+𝜃)−𝑖𝑡	NOUN
iajs-3044	294	11	)	)	PUNCT
iajs-3044	294	12	𝑥	𝑥	NOUN
iajs-3044	295	1	+	+	NUM
iajs-3044	295	2	𝜆(1+𝜃	𝜆(1+𝜃	ADJ
iajs-3044	295	3	)	)	PUNCT
iajs-3044	295	4	2	2	NUM
iajs-3044	295	5	𝑥2	𝑥2	NOUN
iajs-3044	295	6	)	)	PUNCT
iajs-3044	295	7	…	…	PUNCT
iajs-3044	295	8	(	(	PUNCT
iajs-3044	295	9	81	81	NUM
iajs-3044	295	10	)	)	PUNCT
iajs-3044	295	11	ihjpas	ihjpa	NOUN
iajs-3044	295	12	.	.	PUNCT
iajs-3044	296	1	36(2)2023	36(2)2023	NUM
iajs-3044	296	2	405	405	NUM
iajs-3044	296	3	by	by	ADP
iajs-3044	296	4	maclaurin	maclaurin	NOUN
iajs-3044	296	5	series	series	NOUN
iajs-3044	296	6	:	:	PUNCT
iajs-3044	296	7	𝑒−(𝛼(1+𝜃)−it)𝑥	𝑒−(𝛼(1+𝜃)−it)𝑥	X
iajs-3044	296	8	=	=	PUNCT
iajs-3044	296	9	∑	∑	PROPN
iajs-3044	296	10	(	(	PUNCT
iajs-3044	296	11	−(𝛼(1+𝜃)−it))𝑛	−(𝛼(1+𝜃)−it))𝑛	NUM
iajs-3044	296	12	𝑛	𝑛	NOUN
iajs-3044	296	13	!	!	NOUN
iajs-3044	296	14	∞	∞	NUM
iajs-3044	297	1	𝑛=0	𝑛=0	PROPN
iajs-3044	297	2	𝑥𝑛	𝑥𝑛	VERB
iajs-3044	297	3	…	…	PUNCT
iajs-3044	297	4	(	(	PUNCT
iajs-3044	297	5	82	82	NUM
iajs-3044	297	6	)	)	PUNCT
iajs-3044	297	7	substituting	substitute	VERB
iajs-3044	297	8	equation	equation	NOUN
iajs-3044	297	9	(	(	PUNCT
iajs-3044	297	10	82	82	NUM
iajs-3044	297	11	)	)	PUNCT
iajs-3044	297	12	in	in	ADP
iajs-3044	297	13	equation	equation	NOUN
iajs-3044	297	14	(	(	PUNCT
iajs-3044	297	15	8	8	NUM
iajs-3044	297	16	1	1	NUM
iajs-3044	297	17	)	)	PUNCT
iajs-3044	297	18	gives	give	VERB
iajs-3044	297	19	:	:	PUNCT
iajs-3044	297	20	𝐶((𝛼(1	𝐶((𝛼(1	NUM
iajs-3044	298	1	+	+	CCONJ
iajs-3044	298	2	𝜃	𝜃	X
iajs-3044	298	3	)	)	PUNCT
iajs-3044	298	4	−	−	PROPN
iajs-3044	298	5	it	it	PRON
iajs-3044	298	6	)	)	PUNCT
iajs-3044	298	7	,	,	PUNCT
iajs-3044	298	8	𝜆	𝜆	X
iajs-3044	298	9	)	)	PUNCT
iajs-3044	298	10	=	=	SYM
iajs-3044	298	11	∑	∑	PROPN
iajs-3044	298	12	(	(	PUNCT
iajs-3044	298	13	−(𝛼(1+𝜃)−it))𝑛	−(𝛼(1+𝜃)−it))𝑛	NUM
iajs-3044	298	14	𝑛	𝑛	NOUN
iajs-3044	298	15	!	!	PUNCT
iajs-3044	298	16	∞	∞	NUM
iajs-3044	299	1	𝑛=0	𝑛=0	PROPN
iajs-3044	299	2	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	299	3	𝑒−	𝑒−	NOUN
iajs-3044	299	4	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	299	5	)	)	PUNCT
iajs-3044	299	6	2	2	NUM
iajs-3044	299	7	𝑥2	𝑥2	NOUN
iajs-3044	299	8	…	…	PUNCT
iajs-3044	299	9	(	(	PUNCT
iajs-3044	299	10	83	83	NUM
iajs-3044	299	11	)	)	PUNCT
iajs-3044	299	12	substituting	substitute	VERB
iajs-3044	299	13	equation	equation	NOUN
iajs-3044	299	14	(	(	PUNCT
iajs-3044	299	15	83	83	NUM
iajs-3044	299	16	)	)	PUNCT
iajs-3044	299	17	in	in	ADP
iajs-3044	299	18	equation	equation	NOUN
iajs-3044	299	19	(	(	PUNCT
iajs-3044	299	20	80	80	NUM
iajs-3044	299	21	)	)	PUNCT
iajs-3044	299	22	gives	give	VERB
iajs-3044	299	23	:	:	PUNCT
iajs-3044	299	24	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	299	25	=	=	SYM
iajs-3044	299	26	∑	∑	PROPN
iajs-3044	299	27	(	(	PUNCT
iajs-3044	299	28	−(𝛼(1+𝜃)−it))𝑛	−(𝛼(1+𝜃)−it))𝑛	NUM
iajs-3044	299	29	𝑛	𝑛	NOUN
iajs-3044	299	30	!	!	PUNCT
iajs-3044	299	31	∞	∞	NUM
iajs-3044	300	1	𝑛=0	𝑛=0	PROPN
iajs-3044	301	1	[	[	X
iajs-3044	301	2	∫	∫	X
iajs-3044	301	3	𝛼(1	𝛼(1	NOUN
iajs-3044	301	4	+	+	NUM
iajs-3044	301	5	𝜃	𝜃	X
iajs-3044	301	6	)	)	PUNCT
iajs-3044	301	7	𝑥𝑛	𝑥𝑛	AUX
iajs-3044	301	8	𝑒−	𝑒−	NOUN
iajs-3044	301	9	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	301	10	)	)	PUNCT
iajs-3044	301	11	2	2	NUM
iajs-3044	301	12	𝑥2	𝑥2	NOUN
iajs-3044	301	13	∞	∞	NOUN
iajs-3044	301	14	0	0	NUM
iajs-3044	301	15	𝑑𝑥	𝑑𝑥	X
iajs-3044	301	16	+	+	NOUN
iajs-3044	301	17	∫	∫	X
iajs-3044	302	1	𝜆(1	𝜆(1	NOUN
iajs-3044	303	1	+	+	CCONJ
iajs-3044	303	2	∞	∞	NUM
iajs-3044	303	3	0	0	NUM
iajs-3044	303	4	𝜃	𝜃	X
iajs-3044	303	5	)	)	PUNCT
iajs-3044	303	6	𝑥𝑛+1	𝑥𝑛+1	ADJ
iajs-3044	303	7	𝑒−	𝑒−	NOUN
iajs-3044	303	8	𝜆(1+𝜃	𝜆(1+𝜃	NOUN
iajs-3044	303	9	)	)	PUNCT
iajs-3044	303	10	2	2	NUM
iajs-3044	303	11	𝑥2	𝑥2	NOUN
iajs-3044	303	12	𝑑𝑥	𝑑𝑥	VERB
iajs-3044	303	13	]	]	X
iajs-3044	303	14	…	…	PUNCT
iajs-3044	303	15	(	(	PUNCT
iajs-3044	303	16	84	84	NUM
iajs-3044	303	17	)	)	PUNCT
iajs-3044	303	18	now	now	ADV
iajs-3044	303	19	,	,	PUNCT
iajs-3044	303	20	based	base	VERB
iajs-3044	303	21	on	on	ADP
iajs-3044	303	22	equations	equation	NOUN
iajs-3044	303	23	(	(	PUNCT
iajs-3044	303	24	71	71	NUM
iajs-3044	303	25	)	)	PUNCT
iajs-3044	303	26	and	and	CCONJ
iajs-3044	303	27	(	(	PUNCT
iajs-3044	303	28	72	72	X
iajs-3044	303	29	)	)	PUNCT
iajs-3044	303	30	we	we	PRON
iajs-3044	303	31	get	get	VERB
iajs-3044	303	32	:	:	PUNCT
iajs-3044	303	33	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	∅𝑋(𝑖𝑡)𝑀𝑊𝐸𝑅	NOUN
iajs-3044	303	34	=	=	SYM
iajs-3044	303	35	∑	∑	PROPN
iajs-3044	303	36	(	(	PUNCT
iajs-3044	303	37	−(𝛼(1+𝜃)−it))𝑛	−(𝛼(1+𝜃)−it))𝑛	NUM
iajs-3044	303	38	𝑛	𝑛	NOUN
iajs-3044	303	39	!	!	NOUN
iajs-3044	304	1	∞	∞	NUM
iajs-3044	305	1	𝑛=0	𝑛=0	NOUN
iajs-3044	305	2	2	2	NUM
iajs-3044	305	3	𝑛	𝑛	ADP
iajs-3044	305	4	2	2	NUM
iajs-3044	305	5	𝜆	𝜆	NOUN
iajs-3044	305	6	𝑛	𝑛	PRON
iajs-3044	305	7	2	2	NUM
iajs-3044	305	8	(	(	PUNCT
iajs-3044	305	9	1+𝜃	1+𝜃	NUM
iajs-3044	305	10	)	)	PUNCT
iajs-3044	305	11	𝑛	𝑛	DET
iajs-3044	305	12	2	2	NUM
iajs-3044	305	13	[	[	PUNCT
iajs-3044	305	14	𝛼	𝛼	NOUN
iajs-3044	305	15	√𝜃	√𝜃	NUM
iajs-3044	305	16	√2𝜆	√2𝜆	NUM
iajs-3044	305	17	𝛤	𝛤	PROPN
iajs-3044	305	18	(	(	PUNCT
iajs-3044	305	19	𝑛+1	𝑛+1	PROPN
iajs-3044	305	20	2	2	NUM
iajs-3044	305	21	)	)	PUNCT
iajs-3044	306	1	+	+	CCONJ
iajs-3044	306	2	𝛤	𝛤	PROPN
iajs-3044	306	3	(	(	PUNCT
iajs-3044	306	4	𝑛+2	𝑛+2	NUM
iajs-3044	306	5	2	2	NUM
iajs-3044	306	6	)	)	PUNCT
iajs-3044	306	7	]	]	PUNCT
iajs-3044	306	8	…	…	PUNCT
iajs-3044	306	9	(	(	PUNCT
iajs-3044	306	10	85	85	NUM
iajs-3044	306	11	)	)	PUNCT
iajs-3044	306	12	3.2.9	3.2.9	NUM
iajs-3044	306	13	quantile	quantile	NOUN
iajs-3044	306	14	function	function	VERB
iajs-3044	306	15	the	the	DET
iajs-3044	306	16	quantile	quantile	ADJ
iajs-3044	306	17	function	function	NOUN
iajs-3044	306	18	of	of	ADP
iajs-3044	306	19	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	306	20	random	random	ADJ
iajs-3044	306	21	variable	variable	NOUN
iajs-3044	306	22	is	be	AUX
iajs-3044	306	23	defined	define	VERB
iajs-3044	306	24	as	as	ADP
iajs-3044	306	25	a	a	DET
iajs-3044	306	26	solution	solution	NOUN
iajs-3044	306	27	of	of	ADP
iajs-3044	306	28	𝑝(𝑥	𝑝(𝑥	PROPN
iajs-3044	306	29	≤	≤	NOUN
iajs-3044	306	30	𝑥(𝑞	𝑥(𝑞	NUM
iajs-3044	306	31	)	)	PUNCT
iajs-3044	306	32	)	)	PUNCT
iajs-3044	307	1	=	=	SYM
iajs-3044	307	2	𝐹(𝑥(𝑞))𝑀𝑊𝐸𝑅	𝐹(𝑥(𝑞))𝑀𝑊𝐸𝑅	NUM
iajs-3044	307	3	w.r.t	w.r.t	VERB
iajs-3044	307	4	.	.	PUNCT
iajs-3044	308	1	𝑥(𝑞	𝑥(𝑞	X
iajs-3044	308	2	)	)	PUNCT
iajs-3044	308	3	,	,	PUNCT
iajs-3044	308	4	therefore	therefore	ADV
iajs-3044	308	5	,	,	PUNCT
iajs-3044	308	6	via	via	ADP
iajs-3044	308	7	using	use	VERB
iajs-3044	308	8	the	the	DET
iajs-3044	308	9	inverse	inverse	NOUN
iajs-3044	308	10	transformation	transformation	NOUN
iajs-3044	308	11	to	to	ADP
iajs-3044	308	12	equation	equation	NOUN
iajs-3044	308	13	(	(	PUNCT
iajs-3044	308	14	47	47	NUM
iajs-3044	308	15	)	)	PUNCT
iajs-3044	308	16	,	,	PUNCT
iajs-3044	308	17	it	it	PRON
iajs-3044	308	18	can	can	AUX
iajs-3044	308	19	be	be	AUX
iajs-3044	308	20	found	find	VERB
iajs-3044	308	21	as	as	ADP
iajs-3044	308	22	:	:	PUNCT
iajs-3044	308	23	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	308	24	)	)	PUNCT
iajs-3044	308	25	=	=	SYM
iajs-3044	308	26	𝐹−1(𝑞	𝐹−1(𝑞	NUM
iajs-3044	308	27	)	)	PUNCT
iajs-3044	308	28	;	;	PUNCT
iajs-3044	308	29	𝑥(𝑞	𝑥(𝑞	X
iajs-3044	308	30	)	)	PUNCT
iajs-3044	308	31	>	>	X
iajs-3044	308	32	0	0	NUM
iajs-3044	308	33	;	;	PUNCT
iajs-3044	308	34	0	0	NUM
iajs-3044	308	35	<	<	X
iajs-3044	308	36	𝑞	𝑞	X
iajs-3044	308	37	<	<	X
iajs-3044	308	38	1	1	NUM
iajs-3044	308	39	𝑞	𝑞	NOUN
iajs-3044	308	40	=	=	NOUN
iajs-3044	308	41	1	1	NUM
iajs-3044	308	42	−	−	NOUN
iajs-3044	308	43	𝑒−	𝑒−	NOUN
iajs-3044	308	44	(	(	PUNCT
iajs-3044	308	45	𝛼(1+𝜃)𝑥(𝑞	𝛼(1+𝜃)𝑥(𝑞	NOUN
iajs-3044	308	46	)	)	PUNCT
iajs-3044	308	47	+	+	NUM
iajs-3044	308	48	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	308	49	)	)	PUNCT
iajs-3044	308	50	2	2	NUM
iajs-3044	308	51	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	308	52	)	)	PUNCT
iajs-3044	308	53	2	2	NUM
iajs-3044	308	54	)	)	PUNCT
iajs-3044	308	55	1	1	NUM
iajs-3044	308	56	−	−	NOUN
iajs-3044	308	57	𝑞	𝑞	X
iajs-3044	308	58	=	=	PUNCT
iajs-3044	308	59	𝑒−	𝑒−	X
iajs-3044	308	60	(	(	PUNCT
iajs-3044	308	61	𝛼(1+𝜃)𝑥(𝑞	𝛼(1+𝜃)𝑥(𝑞	NOUN
iajs-3044	308	62	)	)	PUNCT
iajs-3044	308	63	+	+	NUM
iajs-3044	308	64	𝜆(1+𝜃	𝜆(1+𝜃	NUM
iajs-3044	308	65	)	)	PUNCT
iajs-3044	308	66	2	2	NUM
iajs-3044	308	67	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	308	68	)	)	PUNCT
iajs-3044	308	69	2	2	NUM
iajs-3044	308	70	)	)	PUNCT
iajs-3044	308	71	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	308	72	(	(	PUNCT
iajs-3044	308	73	1	1	NUM
iajs-3044	308	74	−	−	PROPN
iajs-3044	308	75	𝑞	𝑞	NOUN
iajs-3044	308	76	)	)	PUNCT
iajs-3044	308	77	=	=	SYM
iajs-3044	308	78	−(𝛼(1	−(𝛼(1	NOUN
iajs-3044	308	79	+	+	CCONJ
iajs-3044	308	80	𝜃)𝑥(𝑞	𝜃)𝑥(𝑞	NOUN
iajs-3044	308	81	)	)	PUNCT
iajs-3044	308	82	+	+	CCONJ
iajs-3044	309	1	𝜆(1	𝜆(1	NUM
iajs-3044	309	2	+	+	NUM
iajs-3044	309	3	𝜃	𝜃	X
iajs-3044	309	4	)	)	PUNCT
iajs-3044	309	5	2	2	NUM
iajs-3044	309	6	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	309	7	)	)	PUNCT
iajs-3044	309	8	2	2	NUM
iajs-3044	309	9	)	)	PUNCT
iajs-3044	309	10	𝜆	𝜆	X
iajs-3044	309	11	(	(	PUNCT
iajs-3044	309	12	1	1	NUM
iajs-3044	309	13	+	+	SYM
iajs-3044	309	14	𝜃)𝑥(𝑞	𝜃)𝑥(𝑞	NOUN
iajs-3044	309	15	)	)	PUNCT
iajs-3044	309	16	2	2	NUM
iajs-3044	309	17	+	+	SYM
iajs-3044	309	18	2𝛼(1	2𝛼(1	NUM
iajs-3044	309	19	+	+	CCONJ
iajs-3044	309	20	𝜃)𝑥(𝑞	𝜃)𝑥(𝑞	NOUN
iajs-3044	309	21	)	)	PUNCT
iajs-3044	309	22	+	+	CCONJ
iajs-3044	309	23	2	2	NUM
iajs-3044	309	24	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	309	25	(	(	PUNCT
iajs-3044	309	26	1	1	NUM
iajs-3044	309	27	−	−	PROPN
iajs-3044	309	28	𝑞	𝑞	NOUN
iajs-3044	309	29	)	)	PUNCT
iajs-3044	309	30	=	=	SYM
iajs-3044	309	31	0	0	NUM
iajs-3044	309	32	based	base	VERB
iajs-3044	309	33	on	on	ADP
iajs-3044	309	34	law	law	NOUN
iajs-3044	309	35	of	of	ADP
iajs-3044	309	36	the	the	DET
iajs-3044	309	37	constitution	constitution	NOUN
iajs-3044	309	38	,	,	PUNCT
iajs-3044	309	39	we	we	PRON
iajs-3044	309	40	get	get	VERB
iajs-3044	309	41	:	:	PUNCT
iajs-3044	309	42	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	309	43	)	)	PUNCT
iajs-3044	309	44	=	=	PUNCT
iajs-3044	310	1	−2𝛼(1+𝜃)∓√4𝛼2(1+𝜃)2−	−2𝛼(1+𝜃)∓√4𝛼2(1+𝜃)2−	ADJ
iajs-3044	310	2	8	8	NUM
iajs-3044	310	3	𝜆	𝜆	NOUN
iajs-3044	310	4	(	(	PUNCT
iajs-3044	310	5	1+𝜃	1+𝜃	NUM
iajs-3044	310	6	)	)	PUNCT
iajs-3044	310	7	𝑙𝑛	𝑙𝑛	NOUN
iajs-3044	310	8	(	(	PUNCT
iajs-3044	310	9	1−𝑞	1−𝑞	NUM
iajs-3044	310	10	)	)	PUNCT
iajs-3044	310	11	2	2	NUM
iajs-3044	310	12	𝜆	𝜆	NOUN
iajs-3044	310	13	(	(	PUNCT
iajs-3044	310	14	1+𝜃	1+𝜃	NUM
iajs-3044	310	15	)	)	PUNCT
iajs-3044	310	16	…	…	PUNCT
iajs-3044	310	17	(	(	PUNCT
iajs-3044	310	18	86	86	NUM
iajs-3044	310	19	)	)	PUNCT
iajs-3044	310	20	the	the	DET
iajs-3044	310	21	values	value	NOUN
iajs-3044	310	22	of	of	ADP
iajs-3044	310	23	𝑥(𝑞	𝑥(𝑞	ADJ
iajs-3044	310	24	)	)	PUNCT
iajs-3044	310	25	will	will	AUX
iajs-3044	310	26	be	be	AUX
iajs-3044	310	27	ignored	ignore	VERB
iajs-3044	310	28	when	when	SCONJ
iajs-3044	310	29	𝑥(𝑞	𝑥(𝑞	X
iajs-3044	310	30	)	)	PUNCT
iajs-3044	310	31	<	<	X
iajs-3044	310	32	0	0	X
iajs-3044	310	33	.	.	X
iajs-3044	311	1	4.conclusions	4.conclusion	NOUN
iajs-3044	311	2	in	in	ADP
iajs-3044	311	3	this	this	DET
iajs-3044	311	4	paper	paper	NOUN
iajs-3044	311	5	,	,	PUNCT
iajs-3044	311	6	introduce	introduce	VERB
iajs-3044	311	7	exponential	exponential	ADJ
iajs-3044	311	8	rayleigh	rayleigh	PROPN
iajs-3044	311	9	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	311	10	distribution	distribution	NOUN
iajs-3044	311	11	depending	depend	VERB
iajs-3044	311	12	on	on	ADP
iajs-3044	311	13	mixed	mixed	ADJ
iajs-3044	311	14	between	between	ADP
iajs-3044	311	15	cumulative	cumulative	ADJ
iajs-3044	311	16	distribution	distribution	NOUN
iajs-3044	311	17	function	function	NOUN
iajs-3044	311	18	of	of	ADP
iajs-3044	311	19	exponential	exponential	ADJ
iajs-3044	311	20	and	and	CCONJ
iajs-3044	311	21	rayleigh	rayleigh	ADJ
iajs-3044	311	22	distribution	distribution	NOUN
iajs-3044	311	23	,	,	PUNCT
iajs-3044	311	24	as	as	ADV
iajs-3044	311	25	well	well	ADV
iajs-3044	311	26	as	as	ADP
iajs-3044	311	27	introduce	introduce	VERB
iajs-3044	311	28	a	a	DET
iajs-3044	311	29	new	new	ADJ
iajs-3044	311	30	class	class	NOUN
iajs-3044	311	31	depending	depend	VERB
iajs-3044	311	32	on	on	ADP
iajs-3044	311	33	a	a	DET
iajs-3044	311	34	modified	modify	VERB
iajs-3044	311	35	weighted	weight	VERB
iajs-3044	311	36	version	version	NOUN
iajs-3044	311	37	of	of	ADP
iajs-3044	311	38	azzalini	azzalini	PROPN
iajs-3044	311	39	’s	’s	PART
iajs-3044	311	40	(	(	PUNCT
iajs-3044	311	41	1985	1985	NUM
iajs-3044	311	42	)	)	PUNCT
iajs-3044	311	43	named	name	VERB
iajs-3044	311	44	modified	modify	VERB
iajs-3044	311	45	weighted	weight	VERB
iajs-3044	311	46	exponential	exponential	ADJ
iajs-3044	311	47	rayleigh	rayleigh	PROPN
iajs-3044	311	48	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	311	49	distribution	distribution	NOUN
iajs-3044	311	50	,	,	PUNCT
iajs-3044	311	51	such	such	ADJ
iajs-3044	311	52	that	that	SCONJ
iajs-3044	311	53	the	the	DET
iajs-3044	311	54	exponential	exponential	ADJ
iajs-3044	311	55	rayleigh	rayleigh	PROPN
iajs-3044	311	56	𝐸𝑅	𝐸𝑅	PROPN
iajs-3044	311	57	distribution	distribution	NOUN
iajs-3044	311	58	is	be	AUX
iajs-3044	311	59	special	special	ADJ
iajs-3044	311	60	case	case	NOUN
iajs-3044	311	61	of	of	ADP
iajs-3044	311	62	modified	modify	VERB
iajs-3044	311	63	weighted	weight	VERB
iajs-3044	311	64	exponential	exponential	ADJ
iajs-3044	311	65	rayleigh	rayleigh	PROPN
iajs-3044	311	66	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	311	67	distribution	distribution	NOUN
iajs-3044	311	68	and	and	CCONJ
iajs-3044	311	69	provide	provide	VERB
iajs-3044	311	70	some	some	DET
iajs-3044	311	71	special	special	ADJ
iajs-3044	311	72	models	model	NOUN
iajs-3044	311	73	of	of	ADP
iajs-3044	311	74	the	the	DET
iajs-3044	311	75	𝑀𝑊𝐸𝑅	𝑀𝑊𝐸𝑅	PROPN
iajs-3044	311	76	distribution	distribution	NOUN
iajs-3044	311	77	.	.	PUNCT
iajs-3044	312	1	different	different	ADJ
iajs-3044	312	2	statistical	statistical	ADJ
iajs-3044	312	3	properties	property	NOUN
iajs-3044	312	4	such	such	ADJ
iajs-3044	312	5	as	as	ADP
iajs-3044	312	6	the	the	DET
iajs-3044	312	7	mode	mode	NOUN
iajs-3044	312	8	,	,	PUNCT
iajs-3044	312	9	the	the	DET
iajs-3044	312	10	median	median	NOUN
iajs-3044	312	11	,	,	PUNCT
iajs-3044	312	12	the	the	DET
iajs-3044	312	13	𝑟𝑡ℎ	𝑟𝑡ℎ	NOUN
iajs-3044	312	14	moment	moment	NOUN
iajs-3044	312	15	about	about	ADP
iajs-3044	312	16	the	the	DET
iajs-3044	312	17	origin	origin	NOUN
iajs-3044	312	18	,	,	PUNCT
iajs-3044	312	19	the	the	DET
iajs-3044	312	20	moment	moment	NOUN
iajs-3044	312	21	generating	generate	VERB
iajs-3044	312	22	function	function	NOUN
iajs-3044	312	23	,	,	PUNCT
iajs-3044	312	24	factorial	factorial	ADJ
iajs-3044	312	25	moment	moment	NOUN
iajs-3044	312	26	generating	generate	VERB
iajs-3044	312	27	function	function	NOUN
iajs-3044	312	28	,	,	PUNCT
iajs-3044	312	29	the	the	DET
iajs-3044	312	30	characteristic	characteristic	ADJ
iajs-3044	312	31	function	function	NOUN
iajs-3044	312	32	and	and	CCONJ
iajs-3044	312	33	quantile	quantile	ADJ
iajs-3044	312	34	function	function	NOUN
iajs-3044	312	35	are	be	AUX
iajs-3044	312	36	discuses	discuse	VERB
iajs-3044	312	37	and	and	CCONJ
iajs-3044	312	38	study	study	VERB
iajs-3044	312	39	for	for	ADP
iajs-3044	312	40	these	these	DET
iajs-3044	312	41	two	two	NUM
iajs-3044	312	42	distributions	distribution	NOUN
iajs-3044	312	43	.	.	PUNCT
iajs-3044	313	1	ihjpas	ihjpas	PROPN
iajs-3044	313	2	.	.	PUNCT
iajs-3044	314	1	36(2)2023	36(2)2023	NUM
iajs-3044	314	2	406	406	NUM
iajs-3044	314	3	references	reference	NOUN
iajs-3044	314	4	1	1	NUM
iajs-3044	314	5	.	.	PUNCT
iajs-3044	314	6	rayleigh	rayleigh	PROPN
iajs-3044	314	7	,	,	PUNCT
iajs-3044	314	8	j.	j.	PROPN
iajs-3044	314	9	w.	w.	PROPN
iajs-3044	314	10	s.	s.	PROPN
iajs-3044	314	11	on	on	ADP
iajs-3044	314	12	the	the	DET
iajs-3044	314	13	resultant	resultant	NOUN
iajs-3044	314	14	of	of	ADP
iajs-3044	314	15	a	a	DET
iajs-3044	314	16	large	large	ADJ
iajs-3044	314	17	number	number	NOUN
iajs-3044	314	18	of	of	ADP
iajs-3044	314	19	vibrations	vibration	NOUN
iajs-3044	314	20	of	of	ADP
iajs-3044	314	21	the	the	DET
iajs-3044	314	22	some	some	DET
iajs-3044	314	23	pitch	pitch	NOUN
iajs-3044	314	24	and	and	CCONJ
iajs-3044	314	25	of	of	ADP
iajs-3044	314	26	arbitrary	arbitrary	ADJ
iajs-3044	314	27	phase	phase	NOUN
iajs-3044	314	28	,	,	PUNCT
iajs-3044	314	29	philosophical	philosophical	ADJ
iajs-3044	314	30	magazine	magazine	NOUN
iajs-3044	314	31	series	series	NOUN
iajs-3044	314	32	,	,	PUNCT
iajs-3044	314	33	1880,10	1880,10	PROPN
iajs-3044	314	34	,	,	PUNCT
iajs-3044	314	35	60	60	NUM
iajs-3044	314	36	,	,	PUNCT
iajs-3044	314	37	73	73	NUM
iajs-3044	314	38	–	–	PUNCT
iajs-3044	314	39	78	78	NUM
iajs-3044	314	40	.	.	X
iajs-3044	315	1	2	2	X
iajs-3044	315	2	.	.	X
iajs-3044	315	3	rahiem	rahiem	NOUN
iajs-3044	315	4	,	,	PUNCT
iajs-3044	315	5	n	n	CCONJ
iajs-3044	315	6	,	,	PUNCT
iajs-3044	315	7	a.	a.	NOUN
iajs-3044	315	8	;	;	PUNCT
iajs-3044	315	9	j.	j.	PROPN
iajs-3044	315	10	,	,	PUNCT
iajs-3044	315	11	s.	s.	PROPN
iajs-3044	315	12	h.	h.	PROPN
iajs-3044	315	13	;	;	PUNCT
iajs-3044	315	14	kalaf	kalaf	PROPN
iajs-3044	315	15	b.	b.	PROPN
iajs-3044	315	16	a.	a.	NOUN
iajs-3044	315	17	estimate	estimate	VERB
iajs-3044	315	18	the	the	DET
iajs-3044	315	19	scale	scale	NOUN
iajs-3044	315	20	parameter	parameter	NOUN
iajs-3044	315	21	of	of	ADP
iajs-3044	315	22	exponential	exponential	ADJ
iajs-3044	315	23	distribution	distribution	NOUN
iajs-3044	315	24	via	via	ADP
iajs-3044	315	25	modified	modify	VERB
iajs-3044	315	26	two	two	NUM
iajs-3044	315	27	stage	stage	NOUN
iajs-3044	315	28	shrinkage	shrinkage	NOUN
iajs-3044	315	29	technique	technique	NOUN
iajs-3044	315	30	.	.	PUNCT
iajs-3044	316	1	journal	journal	NOUN
iajs-3044	316	2	of	of	ADP
iajs-3044	316	3	college	college	PROPN
iajs-3044	316	4	of	of	ADP
iajs-3044	316	5	education	education	NOUN
iajs-3044	316	6	,	,	PUNCT
iajs-3044	316	7	2010	2010	NUM
iajs-3044	316	8	,	,	PUNCT
iajs-3044	316	9	(	(	PUNCT
iajs-3044	316	10	6	6	NUM
iajs-3044	316	11	)	)	PUNCT
iajs-3044	316	12	.	.	PUNCT
iajs-3044	317	1	3	3	X
iajs-3044	317	2	.	.	X
iajs-3044	317	3	fatima	fatima	PROPN
iajs-3044	317	4	,	,	PUNCT
iajs-3044	317	5	k.	k.	PROPN
iajs-3044	317	6	;	;	PUNCT
iajs-3044	317	7	ahmad	ahmad	PROPN
iajs-3044	317	8	,	,	PUNCT
iajs-3044	317	9	s.	s.	PROPN
iajs-3044	317	10	statistical	statistical	ADJ
iajs-3044	317	11	properties	property	NOUN
iajs-3044	317	12	of	of	ADP
iajs-3044	317	13	exponential	exponential	ADJ
iajs-3044	317	14	rayleigh	rayleigh	NOUN
iajs-3044	317	15	distribution	distribution	NOUN
iajs-3044	317	16	and	and	CCONJ
iajs-3044	317	17	its	its	PRON
iajs-3044	317	18	applications	application	NOUN
iajs-3044	317	19	to	to	ADP
iajs-3044	317	20	medical	medical	ADJ
iajs-3044	317	21	science	science	NOUN
iajs-3044	317	22	and	and	CCONJ
iajs-3044	317	23	engineering	engineering	NOUN
iajs-3044	317	24	,	,	PUNCT
iajs-3044	317	25	international	international	ADJ
iajs-3044	317	26	conference	conference	NOUN
iajs-3044	317	27	on	on	ADP
iajs-3044	317	28	recent	recent	ADJ
iajs-3044	317	29	innovations	innovation	NOUN
iajs-3044	317	30	in	in	ADP
iajs-3044	317	31	science	science	NOUN
iajs-3044	317	32	,	,	PUNCT
iajs-3044	317	33	agriculture	agriculture	NOUN
iajs-3044	317	34	,	,	PUNCT
iajs-3044	317	35	engineering	engineering	NOUN
iajs-3044	317	36	and	and	CCONJ
iajs-3044	317	37	management	management	NOUN
iajs-3044	317	38	2017	2017	NUM
iajs-3044	317	39	,	,	PUNCT
iajs-3044	317	40	491	491	NUM
iajs-3044	317	41	–	–	PUNCT
iajs-3044	317	42	506	506	NUM
iajs-3044	317	43	.	.	NOUN
iajs-3044	317	44	4	4	NUM
iajs-3044	317	45	.	.	X
iajs-3044	318	1	tahir	tahir	PROPN
iajs-3044	318	2	,	,	PUNCT
iajs-3044	318	3	m	m	PROPN
iajs-3044	318	4	;	;	PUNCT
iajs-3044	318	5	aslam	aslam	PROPN
iajs-3044	318	6	,	,	PUNCT
iajs-3044	318	7	m.	m.	NOUN
iajs-3044	318	8	hussain	hussain	PROPN
iajs-3044	318	9	,	,	PUNCT
iajs-3044	318	10	z.	z.	PROPN
iajs-3044	318	11	;	;	PUNCT
iajs-3044	318	12	abbas	abbas	PROPN
iajs-3044	318	13	,	,	PUNCT
iajs-3044	318	14	n.	n.	NOUN
iajs-3044	318	15	on	on	ADP
iajs-3044	318	16	the	the	DET
iajs-3044	318	17	finite	finite	ADJ
iajs-3044	318	18	mixture	mixture	NOUN
iajs-3044	318	19	of	of	ADP
iajs-3044	318	20	exponential	exponential	NOUN
iajs-3044	318	21	,	,	PUNCT
iajs-3044	318	22	rayleigh	rayleigh	PROPN
iajs-3044	318	23	and	and	CCONJ
iajs-3044	318	24	burr	burr	PROPN
iajs-3044	318	25	type	type	NOUN
iajs-3044	318	26	-	-	PUNCT
iajs-3044	318	27	xii	xii	NOUN
iajs-3044	318	28	distributions	distribution	NOUN
iajs-3044	318	29	:	:	PUNCT
iajs-3044	318	30	estimation	estimation	NOUN
iajs-3044	318	31	of	of	ADP
iajs-3044	318	32	parameters	parameter	NOUN
iajs-3044	318	33	in	in	ADP
iajs-3044	318	34	bayesian	bayesian	NOUN
iajs-3044	318	35	framework	framework	NOUN
iajs-3044	318	36	,	,	PUNCT
iajs-3044	318	37	electronic	electronic	ADJ
iajs-3044	318	38	journal	journal	NOUN
iajs-3044	318	39	of	of	ADP
iajs-3044	318	40	applied	apply	VERB
iajs-3044	318	41	statistical	statistical	ADJ
iajs-3044	318	42	analysis	analysis	NOUN
iajs-3044	318	43	,	,	PUNCT
iajs-3044	318	44	2017,10	2017,10	NUM
iajs-3044	318	45	,	,	PUNCT
iajs-3044	318	46	issue	issue	NOUN
iajs-3044	318	47	01	01	NUM
iajs-3044	318	48	,	,	PUNCT
iajs-3044	318	49	271	271	NUM
iajs-3044	318	50	–	–	PUNCT
iajs-3044	318	51	293	293	NUM
iajs-3044	318	52	.	.	X
iajs-3044	318	53	5	5	NUM
iajs-3044	318	54	.	.	X
iajs-3044	319	1	isaac	isaac	PROPN
iajs-3044	319	2	,	,	PUNCT
iajs-3044	319	3	r	r	PROPN
iajs-3044	319	4	s.	s.	PROPN
iajs-3044	319	5	;	;	PUNCT
iajs-3044	319	6	mehta	mehta	PROPN
iajs-3044	319	7	,	,	PUNCT
iajs-3044	319	8	n.	n.	PROPN
iajs-3044	319	9	b.	b.	PROPN
iajs-3044	319	10	;	;	PUNCT
iajs-3044	319	11	ieee	ieee	PROPN
iajs-3044	319	12	,	,	PUNCT
iajs-3044	319	13	s.	s.	PROPN
iajs-3044	319	14	m.	m.	PROPN
iajs-3044	319	15	efficient	efficient	ADJ
iajs-3044	319	16	computation	computation	NOUN
iajs-3044	319	17	of	of	ADP
iajs-3044	319	18	multivariate	multivariate	NOUN
iajs-3044	319	19	rayleigh	rayleigh	PROPN
iajs-3044	319	20	and	and	CCONJ
iajs-3044	319	21	exponential	exponential	ADJ
iajs-3044	319	22	distributions	distribution	NOUN
iajs-3044	319	23	,	,	PUNCT
iajs-3044	319	24	ieee	ieee	NOUN
iajs-3044	319	25	wireless	wireless	ADJ
iajs-3044	319	26	communications	communication	NOUN
iajs-3044	319	27	letters	letter	NOUN
iajs-3044	319	28	,	,	PUNCT
iajs-3044	319	29	2019,8	2019,8	NUM
iajs-3044	319	30	,	,	PUNCT
iajs-3044	319	31	2	2	NUM
iajs-3044	319	32	,	,	PUNCT
iajs-3044	319	33	456	456	NUM
iajs-3044	319	34	–	–	PUNCT
iajs-3044	319	35	459	459	NUM
iajs-3044	319	36	.	.	NOUN
iajs-3044	320	1	6	6	NUM
iajs-3044	320	2	.	.	PUNCT
iajs-3044	321	1	mohammed	mohammed	PROPN
iajs-3044	321	2	,	,	PUNCT
iajs-3044	321	3	m.	m.	NOUN
iajs-3044	321	4	j.	j.	PROPN
iajs-3044	321	5	;	;	PUNCT
iajs-3044	321	6	hussein	hussein	PROPN
iajs-3044	321	7	,	,	PUNCT
iajs-3044	321	8	i.	i.	PROPN
iajs-3044	321	9	h.	h.	PROPN
iajs-3044	321	10	study	study	PROPN
iajs-3044	321	11	of	of	ADP
iajs-3044	321	12	new	new	ADJ
iajs-3044	321	13	mixture	mixture	NOUN
iajs-3044	321	14	distribution	distribution	NOUN
iajs-3044	321	15	,	,	PUNCT
iajs-3044	321	16	journal	journal	NOUN
iajs-3044	321	17	of	of	ADP
iajs-3044	321	18	engineering	engineering	NOUN
iajs-3044	321	19	and	and	CCONJ
iajs-3044	321	20	applied	apply	VERB
iajs-3044	321	21	sciences	science	NOUN
iajs-3044	321	22	,	,	PUNCT
iajs-3044	321	23	2019,14	2019,14	ADV
iajs-3044	321	24	,	,	PUNCT
iajs-3044	321	25	20	20	NUM
iajs-3044	321	26	,	,	PUNCT
iajs-3044	321	27	7566	7566	NUM
iajs-3044	321	28	–	–	PUNCT
iajs-3044	321	29	7573	7573	NUM
iajs-3044	321	30	.	.	PUNCT
iajs-3044	322	1	7	7	X
iajs-3044	322	2	.	.	X
iajs-3044	322	3	shi	shi	PROPN
iajs-3044	322	4	,	,	PUNCT
iajs-3044	322	5	x	x	X
iajs-3044	322	6	;	;	PUNCT
iajs-3044	322	7	oluyede	oluyede	NOUN
iajs-3044	322	8	,	,	PUNCT
iajs-3044	322	9	b.	b.	PROPN
iajs-3044	322	10	o.	o.	PROPN
iajs-3044	322	11	;	;	PUNCT
iajs-3044	322	12	pararai	pararai	VERB
iajs-3044	322	13	,	,	PUNCT
iajs-3044	322	14	m.	m.	NOUN
iajs-3044	322	15	theoretical	theoretical	ADJ
iajs-3044	322	16	properties	property	NOUN
iajs-3044	322	17	of	of	ADP
iajs-3044	322	18	weighted	weight	VERB
iajs-3044	322	19	generalized	generalized	ADJ
iajs-3044	322	20	rayleigh	rayleigh	PROPN
iajs-3044	322	21	and	and	CCONJ
iajs-3044	322	22	related	related	ADJ
iajs-3044	322	23	distribution	distribution	NOUN
iajs-3044	322	24	,	,	PUNCT
iajs-3044	322	25	theoretical	theoretical	ADJ
iajs-3044	322	26	mathematics	mathematic	NOUN
iajs-3044	322	27	&	&	CCONJ
iajs-3044	322	28	applications	application	NOUN
iajs-3044	322	29	,	,	PUNCT
iajs-3044	322	30	2012	2012	NUM
iajs-3044	322	31	,	,	PUNCT
iajs-3044	322	32	2	2	NUM
iajs-3044	322	33	,	,	PUNCT
iajs-3044	322	34	2	2	NUM
iajs-3044	322	35	,	,	PUNCT
iajs-3044	322	36	45	45	NUM
iajs-3044	322	37	–	–	PUNCT
iajs-3044	322	38	62	62	NUM
iajs-3044	322	39	.	.	NOUN
iajs-3044	322	40	8	8	NUM
iajs-3044	322	41	.	.	X
iajs-3044	323	1	oguntunde	oguntunde	NOUN
iajs-3044	323	2	,	,	PUNCT
iajs-3044	323	3	p.	p.	NOUN
iajs-3044	323	4	e	e	NOUN
iajs-3044	323	5	;	;	PUNCT
iajs-3044	323	6	balogun	balogun	VERB
iajs-3044	323	7	,	,	PUNCT
iajs-3044	323	8	o.	o.	NOUN
iajs-3044	323	9	s	s	PROPN
iajs-3044	323	10	;	;	PUNCT
iajs-3044	324	1	okagbue	okagbue	PROPN
iajs-3044	324	2	,	,	PUNCT
iajs-3044	324	3	h.	h.	PROPN
iajs-3044	324	4	i.	i.	PROPN
iajs-3044	324	5	;	;	PUNCT
iajs-3044	324	6	bishop	bishop	PROPN
iajs-3044	324	7	,	,	PUNCT
iajs-3044	325	1	s.	s.	PROPN
iajs-3044	325	2	a.	a.	PROPN
iajs-3044	325	3	the	the	DET
iajs-3044	325	4	weibull	weibull	PROPN
iajs-3044	325	5	-	-	PUNCT
iajs-3044	325	6	exponential	exponential	ADJ
iajs-3044	325	7	distribution	distribution	NOUN
iajs-3044	325	8	:	:	PUNCT
iajs-3044	325	9	its	its	PRON
iajs-3044	325	10	properties	property	NOUN
iajs-3044	325	11	and	and	CCONJ
iajs-3044	325	12	applications	application	NOUN
iajs-3044	325	13	,	,	PUNCT
iajs-3044	325	14	journal	journal	NOUN
iajs-3044	325	15	of	of	ADP
iajs-3044	325	16	applied	apply	VERB
iajs-3044	325	17	sciences	science	NOUN
iajs-3044	325	18	,	,	PUNCT
iajs-3044	325	19	2015,15,11	2015,15,11	NUM
iajs-3044	325	20	,	,	PUNCT
iajs-3044	325	21	1305	1305	NUM
iajs-3044	325	22	–	–	PUNCT
iajs-3044	325	23	1311	1311	NUM
iajs-3044	325	24	.	.	PUNCT
iajs-3044	326	1	9	9	X
iajs-3044	326	2	.	.	X
iajs-3044	326	3	merovci	merovci	PROPN
iajs-3044	326	4	,	,	PUNCT
iajs-3044	326	5	f.	f.	PROPN
iajs-3044	326	6	;	;	PUNCT
iajs-3044	326	7	elbatal	elbatal	ADJ
iajs-3044	326	8	,	,	PUNCT
iajs-3044	326	9	i.	i.	PROPN
iajs-3044	326	10	weibull	weibull	PROPN
iajs-3044	326	11	rayleigh	rayleigh	PROPN
iajs-3044	326	12	distribution	distribution	PROPN
iajs-3044	326	13	:	:	PUNCT
iajs-3044	326	14	theory	theory	NOUN
iajs-3044	326	15	and	and	CCONJ
iajs-3044	326	16	applications	application	NOUN
iajs-3044	326	17	,	,	PUNCT
iajs-3044	326	18	applied	apply	VERB
iajs-3044	326	19	mathematics	mathematic	NOUN
iajs-3044	326	20	and	and	CCONJ
iajs-3044	326	21	information	information	NOUN
iajs-3044	326	22	sciences	science	NOUN
iajs-3044	326	23	,	,	PUNCT
iajs-3044	326	24	2015,9	2015,9	NUM
iajs-3044	326	25	,	,	PUNCT
iajs-3044	326	26	4	4	NUM
iajs-3044	326	27	,	,	PUNCT
iajs-3044	326	28	2127	2127	NUM
iajs-3044	326	29	–	–	PUNCT
iajs-3044	326	30	2137	2137	NUM
iajs-3044	326	31	10	10	NUM
iajs-3044	326	32	.	.	PUNCT
iajs-3044	327	1	nasiru	nasiru	PROPN
iajs-3044	327	2	,	,	PUNCT
iajs-3044	327	3	s.	s.	PROPN
iajs-3044	327	4	another	another	PRON
iajs-3044	327	5	weighted	weight	VERB
iajs-3044	327	6	weibull	weibull	NOUN
iajs-3044	327	7	distribution	distribution	NOUN
iajs-3044	327	8	from	from	ADP
iajs-3044	327	9	azzalini	azzalini	PROPN
iajs-3044	327	10	’s	’s	PART
iajs-3044	327	11	family	family	NOUN
iajs-3044	327	12	,	,	PUNCT
iajs-3044	327	13	european	european	PROPN
iajs-3044	327	14	scientific	scientific	ADJ
iajs-3044	327	15	journal	journal	PROPN
iajs-3044	327	16	march	march	PROPN
iajs-3044	327	17	,	,	PUNCT
iajs-3044	327	18	2015,11	2015,11	NOUN
iajs-3044	327	19	,	,	PUNCT
iajs-3044	327	20	9	9	NUM
iajs-3044	327	21	,	,	PUNCT
iajs-3044	327	22	134	134	NUM
iajs-3044	327	23	–	–	SYM
iajs-3044	327	24	144	144	NUM
iajs-3044	327	25	.	.	NOUN
iajs-3044	327	26	11	11	NUM
iajs-3044	327	27	.	.	X
iajs-3044	328	1	hussian	hussian	PROPN
iajs-3044	328	2	,	,	PUNCT
iajs-3044	328	3	m.	m.	NOUN
iajs-3044	328	4	a.	a.	PROPN
iajs-3044	328	5	a	a	DET
iajs-3044	328	6	weighted	weight	VERB
iajs-3044	328	7	inverted	invert	VERB
iajs-3044	328	8	exponential	exponential	ADJ
iajs-3044	328	9	distribution	distribution	NOUN
iajs-3044	328	10	,	,	PUNCT
iajs-3044	328	11	international	international	ADJ
iajs-3044	328	12	journal	journal	NOUN
iajs-3044	328	13	of	of	ADP
iajs-3044	328	14	advanced	advanced	ADJ
iajs-3044	328	15	statistics	statistic	NOUN
iajs-3044	328	16	and	and	CCONJ
iajs-3044	328	17	probability	probability	NOUN
iajs-3044	328	18	,	,	PUNCT
iajs-3044	328	19	2013,1	2013,1	NUM
iajs-3044	328	20	,	,	PUNCT
iajs-3044	328	21	3	3	NUM
iajs-3044	328	22	,	,	PUNCT
iajs-3044	328	23	142	142	NUM
iajs-3044	328	24	–	–	SYM
iajs-3044	328	25	150	150	NUM
iajs-3044	328	26	.	.	PUNCT
iajs-3044	329	1	12.oguntunde	12.oguntunde	NUM
iajs-3044	329	2	,	,	PUNCT
iajs-3044	329	3	p	p	NOUN
iajs-3044	329	4	e	e	NOUN
iajs-3044	329	5	;	;	PUNCT
iajs-3044	329	6	owoloko	owoloko	PROPN
iajs-3044	329	7	,	,	PUNCT
iajs-3044	329	8	e.	e.	PROPN
iajs-3044	329	9	a.	a.	PROPN
iajs-3044	329	10	;	;	PUNCT
iajs-3044	329	11	balogun	balogun	VERB
iajs-3044	329	12	,	,	PUNCT
iajs-3044	329	13	o.	o.	PROPN
iajs-3044	329	14	s.	s.	PROPN
iajs-3044	329	15	on	on	ADP
iajs-3044	329	16	a	a	DET
iajs-3044	329	17	new	new	ADJ
iajs-3044	329	18	weighted	weight	VERB
iajs-3044	329	19	exponential	exponential	ADJ
iajs-3044	329	20	distribution	distribution	NOUN
iajs-3044	329	21	:	:	PUNCT
iajs-3044	329	22	theory	theory	NOUN
iajs-3044	329	23	and	and	CCONJ
iajs-3044	329	24	application	application	NOUN
iajs-3044	329	25	,	,	PUNCT
iajs-3044	329	26	asian	asian	ADJ
iajs-3044	329	27	journal	journal	NOUN
iajs-3044	329	28	of	of	ADP
iajs-3044	329	29	applied	apply	VERB
iajs-3044	329	30	sciences	science	NOUN
iajs-3044	329	31	,	,	PUNCT
iajs-3044	329	32	2016,9	2016,9	NUM
iajs-3044	329	33	,	,	PUNCT
iajs-3044	329	34	1	1	NUM
iajs-3044	329	35	,	,	PUNCT
iajs-3044	329	36	1	1	NUM
iajs-3044	329	37	–	–	SYM
iajs-3044	329	38	12	12	NUM
iajs-3044	329	39	.	.	PUNCT
iajs-3044	330	1	https://ieeexplore.ieee.org/xpl/recentissue.jsp?punumber=5962382	https://ieeexplore.ieee.org/xpl/recentissue.jsp?punumber=5962382	NOUN