id	sid	tid	token	lemma	pos
ejpam-6480	1	1	european	european	PROPN
ejpam-6480	1	2	journal	journal	PROPN
ejpam-6480	1	3	of	of	ADP
ejpam-6480	1	4	pure	pure	ADJ
ejpam-6480	1	5	and	and	CCONJ
ejpam-6480	1	6	applied	applied	ADJ
ejpam-6480	1	7	mathematics	mathematic	NOUN
ejpam-6480	1	8	2025	2025	NUM
ejpam-6480	1	9	,	,	PUNCT
ejpam-6480	1	10	vol	vol	NOUN
ejpam-6480	1	11	.	.	PROPN
ejpam-6480	1	12	18	18	NUM
ejpam-6480	1	13	,	,	PUNCT
ejpam-6480	1	14	issue	issue	NOUN
ejpam-6480	1	15	4	4	NUM
ejpam-6480	1	16	,	,	PUNCT
ejpam-6480	1	17	article	article	NOUN
ejpam-6480	1	18	number	number	NOUN
ejpam-6480	1	19	6480	6480	NUM
ejpam-6480	1	20	issn	issn	PROPN
ejpam-6480	1	21	1307	1307	NUM
ejpam-6480	1	22	-	-	SYM
ejpam-6480	1	23	5543	5543	NUM
ejpam-6480	1	24	–	–	PUNCT
ejpam-6480	1	25	ejpam.com	ejpam.com	X
ejpam-6480	1	26	published	publish	VERB
ejpam-6480	1	27	by	by	ADP
ejpam-6480	1	28	new	new	PROPN
ejpam-6480	1	29	york	york	PROPN
ejpam-6480	1	30	business	business	PROPN
ejpam-6480	1	31	global	global	PROPN
ejpam-6480	1	32	mathai	mathai	PROPN
ejpam-6480	1	33	-	-	PUNCT
ejpam-6480	1	34	haubold	haubold	PROPN
ejpam-6480	1	35	interval	interval	NOUN
ejpam-6480	1	36	entropy	entropy	NOUN
ejpam-6480	1	37	and	and	CCONJ
ejpam-6480	1	38	related	related	ADJ
ejpam-6480	1	39	inequalities	inequality	NOUN
ejpam-6480	1	40	javid	javid	PROPN
ejpam-6480	1	41	gani	gani	PROPN
ejpam-6480	1	42	dar1	dar1	PROPN
ejpam-6480	1	43	,	,	PUNCT
ejpam-6480	1	44	sara	sara	PROPN
ejpam-6480	1	45	mohamed	mohamed	PROPN
ejpam-6480	1	46	ahmed	ahmed	PROPN
ejpam-6480	1	47	alsheikh2	alsheikh2	PROPN
ejpam-6480	1	48	,	,	PUNCT
ejpam-6480	1	49	prakash	prakash	PROPN
ejpam-6480	1	50	jadhav3,∗	jadhav3,∗	PROPN
ejpam-6480	1	51	1	1	NUM
ejpam-6480	1	52	department	department	NOUN
ejpam-6480	1	53	of	of	ADP
ejpam-6480	1	54	applied	apply	VERB
ejpam-6480	1	55	sciences	science	NOUN
ejpam-6480	1	56	,	,	PUNCT
ejpam-6480	1	57	symbiosis	symbiosis	NOUN
ejpam-6480	1	58	institute	institute	PROPN
ejpam-6480	1	59	of	of	ADP
ejpam-6480	1	60	technology	technology	PROPN
ejpam-6480	1	61	,	,	PUNCT
ejpam-6480	1	62	symbiosis	symbiosis	NOUN
ejpam-6480	1	63	international	international	ADJ
ejpam-6480	1	64	(	(	PUNCT
ejpam-6480	1	65	deemed	deem	VERB
ejpam-6480	1	66	university	university	NOUN
ejpam-6480	1	67	)	)	PUNCT
ejpam-6480	1	68	(	(	PUNCT
ejpam-6480	1	69	siu	siu	NOUN
ejpam-6480	1	70	)	)	PUNCT
ejpam-6480	1	71	,	,	PUNCT
ejpam-6480	1	72	lavale	lavale	NOUN
ejpam-6480	1	73	,	,	PUNCT
ejpam-6480	1	74	pune	pune	NOUN
ejpam-6480	1	75	,	,	PUNCT
ejpam-6480	1	76	maharashtra	maharashtra	PROPN
ejpam-6480	1	77	,	,	PUNCT
ejpam-6480	1	78	india	india	PROPN
ejpam-6480	1	79	2	2	NUM
ejpam-6480	1	80	department	department	NOUN
ejpam-6480	1	81	of	of	ADP
ejpam-6480	1	82	statistics	statistic	NOUN
ejpam-6480	1	83	,	,	PUNCT
ejpam-6480	1	84	faculty	faculty	NOUN
ejpam-6480	1	85	of	of	ADP
ejpam-6480	1	86	science	science	NOUN
ejpam-6480	1	87	,	,	PUNCT
ejpam-6480	1	88	university	university	NOUN
ejpam-6480	1	89	of	of	ADP
ejpam-6480	1	90	tabuk	tabuk	PROPN
ejpam-6480	1	91	,	,	PUNCT
ejpam-6480	1	92	tabuk	tabuk	PROPN
ejpam-6480	1	93	,	,	PUNCT
ejpam-6480	1	94	saudi	saudi	PROPN
ejpam-6480	1	95	arabia	arabia	PROPN
ejpam-6480	1	96	3	3	NUM
ejpam-6480	1	97	department	department	NOUN
ejpam-6480	1	98	of	of	ADP
ejpam-6480	1	99	mechanical	mechanical	ADJ
ejpam-6480	1	100	engineering	engineering	NOUN
ejpam-6480	1	101	,	,	PUNCT
ejpam-6480	1	102	srm	srm	PROPN
ejpam-6480	1	103	university	university	PROPN
ejpam-6480	1	104	ap	ap	PROPN
ejpam-6480	1	105	,	,	PUNCT
ejpam-6480	1	106	andhra	andhra	PROPN
ejpam-6480	1	107	pradesh	pradesh	PROPN
ejpam-6480	1	108	,	,	PUNCT
ejpam-6480	1	109	522240	522240	NUM
ejpam-6480	1	110	,	,	PUNCT
ejpam-6480	1	111	india	india	PROPN
ejpam-6480	1	112	abstract	abstract	NOUN
ejpam-6480	1	113	.	.	PUNCT
ejpam-6480	2	1	the	the	DET
ejpam-6480	2	2	paper	paper	NOUN
ejpam-6480	2	3	introduces	introduce	VERB
ejpam-6480	2	4	a	a	DET
ejpam-6480	2	5	generalized	generalized	ADJ
ejpam-6480	2	6	interval	interval	NOUN
ejpam-6480	2	7	entropy	entropy	NOUN
ejpam-6480	2	8	measure	measure	NOUN
ejpam-6480	2	9	that	that	PRON
ejpam-6480	2	10	provides	provide	VERB
ejpam-6480	2	11	a	a	DET
ejpam-6480	2	12	comprehensive	comprehensive	ADJ
ejpam-6480	2	13	framework	framework	NOUN
ejpam-6480	2	14	for	for	ADP
ejpam-6480	2	15	understanding	understanding	NOUN
ejpam-6480	2	16	and	and	CCONJ
ejpam-6480	2	17	quantifying	quantify	VERB
ejpam-6480	2	18	the	the	DET
ejpam-6480	2	19	uncertainty	uncertainty	NOUN
ejpam-6480	2	20	in	in	ADP
ejpam-6480	2	21	systems	system	NOUN
ejpam-6480	2	22	with	with	ADP
ejpam-6480	2	23	doubly	doubly	ADV
ejpam-6480	2	24	truncated	truncate	VERB
ejpam-6480	2	25	random	random	ADJ
ejpam-6480	2	26	variables	variable	NOUN
ejpam-6480	2	27	.	.	PUNCT
ejpam-6480	3	1	by	by	ADP
ejpam-6480	3	2	characterizing	characterize	VERB
ejpam-6480	3	3	well	well	ADV
ejpam-6480	3	4	-	-	PUNCT
ejpam-6480	3	5	known	know	VERB
ejpam-6480	3	6	lifetime	lifetime	NOUN
ejpam-6480	3	7	distributions	distribution	NOUN
ejpam-6480	3	8	(	(	PUNCT
ejpam-6480	3	9	exponential	exponential	NOUN
ejpam-6480	3	10	,	,	PUNCT
ejpam-6480	3	11	pareto	pareto	ADJ
ejpam-6480	3	12	,	,	PUNCT
ejpam-6480	3	13	and	and	CCONJ
ejpam-6480	3	14	finite	finite	ADJ
ejpam-6480	3	15	range	range	NOUN
ejpam-6480	3	16	distributions	distribution	NOUN
ejpam-6480	3	17	)	)	PUNCT
ejpam-6480	3	18	,	,	PUNCT
ejpam-6480	3	19	deriving	derive	VERB
ejpam-6480	3	20	a	a	DET
ejpam-6480	3	21	lower	lower	ADV
ejpam-6480	3	22	bound	bind	VERB
ejpam-6480	3	23	for	for	ADP
ejpam-6480	3	24	the	the	DET
ejpam-6480	3	25	entropy	entropy	NOUN
ejpam-6480	3	26	,	,	PUNCT
ejpam-6480	3	27	and	and	CCONJ
ejpam-6480	3	28	exploring	explore	VERB
ejpam-6480	3	29	stochastic	stochastic	ADJ
ejpam-6480	3	30	comparisons	comparison	NOUN
ejpam-6480	3	31	,	,	PUNCT
ejpam-6480	3	32	the	the	DET
ejpam-6480	3	33	paper	paper	NOUN
ejpam-6480	3	34	demonstrates	demonstrate	VERB
ejpam-6480	3	35	the	the	DET
ejpam-6480	3	36	usefulness	usefulness	NOUN
ejpam-6480	3	37	of	of	ADP
ejpam-6480	3	38	this	this	DET
ejpam-6480	3	39	measure	measure	NOUN
ejpam-6480	3	40	in	in	ADP
ejpam-6480	3	41	reliability	reliability	NOUN
ejpam-6480	3	42	modelling	modelling	NOUN
ejpam-6480	3	43	,	,	PUNCT
ejpam-6480	3	44	survival	survival	NOUN
ejpam-6480	3	45	analysis	analysis	NOUN
ejpam-6480	3	46	and	and	CCONJ
ejpam-6480	3	47	information	information	NOUN
ejpam-6480	3	48	theory	theory	NOUN
ejpam-6480	3	49	.	.	PUNCT
ejpam-6480	4	1	2020	2020	NUM
ejpam-6480	4	2	mathematics	mathematic	NOUN
ejpam-6480	4	3	subject	subject	NOUN
ejpam-6480	4	4	classifications	classification	NOUN
ejpam-6480	4	5	:	:	PUNCT
ejpam-6480	4	6	62b10	62b10	NUM
ejpam-6480	4	7	,	,	PUNCT
ejpam-6480	4	8	62r07	62r07	NUM
ejpam-6480	4	9	,	,	PUNCT
ejpam-6480	4	10	60g35	60g35	NUM
ejpam-6480	4	11	,	,	PUNCT
ejpam-6480	4	12	62n05	62n05	NUM
ejpam-6480	4	13	key	key	ADJ
ejpam-6480	4	14	words	word	NOUN
ejpam-6480	4	15	and	and	CCONJ
ejpam-6480	4	16	phrases	phrase	NOUN
ejpam-6480	4	17	:	:	PUNCT
ejpam-6480	4	18	entropy	entropy	PROPN
ejpam-6480	4	19	,	,	PUNCT
ejpam-6480	4	20	residual	residual	ADJ
ejpam-6480	4	21	entropy	entropy	NOUN
ejpam-6480	4	22	,	,	PUNCT
ejpam-6480	4	23	interval	interval	NOUN
ejpam-6480	4	24	entropy	entropy	NOUN
ejpam-6480	4	25	,	,	PUNCT
ejpam-6480	4	26	generalized	generalized	ADJ
ejpam-6480	4	27	failure	failure	NOUN
ejpam-6480	4	28	rate	rate	NOUN
ejpam-6480	4	29	,	,	PUNCT
ejpam-6480	4	30	characterization	characterization	NOUN
ejpam-6480	4	31	1	1	NUM
ejpam-6480	4	32	.	.	PUNCT
ejpam-6480	5	1	introduction	introduction	NOUN
ejpam-6480	5	2	differential	differential	PROPN
ejpam-6480	5	3	entropy	entropy	PROPN
ejpam-6480	5	4	,	,	PUNCT
ejpam-6480	5	5	also	also	ADV
ejpam-6480	5	6	referred	refer	VERB
ejpam-6480	5	7	to	to	ADP
ejpam-6480	5	8	as	as	SCONJ
ejpam-6480	5	9	the	the	DET
ejpam-6480	5	10	shannon	shannon	PROPN
ejpam-6480	5	11	information	information	NOUN
ejpam-6480	5	12	measure	measure	NOUN
ejpam-6480	5	13	[	[	X
ejpam-6480	5	14	1	1	X
ejpam-6480	5	15	]	]	PUNCT
ejpam-6480	5	16	is	be	AUX
ejpam-6480	5	17	the	the	DET
ejpam-6480	5	18	traditional	traditional	ADJ
ejpam-6480	5	19	measure	measure	NOUN
ejpam-6480	5	20	of	of	ADP
ejpam-6480	5	21	uncertainty	uncertainty	NOUN
ejpam-6480	5	22	.	.	PUNCT
ejpam-6480	6	1	shannon	shannon	PROPN
ejpam-6480	6	2	outlined	outline	VERB
ejpam-6480	6	3	the	the	DET
ejpam-6480	6	4	features	feature	NOUN
ejpam-6480	6	5	of	of	ADP
ejpam-6480	6	6	information	information	NOUN
ejpam-6480	6	7	sources	source	NOUN
ejpam-6480	6	8	and	and	CCONJ
ejpam-6480	6	9	communication	communication	NOUN
ejpam-6480	6	10	channels	channel	NOUN
ejpam-6480	6	11	in	in	ADP
ejpam-6480	6	12	order	order	NOUN
ejpam-6480	6	13	to	to	PART
ejpam-6480	6	14	evaluate	evaluate	VERB
ejpam-6480	6	15	the	the	DET
ejpam-6480	6	16	outputs	output	NOUN
ejpam-6480	6	17	of	of	ADP
ejpam-6480	6	18	different	different	ADJ
ejpam-6480	6	19	sources	source	NOUN
ejpam-6480	6	20	.	.	PUNCT
ejpam-6480	7	1	in	in	ADP
ejpam-6480	7	2	addition	addition	NOUN
ejpam-6480	7	3	to	to	ADP
ejpam-6480	7	4	providing	provide	VERB
ejpam-6480	7	5	a	a	DET
ejpam-6480	7	6	framework	framework	NOUN
ejpam-6480	7	7	for	for	ADP
ejpam-6480	7	8	tackling	tackle	VERB
ejpam-6480	7	9	a	a	DET
ejpam-6480	7	10	wide	wide	ADJ
ejpam-6480	7	11	range	range	NOUN
ejpam-6480	7	12	of	of	ADP
ejpam-6480	7	13	statistical	statistical	ADJ
ejpam-6480	7	14	problems	problem	NOUN
ejpam-6480	7	15	,	,	PUNCT
ejpam-6480	7	16	statisticians	statistician	NOUN
ejpam-6480	7	17	have	have	AUX
ejpam-6480	7	18	played	play	VERB
ejpam-6480	7	19	a	a	DET
ejpam-6480	7	20	significant	significant	ADJ
ejpam-6480	7	21	role	role	NOUN
ejpam-6480	7	22	in	in	ADP
ejpam-6480	7	23	the	the	DET
ejpam-6480	7	24	development	development	NOUN
ejpam-6480	7	25	of	of	ADP
ejpam-6480	7	26	information	information	NOUN
ejpam-6480	7	27	theory	theory	NOUN
ejpam-6480	7	28	.	.	PUNCT
ejpam-6480	8	1	the	the	DET
ejpam-6480	8	2	use	use	NOUN
ejpam-6480	8	3	of	of	ADP
ejpam-6480	8	4	information	information	NOUN
ejpam-6480	8	5	measures	measure	NOUN
ejpam-6480	8	6	for	for	ADP
ejpam-6480	8	7	doubly	doubly	ADV
ejpam-6480	8	8	truncated	truncate	VERB
ejpam-6480	8	9	random	random	ADJ
ejpam-6480	8	10	variables	variable	NOUN
ejpam-6480	8	11	have	have	AUX
ejpam-6480	8	12	been	be	AUX
ejpam-6480	8	13	investigated	investigate	VERB
ejpam-6480	8	14	by	by	ADP
ejpam-6480	8	15	sunoj	sunoj	PROPN
ejpam-6480	8	16	et	et	PROPN
ejpam-6480	8	17	al	al	PROPN
ejpam-6480	8	18	.	.	PUNCT
ejpam-6480	9	1	[	[	X
ejpam-6480	9	2	2	2	X
ejpam-6480	9	3	]	]	PUNCT
ejpam-6480	9	4	and	and	CCONJ
ejpam-6480	9	5	this	this	DET
ejpam-6480	9	6	work	work	NOUN
ejpam-6480	9	7	is	be	AUX
ejpam-6480	9	8	important	important	ADJ
ejpam-6480	9	9	for	for	ADP
ejpam-6480	9	10	understanding	understand	VERB
ejpam-6480	9	11	the	the	DET
ejpam-6480	9	12	many	many	ADJ
ejpam-6480	9	13	components	component	NOUN
ejpam-6480	9	14	of	of	ADP
ejpam-6480	9	15	a	a	DET
ejpam-6480	9	16	system	system	NOUN
ejpam-6480	9	17	’s	’s	PART
ejpam-6480	9	18	failure	failure	NOUN
ejpam-6480	9	19	between	between	ADP
ejpam-6480	9	20	two	two	NUM
ejpam-6480	9	21	time	time	NOUN
ejpam-6480	9	22	points	point	NOUN
ejpam-6480	9	23	.	.	PUNCT
ejpam-6480	10	1	most	most	ADJ
ejpam-6480	10	2	existing	exist	VERB
ejpam-6480	10	3	studies	study	NOUN
ejpam-6480	10	4	on	on	ADP
ejpam-6480	10	5	information	information	NOUN
ejpam-6480	10	6	and	and	CCONJ
ejpam-6480	10	7	entropy	entropy	NOUN
ejpam-6480	10	8	measures	measure	NOUN
ejpam-6480	10	9	,	,	PUNCT
ejpam-6480	10	10	including	include	VERB
ejpam-6480	10	11	shannon	shannon	PROPN
ejpam-6480	10	12	entropy	entropy	PROPN
ejpam-6480	10	13	and	and	CCONJ
ejpam-6480	10	14	its	its	PRON
ejpam-6480	10	15	variants	variant	NOUN
ejpam-6480	10	16	,	,	PUNCT
ejpam-6480	10	17	have	have	AUX
ejpam-6480	10	18	primarily	primarily	ADV
ejpam-6480	10	19	focused	focus	VERB
ejpam-6480	10	20	on	on	ADP
ejpam-6480	10	21	classical	classical	ADJ
ejpam-6480	10	22	settings	setting	NOUN
ejpam-6480	10	23	or	or	CCONJ
ejpam-6480	10	24	extensions	extension	NOUN
ejpam-6480	10	25	such	such	ADJ
ejpam-6480	10	26	as	as	ADP
ejpam-6480	10	27	rényi	rényi	NOUN
ejpam-6480	10	28	and	and	CCONJ
ejpam-6480	10	29	tsallis	tsalli	NOUN
ejpam-6480	10	30	entropies	entropy	NOUN
ejpam-6480	10	31	.	.	PUNCT
ejpam-6480	11	1	∗corresponding	∗corresponde	VERB
ejpam-6480	11	2	author	author	NOUN
ejpam-6480	11	3	.	.	PUNCT
ejpam-6480	12	1	doi	doi	NOUN
ejpam-6480	12	2	:	:	PUNCT
ejpam-6480	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6480	https://doi.org/10.29020/nybg.ejpam.v18i4.6480	PROPN
ejpam-6480	12	4	email	email	NOUN
ejpam-6480	12	5	addresses	address	NOUN
ejpam-6480	12	6	:	:	PUNCT
ejpam-6480	12	7	javid.dar@sitpune.edu.in	javid.dar@sitpune.edu.in	NOUN
ejpam-6480	12	8	(	(	PUNCT
ejpam-6480	12	9	j.	j.	PROPN
ejpam-6480	12	10	g.	g.	PROPN
ejpam-6480	12	11	dar	dar	PROPN
ejpam-6480	12	12	)	)	PUNCT
ejpam-6480	12	13	,	,	PUNCT
ejpam-6480	12	14	salshekh@ut.edu.sa	salshekh@ut.edu.sa	PROPN
ejpam-6480	12	15	(	(	PUNCT
ejpam-6480	12	16	s.	s.	PROPN
ejpam-6480	12	17	m.	m.	PROPN
ejpam-6480	12	18	a.	a.	PROPN
ejpam-6480	12	19	alsheikh	alsheikh	PROPN
ejpam-6480	12	20	)	)	PUNCT
ejpam-6480	12	21	,	,	PUNCT
ejpam-6480	12	22	prakash.j@srmap.edu.in	prakash.j@srmap.edu.in	PROPN
ejpam-6480	12	23	(	(	PUNCT
ejpam-6480	12	24	p.	p.	PROPN
ejpam-6480	12	25	jadhav	jadhav	PROPN
ejpam-6480	12	26	)	)	PUNCT
ejpam-6480	12	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6480	13	1	1	1	NUM
ejpam-6480	13	2	copyright	copyright	NOUN
ejpam-6480	13	3	:	:	PUNCT
ejpam-6480	13	4	©	©	PROPN
ejpam-6480	13	5	2025	2025	NUM
ejpam-6480	13	6	the	the	DET
ejpam-6480	13	7	author(s	author(s	NOUN
ejpam-6480	13	8	)	)	PUNCT
ejpam-6480	13	9	.	.	PUNCT
ejpam-6480	14	1	(	(	PUNCT
ejpam-6480	14	2	cc	cc	NOUN
ejpam-6480	14	3	by	by	ADP
ejpam-6480	14	4	-	-	PUNCT
ejpam-6480	14	5	nc	nc	PROPN
ejpam-6480	14	6	4.0	4.0	NUM
ejpam-6480	14	7	)	)	PUNCT
ejpam-6480	14	8	j.	j.	PROPN
ejpam-6480	14	9	g.	g.	PROPN
ejpam-6480	14	10	dar	dar	PROPN
ejpam-6480	14	11	,	,	PUNCT
ejpam-6480	14	12	s.	s.	PROPN
ejpam-6480	14	13	m.	m.	PROPN
ejpam-6480	14	14	a.	a.	PROPN
ejpam-6480	14	15	alsheikh	alsheikh	PROPN
ejpam-6480	14	16	,	,	PUNCT
ejpam-6480	14	17	p.	p.	PROPN
ejpam-6480	14	18	jadhav	jadhav	PROPN
ejpam-6480	14	19	/	/	SYM
ejpam-6480	14	20	eur	eur	PROPN
ejpam-6480	14	21	.	.	PUNCT
ejpam-6480	15	1	j.	j.	PROPN
ejpam-6480	15	2	pure	pure	PROPN
ejpam-6480	15	3	appl	appl	PROPN
ejpam-6480	15	4	.	.	PROPN
ejpam-6480	15	5	math	math	PROPN
ejpam-6480	15	6	,	,	PUNCT
ejpam-6480	15	7	18	18	NUM
ejpam-6480	15	8	(	(	PUNCT
ejpam-6480	15	9	4	4	NUM
ejpam-6480	15	10	)	)	PUNCT
ejpam-6480	15	11	(	(	PUNCT
ejpam-6480	15	12	2025	2025	NUM
ejpam-6480	15	13	)	)	PUNCT
ejpam-6480	15	14	,	,	PUNCT
ejpam-6480	15	15	6480	6480	NUM
ejpam-6480	15	16	2	2	NUM
ejpam-6480	15	17	of	of	ADP
ejpam-6480	15	18	14	14	NUM
ejpam-6480	15	19	interval	interval	NOUN
ejpam-6480	15	20	entropy	entropy	NOUN
ejpam-6480	15	21	is	be	AUX
ejpam-6480	15	22	still	still	ADV
ejpam-6480	15	23	a	a	DET
ejpam-6480	15	24	relatively	relatively	ADV
ejpam-6480	15	25	new	new	ADJ
ejpam-6480	15	26	and	and	CCONJ
ejpam-6480	15	27	developing	develop	VERB
ejpam-6480	15	28	measure	measure	NOUN
ejpam-6480	15	29	in	in	ADP
ejpam-6480	15	30	information	information	NOUN
ejpam-6480	15	31	theory	theory	NOUN
ejpam-6480	15	32	and	and	CCONJ
ejpam-6480	15	33	reliability	reliability	NOUN
ejpam-6480	15	34	modeling	modeling	NOUN
ejpam-6480	15	35	,	,	PUNCT
ejpam-6480	15	36	so	so	CCONJ
ejpam-6480	15	37	the	the	DET
ejpam-6480	15	38	research	research	NOUN
ejpam-6480	15	39	gaps	gap	NOUN
ejpam-6480	15	40	mainly	mainly	ADV
ejpam-6480	15	41	lie	lie	VERB
ejpam-6480	15	42	in	in	ADP
ejpam-6480	15	43	its	its	PRON
ejpam-6480	15	44	generalizations	generalization	NOUN
ejpam-6480	15	45	,	,	PUNCT
ejpam-6480	15	46	applications	application	NOUN
ejpam-6480	15	47	,	,	PUNCT
ejpam-6480	15	48	and	and	CCONJ
ejpam-6480	15	49	connections	connection	NOUN
ejpam-6480	15	50	to	to	ADP
ejpam-6480	15	51	other	other	ADJ
ejpam-6480	15	52	measures	measure	NOUN
ejpam-6480	15	53	.	.	PUNCT
ejpam-6480	16	1	the	the	DET
ejpam-6480	16	2	associated	associated	ADJ
ejpam-6480	16	3	inequalities	inequality	NOUN
ejpam-6480	16	4	,	,	PUNCT
ejpam-6480	16	5	bounds	bound	NOUN
ejpam-6480	16	6	,	,	PUNCT
ejpam-6480	16	7	and	and	CCONJ
ejpam-6480	16	8	related	related	ADJ
ejpam-6480	16	9	properties	property	NOUN
ejpam-6480	16	10	have	have	AUX
ejpam-6480	16	11	not	not	PART
ejpam-6480	16	12	been	be	AUX
ejpam-6480	16	13	systematically	systematically	ADV
ejpam-6480	16	14	developed	develop	VERB
ejpam-6480	16	15	or	or	CCONJ
ejpam-6480	16	16	studied	study	VERB
ejpam-6480	16	17	in	in	ADP
ejpam-6480	16	18	depth	depth	NOUN
ejpam-6480	16	19	.	.	PUNCT
ejpam-6480	17	1	in	in	ADP
ejpam-6480	17	2	particular	particular	ADJ
ejpam-6480	17	3	,	,	PUNCT
ejpam-6480	17	4	there	there	PRON
ejpam-6480	17	5	is	be	VERB
ejpam-6480	17	6	a	a	DET
ejpam-6480	17	7	lack	lack	NOUN
ejpam-6480	17	8	of	of	ADP
ejpam-6480	17	9	results	result	NOUN
ejpam-6480	17	10	connecting	connect	VERB
ejpam-6480	17	11	interval	interval	NOUN
ejpam-6480	17	12	entropy	entropy	NOUN
ejpam-6480	17	13	to	to	ADP
ejpam-6480	17	14	fundamental	fundamental	ADJ
ejpam-6480	17	15	mathematical	mathematical	ADJ
ejpam-6480	17	16	inequalities	inequality	NOUN
ejpam-6480	17	17	and	and	CCONJ
ejpam-6480	17	18	their	their	PRON
ejpam-6480	17	19	implications	implication	NOUN
ejpam-6480	17	20	for	for	ADP
ejpam-6480	17	21	statistical	statistical	ADJ
ejpam-6480	17	22	or	or	CCONJ
ejpam-6480	17	23	applied	apply	VERB
ejpam-6480	17	24	problems	problem	NOUN
ejpam-6480	17	25	.	.	PUNCT
ejpam-6480	18	1	some	some	DET
ejpam-6480	18	2	definitions	definition	NOUN
ejpam-6480	18	3	:	:	PUNCT
ejpam-6480	18	4	i	i	NOUN
ejpam-6480	18	5	)	)	PUNCT
ejpam-6480	18	6	probability	probability	NOUN
ejpam-6480	18	7	density	density	NOUN
ejpam-6480	18	8	function	function	NOUN
ejpam-6480	18	9	:	:	PUNCT
ejpam-6480	18	10	a	a	DET
ejpam-6480	18	11	probability	probability	NOUN
ejpam-6480	18	12	density	density	NOUN
ejpam-6480	18	13	function	function	NOUN
ejpam-6480	18	14	(	(	PUNCT
ejpam-6480	18	15	pdf	pdf	NOUN
ejpam-6480	18	16	)	)	PUNCT
ejpam-6480	18	17	is	be	AUX
ejpam-6480	18	18	a	a	DET
ejpam-6480	18	19	function	function	NOUN
ejpam-6480	18	20	that	that	PRON
ejpam-6480	18	21	describes	describe	VERB
ejpam-6480	18	22	the	the	DET
ejpam-6480	18	23	likelihood	likelihood	NOUN
ejpam-6480	18	24	of	of	ADP
ejpam-6480	18	25	a	a	DET
ejpam-6480	18	26	continuous	continuous	ADJ
ejpam-6480	18	27	random	random	ADJ
ejpam-6480	18	28	variable	variable	NOUN
ejpam-6480	18	29	taking	take	VERB
ejpam-6480	18	30	on	on	ADP
ejpam-6480	18	31	a	a	DET
ejpam-6480	18	32	particular	particular	ADJ
ejpam-6480	18	33	value	value	NOUN
ejpam-6480	18	34	.	.	PUNCT
ejpam-6480	19	1	for	for	ADP
ejpam-6480	19	2	a	a	DET
ejpam-6480	19	3	continuous	continuous	ADJ
ejpam-6480	19	4	random	random	ADJ
ejpam-6480	19	5	variable	variable	NOUN
ejpam-6480	19	6	x	x	NOUN
ejpam-6480	19	7	,	,	PUNCT
ejpam-6480	19	8	the	the	DET
ejpam-6480	19	9	pdf	pdf	NOUN
ejpam-6480	19	10	is	be	AUX
ejpam-6480	19	11	denoted	denote	VERB
ejpam-6480	19	12	by	by	ADP
ejpam-6480	19	13	f(x	f(x	PROPN
ejpam-6480	19	14	)	)	PUNCT
ejpam-6480	19	15	and	and	CCONJ
ejpam-6480	19	16	has	have	VERB
ejpam-6480	19	17	the	the	DET
ejpam-6480	19	18	following	follow	VERB
ejpam-6480	19	19	properties	property	NOUN
ejpam-6480	19	20	:	:	PUNCT
ejpam-6480	19	21	a	a	X
ejpam-6480	19	22	)	)	PUNCT
ejpam-6480	19	23	f(x	f(x	PROPN
ejpam-6480	19	24	)	)	PUNCT
ejpam-6480	19	25	≥	≥	NOUN
ejpam-6480	19	26	0	0	NUM
ejpam-6480	19	27	b	b	X
ejpam-6480	19	28	)	)	PUNCT
ejpam-6480	19	29	p	p	NOUN
ejpam-6480	19	30	(	(	PUNCT
ejpam-6480	19	31	a	a	DET
ejpam-6480	19	32	≤	≤	NUM
ejpam-6480	19	33	x	x	PUNCT
ejpam-6480	19	34	≤	≤	NUM
ejpam-6480	19	35	b	b	X
ejpam-6480	19	36	)	)	PUNCT
ejpam-6480	20	1	=	=	SYM
ejpam-6480	20	2	∫	∫	PROPN
ejpam-6480	21	1	b	b	PROPN
ejpam-6480	21	2	a	a	DET
ejpam-6480	21	3	f(x)dx	f(x)dx	NUM
ejpam-6480	21	4	c	c	NOUN
ejpam-6480	21	5	)	)	PUNCT
ejpam-6480	21	6	∫∞	∫∞	NOUN
ejpam-6480	21	7	−∞	−∞	ADP
ejpam-6480	21	8	f(x)dx	f(x)dx	VERB
ejpam-6480	21	9	=	=	SYM
ejpam-6480	21	10	1	1	NUM
ejpam-6480	21	11	ii	ii	NOUN
ejpam-6480	21	12	)	)	PUNCT
ejpam-6480	21	13	survival	survival	NOUN
ejpam-6480	21	14	function	function	NOUN
ejpam-6480	21	15	:	:	PUNCT
ejpam-6480	21	16	for	for	ADP
ejpam-6480	21	17	a	a	DET
ejpam-6480	21	18	non	non	ADJ
ejpam-6480	21	19	-	-	ADJ
ejpam-6480	21	20	negative	negative	ADJ
ejpam-6480	21	21	random	random	ADJ
ejpam-6480	21	22	variable	variable	NOUN
ejpam-6480	21	23	x	x	X
ejpam-6480	21	24	(	(	PUNCT
ejpam-6480	21	25	representing	represent	VERB
ejpam-6480	21	26	lifetime	lifetime	NOUN
ejpam-6480	21	27	or	or	CCONJ
ejpam-6480	21	28	timeto	timeto	NOUN
ejpam-6480	21	29	-	-	PUNCT
ejpam-6480	21	30	event	event	NOUN
ejpam-6480	21	31	)	)	PUNCT
ejpam-6480	21	32	,	,	PUNCT
ejpam-6480	21	33	the	the	DET
ejpam-6480	21	34	survival	survival	NOUN
ejpam-6480	21	35	function	function	NOUN
ejpam-6480	21	36	is	be	AUX
ejpam-6480	21	37	defined	define	VERB
ejpam-6480	21	38	as	as	ADP
ejpam-6480	21	39	rx(x	rx(x	ADJ
ejpam-6480	21	40	)	)	PUNCT
ejpam-6480	21	41	=	=	PUNCT
ejpam-6480	21	42	p(x	p(x	VERB
ejpam-6480	21	43	>	>	X
ejpam-6480	21	44	x	x	PROPN
ejpam-6480	21	45	)	)	PUNCT
ejpam-6480	21	46	iii	iii	NOUN
ejpam-6480	21	47	)	)	PUNCT
ejpam-6480	21	48	hazard	hazard	NOUN
ejpam-6480	21	49	rate	rate	NOUN
ejpam-6480	21	50	function	function	NOUN
ejpam-6480	21	51	:	:	PUNCT
ejpam-6480	21	52	for	for	ADP
ejpam-6480	21	53	a	a	DET
ejpam-6480	21	54	non	non	ADJ
ejpam-6480	21	55	-	-	ADJ
ejpam-6480	21	56	negative	negative	ADJ
ejpam-6480	21	57	lifetime	lifetime	NOUN
ejpam-6480	21	58	random	random	ADJ
ejpam-6480	21	59	variable	variable	NOUN
ejpam-6480	21	60	x	x	NOUN
ejpam-6480	21	61	,	,	PUNCT
ejpam-6480	21	62	the	the	DET
ejpam-6480	21	63	hazard	hazard	NOUN
ejpam-6480	21	64	rate	rate	NOUN
ejpam-6480	21	65	function	function	PROPN
ejpam-6480	21	66	h(x	h(x	PROPN
ejpam-6480	21	67	)	)	PUNCT
ejpam-6480	21	68	is	be	AUX
ejpam-6480	21	69	defined	define	VERB
ejpam-6480	21	70	as	as	ADP
ejpam-6480	21	71	h(x	h(x	PROPN
ejpam-6480	21	72	)	)	PUNCT
ejpam-6480	22	1	=	=	PROPN
ejpam-6480	22	2	lim	lim	PROPN
ejpam-6480	22	3	∆x→0	∆x→0	PROPN
ejpam-6480	22	4	p	p	X
ejpam-6480	22	5	(	(	PUNCT
ejpam-6480	22	6	x	x	X
ejpam-6480	22	7	<	<	X
ejpam-6480	22	8	x	x	X
ejpam-6480	22	9	<	<	X
ejpam-6480	22	10	x+∆x	x+∆x	PROPN
ejpam-6480	22	11	/	/	SYM
ejpam-6480	22	12	x	x	SYM
ejpam-6480	22	13	≥	≥	NUM
ejpam-6480	22	14	x	x	SYM
ejpam-6480	22	15	)	)	PUNCT
ejpam-6480	22	16	∆x	∆x	PROPN
ejpam-6480	22	17	,	,	PUNCT
ejpam-6480	22	18	x	x	X
ejpam-6480	22	19	≥	≥	NOUN
ejpam-6480	22	20	0	0	NUM
ejpam-6480	22	21	.	.	NUM
ejpam-6480	23	1	iv	iv	X
ejpam-6480	23	2	)	)	PUNCT
ejpam-6480	23	3	mean	mean	VERB
ejpam-6480	23	4	residual	residual	ADJ
ejpam-6480	23	5	function	function	NOUN
ejpam-6480	23	6	:	:	PUNCT
ejpam-6480	23	7	it	it	PRON
ejpam-6480	23	8	represents	represent	VERB
ejpam-6480	23	9	the	the	DET
ejpam-6480	23	10	expected	expect	VERB
ejpam-6480	23	11	remaining	remain	VERB
ejpam-6480	23	12	lifetime	lifetime	NOUN
ejpam-6480	23	13	of	of	ADP
ejpam-6480	23	14	an	an	DET
ejpam-6480	23	15	item	item	NOUN
ejpam-6480	23	16	,	,	PUNCT
ejpam-6480	23	17	given	give	VERB
ejpam-6480	23	18	that	that	SCONJ
ejpam-6480	23	19	it	it	PRON
ejpam-6480	23	20	has	have	AUX
ejpam-6480	23	21	already	already	ADV
ejpam-6480	23	22	survived	survive	VERB
ejpam-6480	23	23	up	up	ADP
ejpam-6480	23	24	to	to	ADP
ejpam-6480	23	25	time	time	NOUN
ejpam-6480	23	26	t	t	PROPN
ejpam-6480	23	27	and	and	CCONJ
ejpam-6480	23	28	is	be	AUX
ejpam-6480	23	29	given	give	VERB
ejpam-6480	23	30	by	by	ADP
ejpam-6480	23	31	r(x	r(x	PROPN
ejpam-6480	23	32	)	)	PUNCT
ejpam-6480	23	33	=	=	SYM
ejpam-6480	23	34	1	1	NUM
ejpam-6480	23	35	r(t	r(t	NOUN
ejpam-6480	23	36	)	)	PUNCT
ejpam-6480	23	37	∫	∫	PROPN
ejpam-6480	24	1	∞	∞	PROPN
ejpam-6480	24	2	t	t	PROPN
ejpam-6480	24	3	r(x)dx	r(x)dx	AUX
ejpam-6480	24	4	also	also	ADV
ejpam-6480	24	5	following	follow	VERB
ejpam-6480	24	6	relation	relation	NOUN
ejpam-6480	24	7	holds	hold	VERB
ejpam-6480	24	8	:	:	PUNCT
ejpam-6480	24	9	h(x	h(x	PROPN
ejpam-6480	24	10	)	)	PUNCT
ejpam-6480	25	1	=	=	SYM
ejpam-6480	25	2	f(x	f(x	PROPN
ejpam-6480	25	3	)	)	PUNCT
ejpam-6480	25	4	r(x	r(x	PROPN
ejpam-6480	25	5	)	)	PUNCT
ejpam-6480	25	6	let	let	VERB
ejpam-6480	25	7	x	x	PRON
ejpam-6480	25	8	be	be	AUX
ejpam-6480	25	9	a	a	DET
ejpam-6480	25	10	nonnegative	nonnegative	ADJ
ejpam-6480	25	11	random	random	ADJ
ejpam-6480	25	12	variable	variable	NOUN
ejpam-6480	25	13	denoting	denote	VERB
ejpam-6480	25	14	the	the	DET
ejpam-6480	25	15	life	life	NOUN
ejpam-6480	25	16	time	time	NOUN
ejpam-6480	25	17	of	of	ADP
ejpam-6480	25	18	a	a	DET
ejpam-6480	25	19	system	system	NOUN
ejpam-6480	25	20	,	,	PUNCT
ejpam-6480	25	21	a	a	DET
ejpam-6480	25	22	component	component	NOUN
ejpam-6480	25	23	or	or	CCONJ
ejpam-6480	25	24	living	living	NOUN
ejpam-6480	25	25	organism	organism	NOUN
ejpam-6480	25	26	with	with	ADP
ejpam-6480	25	27	probability	probability	NOUN
ejpam-6480	25	28	density	density	NOUN
ejpam-6480	25	29	function	function	NOUN
ejpam-6480	25	30	f	f	NOUN
ejpam-6480	25	31	,	,	PUNCT
ejpam-6480	25	32	distribution	distribution	NOUN
ejpam-6480	25	33	function	function	NOUN
ejpam-6480	25	34	f	f	PROPN
ejpam-6480	25	35	and	and	CCONJ
ejpam-6480	25	36	reliability	reliability	NOUN
ejpam-6480	25	37	function	function	NOUN
ejpam-6480	25	38	r.	r.	PROPN
ejpam-6480	25	39	it	it	PRON
ejpam-6480	25	40	is	be	AUX
ejpam-6480	25	41	assumed	assume	VERB
ejpam-6480	25	42	that	that	SCONJ
ejpam-6480	25	43	the	the	DET
ejpam-6480	25	44	component	component	NOUN
ejpam-6480	25	45	is	be	AUX
ejpam-6480	25	46	functioning	function	VERB
ejpam-6480	25	47	at	at	ADP
ejpam-6480	25	48	t	t	PROPN
ejpam-6480	25	49	=	=	SYM
ejpam-6480	25	50	0	0	PUNCT
ejpam-6480	25	51	and	and	CCONJ
ejpam-6480	25	52	it	it	PRON
ejpam-6480	25	53	will	will	AUX
ejpam-6480	25	54	fail	fail	VERB
ejpam-6480	25	55	to	to	ADP
ejpam-6480	25	56	some	some	DET
ejpam-6480	25	57	t	t	PROPN
ejpam-6480	25	58	>	>	X
ejpam-6480	25	59	0	0	NUM
ejpam-6480	25	60	,	,	PUNCT
ejpam-6480	25	61	so	so	SCONJ
ejpam-6480	25	62	that	that	SCONJ
ejpam-6480	25	63	r(0	r(0	PROPN
ejpam-6480	25	64	)	)	PUNCT
ejpam-6480	25	65	=	=	PUNCT
ejpam-6480	26	1	1	1	X
ejpam-6480	26	2	.	.	PUNCT
ejpam-6480	27	1	the	the	DET
ejpam-6480	27	2	functional	functional	ADJ
ejpam-6480	27	3	relationship	relationship	NOUN
ejpam-6480	27	4	between	between	ADP
ejpam-6480	27	5	the	the	DET
ejpam-6480	27	6	hazard	hazard	NOUN
ejpam-6480	27	7	rate	rate	NOUN
ejpam-6480	27	8	function	function	NOUN
ejpam-6480	27	9	and	and	CCONJ
ejpam-6480	27	10	mean	mean	VERB
ejpam-6480	27	11	residual	residual	ADJ
ejpam-6480	27	12	life	life	NOUN
ejpam-6480	27	13	function	function	NOUN
ejpam-6480	27	14	is	be	AUX
ejpam-6480	27	15	given	give	VERB
ejpam-6480	27	16	by	by	ADP
ejpam-6480	27	17	h(t	h(t	PROPN
ejpam-6480	27	18	)	)	PUNCT
ejpam-6480	27	19	=	=	PUNCT
ejpam-6480	28	1	r′(t	r′(t	X
ejpam-6480	28	2	)	)	PUNCT
ejpam-6480	28	3	+	+	CCONJ
ejpam-6480	28	4	1	1	NUM
ejpam-6480	28	5	r(t	r(t	NOUN
ejpam-6480	28	6	)	)	PUNCT
ejpam-6480	28	7	(	(	PUNCT
ejpam-6480	28	8	1.1	1.1	NUM
ejpam-6480	28	9	)	)	PUNCT
ejpam-6480	28	10	the	the	DET
ejpam-6480	28	11	average	average	ADJ
ejpam-6480	28	12	amount	amount	NOUN
ejpam-6480	28	13	of	of	ADP
ejpam-6480	28	14	uncertainty	uncertainty	NOUN
ejpam-6480	28	15	associated	associate	VERB
ejpam-6480	28	16	with	with	ADP
ejpam-6480	28	17	the	the	DET
ejpam-6480	28	18	random	random	ADJ
ejpam-6480	28	19	variable	variable	NOUN
ejpam-6480	28	20	x	x	PUNCT
ejpam-6480	28	21	as	as	SCONJ
ejpam-6480	28	22	given	give	VERB
ejpam-6480	28	23	by	by	ADP
ejpam-6480	28	24	shannon	shannon	PROPN
ejpam-6480	28	25	entropy	entropy	PROPN
ejpam-6480	28	26	,	,	PUNCT
ejpam-6480	28	27	is	be	AUX
ejpam-6480	28	28	h(x	h(x	PROPN
ejpam-6480	28	29	)	)	PUNCT
ejpam-6480	29	1	=	=	PUNCT
ejpam-6480	30	1	−	−	PROPN
ejpam-6480	30	2	∫	∫	PROPN
ejpam-6480	30	3	∞	∞	PROPN
ejpam-6480	30	4	0	0	NUM
ejpam-6480	31	1	f(x	f(x	PROPN
ejpam-6480	31	2	)	)	PUNCT
ejpam-6480	31	3	log	log	NOUN
ejpam-6480	31	4	f(x)dx	f(x)dx	NUM
ejpam-6480	31	5	(	(	PUNCT
ejpam-6480	31	6	1.2	1.2	NUM
ejpam-6480	31	7	)	)	PUNCT
ejpam-6480	31	8	j.	j.	PROPN
ejpam-6480	31	9	g.	g.	PROPN
ejpam-6480	31	10	dar	dar	PROPN
ejpam-6480	31	11	,	,	PUNCT
ejpam-6480	31	12	s.	s.	PROPN
ejpam-6480	31	13	m.	m.	PROPN
ejpam-6480	31	14	a.	a.	PROPN
ejpam-6480	31	15	alsheikh	alsheikh	PROPN
ejpam-6480	31	16	,	,	PUNCT
ejpam-6480	31	17	p.	p.	PROPN
ejpam-6480	31	18	jadhav	jadhav	PROPN
ejpam-6480	31	19	/	/	SYM
ejpam-6480	31	20	eur	eur	PROPN
ejpam-6480	31	21	.	.	PUNCT
ejpam-6480	32	1	j.	j.	PROPN
ejpam-6480	32	2	pure	pure	PROPN
ejpam-6480	32	3	appl	appl	PROPN
ejpam-6480	32	4	.	.	PROPN
ejpam-6480	32	5	math	math	PROPN
ejpam-6480	32	6	,	,	PUNCT
ejpam-6480	32	7	18	18	NUM
ejpam-6480	32	8	(	(	PUNCT
ejpam-6480	32	9	4	4	NUM
ejpam-6480	32	10	)	)	PUNCT
ejpam-6480	32	11	(	(	PUNCT
ejpam-6480	32	12	2025	2025	NUM
ejpam-6480	32	13	)	)	PUNCT
ejpam-6480	32	14	,	,	PUNCT
ejpam-6480	32	15	6480	6480	NUM
ejpam-6480	32	16	3	3	NUM
ejpam-6480	32	17	of	of	ADP
ejpam-6480	32	18	14	14	NUM
ejpam-6480	32	19	mathaihaubold	mathaihaubold	ADJ
ejpam-6480	33	1	[	[	X
ejpam-6480	33	2	3	3	NUM
ejpam-6480	33	3	]	]	PUNCT
ejpam-6480	33	4	introduced	introduce	VERB
ejpam-6480	33	5	the	the	DET
ejpam-6480	33	6	generalized	generalized	ADJ
ejpam-6480	33	7	information	information	NOUN
ejpam-6480	33	8	measure	measure	NOUN
ejpam-6480	33	9	kα(x	kα(x	PROPN
ejpam-6480	33	10	)	)	PUNCT
ejpam-6480	34	1	=	=	SYM
ejpam-6480	34	2	1	1	NUM
ejpam-6480	34	3	(	(	PUNCT
ejpam-6480	34	4	α−	α−	ADP
ejpam-6480	34	5	1	1	NUM
ejpam-6480	34	6	)	)	PUNCT
ejpam-6480	34	7	∫	∫	PROPN
ejpam-6480	35	1	∞	∞	PROPN
ejpam-6480	35	2	0	0	NUM
ejpam-6480	36	1	(	(	PUNCT
ejpam-6480	36	2	f(2−α)(x)−	f(2−α)(x)−	PROPN
ejpam-6480	36	3	1	1	NUM
ejpam-6480	36	4	)	)	PUNCT
ejpam-6480	36	5	dx	dx	PROPN
ejpam-6480	36	6	,	,	PUNCT
ejpam-6480	36	7	α	α	PROPN
ejpam-6480	36	8	6=	6=	ADP
ejpam-6480	36	9	1	1	NUM
ejpam-6480	36	10	,	,	PUNCT
ejpam-6480	36	11	0	0	NUM
ejpam-6480	36	12	<	<	X
ejpam-6480	36	13	α	α	X
ejpam-6480	36	14	<	<	X
ejpam-6480	36	15	2	2	NUM
ejpam-6480	36	16	(	(	PUNCT
ejpam-6480	36	17	1.3	1.3	NUM
ejpam-6480	36	18	)	)	PUNCT
ejpam-6480	36	19	ebrahimi	ebrahimi	NOUN
ejpam-6480	37	1	[	[	X
ejpam-6480	37	2	10	10	NUM
ejpam-6480	37	3	]	]	PUNCT
ejpam-6480	37	4	argues	argue	VERB
ejpam-6480	37	5	that	that	SCONJ
ejpam-6480	37	6	(	(	PUNCT
ejpam-6480	37	7	1.1	1.1	NUM
ejpam-6480	37	8	)	)	PUNCT
ejpam-6480	37	9	is	be	AUX
ejpam-6480	37	10	no	no	ADV
ejpam-6480	37	11	longer	long	ADV
ejpam-6480	37	12	effective	effective	ADJ
ejpam-6480	37	13	in	in	ADP
ejpam-6480	37	14	evaluating	evaluate	VERB
ejpam-6480	37	15	the	the	DET
ejpam-6480	37	16	uncertainty	uncertainty	NOUN
ejpam-6480	37	17	about	about	ADP
ejpam-6480	37	18	the	the	DET
ejpam-6480	37	19	remaining	remain	VERB
ejpam-6480	37	20	life	life	NOUN
ejpam-6480	37	21	time	time	NOUN
ejpam-6480	37	22	of	of	ADP
ejpam-6480	37	23	the	the	DET
ejpam-6480	37	24	unit	unit	NOUN
ejpam-6480	37	25	if	if	SCONJ
ejpam-6480	37	26	a	a	DET
ejpam-6480	37	27	unit	unit	NOUN
ejpam-6480	37	28	is	be	AUX
ejpam-6480	37	29	known	know	VERB
ejpam-6480	37	30	to	to	PART
ejpam-6480	37	31	have	have	AUX
ejpam-6480	37	32	survived	survive	VERB
ejpam-6480	37	33	up	up	ADP
ejpam-6480	37	34	to	to	ADP
ejpam-6480	37	35	an	an	DET
ejpam-6480	37	36	age	age	NOUN
ejpam-6480	37	37	t.	t.	PROPN
ejpam-6480	37	38	a	a	DET
ejpam-6480	37	39	unit	unit	NOUN
ejpam-6480	37	40	with	with	ADP
ejpam-6480	37	41	high	high	ADJ
ejpam-6480	37	42	uncertainty	uncertainty	NOUN
ejpam-6480	37	43	is	be	AUX
ejpam-6480	37	44	less	less	ADV
ejpam-6480	37	45	reliable	reliable	ADJ
ejpam-6480	37	46	than	than	ADP
ejpam-6480	37	47	one	one	NUM
ejpam-6480	37	48	with	with	ADP
ejpam-6480	37	49	low	low	ADJ
ejpam-6480	37	50	uncertainty	uncertainty	NOUN
ejpam-6480	37	51	.	.	PUNCT
ejpam-6480	38	1	in	in	ADP
ejpam-6480	38	2	order	order	NOUN
ejpam-6480	38	3	to	to	PART
ejpam-6480	38	4	account	account	VERB
ejpam-6480	38	5	for	for	ADP
ejpam-6480	38	6	this	this	PRON
ejpam-6480	38	7	,	,	PUNCT
ejpam-6480	38	8	he	he	PRON
ejpam-6480	38	9	developed	develop	VERB
ejpam-6480	38	10	a	a	DET
ejpam-6480	38	11	measure	measure	NOUN
ejpam-6480	38	12	of	of	ADP
ejpam-6480	38	13	uncertainty	uncertainty	NOUN
ejpam-6480	38	14	for	for	ADP
ejpam-6480	38	15	the	the	DET
ejpam-6480	38	16	residual	residual	ADJ
ejpam-6480	38	17	life	life	NOUN
ejpam-6480	38	18	time	time	NOUN
ejpam-6480	38	19	distribution	distribution	NOUN
ejpam-6480	38	20	known	know	VERB
ejpam-6480	38	21	as	as	ADP
ejpam-6480	38	22	residual	residual	ADJ
ejpam-6480	38	23	entropy	entropy	NOUN
ejpam-6480	38	24	.	.	PUNCT
ejpam-6480	39	1	the	the	DET
ejpam-6480	39	2	residual	residual	ADJ
ejpam-6480	39	3	entropy	entropy	NOUN
ejpam-6480	39	4	of	of	ADP
ejpam-6480	39	5	a	a	DET
ejpam-6480	39	6	continuous	continuous	ADJ
ejpam-6480	39	7	random	random	ADJ
ejpam-6480	39	8	variable	variable	NOUN
ejpam-6480	39	9	x	x	PUNCT
ejpam-6480	39	10	is	be	AUX
ejpam-6480	39	11	defined	define	VERB
ejpam-6480	39	12	as	as	ADP
ejpam-6480	39	13	k(x	k(x	PROPN
ejpam-6480	39	14	;	;	PUNCT
ejpam-6480	39	15	t	t	X
ejpam-6480	39	16	)	)	PUNCT
ejpam-6480	39	17	=	=	PUNCT
ejpam-6480	40	1	−	−	PROPN
ejpam-6480	40	2	∫	∫	PROPN
ejpam-6480	40	3	∞	∞	PROPN
ejpam-6480	40	4	t	t	PROPN
ejpam-6480	40	5	f(x	f(x	PROPN
ejpam-6480	40	6	)	)	PUNCT
ejpam-6480	40	7	r(t	r(t	NOUN
ejpam-6480	40	8	)	)	PUNCT
ejpam-6480	40	9	log	log	VERB
ejpam-6480	40	10	f(x	f(x	PROPN
ejpam-6480	40	11	)	)	PUNCT
ejpam-6480	40	12	r(t	r(t	NOUN
ejpam-6480	40	13	)	)	PUNCT
ejpam-6480	40	14	dx	dx	PROPN
ejpam-6480	40	15	(	(	PUNCT
ejpam-6480	40	16	1.4	1.4	NUM
ejpam-6480	40	17	)	)	PUNCT
ejpam-6480	40	18	corollary	corollary	NOUN
ejpam-6480	40	19	:	:	PUNCT
ejpam-6480	40	20	for	for	ADP
ejpam-6480	40	21	t	t	NOUN
ejpam-6480	40	22	=	=	SYM
ejpam-6480	40	23	0	0	NUM
ejpam-6480	40	24	,	,	PUNCT
ejpam-6480	40	25	(	(	PUNCT
ejpam-6480	40	26	1.4	1.4	NUM
ejpam-6480	40	27	)	)	PUNCT
ejpam-6480	40	28	reduces	reduce	VERB
ejpam-6480	40	29	to	to	ADP
ejpam-6480	40	30	(	(	PUNCT
ejpam-6480	40	31	1.1	1.1	NUM
ejpam-6480	40	32	)	)	PUNCT
ejpam-6480	40	33	.	.	PUNCT
ejpam-6480	41	1	ebrahimi	ebrahimi	PROPN
ejpam-6480	42	1	[	[	X
ejpam-6480	42	2	4	4	X
ejpam-6480	42	3	]	]	PUNCT
ejpam-6480	42	4	established	establish	VERB
ejpam-6480	42	5	that	that	SCONJ
ejpam-6480	42	6	a	a	DET
ejpam-6480	42	7	specific	specific	ADJ
ejpam-6480	42	8	dynamic	dynamic	ADJ
ejpam-6480	42	9	measure	measure	NOUN
ejpam-6480	42	10	can	can	AUX
ejpam-6480	42	11	uniquely	uniquely	ADV
ejpam-6480	42	12	determine	determine	VERB
ejpam-6480	42	13	the	the	DET
ejpam-6480	42	14	underlying	underlie	VERB
ejpam-6480	42	15	distribution	distribution	NOUN
ejpam-6480	42	16	function	function	NOUN
ejpam-6480	42	17	.	.	PUNCT
ejpam-6480	43	1	this	this	PRON
ejpam-6480	43	2	implies	imply	VERB
ejpam-6480	43	3	that	that	SCONJ
ejpam-6480	43	4	by	by	ADP
ejpam-6480	43	5	using	use	VERB
ejpam-6480	43	6	this	this	DET
ejpam-6480	43	7	dynamic	dynamic	ADJ
ejpam-6480	43	8	measure	measure	NOUN
ejpam-6480	43	9	,	,	PUNCT
ejpam-6480	43	10	one	one	PRON
ejpam-6480	43	11	can	can	AUX
ejpam-6480	43	12	fully	fully	ADV
ejpam-6480	43	13	understand	understand	VERB
ejpam-6480	43	14	the	the	DET
ejpam-6480	43	15	distribution	distribution	NOUN
ejpam-6480	43	16	of	of	ADP
ejpam-6480	43	17	data	datum	NOUN
ejpam-6480	43	18	or	or	CCONJ
ejpam-6480	43	19	a	a	DET
ejpam-6480	43	20	random	random	ADJ
ejpam-6480	43	21	variable	variable	NOUN
ejpam-6480	43	22	.	.	PUNCT
ejpam-6480	44	1	belzunce	belzunce	ADP
ejpam-6480	44	2	et	et	PROPN
ejpam-6480	44	3	al	al	PROPN
ejpam-6480	44	4	.	.	PUNCT
ejpam-6480	45	1	[	[	X
ejpam-6480	45	2	5	5	NUM
ejpam-6480	45	3	]	]	PUNCT
ejpam-6480	45	4	,	,	PUNCT
ejpam-6480	45	5	asadi	asadi	PROPN
ejpam-6480	45	6	et	et	PROPN
ejpam-6480	45	7	al	al	PROPN
ejpam-6480	45	8	.	.	PUNCT
ejpam-6480	46	1	[	[	X
ejpam-6480	46	2	6	6	NUM
ejpam-6480	46	3	]	]	PUNCT
ejpam-6480	46	4	,	,	PUNCT
ejpam-6480	46	5	dar	dar	PROPN
ejpam-6480	46	6	et	et	PROPN
ejpam-6480	46	7	al	al	PROPN
ejpam-6480	46	8	.	.	PUNCT
ejpam-6480	47	1	[	[	X
ejpam-6480	47	2	7	7	X
ejpam-6480	47	3	]	]	PUNCT
ejpam-6480	47	4	and	and	CCONJ
ejpam-6480	47	5	anant	anant	PROPN
ejpam-6480	47	6	et	et	PROPN
ejpam-6480	47	7	al.[8	al.[8	PROPN
ejpam-6480	47	8	]	]	PUNCT
ejpam-6480	47	9	extended	extend	VERB
ejpam-6480	47	10	ebrahimi	ebrahimi	PROPN
ejpam-6480	47	11	’s	’s	PART
ejpam-6480	47	12	work	work	NOUN
ejpam-6480	47	13	,	,	PUNCT
ejpam-6480	47	14	but	but	CCONJ
ejpam-6480	47	15	in	in	ADP
ejpam-6480	47	16	the	the	DET
ejpam-6480	47	17	context	context	NOUN
ejpam-6480	47	18	of	of	ADP
ejpam-6480	47	19	a	a	DET
ejpam-6480	47	20	generalized	generalized	ADJ
ejpam-6480	47	21	residual	residual	ADJ
ejpam-6480	47	22	entropy	entropy	NOUN
ejpam-6480	47	23	.	.	PUNCT
ejpam-6480	48	1	this	this	DET
ejpam-6480	48	2	type	type	NOUN
ejpam-6480	48	3	of	of	ADP
ejpam-6480	48	4	entropy	entropy	NOUN
ejpam-6480	48	5	is	be	AUX
ejpam-6480	48	6	a	a	DET
ejpam-6480	48	7	variation	variation	NOUN
ejpam-6480	48	8	or	or	CCONJ
ejpam-6480	48	9	extension	extension	NOUN
ejpam-6480	48	10	of	of	ADP
ejpam-6480	48	11	classical	classical	ADJ
ejpam-6480	48	12	entropy	entropy	NOUN
ejpam-6480	48	13	measures	measure	NOUN
ejpam-6480	48	14	and	and	CCONJ
ejpam-6480	48	15	is	be	AUX
ejpam-6480	48	16	useful	useful	ADJ
ejpam-6480	48	17	for	for	ADP
ejpam-6480	48	18	studying	study	VERB
ejpam-6480	48	19	the	the	DET
ejpam-6480	48	20	uncertainty	uncertainty	NOUN
ejpam-6480	48	21	or	or	CCONJ
ejpam-6480	48	22	information	information	NOUN
ejpam-6480	48	23	content	content	NOUN
ejpam-6480	48	24	of	of	ADP
ejpam-6480	48	25	a	a	DET
ejpam-6480	48	26	system	system	NOUN
ejpam-6480	48	27	,	,	PUNCT
ejpam-6480	48	28	particularly	particularly	ADV
ejpam-6480	48	29	in	in	ADP
ejpam-6480	48	30	cases	case	NOUN
ejpam-6480	48	31	where	where	SCONJ
ejpam-6480	48	32	there	there	PRON
ejpam-6480	48	33	may	may	AUX
ejpam-6480	48	34	be	be	AUX
ejpam-6480	48	35	a	a	DET
ejpam-6480	48	36	residual	residual	ADJ
ejpam-6480	48	37	or	or	CCONJ
ejpam-6480	48	38	remaining	remaining	ADJ
ejpam-6480	48	39	uncertainty	uncertainty	NOUN
ejpam-6480	48	40	after	after	ADP
ejpam-6480	48	41	some	some	DET
ejpam-6480	48	42	event	event	NOUN
ejpam-6480	48	43	.	.	PUNCT
ejpam-6480	49	1	nair	nair	PROPN
ejpam-6480	49	2	and	and	CCONJ
ejpam-6480	49	3	rajesh	rajesh	PROPN
ejpam-6480	49	4	[	[	X
ejpam-6480	49	5	9	9	NUM
ejpam-6480	49	6	]	]	PUNCT
ejpam-6480	49	7	and	and	CCONJ
ejpam-6480	49	8	asadi	asadi	NOUN
ejpam-6480	49	9	and	and	CCONJ
ejpam-6480	49	10	ebrahimi	ebrahimi	NOUN
ejpam-6480	50	1	[	[	X
ejpam-6480	50	2	10	10	NUM
ejpam-6480	50	3	]	]	PUNCT
ejpam-6480	50	4	further	far	ADV
ejpam-6480	50	5	explored	explore	VERB
ejpam-6480	50	6	characterizations	characterization	NOUN
ejpam-6480	50	7	of	of	ADP
ejpam-6480	50	8	distributions	distribution	NOUN
ejpam-6480	50	9	using	use	VERB
ejpam-6480	50	10	dynamic	dynamic	ADJ
ejpam-6480	50	11	entropies	entropy	NOUN
ejpam-6480	50	12	.	.	PUNCT
ejpam-6480	51	1	in	in	ADP
ejpam-6480	51	2	particular	particular	ADJ
ejpam-6480	51	3	,	,	PUNCT
ejpam-6480	51	4	they	they	PRON
ejpam-6480	51	5	might	might	AUX
ejpam-6480	51	6	have	have	AUX
ejpam-6480	51	7	looked	look	VERB
ejpam-6480	51	8	at	at	ADP
ejpam-6480	51	9	how	how	SCONJ
ejpam-6480	51	10	various	various	ADJ
ejpam-6480	51	11	dynamic	dynamic	ADJ
ejpam-6480	51	12	entropy	entropy	NOUN
ejpam-6480	51	13	measures	measure	NOUN
ejpam-6480	51	14	can	can	AUX
ejpam-6480	51	15	be	be	AUX
ejpam-6480	51	16	used	use	VERB
ejpam-6480	51	17	to	to	PART
ejpam-6480	51	18	derive	derive	VERB
ejpam-6480	51	19	useful	useful	ADJ
ejpam-6480	51	20	properties	property	NOUN
ejpam-6480	51	21	of	of	ADP
ejpam-6480	51	22	distributions	distribution	NOUN
ejpam-6480	51	23	that	that	PRON
ejpam-6480	51	24	are	be	AUX
ejpam-6480	51	25	relevant	relevant	ADJ
ejpam-6480	51	26	in	in	ADP
ejpam-6480	51	27	engineering	engineering	NOUN
ejpam-6480	51	28	,	,	PUNCT
ejpam-6480	51	29	decision	decision	NOUN
ejpam-6480	51	30	-	-	PUNCT
ejpam-6480	51	31	making	making	NOUN
ejpam-6480	51	32	,	,	PUNCT
ejpam-6480	51	33	or	or	CCONJ
ejpam-6480	51	34	risk	risk	NOUN
ejpam-6480	51	35	assessment	assessment	NOUN
ejpam-6480	51	36	.	.	PUNCT
ejpam-6480	52	1	di	di	PROPN
ejpam-6480	52	2	crescenzo	crescenzo	PROPN
ejpam-6480	52	3	and	and	CCONJ
ejpam-6480	52	4	m.	m.	PROPN
ejpam-6480	52	5	longobardi	longobardi	PROPN
ejpam-6480	53	1	[	[	X
ejpam-6480	53	2	11	11	NUM
ejpam-6480	53	3	,	,	PUNCT
ejpam-6480	53	4	12	12	NUM
ejpam-6480	53	5	]	]	PUNCT
ejpam-6480	53	6	and	and	CCONJ
ejpam-6480	53	7	nanda	nanda	ADV
ejpam-6480	53	8	,	,	PUNCT
ejpam-6480	53	9	and	and	CCONJ
ejpam-6480	53	10	p.	p.	NOUN
ejpam-6480	53	11	paul	paul	PROPN
ejpam-6480	54	1	[	[	X
ejpam-6480	54	2	13	13	NUM
ejpam-6480	54	3	]	]	PUNCT
ejpam-6480	54	4	introduces	introduce	VERB
ejpam-6480	54	5	a	a	DET
ejpam-6480	54	6	new	new	ADJ
ejpam-6480	54	7	measure	measure	NOUN
ejpam-6480	54	8	of	of	ADP
ejpam-6480	54	9	uncertainty	uncertainty	NOUN
ejpam-6480	54	10	related	relate	VERB
ejpam-6480	54	11	to	to	ADP
ejpam-6480	54	12	the	the	DET
ejpam-6480	54	13	past	past	ADJ
ejpam-6480	54	14	lifetime	lifetime	NOUN
ejpam-6480	54	15	of	of	ADP
ejpam-6480	54	16	a	a	DET
ejpam-6480	54	17	system	system	NOUN
ejpam-6480	54	18	or	or	CCONJ
ejpam-6480	54	19	component	component	NOUN
ejpam-6480	54	20	,	,	PUNCT
ejpam-6480	54	21	given	give	VERB
ejpam-6480	54	22	that	that	DET
ejpam-6480	54	23	failure	failure	NOUN
ejpam-6480	54	24	has	have	AUX
ejpam-6480	54	25	already	already	ADV
ejpam-6480	54	26	occurred	occur	VERB
ejpam-6480	54	27	before	before	ADP
ejpam-6480	54	28	a	a	DET
ejpam-6480	54	29	certain	certain	ADJ
ejpam-6480	54	30	time	time	NOUN
ejpam-6480	54	31	.	.	PUNCT
ejpam-6480	55	1	n.	n.	PROPN
ejpam-6480	55	2	ebrahimi	ebrahimi	PROPN
ejpam-6480	55	3	and	and	CCONJ
ejpam-6480	55	4	f.	f.	PROPN
ejpam-6480	55	5	pellerey	pellerey	PROPN
ejpam-6480	56	1	[	[	X
ejpam-6480	56	2	14	14	NUM
ejpam-6480	56	3	]	]	PUNCT
ejpam-6480	56	4	introduce	introduce	VERB
ejpam-6480	56	5	a	a	DET
ejpam-6480	56	6	partial	partial	ADJ
ejpam-6480	56	7	ordering	ordering	NOUN
ejpam-6480	56	8	of	of	ADP
ejpam-6480	56	9	survival	survival	NOUN
ejpam-6480	56	10	functions	function	NOUN
ejpam-6480	56	11	that	that	PRON
ejpam-6480	56	12	reflects	reflect	VERB
ejpam-6480	56	13	the	the	DET
ejpam-6480	56	14	degree	degree	NOUN
ejpam-6480	56	15	of	of	ADP
ejpam-6480	56	16	uncertainty	uncertainty	NOUN
ejpam-6480	56	17	or	or	CCONJ
ejpam-6480	56	18	randomness	randomness	NOUN
ejpam-6480	56	19	associated	associate	VERB
ejpam-6480	56	20	with	with	ADP
ejpam-6480	56	21	the	the	DET
ejpam-6480	56	22	lifetime	lifetime	NOUN
ejpam-6480	56	23	of	of	ADP
ejpam-6480	56	24	systems	system	NOUN
ejpam-6480	56	25	.	.	PUNCT
ejpam-6480	57	1	this	this	DET
ejpam-6480	57	2	ordering	ordering	NOUN
ejpam-6480	57	3	helps	help	VERB
ejpam-6480	57	4	in	in	ADP
ejpam-6480	57	5	characterizing	characterize	VERB
ejpam-6480	57	6	and	and	CCONJ
ejpam-6480	57	7	distinguishing	distinguish	VERB
ejpam-6480	57	8	different	different	ADJ
ejpam-6480	57	9	reliability	reliability	NOUN
ejpam-6480	57	10	behaviors	behavior	NOUN
ejpam-6480	57	11	,	,	PUNCT
ejpam-6480	57	12	such	such	ADJ
ejpam-6480	57	13	as	as	ADP
ejpam-6480	57	14	aging	age	VERB
ejpam-6480	57	15	and	and	CCONJ
ejpam-6480	57	16	variability	variability	NOUN
ejpam-6480	57	17	in	in	ADP
ejpam-6480	57	18	lifetimes	lifetime	NOUN
ejpam-6480	57	19	.	.	PUNCT
ejpam-6480	58	1	in	in	ADP
ejpam-6480	58	2	many	many	ADJ
ejpam-6480	58	3	situations	situation	NOUN
ejpam-6480	58	4	,	,	PUNCT
ejpam-6480	58	5	we	we	PRON
ejpam-6480	58	6	only	only	ADV
ejpam-6480	58	7	have	have	VERB
ejpam-6480	58	8	information	information	NOUN
ejpam-6480	58	9	between	between	ADP
ejpam-6480	58	10	two	two	NUM
ejpam-6480	58	11	points	point	NOUN
ejpam-6480	58	12	,	,	PUNCT
ejpam-6480	58	13	so	so	SCONJ
ejpam-6480	58	14	we	we	PRON
ejpam-6480	58	15	should	should	AUX
ejpam-6480	58	16	study	study	VERB
ejpam-6480	58	17	the	the	DET
ejpam-6480	58	18	statistical	statistical	ADJ
ejpam-6480	58	19	measures	measure	NOUN
ejpam-6480	58	20	under	under	ADP
ejpam-6480	58	21	the	the	DET
ejpam-6480	58	22	condition	condition	NOUN
ejpam-6480	58	23	of	of	ADP
ejpam-6480	58	24	doubly	doubly	ADV
ejpam-6480	58	25	truncated	truncate	VERB
ejpam-6480	58	26	random	random	ADJ
ejpam-6480	58	27	variables	variable	NOUN
ejpam-6480	58	28	.	.	PUNCT
ejpam-6480	59	1	the	the	DET
ejpam-6480	59	2	doubly	doubly	ADV
ejpam-6480	59	3	truncated	truncate	VERB
ejpam-6480	59	4	measures	measure	NOUN
ejpam-6480	59	5	are	be	AUX
ejpam-6480	59	6	applicable	applicable	ADJ
ejpam-6480	59	7	to	to	ADP
ejpam-6480	59	8	engineering	engineering	NOUN
ejpam-6480	59	9	systems	system	NOUN
ejpam-6480	59	10	when	when	SCONJ
ejpam-6480	59	11	the	the	DET
ejpam-6480	59	12	observations	observation	NOUN
ejpam-6480	59	13	are	be	AUX
ejpam-6480	59	14	measured	measure	VERB
ejpam-6480	59	15	after	after	SCONJ
ejpam-6480	59	16	it	it	PRON
ejpam-6480	59	17	starts	start	VERB
ejpam-6480	59	18	operating	operate	VERB
ejpam-6480	59	19	and	and	CCONJ
ejpam-6480	59	20	before	before	SCONJ
ejpam-6480	59	21	it	it	PRON
ejpam-6480	59	22	fails	fail	VERB
ejpam-6480	59	23	.	.	PUNCT
ejpam-6480	60	1	if	if	SCONJ
ejpam-6480	60	2	the	the	DET
ejpam-6480	60	3	random	random	ADJ
ejpam-6480	60	4	variable	variable	NOUN
ejpam-6480	60	5	x	x	PRON
ejpam-6480	60	6	denotes	denote	VERB
ejpam-6480	60	7	the	the	DET
ejpam-6480	60	8	lifetime	lifetime	NOUN
ejpam-6480	60	9	of	of	ADP
ejpam-6480	60	10	a	a	DET
ejpam-6480	60	11	unit	unit	NOUN
ejpam-6480	60	12	,	,	PUNCT
ejpam-6480	60	13	then	then	ADV
ejpam-6480	60	14	the	the	DET
ejpam-6480	60	15	random	random	ADJ
ejpam-6480	60	16	variable	variable	NOUN
ejpam-6480	60	17	(	(	PUNCT
ejpam-6480	60	18	x	x	X
ejpam-6480	60	19	/	/	SYM
ejpam-6480	60	20	t1	t1	NOUN
ejpam-6480	60	21	<	<	X
ejpam-6480	60	22	x	x	X
ejpam-6480	60	23	<	<	X
ejpam-6480	60	24	t2	t2	PROPN
ejpam-6480	60	25	)	)	PUNCT
ejpam-6480	60	26	;	;	PUNCT
ejpam-6480	60	27	where	where	SCONJ
ejpam-6480	60	28	t1	t1	NOUN
ejpam-6480	60	29	,	,	PUNCT
ejpam-6480	60	30	t2	t2	NOUN
ejpam-6480	60	31	∈	∈	PROPN
ejpam-6480	60	32	d	d	X
ejpam-6480	60	33	=	=	PRON
ejpam-6480	60	34	{	{	PUNCT
ejpam-6480	60	35	(	(	PUNCT
ejpam-6480	60	36	u	u	NOUN
ejpam-6480	60	37	,	,	PUNCT
ejpam-6480	60	38	v	v	NOUN
ejpam-6480	60	39	)	)	PUNCT
ejpam-6480	60	40	∈	∈	NOUN
ejpam-6480	60	41	r2	r2	NOUN
ejpam-6480	60	42	:	:	PUNCT
ejpam-6480	61	1	f	f	PROPN
ejpam-6480	61	2	(	(	PUNCT
ejpam-6480	61	3	u	u	NOUN
ejpam-6480	61	4	)	)	PUNCT
ejpam-6480	61	5	<	<	X
ejpam-6480	61	6	f	f	X
ejpam-6480	61	7	(	(	PUNCT
ejpam-6480	61	8	v	v	NOUN
ejpam-6480	61	9	)	)	PUNCT
ejpam-6480	61	10	}	}	PUNCT
ejpam-6480	61	11	is	be	AUX
ejpam-6480	61	12	called	call	VERB
ejpam-6480	61	13	a	a	DET
ejpam-6480	61	14	doubly	doubly	ADV
ejpam-6480	61	15	truncated	truncated	ADJ
ejpam-6480	61	16	lifetime	lifetime	NOUN
ejpam-6480	61	17	variable	variable	NOUN
ejpam-6480	61	18	.	.	PUNCT
ejpam-6480	62	1	another	another	DET
ejpam-6480	62	2	extension	extension	NOUN
ejpam-6480	62	3	of	of	ADP
ejpam-6480	62	4	shannon	shannon	PROPN
ejpam-6480	62	5	entropy	entropy	PROPN
ejpam-6480	62	6	is	be	AUX
ejpam-6480	62	7	based	base	VERB
ejpam-6480	62	8	on	on	ADP
ejpam-6480	62	9	a	a	DET
ejpam-6480	62	10	doubly	doubly	ADV
ejpam-6480	62	11	truncated	truncate	VERB
ejpam-6480	62	12	random	random	ADJ
ejpam-6480	62	13	variable	variable	NOUN
ejpam-6480	62	14	(	(	PUNCT
ejpam-6480	62	15	x	x	X
ejpam-6480	62	16	/	/	SYM
ejpam-6480	62	17	t1	t1	NOUN
ejpam-6480	62	18	<	<	X
ejpam-6480	62	19	x	x	X
ejpam-6480	62	20	<	<	X
ejpam-6480	62	21	t2	t2	PROPN
ejpam-6480	62	22	)	)	PUNCT
ejpam-6480	62	23	,	,	PUNCT
ejpam-6480	62	24	which	which	PRON
ejpam-6480	62	25	is	be	AUX
ejpam-6480	62	26	defined	define	VERB
ejpam-6480	62	27	as	as	ADP
ejpam-6480	62	28	k(x	k(x	PROPN
ejpam-6480	62	29	;	;	PUNCT
ejpam-6480	62	30	t1	t1	NOUN
ejpam-6480	62	31	,	,	PUNCT
ejpam-6480	62	32	t2	t2	NOUN
ejpam-6480	62	33	)	)	PUNCT
ejpam-6480	62	34	=	=	SYM
ejpam-6480	63	1	−	−	PROPN
ejpam-6480	63	2	∫	∫	PROPN
ejpam-6480	63	3	t2	t2	PROPN
ejpam-6480	63	4	t1	t1	PROPN
ejpam-6480	63	5	f(x	f(x	PROPN
ejpam-6480	63	6	)	)	PUNCT
ejpam-6480	63	7	r	r	NOUN
ejpam-6480	63	8	(	(	PUNCT
ejpam-6480	63	9	t1)−	t1)−	NOUN
ejpam-6480	63	10	r(t2	r(t2	NOUN
ejpam-6480	63	11	)	)	PUNCT
ejpam-6480	63	12	log	log	VERB
ejpam-6480	63	13	f(x	f(x	PROPN
ejpam-6480	63	14	)	)	PUNCT
ejpam-6480	64	1	r	r	NOUN
ejpam-6480	64	2	(	(	PUNCT
ejpam-6480	64	3	t1)−	t1)−	NOUN
ejpam-6480	64	4	r(t2	r(t2	NOUN
ejpam-6480	64	5	)	)	PUNCT
ejpam-6480	64	6	dx	dx	PROPN
ejpam-6480	64	7	(	(	PUNCT
ejpam-6480	64	8	1.5	1.5	NUM
ejpam-6480	64	9	)	)	PUNCT
ejpam-6480	64	10	j.	j.	PROPN
ejpam-6480	64	11	g.	g.	PROPN
ejpam-6480	64	12	dar	dar	PROPN
ejpam-6480	64	13	,	,	PUNCT
ejpam-6480	64	14	s.	s.	PROPN
ejpam-6480	64	15	m.	m.	PROPN
ejpam-6480	64	16	a.	a.	PROPN
ejpam-6480	64	17	alsheikh	alsheikh	PROPN
ejpam-6480	64	18	,	,	PUNCT
ejpam-6480	64	19	p.	p.	PROPN
ejpam-6480	64	20	jadhav	jadhav	PROPN
ejpam-6480	64	21	/	/	SYM
ejpam-6480	64	22	eur	eur	PROPN
ejpam-6480	64	23	.	.	PUNCT
ejpam-6480	65	1	j.	j.	PROPN
ejpam-6480	65	2	pure	pure	PROPN
ejpam-6480	65	3	appl	appl	PROPN
ejpam-6480	65	4	.	.	PROPN
ejpam-6480	65	5	math	math	PROPN
ejpam-6480	65	6	,	,	PUNCT
ejpam-6480	65	7	18	18	NUM
ejpam-6480	65	8	(	(	PUNCT
ejpam-6480	65	9	4	4	NUM
ejpam-6480	65	10	)	)	PUNCT
ejpam-6480	65	11	(	(	PUNCT
ejpam-6480	65	12	2025	2025	NUM
ejpam-6480	65	13	)	)	PUNCT
ejpam-6480	65	14	,	,	PUNCT
ejpam-6480	65	15	6480	6480	NUM
ejpam-6480	65	16	4	4	NUM
ejpam-6480	65	17	of	of	ADP
ejpam-6480	65	18	14	14	NUM
ejpam-6480	65	19	given	give	VERB
ejpam-6480	65	20	that	that	SCONJ
ejpam-6480	65	21	a	a	DET
ejpam-6480	65	22	system	system	NOUN
ejpam-6480	65	23	has	have	AUX
ejpam-6480	65	24	survived	survive	VERB
ejpam-6480	65	25	up	up	ADP
ejpam-6480	65	26	to	to	ADP
ejpam-6480	65	27	time	time	NOUN
ejpam-6480	65	28	t1	t1	NOUN
ejpam-6480	65	29	and	and	CCONJ
ejpam-6480	65	30	has	have	AUX
ejpam-6480	65	31	been	be	AUX
ejpam-6480	65	32	found	find	VERB
ejpam-6480	65	33	to	to	PART
ejpam-6480	65	34	be	be	AUX
ejpam-6480	65	35	down	down	ADV
ejpam-6480	65	36	at	at	ADP
ejpam-6480	65	37	time	time	NOUN
ejpam-6480	65	38	t2	t2	PROPN
ejpam-6480	65	39	,	,	PUNCT
ejpam-6480	65	40	then	then	ADV
ejpam-6480	65	41	k	k	X
ejpam-6480	65	42	(	(	PUNCT
ejpam-6480	65	43	x	x	X
ejpam-6480	65	44	;	;	PUNCT
ejpam-6480	65	45	t1	t1	NOUN
ejpam-6480	65	46	,	,	PUNCT
ejpam-6480	65	47	t2	t2	NOUN
ejpam-6480	65	48	)	)	PUNCT
ejpam-6480	65	49	measures	measure	VERB
ejpam-6480	65	50	the	the	DET
ejpam-6480	65	51	uncertainty	uncertainty	NOUN
ejpam-6480	65	52	about	about	ADP
ejpam-6480	65	53	its	its	PRON
ejpam-6480	65	54	lifetimes	lifetime	NOUN
ejpam-6480	65	55	between	between	ADP
ejpam-6480	65	56	t1	t1	NOUN
ejpam-6480	65	57	and	and	CCONJ
ejpam-6480	65	58	t2	t2	PROPN
ejpam-6480	65	59	.	.	PUNCT
ejpam-6480	66	1	sunoj	sunoj	PROPN
ejpam-6480	66	2	et	et	PROPN
ejpam-6480	66	3	al	al	PROPN
ejpam-6480	66	4	.	.	PUNCT
ejpam-6480	67	1	[	[	X
ejpam-6480	67	2	19	19	NUM
ejpam-6480	67	3	]	]	PUNCT
ejpam-6480	67	4	have	have	AUX
ejpam-6480	67	5	explored	explore	VERB
ejpam-6480	67	6	the	the	DET
ejpam-6480	67	7	use	use	NOUN
ejpam-6480	67	8	of	of	ADP
ejpam-6480	67	9	information	information	NOUN
ejpam-6480	67	10	measures	measure	NOUN
ejpam-6480	67	11	for	for	ADP
ejpam-6480	67	12	double	double	ADJ
ejpam-6480	67	13	truncated	truncate	VERB
ejpam-6480	67	14	random	random	ADJ
ejpam-6480	67	15	variables	variable	NOUN
ejpam-6480	67	16	.	.	PUNCT
ejpam-6480	68	1	furthermore	furthermore	ADV
ejpam-6480	68	2	,	,	PUNCT
ejpam-6480	68	3	misagh	misagh	PROPN
ejpam-6480	68	4	and	and	CCONJ
ejpam-6480	68	5	yari	yari	PROPN
ejpam-6480	69	1	[	[	X
ejpam-6480	69	2	15	15	NUM
ejpam-6480	69	3	,	,	PUNCT
ejpam-6480	69	4	16	16	NUM
ejpam-6480	69	5	]	]	PUNCT
ejpam-6480	69	6	explored	explore	VERB
ejpam-6480	69	7	the	the	DET
ejpam-6480	69	8	use	use	NOUN
ejpam-6480	69	9	of	of	ADP
ejpam-6480	69	10	weighted	weight	VERB
ejpam-6480	69	11	information	information	NOUN
ejpam-6480	69	12	measures	measure	NOUN
ejpam-6480	69	13	for	for	ADP
ejpam-6480	69	14	doubly	doubly	ADV
ejpam-6480	69	15	truncated	truncate	VERB
ejpam-6480	69	16	random	random	ADJ
ejpam-6480	69	17	variables	variable	NOUN
ejpam-6480	69	18	.	.	PUNCT
ejpam-6480	70	1	for	for	ADP
ejpam-6480	70	2	various	various	ADJ
ejpam-6480	70	3	results	result	NOUN
ejpam-6480	70	4	on	on	ADP
ejpam-6480	70	5	doubly	doubly	ADV
ejpam-6480	70	6	truncated	truncate	VERB
ejpam-6480	70	7	random	random	ADJ
ejpam-6480	70	8	variable	variable	NOUN
ejpam-6480	70	9	,	,	PUNCT
ejpam-6480	70	10	we	we	PRON
ejpam-6480	70	11	refer	refer	VERB
ejpam-6480	70	12	to	to	ADP
ejpam-6480	70	13	kayal	kayal	PROPN
ejpam-6480	70	14	and	and	CCONJ
ejpam-6480	70	15	moharana	moharana	PROPN
ejpam-6480	71	1	[	[	X
ejpam-6480	71	2	17	17	NUM
ejpam-6480	71	3	]	]	PUNCT
ejpam-6480	71	4	,	,	PUNCT
ejpam-6480	71	5	kundu	kundu	NOUN
ejpam-6480	72	1	[	[	X
ejpam-6480	72	2	18	18	NUM
ejpam-6480	72	3	]	]	PUNCT
ejpam-6480	72	4	,	,	PUNCT
ejpam-6480	72	5	jalayeri	jalayeri	PROPN
ejpam-6480	72	6	et.al	et.al	PROPN
ejpam-6480	73	1	[	[	X
ejpam-6480	73	2	19	19	NUM
ejpam-6480	73	3	]	]	PUNCT
ejpam-6480	73	4	,	,	PUNCT
ejpam-6480	73	5	kumar	kumar	PROPN
ejpam-6480	73	6	[	[	X
ejpam-6480	73	7	20	20	NUM
ejpam-6480	73	8	]	]	PUNCT
ejpam-6480	73	9	and	and	CCONJ
ejpam-6480	73	10	in	in	ADP
ejpam-6480	73	11	[	[	X
ejpam-6480	73	12	21	21	NUM
ejpam-6480	73	13	,	,	PUNCT
ejpam-6480	73	14	22	22	NUM
ejpam-6480	73	15	]	]	PUNCT
ejpam-6480	73	16	.	.	PUNCT
ejpam-6480	74	1	joshi	joshi	PROPN
ejpam-6480	74	2	and	and	CCONJ
ejpam-6480	74	3	dar	dar	PROPN
ejpam-6480	75	1	[	[	X
ejpam-6480	75	2	23	23	NUM
ejpam-6480	75	3	]	]	X
ejpam-6480	75	4	develop	develop	VERB
ejpam-6480	75	5	mathaihaubold	mathaihaubold	ADJ
ejpam-6480	75	6	fuzzy	fuzzy	ADJ
ejpam-6480	75	7	entropy	entropy	NOUN
ejpam-6480	75	8	extends	extend	VERB
ejpam-6480	75	9	the	the	DET
ejpam-6480	75	10	mathaihaubold	mathaihaubold	PROPN
ejpam-6480	75	11	entropy	entropy	NOUN
ejpam-6480	75	12	framework	framework	NOUN
ejpam-6480	75	13	to	to	ADP
ejpam-6480	75	14	the	the	DET
ejpam-6480	75	15	domain	domain	NOUN
ejpam-6480	75	16	of	of	ADP
ejpam-6480	75	17	fuzzy	fuzzy	ADJ
ejpam-6480	75	18	set	set	NOUN
ejpam-6480	75	19	theory	theory	NOUN
ejpam-6480	75	20	,	,	PUNCT
ejpam-6480	75	21	providing	provide	VERB
ejpam-6480	75	22	a	a	DET
ejpam-6480	75	23	generalized	generalized	ADJ
ejpam-6480	75	24	measure	measure	NOUN
ejpam-6480	75	25	of	of	ADP
ejpam-6480	75	26	uncertainty	uncertainty	NOUN
ejpam-6480	75	27	and	and	CCONJ
ejpam-6480	75	28	fuzziness	fuzziness	NOUN
ejpam-6480	75	29	in	in	ADP
ejpam-6480	75	30	imprecise	imprecise	ADJ
ejpam-6480	75	31	or	or	CCONJ
ejpam-6480	75	32	vague	vague	ADJ
ejpam-6480	75	33	systems	system	NOUN
ejpam-6480	75	34	.	.	PUNCT
ejpam-6480	76	1	this	this	DET
ejpam-6480	76	2	formulation	formulation	NOUN
ejpam-6480	76	3	integrates	integrate	VERB
ejpam-6480	76	4	the	the	DET
ejpam-6480	76	5	pathway	pathway	NOUN
ejpam-6480	76	6	model	model	NOUN
ejpam-6480	76	7	of	of	ADP
ejpam-6480	76	8	mathai	mathai	PROPN
ejpam-6480	76	9	and	and	CCONJ
ejpam-6480	76	10	haubold	haubold	VERB
ejpam-6480	76	11	with	with	ADP
ejpam-6480	76	12	the	the	DET
ejpam-6480	76	13	principles	principle	NOUN
ejpam-6480	76	14	of	of	ADP
ejpam-6480	76	15	fuzzy	fuzzy	ADJ
ejpam-6480	76	16	entropy	entropy	NOUN
ejpam-6480	76	17	,	,	PUNCT
ejpam-6480	76	18	allowing	allow	VERB
ejpam-6480	76	19	for	for	ADP
ejpam-6480	76	20	a	a	DET
ejpam-6480	76	21	more	more	ADV
ejpam-6480	76	22	flexible	flexible	ADJ
ejpam-6480	76	23	quantification	quantification	NOUN
ejpam-6480	76	24	of	of	ADP
ejpam-6480	76	25	uncertainty	uncertainty	NOUN
ejpam-6480	76	26	when	when	SCONJ
ejpam-6480	76	27	dealing	deal	VERB
ejpam-6480	76	28	with	with	ADP
ejpam-6480	76	29	fuzzy	fuzzy	ADJ
ejpam-6480	76	30	membership	membership	NOUN
ejpam-6480	76	31	functions	function	NOUN
ejpam-6480	76	32	.	.	PUNCT
ejpam-6480	77	1	oindrali	oindrali	PROPN
ejpam-6480	77	2	das	das	PROPN
ejpam-6480	77	3	,	,	PUNCT
ejpam-6480	77	4	siddhartha	siddhartha	PROPN
ejpam-6480	77	5	chakraborty	chakraborty	PROPN
ejpam-6480	77	6	and	and	CCONJ
ejpam-6480	77	7	biswabrata	biswabrata	ADJ
ejpam-6480	77	8	pradhan	pradhan	NOUN
ejpam-6480	78	1	[	[	X
ejpam-6480	78	2	24	24	NUM
ejpam-6480	78	3	]	]	PUNCT
ejpam-6480	78	4	proposed	propose	VERB
ejpam-6480	78	5	the	the	DET
ejpam-6480	78	6	mathaihaubold	mathaihaubold	NOUN
ejpam-6480	78	7	and	and	CCONJ
ejpam-6480	78	8	study	study	VERB
ejpam-6480	78	9	its	its	PRON
ejpam-6480	78	10	properties	property	NOUN
ejpam-6480	78	11	.	.	PUNCT
ejpam-6480	79	1	since	since	SCONJ
ejpam-6480	79	2	generalized	generalized	ADJ
ejpam-6480	79	3	entropy	entropy	NOUN
ejpam-6480	79	4	plays	play	VERB
ejpam-6480	79	5	an	an	DET
ejpam-6480	79	6	important	important	ADJ
ejpam-6480	79	7	role	role	NOUN
ejpam-6480	79	8	,	,	PUNCT
ejpam-6480	79	9	in	in	ADP
ejpam-6480	79	10	the	the	DET
ejpam-6480	79	11	field	field	NOUN
ejpam-6480	79	12	of	of	ADP
ejpam-6480	79	13	reliability	reliability	NOUN
ejpam-6480	79	14	theory	theory	NOUN
ejpam-6480	79	15	and	and	CCONJ
ejpam-6480	79	16	survival	survival	NOUN
ejpam-6480	79	17	analysis	analysis	NOUN
ejpam-6480	79	18	,	,	PUNCT
ejpam-6480	79	19	when	when	SCONJ
ejpam-6480	79	20	a	a	DET
ejpam-6480	79	21	system	system	NOUN
ejpam-6480	79	22	has	have	VERB
ejpam-6480	79	23	lifetime	lifetime	NOUN
ejpam-6480	79	24	between	between	ADP
ejpam-6480	79	25	two	two	NUM
ejpam-6480	79	26	time	time	NOUN
ejpam-6480	79	27	points	point	NOUN
ejpam-6480	79	28	(	(	PUNCT
ejpam-6480	79	29	t1	t1	NOUN
ejpam-6480	79	30	,	,	PUNCT
ejpam-6480	79	31	t2	t2	PROPN
ejpam-6480	79	32	)	)	PUNCT
ejpam-6480	79	33	,	,	PUNCT
ejpam-6480	79	34	the	the	DET
ejpam-6480	79	35	concept	concept	NOUN
ejpam-6480	79	36	of	of	ADP
ejpam-6480	79	37	doubly	doubly	ADV
ejpam-6480	79	38	truncated	truncate	VERB
ejpam-6480	79	39	data	datum	NOUN
ejpam-6480	79	40	is	be	AUX
ejpam-6480	79	41	also	also	ADV
ejpam-6480	79	42	applied	apply	VERB
ejpam-6480	79	43	to	to	ADP
ejpam-6480	79	44	medical	medical	ADJ
ejpam-6480	79	45	research	research	NOUN
ejpam-6480	79	46	,	,	PUNCT
ejpam-6480	79	47	specifically	specifically	ADV
ejpam-6480	79	48	in	in	ADP
ejpam-6480	79	49	the	the	DET
ejpam-6480	79	50	study	study	NOUN
ejpam-6480	79	51	of	of	ADP
ejpam-6480	79	52	tumor	tumor	NOUN
ejpam-6480	79	53	progression	progression	NOUN
ejpam-6480	79	54	in	in	ADP
ejpam-6480	79	55	cancer	cancer	NOUN
ejpam-6480	79	56	patients	patient	NOUN
ejpam-6480	79	57	who	who	PRON
ejpam-6480	79	58	receive	receive	VERB
ejpam-6480	79	59	chemotherapy	chemotherapy	NOUN
ejpam-6480	79	60	.	.	PUNCT
ejpam-6480	80	1	in	in	ADP
ejpam-6480	80	2	these	these	DET
ejpam-6480	80	3	studies	study	NOUN
ejpam-6480	80	4	,	,	PUNCT
ejpam-6480	80	5	patients	patient	NOUN
ejpam-6480	80	6	’	'	PUNCT
ejpam-6480	80	7	times	time	NOUN
ejpam-6480	80	8	to	to	ADP
ejpam-6480	80	9	progression	progression	NOUN
ejpam-6480	80	10	(	(	PUNCT
ejpam-6480	80	11	i.e.	i.e.	X
ejpam-6480	80	12	,	,	PUNCT
ejpam-6480	80	13	the	the	DET
ejpam-6480	80	14	time	time	NOUN
ejpam-6480	80	15	it	it	PRON
ejpam-6480	80	16	takes	take	VERB
ejpam-6480	80	17	for	for	SCONJ
ejpam-6480	80	18	their	their	PRON
ejpam-6480	80	19	condition	condition	NOUN
ejpam-6480	80	20	to	to	PART
ejpam-6480	80	21	worsen	worsen	VERB
ejpam-6480	80	22	)	)	PUNCT
ejpam-6480	80	23	are	be	AUX
ejpam-6480	80	24	truncated	truncate	VERB
ejpam-6480	80	25	:	:	PUNCT
ejpam-6480	80	26	they	they	PRON
ejpam-6480	80	27	are	be	AUX
ejpam-6480	80	28	observed	observe	VERB
ejpam-6480	80	29	between	between	ADP
ejpam-6480	80	30	two	two	NUM
ejpam-6480	80	31	points	point	NOUN
ejpam-6480	80	32	in	in	ADP
ejpam-6480	80	33	time	time	NOUN
ejpam-6480	80	34	,	,	PUNCT
ejpam-6480	80	35	possibly	possibly	ADV
ejpam-6480	80	36	between	between	ADP
ejpam-6480	80	37	when	when	SCONJ
ejpam-6480	80	38	they	they	PRON
ejpam-6480	80	39	start	start	VERB
ejpam-6480	80	40	treatment	treatment	NOUN
ejpam-6480	80	41	and	and	CCONJ
ejpam-6480	80	42	when	when	SCONJ
ejpam-6480	80	43	they	they	PRON
ejpam-6480	80	44	either	either	CCONJ
ejpam-6480	80	45	progress	progress	VERB
ejpam-6480	80	46	or	or	CCONJ
ejpam-6480	80	47	die	die	VERB
ejpam-6480	80	48	.	.	PUNCT
ejpam-6480	81	1	this	this	DET
ejpam-6480	81	2	doubly	doubly	ADV
ejpam-6480	81	3	truncated	truncate	VERB
ejpam-6480	81	4	data	datum	NOUN
ejpam-6480	81	5	can	can	AUX
ejpam-6480	81	6	be	be	AUX
ejpam-6480	81	7	modelled	model	VERB
ejpam-6480	81	8	effectively	effectively	ADV
ejpam-6480	81	9	using	use	VERB
ejpam-6480	81	10	generalized	generalized	ADJ
ejpam-6480	81	11	entropy	entropy	NOUN
ejpam-6480	81	12	.	.	PUNCT
ejpam-6480	82	1	2	2	X
ejpam-6480	82	2	.	.	X
ejpam-6480	82	3	mathai	mathai	PROPN
ejpam-6480	82	4	-	-	PUNCT
ejpam-6480	82	5	haubold	haubold	PROPN
ejpam-6480	82	6	interval	interval	NOUN
ejpam-6480	82	7	entropy	entropy	NOUN
ejpam-6480	82	8	based	base	VERB
ejpam-6480	82	9	on	on	ADP
ejpam-6480	82	10	the	the	DET
ejpam-6480	82	11	measure	measure	NOUN
ejpam-6480	82	12	defined	define	VERB
ejpam-6480	82	13	in	in	ADP
ejpam-6480	82	14	(	(	PUNCT
ejpam-6480	82	15	1.3	1.3	NUM
ejpam-6480	82	16	)	)	PUNCT
ejpam-6480	82	17	,	,	PUNCT
ejpam-6480	82	18	dar	dar	NOUN
ejpam-6480	82	19	and	and	CCONJ
ejpam-6480	82	20	bander	bander	NOUN
ejpam-6480	83	1	[	[	X
ejpam-6480	83	2	25	25	NUM
ejpam-6480	83	3	]	]	PUNCT
ejpam-6480	83	4	,	,	PUNCT
ejpam-6480	83	5	introduce	introduce	VERB
ejpam-6480	83	6	the	the	DET
ejpam-6480	83	7	information	information	NOUN
ejpam-6480	83	8	measure	measure	NOUN
ejpam-6480	83	9	that	that	PRON
ejpam-6480	83	10	takes	take	VERB
ejpam-6480	83	11	the	the	DET
ejpam-6480	83	12	current	current	ADJ
ejpam-6480	83	13	age	age	NOUN
ejpam-6480	83	14	of	of	ADP
ejpam-6480	83	15	the	the	DET
ejpam-6480	83	16	system	system	NOUN
ejpam-6480	83	17	into	into	ADP
ejpam-6480	83	18	consideration	consideration	NOUN
ejpam-6480	83	19	and	and	CCONJ
ejpam-6480	83	20	generalizes	generalize	VERB
ejpam-6480	83	21	(	(	PUNCT
ejpam-6480	83	22	1.4	1.4	NUM
ejpam-6480	83	23	)	)	PUNCT
ejpam-6480	83	24	as	as	ADP
ejpam-6480	83	25	kα(x	kα(x	PROPN
ejpam-6480	83	26	;	;	PUNCT
ejpam-6480	83	27	t	t	X
ejpam-6480	83	28	)	)	PUNCT
ejpam-6480	83	29	=	=	SYM
ejpam-6480	83	30	1	1	NUM
ejpam-6480	83	31	(	(	PUNCT
ejpam-6480	83	32	α−	α−	ADP
ejpam-6480	83	33	1	1	NUM
ejpam-6480	83	34	)	)	PUNCT
ejpam-6480	84	1	[	[	X
ejpam-6480	84	2	∫∞	∫∞	NOUN
ejpam-6480	84	3	t	t	PROPN
ejpam-6480	84	4	f2−α(x)dx	f2−α(x)dx	VERB
ejpam-6480	84	5	r2−α(t	r2−α(t	VERB
ejpam-6480	84	6	)	)	PUNCT
ejpam-6480	84	7	−	−	PROPN
ejpam-6480	84	8	1	1	NUM
ejpam-6480	84	9	]	]	PUNCT
ejpam-6480	84	10	,	,	PUNCT
ejpam-6480	84	11	α	α	PROPN
ejpam-6480	84	12	6=	6=	ADP
ejpam-6480	84	13	1	1	NUM
ejpam-6480	84	14	,	,	PUNCT
ejpam-6480	84	15	0	0	NUM
ejpam-6480	84	16	<	<	X
ejpam-6480	84	17	α	α	X
ejpam-6480	84	18	<	<	X
ejpam-6480	84	19	2	2	NUM
ejpam-6480	84	20	(	(	PUNCT
ejpam-6480	84	21	2.1	2.1	NUM
ejpam-6480	84	22	)	)	PUNCT
ejpam-6480	84	23	using	use	VERB
ejpam-6480	84	24	equation	equation	NOUN
ejpam-6480	84	25	(	(	PUNCT
ejpam-6480	84	26	2.1),the	2.1),the	DET
ejpam-6480	84	27	interval	interval	NOUN
ejpam-6480	84	28	entropy	entropy	NOUN
ejpam-6480	84	29	of	of	ADP
ejpam-6480	84	30	order	order	NOUN
ejpam-6480	84	31	α	α	NOUN
ejpam-6480	84	32	(	(	PUNCT
ejpam-6480	84	33	now	now	ADV
ejpam-6480	84	34	onwards	onwards	ADP
ejpam-6480	84	35	mhie	mhie	NOUN
ejpam-6480	84	36	)	)	PUNCT
ejpam-6480	84	37	of	of	ADP
ejpam-6480	84	38	the	the	DET
ejpam-6480	84	39	double	double	ADJ
ejpam-6480	84	40	truncated	truncate	VERB
ejpam-6480	84	41	random	random	ADJ
ejpam-6480	84	42	variable	variable	NOUN
ejpam-6480	84	43	(	(	PUNCT
ejpam-6480	84	44	x	x	X
ejpam-6480	84	45	/	/	SYM
ejpam-6480	84	46	t1	t1	NOUN
ejpam-6480	84	47	<	<	X
ejpam-6480	84	48	x	x	X
ejpam-6480	84	49	<	<	X
ejpam-6480	84	50	t2	t2	PROPN
ejpam-6480	84	51	)	)	PUNCT
ejpam-6480	84	52	is	be	AUX
ejpam-6480	84	53	given	give	VERB
ejpam-6480	84	54	by	by	ADP
ejpam-6480	84	55	:	:	PUNCT
ejpam-6480	84	56	kα	kα	PROPN
ejpam-6480	84	57	(	(	PUNCT
ejpam-6480	84	58	x	x	X
ejpam-6480	84	59	;	;	PUNCT
ejpam-6480	84	60	t1	t1	NOUN
ejpam-6480	84	61	,	,	PUNCT
ejpam-6480	84	62	t2	t2	NOUN
ejpam-6480	84	63	)	)	PUNCT
ejpam-6480	84	64	=	=	SYM
ejpam-6480	84	65	1	1	NUM
ejpam-6480	84	66	(	(	PUNCT
ejpam-6480	84	67	α−	α−	ADP
ejpam-6480	84	68	1	1	NUM
ejpam-6480	84	69	)	)	PUNCT
ejpam-6480	85	1	[	[	X
ejpam-6480	85	2	∫	∫	X
ejpam-6480	85	3	t2	t2	PROPN
ejpam-6480	85	4	t1	t1	PROPN
ejpam-6480	85	5	(	(	PUNCT
ejpam-6480	85	6	f(x	f(x	PROPN
ejpam-6480	85	7	)	)	PUNCT
ejpam-6480	85	8	f	f	PROPN
ejpam-6480	85	9	(	(	PUNCT
ejpam-6480	85	10	t2)−	t2)−	NOUN
ejpam-6480	85	11	f	f	X
ejpam-6480	85	12	(	(	PUNCT
ejpam-6480	85	13	t1	t1	PROPN
ejpam-6480	85	14	)	)	PUNCT
ejpam-6480	85	15	)	)	PUNCT
ejpam-6480	85	16	2−α	2−α	NUM
ejpam-6480	86	1	dx−	dx−	NUM
ejpam-6480	86	2	1	1	X
ejpam-6480	86	3	]	]	PUNCT
ejpam-6480	86	4	,	,	PUNCT
ejpam-6480	86	5	α	α	PROPN
ejpam-6480	86	6	6=	6=	ADP
ejpam-6480	86	7	1	1	NUM
ejpam-6480	86	8	,	,	PUNCT
ejpam-6480	86	9	0	0	NUM
ejpam-6480	86	10	<	<	X
ejpam-6480	86	11	α	α	X
ejpam-6480	86	12	<	<	X
ejpam-6480	86	13	2	2	NUM
ejpam-6480	86	14	(	(	PUNCT
ejpam-6480	86	15	2.2	2.2	NUM
ejpam-6480	86	16	)	)	PUNCT
ejpam-6480	86	17	when	when	SCONJ
ejpam-6480	86	18	the	the	DET
ejpam-6480	86	19	system	system	NOUN
ejpam-6480	86	20	has	have	VERB
ejpam-6480	86	21	age	age	NOUN
ejpam-6480	86	22	t1	t1	PROPN
ejpam-6480	86	23	,	,	PUNCT
ejpam-6480	86	24	(	(	PUNCT
ejpam-6480	86	25	2.2	2.2	NUM
ejpam-6480	86	26	)	)	PUNCT
ejpam-6480	86	27	provides	provide	VERB
ejpam-6480	86	28	the	the	DET
ejpam-6480	86	29	information	information	NOUN
ejpam-6480	86	30	spectrum	spectrum	NOUN
ejpam-6480	86	31	of	of	ADP
ejpam-6480	86	32	the	the	DET
ejpam-6480	86	33	remaining	remain	VERB
ejpam-6480	86	34	life	life	NOUN
ejpam-6480	86	35	of	of	ADP
ejpam-6480	86	36	the	the	DET
ejpam-6480	86	37	system	system	NOUN
ejpam-6480	86	38	until	until	ADP
ejpam-6480	86	39	age	age	NOUN
ejpam-6480	86	40	t2	t2	NOUN
ejpam-6480	86	41	.	.	PUNCT
ejpam-6480	87	1	corollary	corollary	NOUN
ejpam-6480	87	2	:	:	PUNCT
ejpam-6480	87	3	for	for	ADP
ejpam-6480	87	4	t1	t1	PROPN
ejpam-6480	87	5	=	=	SYM
ejpam-6480	87	6	t	t	PROPN
ejpam-6480	87	7	and	and	CCONJ
ejpam-6480	87	8	t2	t2	PROPN
ejpam-6480	87	9	=	=	SYM
ejpam-6480	87	10	∞	∞	PROPN
ejpam-6480	87	11	,	,	PUNCT
ejpam-6480	87	12	(	(	PUNCT
ejpam-6480	87	13	2.2	2.2	NUM
ejpam-6480	87	14	)	)	PUNCT
ejpam-6480	87	15	reduces	reduce	VERB
ejpam-6480	87	16	to	to	ADP
ejpam-6480	87	17	(	(	PUNCT
ejpam-6480	87	18	2.1	2.1	NUM
ejpam-6480	87	19	)	)	PUNCT
ejpam-6480	87	20	.	.	PUNCT
ejpam-6480	88	1	definition	definition	NOUN
ejpam-6480	88	2	2.1	2.1	NUM
ejpam-6480	88	3	:	:	PUNCT
ejpam-6480	88	4	the	the	DET
ejpam-6480	88	5	general	general	ADJ
ejpam-6480	88	6	failure	failure	NOUN
ejpam-6480	88	7	rate	rate	NOUN
ejpam-6480	88	8	(	(	PUNCT
ejpam-6480	88	9	gfr	gfr	NOUN
ejpam-6480	88	10	)	)	PUNCT
ejpam-6480	88	11	of	of	ADP
ejpam-6480	88	12	a	a	DET
ejpam-6480	88	13	doubly	doubly	ADV
ejpam-6480	88	14	truncated	truncate	VERB
ejpam-6480	88	15	random	random	ADJ
ejpam-6480	88	16	variable	variable	NOUN
ejpam-6480	88	17	(	(	PUNCT
ejpam-6480	88	18	x	x	X
ejpam-6480	88	19	/	/	SYM
ejpam-6480	88	20	t1	t1	NOUN
ejpam-6480	88	21	<	<	X
ejpam-6480	88	22	x	x	X
ejpam-6480	88	23	<	<	X
ejpam-6480	88	24	t2	t2	PROPN
ejpam-6480	88	25	)	)	PUNCT
ejpam-6480	88	26	is	be	AUX
ejpam-6480	88	27	defined	define	VERB
ejpam-6480	88	28	as	as	ADP
ejpam-6480	88	29	hi	hi	PROPN
ejpam-6480	88	30	(	(	PUNCT
ejpam-6480	88	31	t1	t1	NOUN
ejpam-6480	88	32	,	,	PUNCT
ejpam-6480	88	33	t2	t2	NOUN
ejpam-6480	88	34	)	)	PUNCT
ejpam-6480	88	35	=	=	SYM
ejpam-6480	88	36	f(ti	f(ti	NOUN
ejpam-6480	88	37	)	)	PUNCT
ejpam-6480	88	38	f(t2)−f(t1	f(t2)−f(t1	PROPN
ejpam-6480	88	39	)	)	PUNCT
ejpam-6480	88	40	,	,	PUNCT
ejpam-6480	89	1	i	i	PRON
ejpam-6480	89	2	=	=	NOUN
ejpam-6480	89	3	1	1	NUM
ejpam-6480	89	4	,	,	PUNCT
ejpam-6480	89	5	2	2	NUM
ejpam-6480	89	6	.	.	PUNCT
ejpam-6480	89	7	http://et.al	http://et.al	PROPN
ejpam-6480	90	1	j.	j.	PROPN
ejpam-6480	90	2	g.	g.	PROPN
ejpam-6480	90	3	dar	dar	PROPN
ejpam-6480	90	4	,	,	PUNCT
ejpam-6480	90	5	s.	s.	PROPN
ejpam-6480	90	6	m.	m.	PROPN
ejpam-6480	90	7	a.	a.	PROPN
ejpam-6480	90	8	alsheikh	alsheikh	PROPN
ejpam-6480	90	9	,	,	PUNCT
ejpam-6480	90	10	p.	p.	PROPN
ejpam-6480	90	11	jadhav	jadhav	PROPN
ejpam-6480	90	12	/	/	SYM
ejpam-6480	90	13	eur	eur	PROPN
ejpam-6480	90	14	.	.	PUNCT
ejpam-6480	91	1	j.	j.	PROPN
ejpam-6480	91	2	pure	pure	PROPN
ejpam-6480	91	3	appl	appl	PROPN
ejpam-6480	91	4	.	.	PROPN
ejpam-6480	91	5	math	math	PROPN
ejpam-6480	91	6	,	,	PUNCT
ejpam-6480	91	7	18	18	NUM
ejpam-6480	91	8	(	(	PUNCT
ejpam-6480	91	9	4	4	NUM
ejpam-6480	91	10	)	)	PUNCT
ejpam-6480	91	11	(	(	PUNCT
ejpam-6480	91	12	2025	2025	NUM
ejpam-6480	91	13	)	)	PUNCT
ejpam-6480	91	14	,	,	PUNCT
ejpam-6480	91	15	6480	6480	NUM
ejpam-6480	91	16	5	5	NUM
ejpam-6480	91	17	of	of	ADP
ejpam-6480	91	18	14	14	NUM
ejpam-6480	91	19	based	base	VERB
ejpam-6480	91	20	on	on	ADP
ejpam-6480	91	21	(	(	PUNCT
ejpam-6480	91	22	2.2	2.2	NUM
ejpam-6480	91	23	)	)	PUNCT
ejpam-6480	91	24	,	,	PUNCT
ejpam-6480	91	25	we	we	PRON
ejpam-6480	91	26	derive	derive	VERB
ejpam-6480	91	27	the	the	DET
ejpam-6480	91	28	interval	interval	NOUN
ejpam-6480	91	29	entropy	entropy	NOUN
ejpam-6480	91	30	of	of	ADP
ejpam-6480	91	31	some	some	DET
ejpam-6480	91	32	well	well	ADV
ejpam-6480	91	33	-	-	PUNCT
ejpam-6480	91	34	known	know	VERB
ejpam-6480	91	35	lifetime	lifetime	NOUN
ejpam-6480	91	36	distributions	distribution	NOUN
ejpam-6480	91	37	:	:	PUNCT
ejpam-6480	91	38	(	(	PUNCT
ejpam-6480	91	39	i	i	NOUN
ejpam-6480	91	40	)	)	PUNCT
ejpam-6480	91	41	uniform	uniform	ADJ
ejpam-6480	91	42	distribution	distribution	NOUN
ejpam-6480	91	43	:	:	PUNCT
ejpam-6480	91	44	the	the	DET
ejpam-6480	91	45	probability	probability	NOUN
ejpam-6480	91	46	density	density	NOUN
ejpam-6480	91	47	function	function	NOUN
ejpam-6480	91	48	and	and	CCONJ
ejpam-6480	91	49	corresponding	correspond	VERB
ejpam-6480	91	50	cdf	cdf	PROPN
ejpam-6480	91	51	of	of	ADP
ejpam-6480	91	52	uniform	uniform	ADJ
ejpam-6480	91	53	distribution	distribution	NOUN
ejpam-6480	91	54	is	be	AUX
ejpam-6480	91	55	given	give	VERB
ejpam-6480	91	56	by	by	ADP
ejpam-6480	91	57	f(x	f(x	PROPN
ejpam-6480	91	58	)	)	PUNCT
ejpam-6480	91	59	=	=	SYM
ejpam-6480	92	1	1	1	NUM
ejpam-6480	92	2	b−a	b−a	NOUN
ejpam-6480	92	3	,	,	PUNCT
ejpam-6480	92	4	a	a	DET
ejpam-6480	92	5	<	<	X
ejpam-6480	92	6	x	x	X
ejpam-6480	92	7	<	<	X
ejpam-6480	92	8	b	b	PROPN
ejpam-6480	92	9	,	,	PUNCT
ejpam-6480	92	10	f(x	f(x	PROPN
ejpam-6480	92	11	)	)	PUNCT
ejpam-6480	92	12	=	=	SYM
ejpam-6480	92	13	1−	1−	NUM
ejpam-6480	92	14	b−x	b−x	NOUN
ejpam-6480	92	15	b−a	b−a	ADV
ejpam-6480	92	16	respectively	respectively	ADV
ejpam-6480	92	17	.	.	PUNCT
ejpam-6480	93	1	the	the	DET
ejpam-6480	93	2	mhie	mhie	NOUN
ejpam-6480	93	3	is	be	AUX
ejpam-6480	93	4	given	give	VERB
ejpam-6480	93	5	by	by	ADP
ejpam-6480	93	6	(	(	PUNCT
ejpam-6480	93	7	α−	α−	ADP
ejpam-6480	93	8	1)kα	1)kα	PROPN
ejpam-6480	93	9	(	(	PUNCT
ejpam-6480	93	10	x	x	NOUN
ejpam-6480	93	11	;	;	PUNCT
ejpam-6480	93	12	t1	t1	NOUN
ejpam-6480	93	13	,	,	PUNCT
ejpam-6480	93	14	t2	t2	NOUN
ejpam-6480	93	15	)	)	PUNCT
ejpam-6480	93	16	=	=	SYM
ejpam-6480	93	17	1	1	NUM
ejpam-6480	93	18	(	(	PUNCT
ejpam-6480	93	19	t2−t1	t2−t1	NUM
ejpam-6480	93	20	)	)	PUNCT
ejpam-6480	93	21	2−α	2−α	NUM
ejpam-6480	94	1	(	(	PUNCT
ejpam-6480	94	2	∫	∫	PROPN
ejpam-6480	94	3	t2	t2	PROPN
ejpam-6480	94	4	t1	t1	PROPN
ejpam-6480	94	5	dx	dx	PROPN
ejpam-6480	94	6	)	)	PUNCT
ejpam-6480	95	1	−	−	PROPN
ejpam-6480	95	2	1	1	NUM
ejpam-6480	95	3	or	or	CCONJ
ejpam-6480	95	4	kα	kα	X
ejpam-6480	95	5	(	(	PUNCT
ejpam-6480	95	6	x	x	X
ejpam-6480	95	7	;	;	PUNCT
ejpam-6480	95	8	t1	t1	NOUN
ejpam-6480	95	9	,	,	PUNCT
ejpam-6480	95	10	t2	t2	NOUN
ejpam-6480	95	11	)	)	PUNCT
ejpam-6480	95	12	=	=	SYM
ejpam-6480	95	13	1	1	NUM
ejpam-6480	95	14	(	(	PUNCT
ejpam-6480	95	15	α−	α−	ADP
ejpam-6480	95	16	1	1	NUM
ejpam-6480	95	17	)	)	PUNCT
ejpam-6480	95	18	[	[	PUNCT
ejpam-6480	95	19	t2	t2	NOUN
ejpam-6480	95	20	h2−α	h2−α	PROPN
ejpam-6480	95	21	2	2	NUM
ejpam-6480	95	22	(	(	PUNCT
ejpam-6480	95	23	t1	t1	NOUN
ejpam-6480	95	24	,	,	PUNCT
ejpam-6480	95	25	t2)−	t2)−	VERB
ejpam-6480	95	26	t1	t1	PROPN
ejpam-6480	95	27	h2−α	h2−α	PROPN
ejpam-6480	95	28	1	1	NUM
ejpam-6480	95	29	(	(	PUNCT
ejpam-6480	95	30	t1	t1	NOUN
ejpam-6480	95	31	,	,	PUNCT
ejpam-6480	95	32	t2)−	t2)−	VERB
ejpam-6480	95	33	1	1	NUM
ejpam-6480	95	34	]	]	PUNCT
ejpam-6480	95	35	(	(	PUNCT
ejpam-6480	95	36	ii	ii	NOUN
ejpam-6480	95	37	)	)	PUNCT
ejpam-6480	95	38	exponential	exponential	ADJ
ejpam-6480	95	39	distribution	distribution	NOUN
ejpam-6480	95	40	:	:	PUNCT
ejpam-6480	95	41	the	the	DET
ejpam-6480	95	42	probability	probability	NOUN
ejpam-6480	95	43	density	density	NOUN
ejpam-6480	95	44	function	function	NOUN
ejpam-6480	95	45	and	and	CCONJ
ejpam-6480	95	46	corresponding	correspond	VERB
ejpam-6480	95	47	cdf	cdf	PROPN
ejpam-6480	95	48	of	of	ADP
ejpam-6480	95	49	exponential	exponential	ADJ
ejpam-6480	95	50	distribution	distribution	NOUN
ejpam-6480	95	51	is	be	AUX
ejpam-6480	95	52	given	give	VERB
ejpam-6480	95	53	by	by	ADP
ejpam-6480	95	54	f(x	f(x	PROPN
ejpam-6480	95	55	)	)	PUNCT
ejpam-6480	95	56	=	=	PUNCT
ejpam-6480	96	1	θe−θx	θe−θx	PROPN
ejpam-6480	96	2	,	,	PUNCT
ejpam-6480	96	3	x	x	X
ejpam-6480	96	4	>	>	X
ejpam-6480	96	5	0	0	PROPN
ejpam-6480	96	6	,	,	PUNCT
ejpam-6480	96	7	θ	θ	PROPN
ejpam-6480	96	8	>	>	X
ejpam-6480	96	9	0	0	PROPN
ejpam-6480	96	10	,	,	PUNCT
ejpam-6480	96	11	f	f	PROPN
ejpam-6480	96	12	(	(	PUNCT
ejpam-6480	96	13	x	x	X
ejpam-6480	96	14	)	)	PUNCT
ejpam-6480	96	15	=	=	SYM
ejpam-6480	96	16	1−	1−	NUM
ejpam-6480	96	17	e−θx	e−θx	NUM
ejpam-6480	96	18	respectively	respectively	ADV
ejpam-6480	96	19	.	.	PUNCT
ejpam-6480	97	1	(	(	PUNCT
ejpam-6480	97	2	α−	α−	ADP
ejpam-6480	97	3	1)kα	1)kα	PROPN
ejpam-6480	97	4	(	(	PUNCT
ejpam-6480	97	5	x	x	NOUN
ejpam-6480	97	6	;	;	PUNCT
ejpam-6480	97	7	t1	t1	NOUN
ejpam-6480	97	8	,	,	PUNCT
ejpam-6480	97	9	t2	t2	NOUN
ejpam-6480	97	10	)	)	PUNCT
ejpam-6480	97	11	=	=	PUNCT
ejpam-6480	97	12	(	(	PUNCT
ejpam-6480	97	13	θ	θ	PROPN
ejpam-6480	97	14	e−θt1−e−θt2	e−θt1−e−θt2	PROPN
ejpam-6480	97	15	)	)	PUNCT
ejpam-6480	97	16	2−α	2−α	PROPN
ejpam-6480	98	1	[	[	X
ejpam-6480	98	2	∫	∫	X
ejpam-6480	98	3	t2	t2	PROPN
ejpam-6480	98	4	t1	t1	PROPN
ejpam-6480	98	5	e−(2−α)θxdx	e−(2−α)θxdx	NOUN
ejpam-6480	98	6	]	]	PUNCT
ejpam-6480	99	1	−	−	PROPN
ejpam-6480	99	2	1	1	NUM
ejpam-6480	99	3	=	=	SYM
ejpam-6480	99	4	1	1	NUM
ejpam-6480	99	5	θ(2−	θ(2−	NOUN
ejpam-6480	99	6	α	α	NOUN
ejpam-6480	99	7	)	)	PUNCT
ejpam-6480	100	1	[	[	X
ejpam-6480	100	2	(	(	PUNCT
ejpam-6480	100	3	θe−θt1	θe−θt1	NOUN
ejpam-6480	100	4	e−θt1−e−θt2	e−θt1−e−θt2	PROPN
ejpam-6480	100	5	)	)	PUNCT
ejpam-6480	100	6	2−α	2−α	PROPN
ejpam-6480	101	1	−	−	PROPN
ejpam-6480	101	2	(	(	PUNCT
ejpam-6480	101	3	θe−θt2	θe−θt2	X
ejpam-6480	101	4	e−θt1−e−θt2	e−θt1−e−θt2	PROPN
ejpam-6480	101	5	)	)	PUNCT
ejpam-6480	101	6	2−α	2−α	NUM
ejpam-6480	101	7	]	]	PUNCT
ejpam-6480	102	1	−	−	NOUN
ejpam-6480	102	2	1	1	NUM
ejpam-6480	102	3	or	or	CCONJ
ejpam-6480	102	4	kα	kα	X
ejpam-6480	102	5	(	(	PUNCT
ejpam-6480	102	6	x	x	X
ejpam-6480	102	7	;	;	PUNCT
ejpam-6480	102	8	t1	t1	NOUN
ejpam-6480	102	9	,	,	PUNCT
ejpam-6480	102	10	t2	t2	NOUN
ejpam-6480	102	11	)	)	PUNCT
ejpam-6480	102	12	=	=	SYM
ejpam-6480	102	13	1	1	NUM
ejpam-6480	102	14	(	(	PUNCT
ejpam-6480	102	15	α−	α−	ADP
ejpam-6480	102	16	1	1	NUM
ejpam-6480	102	17	)	)	PUNCT
ejpam-6480	102	18	[	[	PUNCT
ejpam-6480	102	19	1	1	NUM
ejpam-6480	102	20	θ(2−	θ(2−	NOUN
ejpam-6480	102	21	α	α	NOUN
ejpam-6480	102	22	)	)	PUNCT
ejpam-6480	102	23	(	(	PUNCT
ejpam-6480	102	24	h2−α	h2−α	PROPN
ejpam-6480	102	25	1	1	NUM
ejpam-6480	102	26	(	(	PUNCT
ejpam-6480	102	27	t1	t1	NOUN
ejpam-6480	102	28	,	,	PUNCT
ejpam-6480	102	29	t2)−	t2)−	VERB
ejpam-6480	102	30	h2−α	h2−α	PROPN
ejpam-6480	102	31	2	2	NUM
ejpam-6480	102	32	(	(	PUNCT
ejpam-6480	102	33	t1	t1	NOUN
ejpam-6480	102	34	,	,	PUNCT
ejpam-6480	102	35	t2	t2	NOUN
ejpam-6480	102	36	)	)	PUNCT
ejpam-6480	102	37	)	)	PUNCT
ejpam-6480	102	38	−	−	PROPN
ejpam-6480	103	1	1	1	NUM
ejpam-6480	103	2	]	]	PUNCT
ejpam-6480	103	3	(	(	PUNCT
ejpam-6480	103	4	iii	iii	X
ejpam-6480	103	5	)	)	PUNCT
ejpam-6480	103	6	finite	finite	ADJ
ejpam-6480	103	7	range	range	NOUN
ejpam-6480	103	8	distribution	distribution	NOUN
ejpam-6480	103	9	:	:	PUNCT
ejpam-6480	103	10	the	the	DET
ejpam-6480	103	11	probability	probability	NOUN
ejpam-6480	103	12	density	density	NOUN
ejpam-6480	103	13	function	function	NOUN
ejpam-6480	103	14	and	and	CCONJ
ejpam-6480	103	15	corresponding	correspond	VERB
ejpam-6480	103	16	cdf	cdf	PROPN
ejpam-6480	103	17	of	of	ADP
ejpam-6480	103	18	finite	finite	ADJ
ejpam-6480	103	19	range	range	NOUN
ejpam-6480	103	20	distribution	distribution	NOUN
ejpam-6480	103	21	is	be	AUX
ejpam-6480	103	22	given	give	VERB
ejpam-6480	103	23	by	by	ADP
ejpam-6480	103	24	f(x	f(x	PROPN
ejpam-6480	103	25	)	)	PUNCT
ejpam-6480	104	1	=	=	SYM
ejpam-6480	105	1	ab(1−	ab(1−	ADJ
ejpam-6480	105	2	ax)b−1	ax)b−1	NOUN
ejpam-6480	105	3	,	,	PUNCT
ejpam-6480	105	4	0	0	NUM
ejpam-6480	105	5	<	<	X
ejpam-6480	105	6	x	x	X
ejpam-6480	105	7	<	<	X
ejpam-6480	105	8	1	1	NUM
ejpam-6480	105	9	b	b	PROPN
ejpam-6480	105	10	,	,	PUNCT
ejpam-6480	105	11	a	a	PRON
ejpam-6480	105	12	,	,	PUNCT
ejpam-6480	105	13	b	b	X
ejpam-6480	105	14	>	>	X
ejpam-6480	105	15	0	0	PROPN
ejpam-6480	105	16	,	,	PUNCT
ejpam-6480	105	17	f(x	f(x	PROPN
ejpam-6480	105	18	)	)	PUNCT
ejpam-6480	105	19	=	=	SYM
ejpam-6480	105	20	1−	1−	NUM
ejpam-6480	105	21	(	(	PUNCT
ejpam-6480	105	22	1−	1−	NUM
ejpam-6480	105	23	ax)b	ax)b	PROPN
ejpam-6480	105	24	respectively	respectively	ADV
ejpam-6480	105	25	.	.	PUNCT
ejpam-6480	106	1	(	(	PUNCT
ejpam-6480	106	2	α−	α−	ADP
ejpam-6480	106	3	1)kα	1)kα	PROPN
ejpam-6480	106	4	(	(	PUNCT
ejpam-6480	106	5	x	x	NOUN
ejpam-6480	106	6	;	;	PUNCT
ejpam-6480	106	7	t1	t1	NOUN
ejpam-6480	106	8	,	,	PUNCT
ejpam-6480	106	9	t2	t2	NOUN
ejpam-6480	106	10	)	)	PUNCT
ejpam-6480	106	11	=	=	SYM
ejpam-6480	106	12	(	(	PUNCT
ejpam-6480	106	13	ab	ab	X
ejpam-6480	106	14	(	(	PUNCT
ejpam-6480	106	15	1−	1−	NUM
ejpam-6480	106	16	at1	at1	PROPN
ejpam-6480	106	17	)	)	PUNCT
ejpam-6480	106	18	b	b	NOUN
ejpam-6480	106	19	−	−	PROPN
ejpam-6480	106	20	(	(	PUNCT
ejpam-6480	106	21	1−	1−	NUM
ejpam-6480	106	22	at2	at2	PROPN
ejpam-6480	106	23	)	)	PUNCT
ejpam-6480	106	24	b	b	NOUN
ejpam-6480	106	25	)	)	PUNCT
ejpam-6480	106	26	2−α	2−α	PROPN
ejpam-6480	107	1	[	[	X
ejpam-6480	107	2	∫	∫	X
ejpam-6480	107	3	t2	t2	PROPN
ejpam-6480	107	4	t1	t1	PROPN
ejpam-6480	107	5	(	(	PUNCT
ejpam-6480	107	6	1−	1−	NUM
ejpam-6480	107	7	ax)(b−1)(2−α)dx	ax)(b−1)(2−α)dx	ADV
ejpam-6480	107	8	]	]	PUNCT
ejpam-6480	107	9	−	−	PROPN
ejpam-6480	107	10	1	1	NUM
ejpam-6480	107	11	kα	kα	NOUN
ejpam-6480	107	12	(	(	PUNCT
ejpam-6480	107	13	x	x	NOUN
ejpam-6480	107	14	;	;	PUNCT
ejpam-6480	107	15	t1	t1	NOUN
ejpam-6480	107	16	,	,	PUNCT
ejpam-6480	107	17	t2	t2	NOUN
ejpam-6480	107	18	)	)	PUNCT
ejpam-6480	107	19	=	=	SYM
ejpam-6480	107	20	1	1	NUM
ejpam-6480	107	21	(	(	PUNCT
ejpam-6480	107	22	α−	α−	ADP
ejpam-6480	107	23	1	1	NUM
ejpam-6480	107	24	)	)	PUNCT
ejpam-6480	107	25	)	)	PUNCT
ejpam-6480	108	1	[	[	PUNCT
ejpam-6480	108	2	1	1	NUM
ejpam-6480	108	3	a((2−	a((2−	NUM
ejpam-6480	108	4	α)(b−	α)(b−	NOUN
ejpam-6480	108	5	1	1	NUM
ejpam-6480	108	6	)	)	PUNCT
ejpam-6480	108	7	+	+	CCONJ
ejpam-6480	108	8	1	1	NUM
ejpam-6480	108	9	(	(	PUNCT
ejpam-6480	108	10	(	(	PUNCT
ejpam-6480	108	11	1−	1−	NUM
ejpam-6480	108	12	at1	at1	PROPN
ejpam-6480	108	13	)	)	PUNCT
ejpam-6480	108	14	h	h	NOUN
ejpam-6480	108	15	2−α	2−α	NUM
ejpam-6480	108	16	1	1	NUM
ejpam-6480	108	17	(	(	PUNCT
ejpam-6480	108	18	t1	t1	NOUN
ejpam-6480	108	19	,	,	PUNCT
ejpam-6480	108	20	t2)−	t2)−	NOUN
ejpam-6480	108	21	(	(	PUNCT
ejpam-6480	108	22	1−	1−	NUM
ejpam-6480	108	23	at2	at2	NOUN
ejpam-6480	108	24	)	)	PUNCT
ejpam-6480	108	25	h2−α	h2−α	PROPN
ejpam-6480	108	26	2	2	NUM
ejpam-6480	108	27	(	(	PUNCT
ejpam-6480	108	28	t1	t1	NOUN
ejpam-6480	108	29	,	,	PUNCT
ejpam-6480	108	30	t2	t2	NOUN
ejpam-6480	108	31	)	)	PUNCT
ejpam-6480	108	32	)	)	PUNCT
ejpam-6480	109	1	−	−	PROPN
ejpam-6480	109	2	1	1	NUM
ejpam-6480	109	3	]	]	PUNCT
ejpam-6480	109	4	(	(	PUNCT
ejpam-6480	109	5	iv	iv	X
ejpam-6480	109	6	)	)	PUNCT
ejpam-6480	109	7	power	power	NOUN
ejpam-6480	109	8	distribution	distribution	NOUN
ejpam-6480	109	9	:	:	PUNCT
ejpam-6480	109	10	the	the	DET
ejpam-6480	109	11	density	density	NOUN
ejpam-6480	109	12	function	function	NOUN
ejpam-6480	109	13	and	and	CCONJ
ejpam-6480	109	14	cdf	cdf	PROPN
ejpam-6480	109	15	of	of	ADP
ejpam-6480	109	16	power	power	NOUN
ejpam-6480	109	17	distribution	distribution	NOUN
ejpam-6480	109	18	is	be	AUX
ejpam-6480	109	19	given	give	VERB
ejpam-6480	109	20	as	as	ADP
ejpam-6480	109	21	j.	j.	PROPN
ejpam-6480	109	22	g.	g.	PROPN
ejpam-6480	109	23	dar	dar	PROPN
ejpam-6480	109	24	,	,	PUNCT
ejpam-6480	109	25	s.	s.	PROPN
ejpam-6480	109	26	m.	m.	PROPN
ejpam-6480	109	27	a.	a.	PROPN
ejpam-6480	109	28	alsheikh	alsheikh	PROPN
ejpam-6480	109	29	,	,	PUNCT
ejpam-6480	109	30	p.	p.	PROPN
ejpam-6480	109	31	jadhav	jadhav	PROPN
ejpam-6480	109	32	/	/	SYM
ejpam-6480	109	33	eur	eur	PROPN
ejpam-6480	109	34	.	.	PUNCT
ejpam-6480	110	1	j.	j.	PROPN
ejpam-6480	110	2	pure	pure	PROPN
ejpam-6480	110	3	appl	appl	PROPN
ejpam-6480	110	4	.	.	PROPN
ejpam-6480	110	5	math	math	PROPN
ejpam-6480	110	6	,	,	PUNCT
ejpam-6480	110	7	18	18	NUM
ejpam-6480	110	8	(	(	PUNCT
ejpam-6480	110	9	4	4	NUM
ejpam-6480	110	10	)	)	PUNCT
ejpam-6480	110	11	(	(	PUNCT
ejpam-6480	110	12	2025	2025	NUM
ejpam-6480	110	13	)	)	PUNCT
ejpam-6480	110	14	,	,	PUNCT
ejpam-6480	110	15	6480	6480	NUM
ejpam-6480	110	16	6	6	NUM
ejpam-6480	110	17	of	of	ADP
ejpam-6480	110	18	14	14	NUM
ejpam-6480	110	19	f(x	f(x	PROPN
ejpam-6480	110	20	)	)	PUNCT
ejpam-6480	111	1	=	=	PUNCT
ejpam-6480	112	1	b	b	X
ejpam-6480	112	2	a	a	PRON
ejpam-6480	112	3	(	(	PUNCT
ejpam-6480	112	4	x	x	NOUN
ejpam-6480	112	5	a	a	X
ejpam-6480	112	6	)	)	PUNCT
ejpam-6480	112	7	b−1	b−1	PROPN
ejpam-6480	112	8	,	,	PUNCT
ejpam-6480	112	9	0	0	PUNCT
ejpam-6480	112	10	<	<	X
ejpam-6480	112	11	x	x	X
ejpam-6480	112	12	<	<	X
ejpam-6480	112	13	b	b	PROPN
ejpam-6480	112	14	,	,	PUNCT
ejpam-6480	112	15	b	b	PROPN
ejpam-6480	112	16	>	>	X
ejpam-6480	112	17	0	0	PROPN
ejpam-6480	112	18	,	,	PUNCT
ejpam-6480	112	19	f	f	PROPN
ejpam-6480	112	20	(	(	PUNCT
ejpam-6480	112	21	x	x	X
ejpam-6480	112	22	)	)	PUNCT
ejpam-6480	112	23	=	=	SYM
ejpam-6480	113	1	(	(	PUNCT
ejpam-6480	113	2	x	x	X
ejpam-6480	113	3	a	a	X
ejpam-6480	113	4	)	)	PUNCT
ejpam-6480	113	5	b	b	NOUN
ejpam-6480	113	6	(	(	PUNCT
ejpam-6480	113	7	α−	α−	ADP
ejpam-6480	113	8	1)kα	1)kα	PROPN
ejpam-6480	113	9	(	(	PUNCT
ejpam-6480	113	10	x	x	NOUN
ejpam-6480	113	11	;	;	PUNCT
ejpam-6480	113	12	t1	t1	NOUN
ejpam-6480	113	13	,	,	PUNCT
ejpam-6480	113	14	t2	t2	NOUN
ejpam-6480	113	15	)	)	PUNCT
ejpam-6480	113	16	=	=	PUNCT
ejpam-6480	114	1	(	(	PUNCT
ejpam-6480	114	2	b	b	X
ejpam-6480	114	3	tb2	tb2	PROPN
ejpam-6480	114	4	−	−	PROPN
ejpam-6480	114	5	tb1	tb1	PROPN
ejpam-6480	114	6	)	)	PUNCT
ejpam-6480	114	7	2−α	2−α	PROPN
ejpam-6480	115	1	[	[	X
ejpam-6480	115	2	∫	∫	X
ejpam-6480	115	3	t2	t2	PROPN
ejpam-6480	115	4	t1	t1	PROPN
ejpam-6480	115	5	x(b−1)(2−α)dx	x(b−1)(2−α)dx	PROPN
ejpam-6480	115	6	]	]	PUNCT
ejpam-6480	115	7	−	−	PROPN
ejpam-6480	115	8	1	1	NUM
ejpam-6480	115	9	=	=	SYM
ejpam-6480	115	10	1	1	NUM
ejpam-6480	115	11	(	(	PUNCT
ejpam-6480	115	12	(	(	PUNCT
ejpam-6480	115	13	2−	2−	NUM
ejpam-6480	115	14	α)(b−	α)(b−	NOUN
ejpam-6480	115	15	1	1	NUM
ejpam-6480	115	16	)	)	PUNCT
ejpam-6480	115	17	+	+	CCONJ
ejpam-6480	115	18	1	1	X
ejpam-6480	115	19	)	)	PUNCT
ejpam-6480	115	20	t2	t2	NOUN
ejpam-6480	115	21	(	(	PUNCT
ejpam-6480	115	22	btb−1	btb−1	PROPN
ejpam-6480	115	23	2	2	NUM
ejpam-6480	115	24	tb2	tb2	NOUN
ejpam-6480	115	25	−	−	PROPN
ejpam-6480	115	26	tb1	tb1	PROPN
ejpam-6480	115	27	)	)	PUNCT
ejpam-6480	115	28	2−α	2−α	PROPN
ejpam-6480	116	1	−	−	PROPN
ejpam-6480	116	2	t1	t1	NOUN
ejpam-6480	116	3	(	(	PUNCT
ejpam-6480	116	4	btb−1	btb−1	PROPN
ejpam-6480	116	5	1	1	NUM
ejpam-6480	116	6	tb2	tb2	NOUN
ejpam-6480	116	7	−	−	PROPN
ejpam-6480	116	8	tb1	tb1	PROPN
ejpam-6480	116	9	)	)	PUNCT
ejpam-6480	116	10	2−α	2−α	PROPN
ejpam-6480	117	1	−	−	X
ejpam-6480	117	2	1	1	NUM
ejpam-6480	117	3	or	or	CCONJ
ejpam-6480	117	4	kα	kα	X
ejpam-6480	117	5	(	(	PUNCT
ejpam-6480	117	6	x	x	X
ejpam-6480	117	7	;	;	PUNCT
ejpam-6480	117	8	t1	t1	NOUN
ejpam-6480	117	9	,	,	PUNCT
ejpam-6480	117	10	t2	t2	NOUN
ejpam-6480	117	11	)	)	PUNCT
ejpam-6480	117	12	=	=	SYM
ejpam-6480	117	13	1	1	NUM
ejpam-6480	117	14	(	(	PUNCT
ejpam-6480	117	15	α−	α−	ADP
ejpam-6480	117	16	1	1	NUM
ejpam-6480	117	17	)	)	PUNCT
ejpam-6480	117	18	[	[	PUNCT
ejpam-6480	117	19	1	1	NUM
ejpam-6480	117	20	(	(	PUNCT
ejpam-6480	117	21	(	(	PUNCT
ejpam-6480	117	22	2−	2−	NUM
ejpam-6480	117	23	α)(b−	α)(b−	NOUN
ejpam-6480	117	24	1	1	NUM
ejpam-6480	117	25	)	)	PUNCT
ejpam-6480	117	26	+	+	CCONJ
ejpam-6480	117	27	1	1	X
ejpam-6480	117	28	)	)	PUNCT
ejpam-6480	117	29	(	(	PUNCT
ejpam-6480	117	30	t2	t2	PROPN
ejpam-6480	117	31	h2−α	h2−α	PROPN
ejpam-6480	117	32	2	2	NUM
ejpam-6480	117	33	−	−	NOUN
ejpam-6480	118	1	t1	t1	NOUN
ejpam-6480	118	2	h2−α	h2−α	PROPN
ejpam-6480	118	3	1	1	NUM
ejpam-6480	118	4	(	(	PUNCT
ejpam-6480	118	5	t1	t1	NOUN
ejpam-6480	118	6	,	,	PUNCT
ejpam-6480	118	7	t2	t2	NOUN
ejpam-6480	118	8	)	)	PUNCT
ejpam-6480	118	9	)	)	PUNCT
ejpam-6480	119	1	−	−	PROPN
ejpam-6480	119	2	1	1	NUM
ejpam-6480	119	3	]	]	PUNCT
ejpam-6480	119	4	.	.	PUNCT
ejpam-6480	120	1	to	to	PART
ejpam-6480	120	2	gain	gain	VERB
ejpam-6480	120	3	further	further	ADJ
ejpam-6480	120	4	insights	insight	NOUN
ejpam-6480	120	5	into	into	ADP
ejpam-6480	120	6	the	the	DET
ejpam-6480	120	7	behavior	behavior	NOUN
ejpam-6480	120	8	of	of	ADP
ejpam-6480	120	9	the	the	DET
ejpam-6480	120	10	mathai	mathai	PROPN
ejpam-6480	120	11	-	-	PUNCT
ejpam-6480	120	12	haubold	haubold	PROPN
ejpam-6480	120	13	interval	interval	NOUN
ejpam-6480	120	14	entropy	entropy	NOUN
ejpam-6480	120	15	(	(	PUNCT
ejpam-6480	120	16	mhie	mhie	PROPN
ejpam-6480	120	17	)	)	PUNCT
ejpam-6480	120	18	,	,	PUNCT
ejpam-6480	120	19	we	we	PRON
ejpam-6480	120	20	provide	provide	VERB
ejpam-6480	120	21	graphical	graphical	ADJ
ejpam-6480	120	22	representations	representation	NOUN
ejpam-6480	120	23	of	of	ADP
ejpam-6480	120	24	mhie	mhie	NOUN
ejpam-6480	120	25	for	for	ADP
ejpam-6480	120	26	several	several	ADJ
ejpam-6480	120	27	standard	standard	ADJ
ejpam-6480	120	28	lifetime	lifetime	NOUN
ejpam-6480	120	29	distributions	distribution	NOUN
ejpam-6480	120	30	.	.	PUNCT
ejpam-6480	121	1	figure	figure	VERB
ejpam-6480	121	2	1	1	NUM
ejpam-6480	121	3	:	:	PUNCT
ejpam-6480	121	4	uniform	uniform	ADJ
ejpam-6480	121	5	distribution	distribution	NOUN
ejpam-6480	121	6	figure	figure	NOUN
ejpam-6480	121	7	2	2	NUM
ejpam-6480	121	8	:	:	PUNCT
ejpam-6480	121	9	uniform	uniform	ADJ
ejpam-6480	121	10	distribution	distribution	NOUN
ejpam-6480	121	11	figure	figure	NOUN
ejpam-6480	121	12	3	3	NUM
ejpam-6480	121	13	:	:	PUNCT
ejpam-6480	121	14	exponential	exponential	ADJ
ejpam-6480	121	15	distribution	distribution	NOUN
ejpam-6480	121	16	figure	figure	NOUN
ejpam-6480	121	17	4	4	NUM
ejpam-6480	121	18	:	:	PUNCT
ejpam-6480	121	19	exponential	exponential	ADJ
ejpam-6480	121	20	distribution	distribution	NOUN
ejpam-6480	121	21	j.	j.	PROPN
ejpam-6480	121	22	g.	g.	PROPN
ejpam-6480	121	23	dar	dar	PROPN
ejpam-6480	121	24	,	,	PUNCT
ejpam-6480	121	25	s.	s.	PROPN
ejpam-6480	121	26	m.	m.	PROPN
ejpam-6480	121	27	a.	a.	PROPN
ejpam-6480	121	28	alsheikh	alsheikh	PROPN
ejpam-6480	121	29	,	,	PUNCT
ejpam-6480	121	30	p.	p.	PROPN
ejpam-6480	121	31	jadhav	jadhav	PROPN
ejpam-6480	121	32	/	/	SYM
ejpam-6480	121	33	eur	eur	PROPN
ejpam-6480	121	34	.	.	PUNCT
ejpam-6480	122	1	j.	j.	PROPN
ejpam-6480	122	2	pure	pure	PROPN
ejpam-6480	122	3	appl	appl	PROPN
ejpam-6480	122	4	.	.	PROPN
ejpam-6480	122	5	math	math	PROPN
ejpam-6480	122	6	,	,	PUNCT
ejpam-6480	122	7	18	18	NUM
ejpam-6480	122	8	(	(	PUNCT
ejpam-6480	122	9	4	4	NUM
ejpam-6480	122	10	)	)	PUNCT
ejpam-6480	122	11	(	(	PUNCT
ejpam-6480	122	12	2025	2025	NUM
ejpam-6480	122	13	)	)	PUNCT
ejpam-6480	122	14	,	,	PUNCT
ejpam-6480	122	15	6480	6480	NUM
ejpam-6480	122	16	7	7	NUM
ejpam-6480	122	17	of	of	ADP
ejpam-6480	122	18	14	14	NUM
ejpam-6480	122	19	figure	figure	NOUN
ejpam-6480	122	20	5	5	NUM
ejpam-6480	122	21	:	:	PUNCT
ejpam-6480	122	22	power	power	NOUN
ejpam-6480	122	23	distribution	distribution	NOUN
ejpam-6480	122	24	figure	figure	NOUN
ejpam-6480	122	25	6	6	NUM
ejpam-6480	122	26	:	:	PUNCT
ejpam-6480	122	27	power	power	NOUN
ejpam-6480	122	28	distribution	distribution	NOUN
ejpam-6480	122	29	3	3	X
ejpam-6480	122	30	.	.	PUNCT
ejpam-6480	123	1	some	some	DET
ejpam-6480	123	2	characterization	characterization	NOUN
ejpam-6480	123	3	results	result	NOUN
ejpam-6480	123	4	:	:	PUNCT
ejpam-6480	123	5	theorem	theorem	VERB
ejpam-6480	123	6	3.1	3.1	NUM
ejpam-6480	123	7	.	.	PUNCT
ejpam-6480	124	1	let	let	VERB
ejpam-6480	124	2	x	x	PRON
ejpam-6480	124	3	be	be	AUX
ejpam-6480	124	4	the	the	DET
ejpam-6480	124	5	non	non	ADJ
ejpam-6480	124	6	-	-	ADJ
ejpam-6480	124	7	negative	negative	ADJ
ejpam-6480	124	8	random	random	ADJ
ejpam-6480	124	9	variable	variable	NOUN
ejpam-6480	124	10	having	have	VERB
ejpam-6480	124	11	continuous	continuous	ADJ
ejpam-6480	124	12	density	density	NOUN
ejpam-6480	124	13	function	function	NOUN
ejpam-6480	124	14	f(x	f(x	PROPN
ejpam-6480	124	15	)	)	PUNCT
ejpam-6480	124	16	and	and	CCONJ
ejpam-6480	124	17	distribution	distribution	NOUN
ejpam-6480	124	18	function	function	NOUN
ejpam-6480	124	19	f(x	f(x	PROPN
ejpam-6480	124	20	)	)	PUNCT
ejpam-6480	124	21	.	.	PUNCT
ejpam-6480	125	1	assume	assume	VERB
ejpam-6480	125	2	that	that	SCONJ
ejpam-6480	125	3	kα	kα	PROPN
ejpam-6480	125	4	(	(	PUNCT
ejpam-6480	125	5	x	x	X
ejpam-6480	125	6	;	;	PUNCT
ejpam-6480	125	7	t1	t1	NOUN
ejpam-6480	125	8	,	,	PUNCT
ejpam-6480	125	9	t2	t2	NOUN
ejpam-6480	125	10	)	)	PUNCT
ejpam-6480	125	11	is	be	AUX
ejpam-6480	125	12	increasing	increase	VERB
ejpam-6480	125	13	with	with	ADP
ejpam-6480	125	14	respect	respect	NOUN
ejpam-6480	125	15	to	to	ADP
ejpam-6480	125	16	t1	t1	NOUN
ejpam-6480	125	17	and	and	CCONJ
ejpam-6480	125	18	t2	t2	PROPN
ejpam-6480	125	19	,	,	PUNCT
ejpam-6480	125	20	then	then	ADV
ejpam-6480	125	21	kα	kα	X
ejpam-6480	125	22	(	(	PUNCT
ejpam-6480	125	23	x	x	X
ejpam-6480	125	24	;	;	PUNCT
ejpam-6480	125	25	t1	t1	NOUN
ejpam-6480	125	26	,	,	PUNCT
ejpam-6480	125	27	t2	t2	NOUN
ejpam-6480	125	28	)	)	PUNCT
ejpam-6480	125	29	uniquely	uniquely	ADV
ejpam-6480	125	30	determine	determine	VERB
ejpam-6480	125	31	the	the	DET
ejpam-6480	125	32	distribution	distribution	NOUN
ejpam-6480	125	33	function	function	NOUN
ejpam-6480	125	34	f(x	f(x	PROPN
ejpam-6480	125	35	)	)	PUNCT
ejpam-6480	125	36	.	.	PUNCT
ejpam-6480	126	1	proof	proof	NOUN
ejpam-6480	126	2	:	:	PUNCT
ejpam-6480	126	3	differentiating	differentiate	VERB
ejpam-6480	126	4	(	(	PUNCT
ejpam-6480	126	5	2.2	2.2	NUM
ejpam-6480	126	6	)	)	PUNCT
ejpam-6480	126	7	partially	partially	ADV
ejpam-6480	126	8	with	with	ADP
ejpam-6480	126	9	respect	respect	NOUN
ejpam-6480	126	10	to	to	ADP
ejpam-6480	126	11	t1	t1	NOUN
ejpam-6480	126	12	and	and	CCONJ
ejpam-6480	126	13	t2	t2	NOUN
ejpam-6480	126	14	,	,	PUNCT
ejpam-6480	126	15	we	we	PRON
ejpam-6480	126	16	get	get	VERB
ejpam-6480	126	17	(	(	PUNCT
ejpam-6480	126	18	α−	α−	ADP
ejpam-6480	126	19	1	1	NUM
ejpam-6480	126	20	)	)	PUNCT
ejpam-6480	126	21	∂	∂	NOUN
ejpam-6480	127	1	∂t1	∂t1	NOUN
ejpam-6480	127	2	kα	kα	PROPN
ejpam-6480	127	3	(	(	PUNCT
ejpam-6480	127	4	x	x	NOUN
ejpam-6480	127	5	;	;	PUNCT
ejpam-6480	127	6	t1	t1	NOUN
ejpam-6480	127	7	,	,	PUNCT
ejpam-6480	127	8	t2	t2	NOUN
ejpam-6480	127	9	)	)	PUNCT
ejpam-6480	127	10	=	=	PUNCT
ejpam-6480	127	11	(	(	PUNCT
ejpam-6480	127	12	2−	2−	NUM
ejpam-6480	127	13	α	α	NOUN
ejpam-6480	127	14	)	)	PUNCT
ejpam-6480	127	15	∫	∫	PROPN
ejpam-6480	127	16	t2	t2	PROPN
ejpam-6480	127	17	t1	t1	PROPN
ejpam-6480	127	18	f2−α(x)f	f2−α(x)f	NUM
ejpam-6480	127	19	(	(	PUNCT
ejpam-6480	127	20	t1	t1	NOUN
ejpam-6480	127	21	)	)	PUNCT
ejpam-6480	127	22	dx	dx	PROPN
ejpam-6480	127	23	(	(	PUNCT
ejpam-6480	127	24	f	f	X
ejpam-6480	127	25	(	(	PUNCT
ejpam-6480	127	26	t2)−	t2)−	NOUN
ejpam-6480	127	27	f	f	X
ejpam-6480	127	28	(	(	PUNCT
ejpam-6480	127	29	t1	t1	NOUN
ejpam-6480	127	30	)	)	PUNCT
ejpam-6480	127	31	)	)	PUNCT
ejpam-6480	128	1	3−α	3−α	NUM
ejpam-6480	128	2	−	−	PROPN
ejpam-6480	128	3	(	(	PUNCT
ejpam-6480	128	4	f	f	PROPN
ejpam-6480	128	5	(	(	PUNCT
ejpam-6480	128	6	t1	t1	NOUN
ejpam-6480	128	7	)	)	PUNCT
ejpam-6480	128	8	f	f	PROPN
ejpam-6480	128	9	(	(	PUNCT
ejpam-6480	128	10	t2)−	t2)−	NOUN
ejpam-6480	128	11	f	f	X
ejpam-6480	128	12	(	(	PUNCT
ejpam-6480	128	13	t1	t1	PROPN
ejpam-6480	128	14	)	)	PUNCT
ejpam-6480	128	15	)	)	PUNCT
ejpam-6480	128	16	2−α	2−α	NUM
ejpam-6480	129	1	and	and	CCONJ
ejpam-6480	129	2	(	(	PUNCT
ejpam-6480	129	3	α−	α−	ADP
ejpam-6480	129	4	1	1	NUM
ejpam-6480	129	5	)	)	PUNCT
ejpam-6480	129	6	∂	∂	NOUN
ejpam-6480	129	7	∂t2	∂t2	NOUN
ejpam-6480	129	8	kα	kα	X
ejpam-6480	129	9	(	(	PUNCT
ejpam-6480	129	10	x	x	NOUN
ejpam-6480	129	11	;	;	PUNCT
ejpam-6480	129	12	t1	t1	NOUN
ejpam-6480	129	13	,	,	PUNCT
ejpam-6480	129	14	t2	t2	NOUN
ejpam-6480	129	15	)	)	PUNCT
ejpam-6480	129	16	=	=	PUNCT
ejpam-6480	129	17	(	(	PUNCT
ejpam-6480	129	18	2−	2−	NUM
ejpam-6480	129	19	α	α	NOUN
ejpam-6480	129	20	)	)	PUNCT
ejpam-6480	129	21	∫	∫	PROPN
ejpam-6480	129	22	t2	t2	PROPN
ejpam-6480	129	23	t1	t1	PROPN
ejpam-6480	129	24	f2−α(x)f	f2−α(x)f	NUM
ejpam-6480	129	25	(	(	PUNCT
ejpam-6480	129	26	t1	t1	NOUN
ejpam-6480	129	27	)	)	PUNCT
ejpam-6480	129	28	dx	dx	PROPN
ejpam-6480	129	29	(	(	PUNCT
ejpam-6480	129	30	f	f	X
ejpam-6480	129	31	(	(	PUNCT
ejpam-6480	129	32	t2)−	t2)−	NOUN
ejpam-6480	129	33	f	f	X
ejpam-6480	129	34	(	(	PUNCT
ejpam-6480	129	35	t1	t1	NOUN
ejpam-6480	129	36	)	)	PUNCT
ejpam-6480	129	37	)	)	PUNCT
ejpam-6480	130	1	3−α	3−α	NUM
ejpam-6480	130	2	−	−	PROPN
ejpam-6480	130	3	(	(	PUNCT
ejpam-6480	130	4	f	f	PROPN
ejpam-6480	130	5	(	(	PUNCT
ejpam-6480	130	6	t2	t2	PROPN
ejpam-6480	130	7	)	)	PUNCT
ejpam-6480	130	8	f	f	PROPN
ejpam-6480	130	9	(	(	PUNCT
ejpam-6480	130	10	t2)−	t2)−	NOUN
ejpam-6480	130	11	f	f	X
ejpam-6480	130	12	(	(	PUNCT
ejpam-6480	130	13	t1	t1	PROPN
ejpam-6480	130	14	)	)	PUNCT
ejpam-6480	130	15	)	)	PUNCT
ejpam-6480	130	16	2−α	2−α	PROPN
ejpam-6480	130	17	after	after	ADP
ejpam-6480	130	18	simplification	simplification	NOUN
ejpam-6480	130	19	,	,	PUNCT
ejpam-6480	130	20	we	we	PRON
ejpam-6480	130	21	get	get	VERB
ejpam-6480	130	22	(	(	PUNCT
ejpam-6480	130	23	α−	α−	ADP
ejpam-6480	130	24	1	1	NUM
ejpam-6480	130	25	)	)	PUNCT
ejpam-6480	130	26	∂	∂	NOUN
ejpam-6480	131	1	∂t1	∂t1	NOUN
ejpam-6480	131	2	kα	kα	PROPN
ejpam-6480	131	3	(	(	PUNCT
ejpam-6480	131	4	x	x	NOUN
ejpam-6480	131	5	;	;	PUNCT
ejpam-6480	131	6	t1	t1	NOUN
ejpam-6480	131	7	,	,	PUNCT
ejpam-6480	131	8	t2	t2	NOUN
ejpam-6480	131	9	)	)	PUNCT
ejpam-6480	131	10	=	=	PUNCT
ejpam-6480	132	1	−h2−α	−h2−α	PROPN
ejpam-6480	132	2	1	1	NUM
ejpam-6480	132	3	(	(	PUNCT
ejpam-6480	132	4	t1	t1	NOUN
ejpam-6480	132	5	,	,	PUNCT
ejpam-6480	132	6	t2	t2	NOUN
ejpam-6480	132	7	)	)	PUNCT
ejpam-6480	132	8	+	+	CCONJ
ejpam-6480	132	9	(	(	PUNCT
ejpam-6480	132	10	2−	2−	NUM
ejpam-6480	132	11	α)(α−	α)(α−	NOUN
ejpam-6480	132	12	1)h1	1)h1	PROPN
ejpam-6480	132	13	(	(	PUNCT
ejpam-6480	132	14	t1	t1	PROPN
ejpam-6480	132	15	,	,	PUNCT
ejpam-6480	132	16	t2)kα	t2)kα	PROPN
ejpam-6480	132	17	(	(	PUNCT
ejpam-6480	132	18	x	x	NOUN
ejpam-6480	132	19	;	;	PUNCT
ejpam-6480	132	20	t1	t1	NOUN
ejpam-6480	132	21	,	,	PUNCT
ejpam-6480	132	22	t2	t2	NOUN
ejpam-6480	132	23	)	)	PUNCT
ejpam-6480	132	24	(	(	PUNCT
ejpam-6480	132	25	α−	α−	ADP
ejpam-6480	132	26	1	1	NUM
ejpam-6480	132	27	)	)	PUNCT
ejpam-6480	132	28	∂	∂	NOUN
ejpam-6480	132	29	∂t2	∂t2	NOUN
ejpam-6480	132	30	kα	kα	X
ejpam-6480	132	31	(	(	PUNCT
ejpam-6480	132	32	x	x	NOUN
ejpam-6480	132	33	;	;	PUNCT
ejpam-6480	132	34	t1	t1	NOUN
ejpam-6480	132	35	,	,	PUNCT
ejpam-6480	132	36	t2	t2	NOUN
ejpam-6480	132	37	)	)	PUNCT
ejpam-6480	132	38	=	=	PUNCT
ejpam-6480	133	1	−h2−α	−h2−α	PROPN
ejpam-6480	133	2	2	2	NUM
ejpam-6480	133	3	(	(	PUNCT
ejpam-6480	133	4	t1	t1	NOUN
ejpam-6480	133	5	,	,	PUNCT
ejpam-6480	133	6	t2	t2	NOUN
ejpam-6480	133	7	)	)	PUNCT
ejpam-6480	133	8	+	+	CCONJ
ejpam-6480	133	9	(	(	PUNCT
ejpam-6480	133	10	2−	2−	NUM
ejpam-6480	133	11	α)(α−	α)(α−	NUM
ejpam-6480	133	12	1)h2	1)h2	NUM
ejpam-6480	133	13	(	(	PUNCT
ejpam-6480	133	14	t1	t1	PROPN
ejpam-6480	133	15	,	,	PUNCT
ejpam-6480	133	16	t2)kα	t2)kα	PROPN
ejpam-6480	133	17	(	(	PUNCT
ejpam-6480	133	18	x	x	NOUN
ejpam-6480	133	19	;	;	PUNCT
ejpam-6480	133	20	t1	t1	NOUN
ejpam-6480	133	21	,	,	PUNCT
ejpam-6480	133	22	t2	t2	NOUN
ejpam-6480	133	23	)	)	PUNCT
ejpam-6480	133	24	or	or	CCONJ
ejpam-6480	133	25	h2−α	h2−α	PROPN
ejpam-6480	133	26	1	1	NUM
ejpam-6480	133	27	(	(	PUNCT
ejpam-6480	133	28	t1	t1	NOUN
ejpam-6480	133	29	,	,	PUNCT
ejpam-6480	133	30	t2	t2	NOUN
ejpam-6480	133	31	)	)	PUNCT
ejpam-6480	133	32	=	=	PUNCT
ejpam-6480	133	33	(	(	PUNCT
ejpam-6480	133	34	2−	2−	NUM
ejpam-6480	133	35	α)(α−	α)(α−	PROPN
ejpam-6480	133	36	1)h1	1)h1	PROPN
ejpam-6480	133	37	(	(	PUNCT
ejpam-6480	133	38	t1	t1	PROPN
ejpam-6480	133	39	,	,	PUNCT
ejpam-6480	133	40	t2)kα	t2)kα	PROPN
ejpam-6480	133	41	(	(	PUNCT
ejpam-6480	133	42	x	x	NOUN
ejpam-6480	133	43	;	;	PUNCT
ejpam-6480	133	44	t1	t1	NUM
ejpam-6480	133	45	,	,	PUNCT
ejpam-6480	133	46	t2)−	t2)−	X
ejpam-6480	133	47	(	(	PUNCT
ejpam-6480	133	48	α−	α−	ADP
ejpam-6480	133	49	1	1	NUM
ejpam-6480	133	50	)	)	PUNCT
ejpam-6480	133	51	∂	∂	NOUN
ejpam-6480	133	52	∂t1	∂t1	NOUN
ejpam-6480	133	53	kα	kα	PROPN
ejpam-6480	133	54	(	(	PUNCT
ejpam-6480	133	55	x	x	NOUN
ejpam-6480	133	56	;	;	PUNCT
ejpam-6480	133	57	t1	t1	NOUN
ejpam-6480	133	58	,	,	PUNCT
ejpam-6480	133	59	t2	t2	NOUN
ejpam-6480	133	60	)	)	PUNCT
ejpam-6480	133	61	h2−α	h2−α	PROPN
ejpam-6480	133	62	2	2	NUM
ejpam-6480	133	63	(	(	PUNCT
ejpam-6480	133	64	t1	t1	NOUN
ejpam-6480	133	65	,	,	PUNCT
ejpam-6480	133	66	t2	t2	NOUN
ejpam-6480	133	67	)	)	PUNCT
ejpam-6480	133	68	=	=	PUNCT
ejpam-6480	133	69	(	(	PUNCT
ejpam-6480	133	70	2−	2−	NUM
ejpam-6480	133	71	α)(α−	α)(α−	NUM
ejpam-6480	133	72	1)h2	1)h2	NUM
ejpam-6480	133	73	(	(	PUNCT
ejpam-6480	133	74	t1	t1	PROPN
ejpam-6480	133	75	,	,	PUNCT
ejpam-6480	133	76	t2)kα	t2)kα	PROPN
ejpam-6480	133	77	(	(	PUNCT
ejpam-6480	133	78	x	x	NOUN
ejpam-6480	133	79	;	;	PUNCT
ejpam-6480	133	80	t1	t1	NOUN
ejpam-6480	133	81	,	,	PUNCT
ejpam-6480	133	82	t2	t2	NOUN
ejpam-6480	133	83	)	)	PUNCT
ejpam-6480	133	84	+	+	CCONJ
ejpam-6480	133	85	(	(	PUNCT
ejpam-6480	133	86	α−	α−	ADP
ejpam-6480	133	87	j.	j.	PROPN
ejpam-6480	133	88	g.	g.	PROPN
ejpam-6480	133	89	dar	dar	PROPN
ejpam-6480	133	90	,	,	PUNCT
ejpam-6480	133	91	s.	s.	PROPN
ejpam-6480	133	92	m.	m.	PROPN
ejpam-6480	133	93	a.	a.	PROPN
ejpam-6480	133	94	alsheikh	alsheikh	PROPN
ejpam-6480	133	95	,	,	PUNCT
ejpam-6480	133	96	p.	p.	PROPN
ejpam-6480	133	97	jadhav	jadhav	PROPN
ejpam-6480	133	98	/	/	SYM
ejpam-6480	133	99	eur	eur	PROPN
ejpam-6480	133	100	.	.	PUNCT
ejpam-6480	134	1	j.	j.	PROPN
ejpam-6480	134	2	pure	pure	PROPN
ejpam-6480	134	3	appl	appl	PROPN
ejpam-6480	134	4	.	.	PROPN
ejpam-6480	134	5	math	math	PROPN
ejpam-6480	134	6	,	,	PUNCT
ejpam-6480	134	7	18	18	NUM
ejpam-6480	134	8	(	(	PUNCT
ejpam-6480	134	9	4	4	NUM
ejpam-6480	134	10	)	)	PUNCT
ejpam-6480	134	11	(	(	PUNCT
ejpam-6480	134	12	2025	2025	NUM
ejpam-6480	134	13	)	)	PUNCT
ejpam-6480	134	14	,	,	PUNCT
ejpam-6480	134	15	6480	6480	NUM
ejpam-6480	134	16	8	8	NUM
ejpam-6480	134	17	of	of	ADP
ejpam-6480	134	18	14	14	NUM
ejpam-6480	134	19	(	(	PUNCT
ejpam-6480	134	20	i	i	NOUN
ejpam-6480	134	21	)	)	PUNCT
ejpam-6480	134	22	∂	∂	PUNCT
ejpam-6480	135	1	∂t2	∂t2	NOUN
ejpam-6480	136	1	kα	kα	X
ejpam-6480	136	2	(	(	PUNCT
ejpam-6480	136	3	x	x	NOUN
ejpam-6480	136	4	;	;	PUNCT
ejpam-6480	136	5	t1	t1	NOUN
ejpam-6480	136	6	,	,	PUNCT
ejpam-6480	136	7	t2	t2	NOUN
ejpam-6480	136	8	)	)	PUNCT
ejpam-6480	136	9	now	now	ADV
ejpam-6480	136	10	for	for	ADP
ejpam-6480	136	11	any	any	DET
ejpam-6480	136	12	fixed	fix	VERB
ejpam-6480	136	13	t1	t1	NOUN
ejpam-6480	136	14	and	and	CCONJ
ejpam-6480	136	15	t2	t2	NOUN
ejpam-6480	136	16	,	,	PUNCT
ejpam-6480	136	17	h1	h1	PROPN
ejpam-6480	136	18	(	(	PUNCT
ejpam-6480	136	19	t1	t1	NOUN
ejpam-6480	136	20	,	,	PUNCT
ejpam-6480	136	21	t2	t2	NOUN
ejpam-6480	136	22	)	)	PUNCT
ejpam-6480	136	23	and	and	CCONJ
ejpam-6480	136	24	h2	h2	PROPN
ejpam-6480	136	25	(	(	PUNCT
ejpam-6480	136	26	t1	t1	NOUN
ejpam-6480	136	27	,	,	PUNCT
ejpam-6480	136	28	t2	t2	NOUN
ejpam-6480	136	29	)	)	PUNCT
ejpam-6480	136	30	is	be	AUX
ejpam-6480	136	31	a	a	DET
ejpam-6480	136	32	positive	positive	ADJ
ejpam-6480	136	33	solution	solution	NOUN
ejpam-6480	136	34	of	of	ADP
ejpam-6480	136	35	the	the	DET
ejpam-6480	136	36	equation	equation	NOUN
ejpam-6480	136	37	ξ	ξ	X
ejpam-6480	136	38	(	(	PUNCT
ejpam-6480	136	39	xt2	xt2	X
ejpam-6480	136	40	)	)	PUNCT
ejpam-6480	136	41	=	=	SYM
ejpam-6480	136	42	0	0	NUM
ejpam-6480	136	43	and	and	CCONJ
ejpam-6480	136	44	ψ	ψ	X
ejpam-6480	136	45	(	(	PUNCT
ejpam-6480	136	46	yt1	yt1	NOUN
ejpam-6480	136	47	)	)	PUNCT
ejpam-6480	136	48	=	=	SYM
ejpam-6480	136	49	0	0	NUM
ejpam-6480	136	50	,	,	PUNCT
ejpam-6480	136	51	where	where	SCONJ
ejpam-6480	136	52	ξ	ξ	X
ejpam-6480	136	53	(	(	PUNCT
ejpam-6480	136	54	xt2	xt2	PROPN
ejpam-6480	136	55	)	)	PUNCT
ejpam-6480	136	56	=	=	PUNCT
ejpam-6480	136	57	(	(	PUNCT
ejpam-6480	136	58	xt2	xt2	PROPN
ejpam-6480	136	59	)	)	PUNCT
ejpam-6480	136	60	2−α	2−α	NUM
ejpam-6480	137	1	−	−	PROPN
ejpam-6480	137	2	(	(	PUNCT
ejpam-6480	137	3	2−	2−	NUM
ejpam-6480	137	4	α)(α−	α)(α−	PRON
ejpam-6480	137	5	1)xt2	1)xt2	NUM
ejpam-6480	137	6	kα	kα	PROPN
ejpam-6480	137	7	(	(	PUNCT
ejpam-6480	137	8	x	x	X
ejpam-6480	137	9	;	;	PUNCT
ejpam-6480	137	10	t1	t1	NUM
ejpam-6480	137	11	,	,	PUNCT
ejpam-6480	137	12	t2)−	t2)−	X
ejpam-6480	137	13	(	(	PUNCT
ejpam-6480	137	14	α−	α−	ADP
ejpam-6480	137	15	1	1	NUM
ejpam-6480	137	16	)	)	PUNCT
ejpam-6480	137	17	∂	∂	NOUN
ejpam-6480	137	18	∂t2	∂t2	NOUN
ejpam-6480	137	19	kα	kα	X
ejpam-6480	137	20	(	(	PUNCT
ejpam-6480	137	21	x	x	NOUN
ejpam-6480	137	22	;	;	PUNCT
ejpam-6480	137	23	t1	t1	NOUN
ejpam-6480	137	24	,	,	PUNCT
ejpam-6480	137	25	t2	t2	NOUN
ejpam-6480	137	26	)	)	PUNCT
ejpam-6480	137	27	(	(	PUNCT
ejpam-6480	137	28	3.1	3.1	NUM
ejpam-6480	137	29	)	)	PUNCT
ejpam-6480	137	30	and	and	CCONJ
ejpam-6480	137	31	ψ	ψ	X
ejpam-6480	137	32	(	(	PUNCT
ejpam-6480	137	33	yt1	yt1	NOUN
ejpam-6480	137	34	)	)	PUNCT
ejpam-6480	137	35	=	=	SYM
ejpam-6480	137	36	(	(	PUNCT
ejpam-6480	137	37	yt1	yt1	PROPN
ejpam-6480	137	38	)	)	PUNCT
ejpam-6480	137	39	2−α	2−α	NUM
ejpam-6480	138	1	−	−	PROPN
ejpam-6480	138	2	(	(	PUNCT
ejpam-6480	138	3	2−	2−	NUM
ejpam-6480	138	4	α)(α−	α)(α−	NUM
ejpam-6480	138	5	1)yt1	1)yt1	NUM
ejpam-6480	138	6	kα	kα	NOUN
ejpam-6480	138	7	(	(	PUNCT
ejpam-6480	138	8	x	x	NOUN
ejpam-6480	138	9	;	;	PUNCT
ejpam-6480	138	10	t1	t1	NOUN
ejpam-6480	138	11	,	,	PUNCT
ejpam-6480	138	12	t2	t2	NOUN
ejpam-6480	138	13	)	)	PUNCT
ejpam-6480	138	14	+	+	CCONJ
ejpam-6480	138	15	(	(	PUNCT
ejpam-6480	138	16	α−	α−	ADP
ejpam-6480	138	17	1	1	NUM
ejpam-6480	138	18	)	)	PUNCT
ejpam-6480	138	19	∂	∂	NOUN
ejpam-6480	138	20	∂t1	∂t1	NOUN
ejpam-6480	138	21	kα	kα	PROPN
ejpam-6480	138	22	(	(	PUNCT
ejpam-6480	138	23	x	x	NOUN
ejpam-6480	138	24	;	;	PUNCT
ejpam-6480	138	25	t1	t1	NOUN
ejpam-6480	138	26	,	,	PUNCT
ejpam-6480	138	27	t2	t2	NOUN
ejpam-6480	138	28	)	)	PUNCT
ejpam-6480	138	29	(	(	PUNCT
ejpam-6480	138	30	3.2	3.2	NUM
ejpam-6480	138	31	)	)	PUNCT
ejpam-6480	138	32	differentiating	differentiate	VERB
ejpam-6480	138	33	partially	partially	ADV
ejpam-6480	138	34	with	with	ADP
ejpam-6480	138	35	respect	respect	NOUN
ejpam-6480	138	36	to	to	ADP
ejpam-6480	138	37	xt2	xt2	PROPN
ejpam-6480	138	38	and	and	CCONJ
ejpam-6480	138	39	yt1	yt1	X
ejpam-6480	138	40	,	,	PUNCT
ejpam-6480	138	41	we	we	PRON
ejpam-6480	138	42	obtain	obtain	VERB
ejpam-6480	138	43	ξ′	ξ′	NOUN
ejpam-6480	138	44	(	(	PUNCT
ejpam-6480	138	45	xt2	xt2	PROPN
ejpam-6480	138	46	)	)	PUNCT
ejpam-6480	138	47	=	=	PUNCT
ejpam-6480	139	1	(	(	PUNCT
ejpam-6480	139	2	2−	2−	NUM
ejpam-6480	139	3	α	α	NOUN
ejpam-6480	139	4	)	)	PUNCT
ejpam-6480	139	5	(	(	PUNCT
ejpam-6480	139	6	xt2	xt2	PROPN
ejpam-6480	139	7	)	)	PUNCT
ejpam-6480	139	8	1−α	1−α	NUM
ejpam-6480	140	1	−	−	PROPN
ejpam-6480	140	2	(	(	PUNCT
ejpam-6480	140	3	2−	2−	NUM
ejpam-6480	140	4	α)(α−	α)(α−	PROPN
ejpam-6480	140	5	1)kα	1)kα	PROPN
ejpam-6480	140	6	(	(	PUNCT
ejpam-6480	140	7	x	x	NOUN
ejpam-6480	140	8	;	;	PUNCT
ejpam-6480	140	9	t1	t1	NOUN
ejpam-6480	140	10	,	,	PUNCT
ejpam-6480	140	11	t2	t2	NOUN
ejpam-6480	140	12	)	)	PUNCT
ejpam-6480	140	13	(	(	PUNCT
ejpam-6480	140	14	3.3	3.3	NUM
ejpam-6480	140	15	)	)	PUNCT
ejpam-6480	140	16	ψ′	ψ′	PUNCT
ejpam-6480	140	17	(	(	PUNCT
ejpam-6480	140	18	yt1	yt1	NOUN
ejpam-6480	140	19	)	)	PUNCT
ejpam-6480	140	20	=	=	PUNCT
ejpam-6480	141	1	(	(	PUNCT
ejpam-6480	141	2	2−	2−	NUM
ejpam-6480	141	3	α	α	NOUN
ejpam-6480	141	4	)	)	PUNCT
ejpam-6480	141	5	(	(	PUNCT
ejpam-6480	141	6	yt1	yt1	PROPN
ejpam-6480	141	7	)	)	PUNCT
ejpam-6480	141	8	1−α	1−α	NUM
ejpam-6480	142	1	−	−	PROPN
ejpam-6480	142	2	(	(	PUNCT
ejpam-6480	142	3	2−	2−	NUM
ejpam-6480	142	4	α)(α−	α)(α−	PROPN
ejpam-6480	142	5	1)kα	1)kα	PROPN
ejpam-6480	142	6	(	(	PUNCT
ejpam-6480	142	7	x	x	NOUN
ejpam-6480	142	8	;	;	PUNCT
ejpam-6480	142	9	t1	t1	NOUN
ejpam-6480	142	10	,	,	PUNCT
ejpam-6480	142	11	t2	t2	NOUN
ejpam-6480	142	12	)	)	PUNCT
ejpam-6480	142	13	(	(	PUNCT
ejpam-6480	142	14	3.4	3.4	NUM
ejpam-6480	142	15	)	)	PUNCT
ejpam-6480	142	16	for	for	ADP
ejpam-6480	142	17	extreme	extreme	ADJ
ejpam-6480	142	18	values	value	NOUN
ejpam-6480	142	19	,	,	PUNCT
ejpam-6480	142	20	ξ′	ξ′	X
ejpam-6480	142	21	(	(	PUNCT
ejpam-6480	142	22	xt2	xt2	PROPN
ejpam-6480	142	23	)	)	PUNCT
ejpam-6480	142	24	=	=	SYM
ejpam-6480	143	1	0	0	NUM
ejpam-6480	143	2	,	,	PUNCT
ejpam-6480	143	3	ψ′	ψ′	PUNCT
ejpam-6480	143	4	(	(	PUNCT
ejpam-6480	143	5	yt1	yt1	NOUN
ejpam-6480	143	6	)	)	PUNCT
ejpam-6480	143	7	=	=	SYM
ejpam-6480	144	1	0	0	NUM
ejpam-6480	144	2	,	,	PUNCT
ejpam-6480	144	3	which	which	PRON
ejpam-6480	144	4	gives	give	VERB
ejpam-6480	144	5	xt2	xt2	PROPN
ejpam-6480	144	6	=	=	PUNCT
ejpam-6480	145	1	[	[	X
ejpam-6480	145	2	(	(	PUNCT
ejpam-6480	145	3	α−	α−	ADP
ejpam-6480	145	4	1)kα	1)kα	PROPN
ejpam-6480	145	5	(	(	PUNCT
ejpam-6480	145	6	x	x	NOUN
ejpam-6480	145	7	;	;	PUNCT
ejpam-6480	145	8	t1	t1	NOUN
ejpam-6480	145	9	,	,	PUNCT
ejpam-6480	145	10	t2	t2	NOUN
ejpam-6480	145	11	)	)	PUNCT
ejpam-6480	145	12	]	]	PUNCT
ejpam-6480	145	13	1	1	NUM
ejpam-6480	145	14	1−α	1−α	NUM
ejpam-6480	145	15	=	=	SYM
ejpam-6480	145	16	yt1	yt1	X
ejpam-6480	145	17	.	.	PUNCT
ejpam-6480	146	1	further	far	ADV
ejpam-6480	146	2	more	more	ADJ
ejpam-6480	146	3	ξ′′	ξ′′	NOUN
ejpam-6480	146	4	(	(	PUNCT
ejpam-6480	146	5	xt2	xt2	PROPN
ejpam-6480	146	6	)	)	PUNCT
ejpam-6480	146	7	=	=	PUNCT
ejpam-6480	146	8	(	(	PUNCT
ejpam-6480	146	9	2−	2−	NUM
ejpam-6480	146	10	α)(1−	α)(1−	PROPN
ejpam-6480	146	11	α	α	NOUN
ejpam-6480	146	12	)	)	PUNCT
ejpam-6480	146	13	(	(	PUNCT
ejpam-6480	146	14	xt2	xt2	PROPN
ejpam-6480	146	15	)	)	PUNCT
ejpam-6480	146	16	−α	−α	PROPN
ejpam-6480	146	17	and	and	CCONJ
ejpam-6480	146	18	ψ′′	ψ′′	PROPN
ejpam-6480	146	19	(	(	PUNCT
ejpam-6480	146	20	yt1	yt1	NOUN
ejpam-6480	146	21	)	)	PUNCT
ejpam-6480	146	22	=	=	NOUN
ejpam-6480	146	23	(	(	PUNCT
ejpam-6480	146	24	2−	2−	NUM
ejpam-6480	146	25	α)(1−	α)(1−	PROPN
ejpam-6480	146	26	α	α	NOUN
ejpam-6480	146	27	)	)	PUNCT
ejpam-6480	146	28	(	(	PUNCT
ejpam-6480	146	29	yt1	yt1	PROPN
ejpam-6480	146	30	)	)	PUNCT
ejpam-6480	146	31	−α	−α	NOUN
ejpam-6480	146	32	two	two	NUM
ejpam-6480	146	33	cases	case	NOUN
ejpam-6480	146	34	arise	arise	VERB
ejpam-6480	146	35	:	:	PUNCT
ejpam-6480	146	36	case	case	NOUN
ejpam-6480	146	37	i	i	PRON
ejpam-6480	146	38	:	:	PUNCT
ejpam-6480	146	39	α	α	X
ejpam-6480	146	40	<	<	X
ejpam-6480	146	41	1	1	NUM
ejpam-6480	146	42	,	,	PUNCT
ejpam-6480	146	43	then	then	ADV
ejpam-6480	146	44	ξ′′	ξ′′	PROPN
ejpam-6480	146	45	(	(	PUNCT
ejpam-6480	146	46	xt2	xt2	PROPN
ejpam-6480	146	47	)	)	PUNCT
ejpam-6480	146	48	=	=	SYM
ejpam-6480	146	49	ψ′′	ψ′′	PROPN
ejpam-6480	146	50	(	(	PUNCT
ejpam-6480	146	51	yt1	yt1	PROPN
ejpam-6480	146	52	)	)	PUNCT
ejpam-6480	146	53	>	>	X
ejpam-6480	147	1	0	0	X
ejpam-6480	147	2	.	.	PUNCT
ejpam-6480	148	1	thus	thus	ADV
ejpam-6480	148	2	both	both	DET
ejpam-6480	148	3	ξ	ξ	X
ejpam-6480	148	4	(	(	PUNCT
ejpam-6480	148	5	xt2	xt2	PROPN
ejpam-6480	148	6	)	)	PUNCT
ejpam-6480	148	7	and	and	CCONJ
ejpam-6480	148	8	ψ	ψ	X
ejpam-6480	148	9	(	(	PUNCT
ejpam-6480	148	10	yt1	yt1	NOUN
ejpam-6480	148	11	)	)	PUNCT
ejpam-6480	148	12	are	be	AUX
ejpam-6480	148	13	minimized	minimize	VERB
ejpam-6480	148	14	at	at	ADP
ejpam-6480	148	15	xt2	xt2	PROPN
ejpam-6480	148	16	and	and	CCONJ
ejpam-6480	148	17	yt1	yt1	X
ejpam-6480	148	18	respectively	respectively	ADV
ejpam-6480	148	19	.	.	PUNCT
ejpam-6480	149	1	also	also	ADV
ejpam-6480	149	2	,	,	PUNCT
ejpam-6480	149	3	ξ(0	ξ(0	PROPN
ejpam-6480	149	4	)	)	PUNCT
ejpam-6480	149	5	<	<	X
ejpam-6480	149	6	0	0	NUM
ejpam-6480	149	7	and	and	CCONJ
ejpam-6480	149	8	ξ(∞	ξ(∞	PRON
ejpam-6480	149	9	)	)	PUNCT
ejpam-6480	150	1	=	=	SYM
ejpam-6480	150	2	∞.	∞.	PROPN
ejpam-6480	150	3	similarly	similarly	ADV
ejpam-6480	150	4	,	,	PUNCT
ejpam-6480	150	5	ψ(0	ψ(0	NOUN
ejpam-6480	150	6	)	)	PUNCT
ejpam-6480	150	7	>	>	X
ejpam-6480	150	8	0	0	NUM
ejpam-6480	150	9	,	,	PUNCT
ejpam-6480	150	10	ψ(∞	ψ(∞	NOUN
ejpam-6480	150	11	)	)	PUNCT
ejpam-6480	151	1	=	=	SYM
ejpam-6480	151	2	∞.	∞.	PROPN
ejpam-6480	151	3	hence	hence	ADV
ejpam-6480	151	4	both	both	CCONJ
ejpam-6480	151	5	the	the	DET
ejpam-6480	151	6	equations	equation	NOUN
ejpam-6480	151	7	ξ	ξ	X
ejpam-6480	151	8	(	(	PUNCT
ejpam-6480	151	9	xt2	xt2	X
ejpam-6480	151	10	)	)	PUNCT
ejpam-6480	151	11	=	=	SYM
ejpam-6480	151	12	0	0	NUM
ejpam-6480	151	13	and	and	CCONJ
ejpam-6480	151	14	ψ	ψ	X
ejpam-6480	151	15	(	(	PUNCT
ejpam-6480	151	16	yt1	yt1	NOUN
ejpam-6480	151	17	)	)	PUNCT
ejpam-6480	151	18	=	=	SYM
ejpam-6480	151	19	0	0	PUNCT
ejpam-6480	151	20	have	have	VERB
ejpam-6480	151	21	unique	unique	ADJ
ejpam-6480	151	22	positive	positive	ADJ
ejpam-6480	151	23	solutions	solution	NOUN
ejpam-6480	151	24	h1	h1	NOUN
ejpam-6480	151	25	(	(	PUNCT
ejpam-6480	151	26	t1	t1	NOUN
ejpam-6480	151	27	,	,	PUNCT
ejpam-6480	151	28	t2	t2	NOUN
ejpam-6480	151	29	)	)	PUNCT
ejpam-6480	151	30	and	and	CCONJ
ejpam-6480	151	31	h2	h2	PROPN
ejpam-6480	151	32	(	(	PUNCT
ejpam-6480	151	33	t1	t1	NOUN
ejpam-6480	151	34	,	,	PUNCT
ejpam-6480	151	35	t2	t2	NOUN
ejpam-6480	151	36	)	)	PUNCT
ejpam-6480	151	37	respectively	respectively	ADV
ejpam-6480	151	38	.	.	PUNCT
ejpam-6480	152	1	case	case	NOUN
ejpam-6480	152	2	ii	ii	PROPN
ejpam-6480	152	3	:	:	PUNCT
ejpam-6480	152	4	α	α	PROPN
ejpam-6480	152	5	>	>	X
ejpam-6480	152	6	1	1	NUM
ejpam-6480	152	7	,	,	PUNCT
ejpam-6480	152	8	then	then	ADV
ejpam-6480	152	9	ξ′′	ξ′′	PROPN
ejpam-6480	152	10	(	(	PUNCT
ejpam-6480	152	11	xt2	xt2	PROPN
ejpam-6480	152	12	)	)	PUNCT
ejpam-6480	153	1	=	=	SYM
ejpam-6480	153	2	ψ′′	ψ′′	PROPN
ejpam-6480	153	3	(	(	PUNCT
ejpam-6480	153	4	yt1	yt1	PROPN
ejpam-6480	153	5	)	)	PUNCT
ejpam-6480	153	6	<	<	X
ejpam-6480	153	7	0	0	X
ejpam-6480	153	8	.	.	PUNCT
ejpam-6480	154	1	thus	thus	ADV
ejpam-6480	154	2	both	both	DET
ejpam-6480	154	3	ξ	ξ	X
ejpam-6480	154	4	(	(	PUNCT
ejpam-6480	154	5	xt2	xt2	PROPN
ejpam-6480	154	6	)	)	PUNCT
ejpam-6480	154	7	and	and	CCONJ
ejpam-6480	154	8	ψ	ψ	X
ejpam-6480	154	9	(	(	PUNCT
ejpam-6480	154	10	yt1	yt1	NOUN
ejpam-6480	154	11	)	)	PUNCT
ejpam-6480	154	12	are	be	AUX
ejpam-6480	154	13	maximized	maximize	VERB
ejpam-6480	154	14	at	at	ADP
ejpam-6480	154	15	xt2	xt2	PROPN
ejpam-6480	154	16	and	and	CCONJ
ejpam-6480	154	17	yt1	yt1	X
ejpam-6480	154	18	respectively	respectively	ADV
ejpam-6480	154	19	.	.	PUNCT
ejpam-6480	155	1	also	also	ADV
ejpam-6480	155	2	,	,	PUNCT
ejpam-6480	155	3	ξ(0	ξ(0	PROPN
ejpam-6480	155	4	)	)	PUNCT
ejpam-6480	155	5	<	<	X
ejpam-6480	155	6	0	0	NUM
ejpam-6480	155	7	and	and	CCONJ
ejpam-6480	155	8	ξ(∞	ξ(∞	PRON
ejpam-6480	155	9	)	)	PUNCT
ejpam-6480	156	1	=	=	SYM
ejpam-6480	156	2	∞.	∞.	PROPN
ejpam-6480	156	3	similarly	similarly	ADV
ejpam-6480	156	4	,	,	PUNCT
ejpam-6480	156	5	ψ(0	ψ(0	NOUN
ejpam-6480	156	6	)	)	PUNCT
ejpam-6480	156	7	>	>	X
ejpam-6480	156	8	0	0	NUM
ejpam-6480	156	9	,	,	PUNCT
ejpam-6480	156	10	ψ(∞	ψ(∞	NOUN
ejpam-6480	156	11	)	)	PUNCT
ejpam-6480	157	1	=	=	SYM
ejpam-6480	157	2	∞.	∞.	PROPN
ejpam-6480	157	3	hence	hence	ADV
ejpam-6480	157	4	both	both	CCONJ
ejpam-6480	157	5	the	the	DET
ejpam-6480	157	6	equations	equation	NOUN
ejpam-6480	157	7	ξ	ξ	X
ejpam-6480	157	8	(	(	PUNCT
ejpam-6480	157	9	xt2	xt2	X
ejpam-6480	157	10	)	)	PUNCT
ejpam-6480	157	11	=	=	SYM
ejpam-6480	157	12	0	0	NUM
ejpam-6480	157	13	and	and	CCONJ
ejpam-6480	157	14	ψ	ψ	X
ejpam-6480	157	15	(	(	PUNCT
ejpam-6480	157	16	yt1	yt1	NOUN
ejpam-6480	157	17	)	)	PUNCT
ejpam-6480	157	18	=	=	SYM
ejpam-6480	157	19	0	0	PUNCT
ejpam-6480	157	20	have	have	VERB
ejpam-6480	157	21	unique	unique	ADJ
ejpam-6480	157	22	positive	positive	ADJ
ejpam-6480	157	23	solutions	solution	NOUN
ejpam-6480	157	24	h1	h1	NOUN
ejpam-6480	157	25	(	(	PUNCT
ejpam-6480	157	26	t1	t1	NOUN
ejpam-6480	157	27	,	,	PUNCT
ejpam-6480	157	28	t2	t2	NOUN
ejpam-6480	157	29	)	)	PUNCT
ejpam-6480	157	30	and	and	CCONJ
ejpam-6480	157	31	h2	h2	PROPN
ejpam-6480	157	32	(	(	PUNCT
ejpam-6480	157	33	t1	t1	NOUN
ejpam-6480	157	34	,	,	PUNCT
ejpam-6480	157	35	t2	t2	NOUN
ejpam-6480	157	36	)	)	PUNCT
ejpam-6480	157	37	respectively	respectively	ADV
ejpam-6480	157	38	.	.	PUNCT
ejpam-6480	158	1	combining	combine	VERB
ejpam-6480	158	2	both	both	DET
ejpam-6480	158	3	the	the	DET
ejpam-6480	158	4	cases	case	NOUN
ejpam-6480	158	5	,	,	PUNCT
ejpam-6480	158	6	we	we	PRON
ejpam-6480	158	7	conclude	conclude	VERB
ejpam-6480	158	8	kα	kα	PRON
ejpam-6480	158	9	(	(	PUNCT
ejpam-6480	158	10	x	x	X
ejpam-6480	158	11	;	;	PUNCT
ejpam-6480	158	12	t1	t1	NOUN
ejpam-6480	158	13	,	,	PUNCT
ejpam-6480	158	14	t2	t2	NOUN
ejpam-6480	158	15	)	)	PUNCT
ejpam-6480	158	16	determines	determine	VERB
ejpam-6480	158	17	the	the	DET
ejpam-6480	158	18	hi	hi	INTJ
ejpam-6480	158	19	(	(	PUNCT
ejpam-6480	158	20	t1	t1	NOUN
ejpam-6480	158	21	,	,	PUNCT
ejpam-6480	158	22	t2	t2	PROPN
ejpam-6480	158	23	)	)	PUNCT
ejpam-6480	158	24	,	,	PUNCT
ejpam-6480	159	1	i	i	PRON
ejpam-6480	159	2	=	=	NOUN
ejpam-6480	159	3	1	1	NUM
ejpam-6480	159	4	,	,	PUNCT
ejpam-6480	159	5	2	2	NUM
ejpam-6480	159	6	uniquely	uniquely	ADV
ejpam-6480	159	7	.	.	PUNCT
ejpam-6480	160	1	j.	j.	PROPN
ejpam-6480	160	2	g.	g.	PROPN
ejpam-6480	160	3	dar	dar	PROPN
ejpam-6480	160	4	,	,	PUNCT
ejpam-6480	160	5	s.	s.	PROPN
ejpam-6480	160	6	m.	m.	PROPN
ejpam-6480	160	7	a.	a.	PROPN
ejpam-6480	160	8	alsheikh	alsheikh	PROPN
ejpam-6480	160	9	,	,	PUNCT
ejpam-6480	160	10	p.	p.	PROPN
ejpam-6480	160	11	jadhav	jadhav	PROPN
ejpam-6480	160	12	/	/	SYM
ejpam-6480	160	13	eur	eur	PROPN
ejpam-6480	160	14	.	.	PUNCT
ejpam-6480	161	1	j.	j.	PROPN
ejpam-6480	161	2	pure	pure	PROPN
ejpam-6480	161	3	appl	appl	PROPN
ejpam-6480	161	4	.	.	PROPN
ejpam-6480	161	5	math	math	PROPN
ejpam-6480	161	6	,	,	PUNCT
ejpam-6480	161	7	18	18	NUM
ejpam-6480	161	8	(	(	PUNCT
ejpam-6480	161	9	4	4	NUM
ejpam-6480	161	10	)	)	PUNCT
ejpam-6480	161	11	(	(	PUNCT
ejpam-6480	161	12	2025	2025	NUM
ejpam-6480	161	13	)	)	PUNCT
ejpam-6480	161	14	,	,	PUNCT
ejpam-6480	161	15	6480	6480	NUM
ejpam-6480	161	16	9	9	NUM
ejpam-6480	161	17	of	of	ADP
ejpam-6480	161	18	14	14	NUM
ejpam-6480	161	19	theorem	theorem	NOUN
ejpam-6480	161	20	3.2	3.2	NUM
ejpam-6480	161	21	.	.	PUNCT
ejpam-6480	162	1	let	let	VERB
ejpam-6480	162	2	x	x	PRON
ejpam-6480	162	3	be	be	AUX
ejpam-6480	162	4	the	the	DET
ejpam-6480	162	5	non	non	ADJ
ejpam-6480	162	6	-	-	ADJ
ejpam-6480	162	7	negative	negative	ADJ
ejpam-6480	162	8	random	random	ADJ
ejpam-6480	162	9	variable	variable	NOUN
ejpam-6480	162	10	follows	follow	VERB
ejpam-6480	162	11	uniform	uniform	ADJ
ejpam-6480	162	12	distribution	distribution	NOUN
ejpam-6480	162	13	over	over	ADP
ejpam-6480	162	14	(	(	PUNCT
ejpam-6480	162	15	a	a	DET
ejpam-6480	162	16	,	,	PUNCT
ejpam-6480	162	17	b	b	NOUN
ejpam-6480	162	18	)	)	PUNCT
ejpam-6480	162	19	,	,	PUNCT
ejpam-6480	163	1	a	a	DET
ejpam-6480	163	2	<	<	X
ejpam-6480	163	3	b	b	X
ejpam-6480	163	4	if	if	SCONJ
ejpam-6480	164	1	and	and	CCONJ
ejpam-6480	164	2	only	only	ADV
ejpam-6480	164	3	if	if	SCONJ
ejpam-6480	164	4	kα	kα	PROPN
ejpam-6480	164	5	(	(	PUNCT
ejpam-6480	164	6	x	x	NOUN
ejpam-6480	164	7	;	;	PUNCT
ejpam-6480	164	8	t1	t1	NOUN
ejpam-6480	164	9	,	,	PUNCT
ejpam-6480	164	10	t2	t2	NOUN
ejpam-6480	164	11	)	)	PUNCT
ejpam-6480	164	12	=	=	SYM
ejpam-6480	165	1	1	1	NUM
ejpam-6480	165	2	α−	α−	ADP
ejpam-6480	165	3	1	1	NUM
ejpam-6480	165	4	[	[	PUNCT
ejpam-6480	165	5	t2	t2	PROPN
ejpam-6480	165	6	−	−	PROPN
ejpam-6480	165	7	t1	t1	NOUN
ejpam-6480	165	8	(	(	PUNCT
ejpam-6480	165	9	t2	t2	PROPN
ejpam-6480	165	10	−	−	PROPN
ejpam-6480	165	11	t1	t1	PROPN
ejpam-6480	165	12	)	)	PUNCT
ejpam-6480	165	13	2−α	2−α	NUM
ejpam-6480	166	1	−	−	NOUN
ejpam-6480	166	2	1	1	NUM
ejpam-6480	166	3	]	]	PUNCT
ejpam-6480	166	4	(	(	PUNCT
ejpam-6480	166	5	3.5	3.5	NUM
ejpam-6480	166	6	)	)	PUNCT
ejpam-6480	166	7	proof	proof	NOUN
ejpam-6480	166	8	:	:	PUNCT
ejpam-6480	166	9	the	the	DET
ejpam-6480	166	10	probability	probability	NOUN
ejpam-6480	166	11	density	density	NOUN
ejpam-6480	166	12	function	function	NOUN
ejpam-6480	166	13	and	and	CCONJ
ejpam-6480	166	14	corresponding	correspond	VERB
ejpam-6480	166	15	cdf	cdf	PROPN
ejpam-6480	166	16	of	of	ADP
ejpam-6480	166	17	uniform	uniform	ADJ
ejpam-6480	166	18	distribution	distribution	NOUN
ejpam-6480	166	19	is	be	AUX
ejpam-6480	166	20	given	give	VERB
ejpam-6480	166	21	by	by	ADP
ejpam-6480	166	22	f(x	f(x	PROPN
ejpam-6480	166	23	)	)	PUNCT
ejpam-6480	166	24	=	=	SYM
ejpam-6480	166	25	1	1	NUM
ejpam-6480	166	26	b−	b−	PROPN
ejpam-6480	166	27	a	a	PRON
ejpam-6480	166	28	,	,	PUNCT
ejpam-6480	166	29	a	a	DET
ejpam-6480	166	30	<	<	X
ejpam-6480	166	31	x	x	X
ejpam-6480	166	32	<	<	X
ejpam-6480	166	33	b	b	PROPN
ejpam-6480	166	34	,	,	PUNCT
ejpam-6480	166	35	f(x	f(x	PROPN
ejpam-6480	166	36	)	)	PUNCT
ejpam-6480	166	37	=	=	SYM
ejpam-6480	167	1	1−	1−	NUM
ejpam-6480	167	2	b−	b−	NOUN
ejpam-6480	167	3	x	x	PUNCT
ejpam-6480	167	4	b−	b−	PROPN
ejpam-6480	167	5	a	a	PRON
ejpam-6480	167	6	respectively	respectively	ADV
ejpam-6480	167	7	.	.	PUNCT
ejpam-6480	168	1	using	use	VERB
ejpam-6480	168	2	(	(	PUNCT
ejpam-6480	168	3	2.2	2.2	NUM
ejpam-6480	168	4	)	)	PUNCT
ejpam-6480	168	5	,	,	PUNCT
ejpam-6480	168	6	we	we	PRON
ejpam-6480	168	7	get	get	VERB
ejpam-6480	168	8	kα	kα	PRON
ejpam-6480	168	9	(	(	PUNCT
ejpam-6480	168	10	x	x	X
ejpam-6480	168	11	;	;	PUNCT
ejpam-6480	168	12	t1	t1	NOUN
ejpam-6480	168	13	,	,	PUNCT
ejpam-6480	168	14	t2	t2	NOUN
ejpam-6480	168	15	)	)	PUNCT
ejpam-6480	168	16	=	=	SYM
ejpam-6480	169	1	1	1	NUM
ejpam-6480	169	2	α−	α−	ADP
ejpam-6480	169	3	1	1	NUM
ejpam-6480	169	4	[	[	PUNCT
ejpam-6480	169	5	t2	t2	PROPN
ejpam-6480	169	6	−	−	PROPN
ejpam-6480	169	7	t1	t1	NOUN
ejpam-6480	169	8	(	(	PUNCT
ejpam-6480	169	9	t2	t2	PROPN
ejpam-6480	169	10	−	−	PROPN
ejpam-6480	169	11	t1	t1	PROPN
ejpam-6480	169	12	)	)	PUNCT
ejpam-6480	169	13	2−α	2−α	NUM
ejpam-6480	170	1	−	−	NOUN
ejpam-6480	170	2	1	1	NUM
ejpam-6480	170	3	]	]	PUNCT
ejpam-6480	170	4	,	,	PUNCT
ejpam-6480	170	5	which	which	PRON
ejpam-6480	170	6	proves	prove	VERB
ejpam-6480	170	7	only	only	ADV
ejpam-6480	170	8	if	if	SCONJ
ejpam-6480	170	9	part	part	NOUN
ejpam-6480	170	10	of	of	ADP
ejpam-6480	170	11	the	the	DET
ejpam-6480	170	12	theorem	theorem	NOUN
ejpam-6480	170	13	.	.	PROPN
ejpam-6480	170	14	to	to	PART
ejpam-6480	170	15	prove	prove	VERB
ejpam-6480	170	16	the	the	DET
ejpam-6480	170	17	if	if	SCONJ
ejpam-6480	170	18	part	part	NOUN
ejpam-6480	170	19	,	,	PUNCT
ejpam-6480	170	20	let	let	VERB
ejpam-6480	170	21	(	(	PUNCT
ejpam-6480	170	22	3.5	3.5	NUM
ejpam-6480	170	23	)	)	PUNCT
ejpam-6480	170	24	is	be	AUX
ejpam-6480	170	25	valid	valid	ADJ
ejpam-6480	170	26	.	.	PUNCT
ejpam-6480	171	1	thus	thus	ADV
ejpam-6480	171	2	from	from	ADP
ejpam-6480	171	3	(	(	PUNCT
ejpam-6480	171	4	2.2	2.2	NUM
ejpam-6480	171	5	)	)	PUNCT
ejpam-6480	171	6	and	and	CCONJ
ejpam-6480	171	7	(	(	PUNCT
ejpam-6480	171	8	3.5	3.5	NUM
ejpam-6480	171	9	)	)	PUNCT
ejpam-6480	171	10	,	,	PUNCT
ejpam-6480	171	11	we	we	PRON
ejpam-6480	171	12	get∫	get∫	PROPN
ejpam-6480	171	13	t2	t2	PROPN
ejpam-6480	171	14	t1	t1	NOUN
ejpam-6480	171	15	f2−α(x)dx	f2−α(x)dx	VERB
ejpam-6480	171	16	=	=	SYM
ejpam-6480	171	17	(	(	PUNCT
ejpam-6480	171	18	t2	t2	PROPN
ejpam-6480	171	19	−	−	PROPN
ejpam-6480	171	20	t1	t1	PROPN
ejpam-6480	171	21	)	)	PUNCT
ejpam-6480	171	22	2−α	2−α	PROPN
ejpam-6480	171	23	(	(	PUNCT
ejpam-6480	171	24	(	(	PUNCT
ejpam-6480	171	25	f	f	X
ejpam-6480	171	26	(	(	PUNCT
ejpam-6480	171	27	t2)−	t2)−	NOUN
ejpam-6480	171	28	f	f	X
ejpam-6480	171	29	(	(	PUNCT
ejpam-6480	171	30	t1	t1	NOUN
ejpam-6480	171	31	)	)	PUNCT
ejpam-6480	171	32	)	)	PUNCT
ejpam-6480	172	1	α−2	α−2	NOUN
ejpam-6480	172	2	differentiating	differentiate	VERB
ejpam-6480	172	3	with	with	ADP
ejpam-6480	172	4	respect	respect	NOUN
ejpam-6480	172	5	t1	t1	NOUN
ejpam-6480	172	6	and	and	CCONJ
ejpam-6480	172	7	t2	t2	NOUN
ejpam-6480	172	8	,	,	PUNCT
ejpam-6480	172	9	we	we	PRON
ejpam-6480	172	10	obtain	obtain	VERB
ejpam-6480	172	11	h2−α	h2−α	PROPN
ejpam-6480	172	12	1	1	NUM
ejpam-6480	172	13	(	(	PUNCT
ejpam-6480	172	14	t1	t1	NOUN
ejpam-6480	172	15	,	,	PUNCT
ejpam-6480	172	16	t2	t2	NOUN
ejpam-6480	172	17	)	)	PUNCT
ejpam-6480	172	18	=	=	PUNCT
ejpam-6480	173	1	(	(	PUNCT
ejpam-6480	173	2	α−	α−	ADP
ejpam-6480	173	3	1	1	NUM
ejpam-6480	173	4	)	)	PUNCT
ejpam-6480	173	5	(	(	PUNCT
ejpam-6480	173	6	t2	t2	PROPN
ejpam-6480	173	7	−	−	PROPN
ejpam-6480	173	8	t1	t1	NOUN
ejpam-6480	173	9	)	)	PUNCT
ejpam-6480	174	1	α−2	α−2	PROPN
ejpam-6480	174	2	+	+	X
ejpam-6480	174	3	(	(	PUNCT
ejpam-6480	174	4	2−	2−	NUM
ejpam-6480	174	5	α	α	NOUN
ejpam-6480	174	6	)	)	PUNCT
ejpam-6480	174	7	(	(	PUNCT
ejpam-6480	174	8	t2	t2	PROPN
ejpam-6480	174	9	−	−	PROPN
ejpam-6480	174	10	t1	t1	PROPN
ejpam-6480	174	11	)	)	PUNCT
ejpam-6480	174	12	α−1	α−1	PROPN
ejpam-6480	174	13	h1	h1	NOUN
ejpam-6480	174	14	(	(	PUNCT
ejpam-6480	174	15	t1	t1	NOUN
ejpam-6480	174	16	,	,	PUNCT
ejpam-6480	174	17	t2	t2	NOUN
ejpam-6480	174	18	)	)	PUNCT
ejpam-6480	174	19	and	and	CCONJ
ejpam-6480	174	20	h2−α	h2−α	PROPN
ejpam-6480	174	21	2	2	NUM
ejpam-6480	174	22	(	(	PUNCT
ejpam-6480	174	23	t1	t1	NOUN
ejpam-6480	174	24	,	,	PUNCT
ejpam-6480	174	25	t2	t2	NOUN
ejpam-6480	174	26	)	)	PUNCT
ejpam-6480	174	27	=	=	PUNCT
ejpam-6480	174	28	(	(	PUNCT
ejpam-6480	174	29	α−	α−	ADP
ejpam-6480	174	30	1	1	NUM
ejpam-6480	174	31	)	)	PUNCT
ejpam-6480	174	32	(	(	PUNCT
ejpam-6480	174	33	t2	t2	PROPN
ejpam-6480	174	34	−	−	PROPN
ejpam-6480	174	35	t1	t1	NOUN
ejpam-6480	174	36	)	)	PUNCT
ejpam-6480	175	1	α−2	α−2	PROPN
ejpam-6480	175	2	+	+	X
ejpam-6480	175	3	(	(	PUNCT
ejpam-6480	175	4	2−	2−	NUM
ejpam-6480	175	5	α	α	NOUN
ejpam-6480	175	6	)	)	PUNCT
ejpam-6480	175	7	(	(	PUNCT
ejpam-6480	175	8	t2	t2	PROPN
ejpam-6480	175	9	−	−	PROPN
ejpam-6480	175	10	t1	t1	PROPN
ejpam-6480	175	11	)	)	PUNCT
ejpam-6480	175	12	α−1	α−1	PROPN
ejpam-6480	175	13	h2	h2	NOUN
ejpam-6480	175	14	(	(	PUNCT
ejpam-6480	175	15	t1	t1	NOUN
ejpam-6480	175	16	,	,	PUNCT
ejpam-6480	175	17	t2	t2	PROPN
ejpam-6480	175	18	)	)	PUNCT
ejpam-6480	175	19	now	now	ADV
ejpam-6480	175	20	for	for	ADP
ejpam-6480	175	21	any	any	DET
ejpam-6480	175	22	fixed	fix	VERB
ejpam-6480	175	23	t1	t1	NOUN
ejpam-6480	175	24	and	and	CCONJ
ejpam-6480	175	25	t2	t2	NOUN
ejpam-6480	175	26	,	,	PUNCT
ejpam-6480	175	27	h1	h1	PROPN
ejpam-6480	175	28	(	(	PUNCT
ejpam-6480	175	29	t1	t1	NOUN
ejpam-6480	175	30	,	,	PUNCT
ejpam-6480	175	31	t2	t2	NOUN
ejpam-6480	175	32	)	)	PUNCT
ejpam-6480	175	33	and	and	CCONJ
ejpam-6480	175	34	h2	h2	PROPN
ejpam-6480	175	35	(	(	PUNCT
ejpam-6480	175	36	t1	t1	NOUN
ejpam-6480	175	37	,	,	PUNCT
ejpam-6480	175	38	t2	t2	NOUN
ejpam-6480	175	39	)	)	PUNCT
ejpam-6480	175	40	is	be	AUX
ejpam-6480	175	41	a	a	DET
ejpam-6480	175	42	positive	positive	ADJ
ejpam-6480	175	43	solution	solution	NOUN
ejpam-6480	175	44	of	of	ADP
ejpam-6480	175	45	the	the	DET
ejpam-6480	175	46	equation	equation	NOUN
ejpam-6480	175	47	ξ	ξ	X
ejpam-6480	175	48	(	(	PUNCT
ejpam-6480	175	49	xt2	xt2	X
ejpam-6480	175	50	)	)	PUNCT
ejpam-6480	175	51	=	=	SYM
ejpam-6480	175	52	0	0	NUM
ejpam-6480	175	53	and	and	CCONJ
ejpam-6480	175	54	ψ	ψ	X
ejpam-6480	175	55	(	(	PUNCT
ejpam-6480	175	56	yt1	yt1	NOUN
ejpam-6480	175	57	)	)	PUNCT
ejpam-6480	175	58	=	=	SYM
ejpam-6480	175	59	0	0	NUM
ejpam-6480	175	60	,	,	PUNCT
ejpam-6480	175	61	where	where	SCONJ
ejpam-6480	175	62	ξ	ξ	X
ejpam-6480	175	63	(	(	PUNCT
ejpam-6480	175	64	xt2	xt2	PROPN
ejpam-6480	175	65	)	)	PUNCT
ejpam-6480	175	66	=	=	PUNCT
ejpam-6480	175	67	(	(	PUNCT
ejpam-6480	175	68	xt2	xt2	PROPN
ejpam-6480	175	69	)	)	PUNCT
ejpam-6480	175	70	2−α	2−α	NUM
ejpam-6480	176	1	−	−	PROPN
ejpam-6480	176	2	(	(	PUNCT
ejpam-6480	176	3	α−	α−	ADP
ejpam-6480	176	4	1	1	NUM
ejpam-6480	176	5	)	)	PUNCT
ejpam-6480	176	6	(	(	PUNCT
ejpam-6480	176	7	t2	t2	NOUN
ejpam-6480	176	8	−	−	PROPN
ejpam-6480	176	9	t1	t1	PROPN
ejpam-6480	176	10	)	)	PUNCT
ejpam-6480	176	11	2−α	2−α	NUM
ejpam-6480	177	1	−	−	PROPN
ejpam-6480	177	2	(	(	PUNCT
ejpam-6480	177	3	2−	2−	NUM
ejpam-6480	177	4	α	α	NOUN
ejpam-6480	177	5	)	)	PUNCT
ejpam-6480	177	6	(	(	PUNCT
ejpam-6480	177	7	t2	t2	PROPN
ejpam-6480	177	8	−	−	PROPN
ejpam-6480	177	9	t1	t1	NOUN
ejpam-6480	177	10	)	)	PUNCT
ejpam-6480	177	11	1−αxt2	1−αxt2	NUM
ejpam-6480	177	12	(	(	PUNCT
ejpam-6480	177	13	3.6	3.6	NUM
ejpam-6480	177	14	)	)	PUNCT
ejpam-6480	177	15	and	and	CCONJ
ejpam-6480	177	16	ψ	ψ	X
ejpam-6480	177	17	(	(	PUNCT
ejpam-6480	177	18	yt1	yt1	NOUN
ejpam-6480	177	19	)	)	PUNCT
ejpam-6480	177	20	=	=	SYM
ejpam-6480	177	21	(	(	PUNCT
ejpam-6480	177	22	yt1	yt1	PROPN
ejpam-6480	177	23	)	)	PUNCT
ejpam-6480	177	24	2−α	2−α	NUM
ejpam-6480	178	1	−	−	PROPN
ejpam-6480	178	2	(	(	PUNCT
ejpam-6480	178	3	α−	α−	ADP
ejpam-6480	178	4	1	1	NUM
ejpam-6480	178	5	)	)	PUNCT
ejpam-6480	178	6	(	(	PUNCT
ejpam-6480	178	7	t2	t2	NOUN
ejpam-6480	178	8	−	−	PROPN
ejpam-6480	178	9	t1	t1	PROPN
ejpam-6480	178	10	)	)	PUNCT
ejpam-6480	178	11	2−α	2−α	NUM
ejpam-6480	179	1	−	−	PROPN
ejpam-6480	179	2	(	(	PUNCT
ejpam-6480	179	3	2−	2−	NUM
ejpam-6480	179	4	α	α	NOUN
ejpam-6480	179	5	)	)	PUNCT
ejpam-6480	179	6	(	(	PUNCT
ejpam-6480	179	7	t2	t2	PROPN
ejpam-6480	179	8	−	−	PROPN
ejpam-6480	179	9	t1	t1	NOUN
ejpam-6480	179	10	)	)	PUNCT
ejpam-6480	179	11	1−αyt1	1−αyt1	NUM
ejpam-6480	179	12	(	(	PUNCT
ejpam-6480	179	13	3.7	3.7	NUM
ejpam-6480	179	14	)	)	PUNCT
ejpam-6480	179	15	differentiating	differentiate	VERB
ejpam-6480	179	16	both	both	DET
ejpam-6480	179	17	side	side	NOUN
ejpam-6480	179	18	of	of	ADP
ejpam-6480	179	19	(	(	PUNCT
ejpam-6480	179	20	3.6	3.6	NUM
ejpam-6480	179	21	)	)	PUNCT
ejpam-6480	179	22	and	and	CCONJ
ejpam-6480	179	23	(	(	PUNCT
ejpam-6480	179	24	3.7	3.7	NUM
ejpam-6480	179	25	)	)	PUNCT
ejpam-6480	179	26	with	with	ADP
ejpam-6480	179	27	respect	respect	NOUN
ejpam-6480	179	28	to	to	ADP
ejpam-6480	179	29	xt2	xt2	PROPN
ejpam-6480	179	30	and	and	CCONJ
ejpam-6480	179	31	yt1	yt1	PRON
ejpam-6480	179	32	respectively	respectively	ADV
ejpam-6480	179	33	,	,	PUNCT
ejpam-6480	179	34	we	we	PRON
ejpam-6480	179	35	get	get	VERB
ejpam-6480	179	36	ξ′	ξ′	NOUN
ejpam-6480	179	37	(	(	PUNCT
ejpam-6480	179	38	xt2	xt2	PROPN
ejpam-6480	179	39	)	)	PUNCT
ejpam-6480	179	40	=	=	PUNCT
ejpam-6480	180	1	(	(	PUNCT
ejpam-6480	180	2	2−	2−	NUM
ejpam-6480	180	3	α	α	NOUN
ejpam-6480	180	4	)	)	PUNCT
ejpam-6480	180	5	(	(	PUNCT
ejpam-6480	180	6	xt2	xt2	PROPN
ejpam-6480	180	7	)	)	PUNCT
ejpam-6480	181	1	1−α	1−α	NUM
ejpam-6480	181	2	−	−	PROPN
ejpam-6480	182	1	(	(	PUNCT
ejpam-6480	182	2	2−	2−	NUM
ejpam-6480	182	3	α	α	NOUN
ejpam-6480	182	4	)	)	PUNCT
ejpam-6480	182	5	(	(	PUNCT
ejpam-6480	182	6	t2	t2	PROPN
ejpam-6480	182	7	−	−	PROPN
ejpam-6480	182	8	t1	t1	PROPN
ejpam-6480	182	9	)	)	PUNCT
ejpam-6480	182	10	1−α	1−α	NUM
ejpam-6480	182	11	ψ′	ψ′	NUM
ejpam-6480	182	12	(	(	PUNCT
ejpam-6480	182	13	yt1	yt1	NOUN
ejpam-6480	182	14	)	)	PUNCT
ejpam-6480	182	15	=	=	PUNCT
ejpam-6480	183	1	(	(	PUNCT
ejpam-6480	183	2	2−	2−	NUM
ejpam-6480	183	3	α	α	NOUN
ejpam-6480	183	4	)	)	PUNCT
ejpam-6480	183	5	(	(	PUNCT
ejpam-6480	183	6	yt1	yt1	PROPN
ejpam-6480	183	7	)	)	PUNCT
ejpam-6480	183	8	1−α	1−α	NUM
ejpam-6480	184	1	−	−	PROPN
ejpam-6480	184	2	(	(	PUNCT
ejpam-6480	184	3	2−	2−	NUM
ejpam-6480	184	4	α	α	NOUN
ejpam-6480	184	5	)	)	PUNCT
ejpam-6480	184	6	(	(	PUNCT
ejpam-6480	184	7	t2	t2	PROPN
ejpam-6480	184	8	−	−	PROPN
ejpam-6480	184	9	t1	t1	PROPN
ejpam-6480	184	10	)	)	PUNCT
ejpam-6480	184	11	1−α	1−α	NUM
ejpam-6480	185	1	j.	j.	PROPN
ejpam-6480	185	2	g.	g.	PROPN
ejpam-6480	185	3	dar	dar	PROPN
ejpam-6480	185	4	,	,	PUNCT
ejpam-6480	185	5	s.	s.	PROPN
ejpam-6480	185	6	m.	m.	PROPN
ejpam-6480	185	7	a.	a.	PROPN
ejpam-6480	185	8	alsheikh	alsheikh	PROPN
ejpam-6480	185	9	,	,	PUNCT
ejpam-6480	185	10	p.	p.	PROPN
ejpam-6480	185	11	jadhav	jadhav	PROPN
ejpam-6480	185	12	/	/	SYM
ejpam-6480	185	13	eur	eur	PROPN
ejpam-6480	185	14	.	.	PUNCT
ejpam-6480	186	1	j.	j.	PROPN
ejpam-6480	186	2	pure	pure	PROPN
ejpam-6480	186	3	appl	appl	PROPN
ejpam-6480	186	4	.	.	PROPN
ejpam-6480	186	5	math	math	PROPN
ejpam-6480	186	6	,	,	PUNCT
ejpam-6480	186	7	18	18	NUM
ejpam-6480	186	8	(	(	PUNCT
ejpam-6480	186	9	4	4	NUM
ejpam-6480	186	10	)	)	PUNCT
ejpam-6480	186	11	(	(	PUNCT
ejpam-6480	186	12	2025	2025	NUM
ejpam-6480	186	13	)	)	PUNCT
ejpam-6480	186	14	,	,	PUNCT
ejpam-6480	186	15	6480	6480	NUM
ejpam-6480	186	16	10	10	NUM
ejpam-6480	186	17	of	of	ADP
ejpam-6480	186	18	14	14	NUM
ejpam-6480	186	19	for	for	ADP
ejpam-6480	186	20	extreme	extreme	ADJ
ejpam-6480	186	21	values	value	NOUN
ejpam-6480	186	22	,	,	PUNCT
ejpam-6480	186	23	ξ′	ξ′	X
ejpam-6480	186	24	(	(	PUNCT
ejpam-6480	186	25	xt2	xt2	PROPN
ejpam-6480	186	26	)	)	PUNCT
ejpam-6480	186	27	=	=	SYM
ejpam-6480	186	28	0	0	NUM
ejpam-6480	186	29	,	,	PUNCT
ejpam-6480	186	30	ψ′	ψ′	PUNCT
ejpam-6480	186	31	(	(	PUNCT
ejpam-6480	186	32	yt1	yt1	NOUN
ejpam-6480	186	33	)	)	PUNCT
ejpam-6480	186	34	=	=	SYM
ejpam-6480	186	35	0	0	NUM
ejpam-6480	186	36	,	,	PUNCT
ejpam-6480	186	37	which	which	PRON
ejpam-6480	186	38	gives	give	VERB
ejpam-6480	186	39	xt2	xt2	PROPN
ejpam-6480	186	40	=	=	SYM
ejpam-6480	186	41	1	1	NUM
ejpam-6480	186	42	t2	t2	NOUN
ejpam-6480	186	43	−	−	PROPN
ejpam-6480	186	44	t1	t1	NOUN
ejpam-6480	186	45	=	=	PUNCT
ejpam-6480	186	46	h1	h1	PROPN
ejpam-6480	186	47	(	(	PUNCT
ejpam-6480	186	48	t1	t1	NOUN
ejpam-6480	186	49	,	,	PUNCT
ejpam-6480	186	50	t2	t2	NOUN
ejpam-6480	186	51	)	)	PUNCT
ejpam-6480	186	52	and	and	CCONJ
ejpam-6480	186	53	yt1	yt1	NOUN
ejpam-6480	186	54	=	=	SYM
ejpam-6480	186	55	1	1	NUM
ejpam-6480	186	56	t2	t2	NOUN
ejpam-6480	186	57	−	−	PROPN
ejpam-6480	186	58	t1	t1	NOUN
ejpam-6480	186	59	=	=	SYM
ejpam-6480	186	60	h2	h2	PROPN
ejpam-6480	186	61	(	(	PUNCT
ejpam-6480	186	62	t1	t1	NOUN
ejpam-6480	186	63	,	,	PUNCT
ejpam-6480	186	64	t2	t2	PROPN
ejpam-6480	186	65	)	)	PUNCT
ejpam-6480	186	66	,	,	PUNCT
ejpam-6480	186	67	which	which	PRON
ejpam-6480	186	68	proves	prove	VERB
ejpam-6480	186	69	the	the	DET
ejpam-6480	186	70	theorem	theorem	PROPN
ejpam-6480	186	71	.	.	PUNCT
ejpam-6480	186	72	theorem	theorem	VERB
ejpam-6480	186	73	3.3	3.3	NUM
ejpam-6480	186	74	.	.	PUNCT
ejpam-6480	187	1	let	let	VERB
ejpam-6480	187	2	x	x	PRON
ejpam-6480	187	3	be	be	AUX
ejpam-6480	187	4	the	the	DET
ejpam-6480	187	5	non	non	ADJ
ejpam-6480	187	6	-	-	ADJ
ejpam-6480	187	7	negative	negative	ADJ
ejpam-6480	187	8	random	random	ADJ
ejpam-6480	187	9	variable	variable	NOUN
ejpam-6480	187	10	having	have	VERB
ejpam-6480	187	11	continuous	continuous	ADJ
ejpam-6480	187	12	density	density	NOUN
ejpam-6480	187	13	function	function	NOUN
ejpam-6480	187	14	f(x	f(x	PROPN
ejpam-6480	187	15	)	)	PUNCT
ejpam-6480	187	16	and	and	CCONJ
ejpam-6480	187	17	distribution	distribution	NOUN
ejpam-6480	187	18	function	function	NOUN
ejpam-6480	187	19	f	f	PROPN
ejpam-6480	187	20	(	(	PUNCT
ejpam-6480	187	21	x	x	NOUN
ejpam-6480	187	22	)	)	PUNCT
ejpam-6480	187	23	,	,	PUNCT
ejpam-6480	187	24	then	then	ADV
ejpam-6480	187	25	a	a	DET
ejpam-6480	187	26	relation	relation	NOUN
ejpam-6480	187	27	of	of	ADP
ejpam-6480	187	28	the	the	DET
ejpam-6480	187	29	form	form	NOUN
ejpam-6480	187	30	(	(	PUNCT
ejpam-6480	187	31	α−	α−	ADP
ejpam-6480	187	32	1)kα	1)kα	PROPN
ejpam-6480	187	33	(	(	PUNCT
ejpam-6480	187	34	x	x	NOUN
ejpam-6480	187	35	;	;	PUNCT
ejpam-6480	187	36	t1	t1	NOUN
ejpam-6480	187	37	,	,	PUNCT
ejpam-6480	187	38	t2	t2	NOUN
ejpam-6480	187	39	)	)	PUNCT
ejpam-6480	187	40	=	=	SYM
ejpam-6480	188	1	1	1	NUM
ejpam-6480	188	2	c	c	NOUN
ejpam-6480	188	3	[	[	PUNCT
ejpam-6480	188	4	(	(	PUNCT
ejpam-6480	188	5	1	1	NUM
ejpam-6480	188	6	+	+	NUM
ejpam-6480	188	7	kt2	kt2	NOUN
ejpam-6480	188	8	)	)	PUNCT
ejpam-6480	188	9	h	h	NOUN
ejpam-6480	188	10	2−α	2−α	NUM
ejpam-6480	188	11	2	2	NUM
ejpam-6480	188	12	(	(	PUNCT
ejpam-6480	188	13	t1	t1	NOUN
ejpam-6480	188	14	,	,	PUNCT
ejpam-6480	188	15	t2)−	t2)−	X
ejpam-6480	188	16	(	(	PUNCT
ejpam-6480	188	17	1	1	NUM
ejpam-6480	188	18	+	+	NUM
ejpam-6480	188	19	kt1	kt1	NOUN
ejpam-6480	188	20	)	)	PUNCT
ejpam-6480	188	21	h	h	NOUN
ejpam-6480	188	22	2−α	2−α	NUM
ejpam-6480	188	23	1	1	NUM
ejpam-6480	188	24	(	(	PUNCT
ejpam-6480	188	25	t1	t1	NOUN
ejpam-6480	188	26	,	,	PUNCT
ejpam-6480	188	27	t2	t2	NOUN
ejpam-6480	188	28	)	)	PUNCT
ejpam-6480	188	29	]	]	PUNCT
ejpam-6480	189	1	−	−	PROPN
ejpam-6480	189	2	1	1	NUM
ejpam-6480	189	3	(	(	PUNCT
ejpam-6480	189	4	3.8	3.8	NUM
ejpam-6480	189	5	)	)	PUNCT
ejpam-6480	189	6	where	where	SCONJ
ejpam-6480	189	7	c	c	NOUN
ejpam-6480	189	8	is	be	AUX
ejpam-6480	189	9	a	a	DET
ejpam-6480	189	10	constant	constant	ADJ
ejpam-6480	189	11	holds	hold	NOUN
ejpam-6480	189	12	for	for	ADP
ejpam-6480	189	13	all	all	DET
ejpam-6480	189	14	t1	t1	NOUN
ejpam-6480	189	15	,	,	PUNCT
ejpam-6480	189	16	t2	t2	NOUN
ejpam-6480	189	17	.	.	PUNCT
ejpam-6480	190	1	then	then	ADV
ejpam-6480	190	2	x	x	X
ejpam-6480	190	3	has	have	AUX
ejpam-6480	190	4	(	(	PUNCT
ejpam-6480	190	5	i	i	NOUN
ejpam-6480	190	6	)	)	PUNCT
ejpam-6480	190	7	an	an	DET
ejpam-6480	190	8	exponential	exponential	ADJ
ejpam-6480	190	9	distribution	distribution	NOUN
ejpam-6480	190	10	iff	iff	NOUN
ejpam-6480	190	11	c	c	NOUN
ejpam-6480	190	12	=	=	SYM
ejpam-6480	190	13	0	0	NUM
ejpam-6480	190	14	(	(	PUNCT
ejpam-6480	190	15	ii	ii	NOUN
ejpam-6480	190	16	)	)	PUNCT
ejpam-6480	190	17	a	a	DET
ejpam-6480	190	18	pareto	pareto	ADJ
ejpam-6480	190	19	distribution	distribution	NOUN
ejpam-6480	190	20	iff	iff	NOUN
ejpam-6480	190	21	c	c	PROPN
ejpam-6480	190	22	<	<	X
ejpam-6480	190	23	0	0	NUM
ejpam-6480	190	24	(	(	PUNCT
ejpam-6480	190	25	iii	iii	NOUN
ejpam-6480	190	26	)	)	PUNCT
ejpam-6480	190	27	a	a	DET
ejpam-6480	190	28	finite	finite	ADJ
ejpam-6480	190	29	range	range	NOUN
ejpam-6480	190	30	distribution	distribution	NOUN
ejpam-6480	190	31	iff	iff	NOUN
ejpam-6480	191	1	c	c	PROPN
ejpam-6480	191	2	>	>	X
ejpam-6480	191	3	0	0	X
ejpam-6480	191	4	.	.	PUNCT
ejpam-6480	191	5	proof	proof	NOUN
ejpam-6480	191	6	.	.	PUNCT
ejpam-6480	192	1	(	(	PUNCT
ejpam-6480	192	2	i	i	NOUN
ejpam-6480	192	3	)	)	PUNCT
ejpam-6480	192	4	the	the	DET
ejpam-6480	192	5	probability	probability	NOUN
ejpam-6480	192	6	density	density	NOUN
ejpam-6480	192	7	function	function	NOUN
ejpam-6480	192	8	and	and	CCONJ
ejpam-6480	192	9	corresponding	correspond	VERB
ejpam-6480	192	10	cdf	cdf	PROPN
ejpam-6480	192	11	of	of	ADP
ejpam-6480	192	12	exponential	exponential	ADJ
ejpam-6480	192	13	distribution	distribution	NOUN
ejpam-6480	192	14	is	be	AUX
ejpam-6480	192	15	given	give	VERB
ejpam-6480	192	16	by	by	ADP
ejpam-6480	192	17	f(x	f(x	PROPN
ejpam-6480	192	18	)	)	PUNCT
ejpam-6480	192	19	=	=	PUNCT
ejpam-6480	193	1	θe−θx	θe−θx	PROPN
ejpam-6480	193	2	,	,	PUNCT
ejpam-6480	193	3	x	x	X
ejpam-6480	193	4	>	>	X
ejpam-6480	193	5	0	0	PROPN
ejpam-6480	193	6	,	,	PUNCT
ejpam-6480	193	7	θ	θ	PROPN
ejpam-6480	193	8	>	>	X
ejpam-6480	193	9	0	0	PROPN
ejpam-6480	193	10	,	,	PUNCT
ejpam-6480	193	11	f	f	PROPN
ejpam-6480	193	12	(	(	PUNCT
ejpam-6480	193	13	x	x	X
ejpam-6480	193	14	)	)	PUNCT
ejpam-6480	193	15	=	=	SYM
ejpam-6480	193	16	1−	1−	NUM
ejpam-6480	193	17	e−θx	e−θx	PROPN
ejpam-6480	193	18	respectively	respectively	ADV
ejpam-6480	193	19	also	also	ADV
ejpam-6480	193	20	,	,	PUNCT
ejpam-6480	193	21	hi	hi	INTJ
ejpam-6480	193	22	(	(	PUNCT
ejpam-6480	193	23	t1	t1	NOUN
ejpam-6480	193	24	,	,	PUNCT
ejpam-6480	193	25	t2	t2	NOUN
ejpam-6480	193	26	)	)	PUNCT
ejpam-6480	193	27	=	=	PUNCT
ejpam-6480	194	1	θe−θti	θe−θti	X
ejpam-6480	194	2	e−θt1−e−θt2	e−θt1−e−θt2	PROPN
ejpam-6480	194	3	using	use	VERB
ejpam-6480	194	4	(	(	PUNCT
ejpam-6480	194	5	2.2	2.2	NUM
ejpam-6480	194	6	)	)	PUNCT
ejpam-6480	194	7	,	,	PUNCT
ejpam-6480	194	8	we	we	PRON
ejpam-6480	194	9	get	get	VERB
ejpam-6480	194	10	(	(	PUNCT
ejpam-6480	194	11	α−	α−	ADP
ejpam-6480	194	12	1)kα	1)kα	PROPN
ejpam-6480	194	13	(	(	PUNCT
ejpam-6480	194	14	x	x	NOUN
ejpam-6480	194	15	;	;	PUNCT
ejpam-6480	194	16	t1	t1	NOUN
ejpam-6480	194	17	,	,	PUNCT
ejpam-6480	194	18	t2	t2	NOUN
ejpam-6480	194	19	)	)	PUNCT
ejpam-6480	194	20	=	=	SYM
ejpam-6480	194	21	1	1	NUM
ejpam-6480	194	22	c	c	X
ejpam-6480	194	23	[	[	PUNCT
ejpam-6480	194	24	h2−α	h2−α	PROPN
ejpam-6480	194	25	2	2	NUM
ejpam-6480	194	26	(	(	PUNCT
ejpam-6480	194	27	t1	t1	NOUN
ejpam-6480	194	28	,	,	PUNCT
ejpam-6480	194	29	t2)−	t2)−	VERB
ejpam-6480	194	30	h2−α	h2−α	PROPN
ejpam-6480	194	31	1	1	NUM
ejpam-6480	194	32	(	(	PUNCT
ejpam-6480	194	33	t1	t1	NOUN
ejpam-6480	194	34	,	,	PUNCT
ejpam-6480	194	35	t2	t2	NOUN
ejpam-6480	194	36	)	)	PUNCT
ejpam-6480	194	37	]	]	PUNCT
ejpam-6480	195	1	−	−	PROPN
ejpam-6480	195	2	1	1	NUM
ejpam-6480	195	3	(	(	PUNCT
ejpam-6480	195	4	3.9	3.9	NUM
ejpam-6480	195	5	)	)	PUNCT
ejpam-6480	195	6	where	where	SCONJ
ejpam-6480	195	7	c	c	NOUN
ejpam-6480	195	8	=	=	SYM
ejpam-6480	195	9	θ(2−	θ(2−	PROPN
ejpam-6480	195	10	α	α	NOUN
ejpam-6480	195	11	)	)	PUNCT
ejpam-6480	195	12	.	.	PUNCT
ejpam-6480	196	1	thus	thus	ADV
ejpam-6480	196	2	(	(	PUNCT
ejpam-6480	196	3	3.9	3.9	NUM
ejpam-6480	196	4	)	)	PUNCT
ejpam-6480	196	5	is	be	AUX
ejpam-6480	196	6	equivalent	equivalent	ADJ
ejpam-6480	196	7	to	to	ADP
ejpam-6480	196	8	(	(	PUNCT
ejpam-6480	196	9	3.8	3.8	NUM
ejpam-6480	196	10	)	)	PUNCT
ejpam-6480	196	11	for	for	ADP
ejpam-6480	196	12	k	k	PROPN
ejpam-6480	196	13	=	=	SYM
ejpam-6480	196	14	0	0	PROPN
ejpam-6480	196	15	.	.	PUNCT
ejpam-6480	197	1	(	(	PUNCT
ejpam-6480	197	2	ii	ii	NOUN
ejpam-6480	197	3	)	)	PUNCT
ejpam-6480	197	4	the	the	DET
ejpam-6480	197	5	probability	probability	NOUN
ejpam-6480	197	6	density	density	NOUN
ejpam-6480	197	7	function	function	NOUN
ejpam-6480	197	8	and	and	CCONJ
ejpam-6480	197	9	corresponding	correspond	VERB
ejpam-6480	197	10	cdf	cdf	PROPN
ejpam-6480	197	11	of	of	ADP
ejpam-6480	197	12	uniform	uniform	ADJ
ejpam-6480	197	13	distribution	distribution	NOUN
ejpam-6480	197	14	is	be	AUX
ejpam-6480	197	15	given	give	VERB
ejpam-6480	197	16	by	by	ADP
ejpam-6480	197	17	f(x	f(x	PROPN
ejpam-6480	197	18	)	)	PUNCT
ejpam-6480	198	1	=	=	PUNCT
ejpam-6480	199	1	rs(1	rs(1	PROPN
ejpam-6480	199	2	+	+	CCONJ
ejpam-6480	199	3	rx)−(s+1	rx)−(s+1	PROPN
ejpam-6480	199	4	)	)	PUNCT
ejpam-6480	199	5	,	,	PUNCT
ejpam-6480	199	6	r	r	NOUN
ejpam-6480	199	7	,	,	PUNCT
ejpam-6480	199	8	s	s	NOUN
ejpam-6480	199	9	>	>	X
ejpam-6480	199	10	0	0	NUM
ejpam-6480	199	11	,	,	PUNCT
ejpam-6480	199	12	fx(x	fx(x	PUNCT
ejpam-6480	199	13	)	)	PUNCT
ejpam-6480	200	1	=	=	SYM
ejpam-6480	200	2	1−	1−	NUM
ejpam-6480	200	3	(	(	PUNCT
ejpam-6480	200	4	1	1	NUM
ejpam-6480	200	5	+	+	CCONJ
ejpam-6480	200	6	rx)s	rx)s	VERB
ejpam-6480	200	7	thus	thus	ADV
ejpam-6480	200	8	using	use	VERB
ejpam-6480	200	9	(	(	PUNCT
ejpam-6480	200	10	2.2	2.2	NUM
ejpam-6480	200	11	)	)	PUNCT
ejpam-6480	200	12	,	,	PUNCT
ejpam-6480	200	13	we	we	PRON
ejpam-6480	200	14	have	have	VERB
ejpam-6480	200	15	(	(	PUNCT
ejpam-6480	200	16	α−	α−	ADP
ejpam-6480	200	17	1)kα	1)kα	PROPN
ejpam-6480	200	18	(	(	PUNCT
ejpam-6480	200	19	x	x	NOUN
ejpam-6480	200	20	;	;	PUNCT
ejpam-6480	200	21	t1	t1	NOUN
ejpam-6480	200	22	,	,	PUNCT
ejpam-6480	200	23	t2	t2	NOUN
ejpam-6480	200	24	)	)	PUNCT
ejpam-6480	200	25	=	=	SYM
ejpam-6480	201	1	1	1	NUM
ejpam-6480	201	2	c	c	NOUN
ejpam-6480	201	3	[	[	PUNCT
ejpam-6480	201	4	(	(	PUNCT
ejpam-6480	201	5	1	1	NUM
ejpam-6480	201	6	+	+	NUM
ejpam-6480	201	7	rt2	rt2	NOUN
ejpam-6480	201	8	)	)	PUNCT
ejpam-6480	201	9	h	h	NOUN
ejpam-6480	201	10	2−α	2−α	NUM
ejpam-6480	201	11	2	2	NUM
ejpam-6480	201	12	(	(	PUNCT
ejpam-6480	201	13	t1	t1	NOUN
ejpam-6480	201	14	,	,	PUNCT
ejpam-6480	201	15	t2)−	t2)−	X
ejpam-6480	201	16	(	(	PUNCT
ejpam-6480	201	17	1	1	NUM
ejpam-6480	201	18	+	+	NUM
ejpam-6480	201	19	rt1	rt1	PROPN
ejpam-6480	201	20	)	)	PUNCT
ejpam-6480	201	21	h	h	NOUN
ejpam-6480	201	22	2−α	2−α	NUM
ejpam-6480	201	23	1	1	NUM
ejpam-6480	201	24	(	(	PUNCT
ejpam-6480	201	25	t1	t1	NOUN
ejpam-6480	201	26	,	,	PUNCT
ejpam-6480	201	27	t2	t2	NOUN
ejpam-6480	201	28	)	)	PUNCT
ejpam-6480	201	29	]	]	PUNCT
ejpam-6480	202	1	−	−	PROPN
ejpam-6480	202	2	1	1	NUM
ejpam-6480	202	3	where	where	SCONJ
ejpam-6480	202	4	c	c	NOUN
ejpam-6480	202	5	=	=	SYM
ejpam-6480	202	6	1	1	NUM
ejpam-6480	202	7	r[1−(s+1)(2−α	r[1−(s+1)(2−α	NOUN
ejpam-6480	202	8	)	)	PUNCT
ejpam-6480	202	9	]	]	PUNCT
ejpam-6480	202	10	and	and	CCONJ
ejpam-6480	202	11	k	k	X
ejpam-6480	202	12	=	=	SYM
ejpam-6480	202	13	r	r	X
ejpam-6480	202	14	>	>	X
ejpam-6480	202	15	0	0	NUM
ejpam-6480	202	16	.	.	PUNCT
ejpam-6480	203	1	thus	thus	ADV
ejpam-6480	203	2	(	(	PUNCT
ejpam-6480	203	3	3.8	3.8	NUM
ejpam-6480	203	4	)	)	PUNCT
ejpam-6480	203	5	holds	hold	VERB
ejpam-6480	203	6	(	(	PUNCT
ejpam-6480	203	7	iii	iii	NOUN
ejpam-6480	203	8	)	)	PUNCT
ejpam-6480	203	9	the	the	DET
ejpam-6480	203	10	probability	probability	NOUN
ejpam-6480	203	11	density	density	NOUN
ejpam-6480	203	12	function	function	NOUN
ejpam-6480	203	13	and	and	CCONJ
ejpam-6480	203	14	corresponding	correspond	VERB
ejpam-6480	203	15	cdf	cdf	PROPN
ejpam-6480	203	16	of	of	ADP
ejpam-6480	203	17	uniform	uniform	ADJ
ejpam-6480	203	18	distribution	distribution	NOUN
ejpam-6480	203	19	is	be	AUX
ejpam-6480	203	20	given	give	VERB
ejpam-6480	203	21	by	by	ADP
ejpam-6480	203	22	j.	j.	PROPN
ejpam-6480	203	23	g.	g.	PROPN
ejpam-6480	203	24	dar	dar	PROPN
ejpam-6480	203	25	,	,	PUNCT
ejpam-6480	203	26	s.	s.	PROPN
ejpam-6480	203	27	m.	m.	PROPN
ejpam-6480	203	28	a.	a.	PROPN
ejpam-6480	203	29	alsheikh	alsheikh	PROPN
ejpam-6480	203	30	,	,	PUNCT
ejpam-6480	203	31	p.	p.	PROPN
ejpam-6480	203	32	jadhav	jadhav	PROPN
ejpam-6480	203	33	/	/	SYM
ejpam-6480	203	34	eur	eur	PROPN
ejpam-6480	203	35	.	.	PUNCT
ejpam-6480	204	1	j.	j.	PROPN
ejpam-6480	204	2	pure	pure	PROPN
ejpam-6480	204	3	appl	appl	PROPN
ejpam-6480	204	4	.	.	PROPN
ejpam-6480	204	5	math	math	PROPN
ejpam-6480	204	6	,	,	PUNCT
ejpam-6480	204	7	18	18	NUM
ejpam-6480	204	8	(	(	PUNCT
ejpam-6480	204	9	4	4	NUM
ejpam-6480	204	10	)	)	PUNCT
ejpam-6480	204	11	(	(	PUNCT
ejpam-6480	204	12	2025	2025	NUM
ejpam-6480	204	13	)	)	PUNCT
ejpam-6480	204	14	,	,	PUNCT
ejpam-6480	204	15	6480	6480	NUM
ejpam-6480	204	16	11	11	NUM
ejpam-6480	204	17	of	of	ADP
ejpam-6480	204	18	14	14	NUM
ejpam-6480	204	19	f(x	f(x	PROPN
ejpam-6480	204	20	)	)	PUNCT
ejpam-6480	205	1	=	=	SYM
ejpam-6480	206	1	ab(1−	ab(1−	ADJ
ejpam-6480	206	2	ax)b−1	ax)b−1	NOUN
ejpam-6480	206	3	,	,	PUNCT
ejpam-6480	206	4	0	0	NUM
ejpam-6480	206	5	<	<	X
ejpam-6480	206	6	x	x	X
ejpam-6480	206	7	<	<	X
ejpam-6480	206	8	1	1	NUM
ejpam-6480	206	9	b	b	PROPN
ejpam-6480	206	10	,	,	PUNCT
ejpam-6480	206	11	a	a	PRON
ejpam-6480	206	12	,	,	PUNCT
ejpam-6480	206	13	b	b	X
ejpam-6480	206	14	>	>	X
ejpam-6480	206	15	0	0	PROPN
ejpam-6480	206	16	,	,	PUNCT
ejpam-6480	206	17	f(x	f(x	PROPN
ejpam-6480	206	18	)	)	PUNCT
ejpam-6480	206	19	=	=	SYM
ejpam-6480	206	20	1−	1−	NUM
ejpam-6480	206	21	(	(	PUNCT
ejpam-6480	206	22	1−	1−	NUM
ejpam-6480	206	23	ax)b	ax)b	PROPN
ejpam-6480	206	24	respectively	respectively	ADV
ejpam-6480	206	25	.	.	PUNCT
ejpam-6480	207	1	using	use	VERB
ejpam-6480	207	2	(	(	PUNCT
ejpam-6480	207	3	2.2	2.2	NUM
ejpam-6480	207	4	)	)	PUNCT
ejpam-6480	207	5	,	,	PUNCT
ejpam-6480	207	6	one	one	PRON
ejpam-6480	207	7	will	will	AUX
ejpam-6480	207	8	get	get	VERB
ejpam-6480	207	9	(	(	PUNCT
ejpam-6480	207	10	α−	α−	ADP
ejpam-6480	207	11	1)kα	1)kα	PROPN
ejpam-6480	207	12	(	(	PUNCT
ejpam-6480	207	13	x	x	NOUN
ejpam-6480	207	14	;	;	PUNCT
ejpam-6480	207	15	t1	t1	NOUN
ejpam-6480	207	16	,	,	PUNCT
ejpam-6480	207	17	t2	t2	NOUN
ejpam-6480	207	18	)	)	PUNCT
ejpam-6480	207	19	=	=	SYM
ejpam-6480	208	1	1	1	NUM
ejpam-6480	208	2	c	c	NOUN
ejpam-6480	208	3	[	[	PUNCT
ejpam-6480	208	4	(	(	PUNCT
ejpam-6480	208	5	1−	1−	NUM
ejpam-6480	208	6	at2	at2	NOUN
ejpam-6480	208	7	)	)	PUNCT
ejpam-6480	208	8	h	h	NOUN
ejpam-6480	208	9	2−α	2−α	NUM
ejpam-6480	208	10	1	1	NUM
ejpam-6480	208	11	(	(	PUNCT
ejpam-6480	208	12	t1	t1	NOUN
ejpam-6480	208	13	,	,	PUNCT
ejpam-6480	208	14	t2)−	t2)−	NOUN
ejpam-6480	208	15	(	(	PUNCT
ejpam-6480	208	16	1−	1−	NUM
ejpam-6480	208	17	at1	at1	PROPN
ejpam-6480	208	18	)	)	PUNCT
ejpam-6480	208	19	h	h	NOUN
ejpam-6480	208	20	2−α	2−α	NUM
ejpam-6480	208	21	2	2	NUM
ejpam-6480	208	22	(	(	PUNCT
ejpam-6480	208	23	t1	t1	NOUN
ejpam-6480	208	24	,	,	PUNCT
ejpam-6480	208	25	t2	t2	NOUN
ejpam-6480	208	26	)	)	PUNCT
ejpam-6480	208	27	]	]	PUNCT
ejpam-6480	209	1	−	−	PROPN
ejpam-6480	209	2	1	1	NUM
ejpam-6480	210	1	where	where	SCONJ
ejpam-6480	210	2	c	c	NOUN
ejpam-6480	210	3	=	=	SYM
ejpam-6480	210	4	1	1	NUM
ejpam-6480	210	5	−a[1+(b−1)(2−α	−a[1+(b−1)(2−α	NUM
ejpam-6480	210	6	)	)	PUNCT
ejpam-6480	210	7	]	]	PUNCT
ejpam-6480	210	8	and	and	CCONJ
ejpam-6480	210	9	k	k	X
ejpam-6480	210	10	=	=	SYM
ejpam-6480	210	11	−a	−a	ADV
ejpam-6480	210	12	<	<	X
ejpam-6480	210	13	0	0	NUM
ejpam-6480	210	14	.	.	PUNCT
ejpam-6480	211	1	thus	thus	ADV
ejpam-6480	211	2	(	(	PUNCT
ejpam-6480	211	3	3.8	3.8	NUM
ejpam-6480	211	4	)	)	PUNCT
ejpam-6480	211	5	holds	hold	VERB
ejpam-6480	211	6	.	.	PUNCT
ejpam-6480	212	1	conversely	conversely	ADV
ejpam-6480	212	2	,	,	PUNCT
ejpam-6480	212	3	let	let	VERB
ejpam-6480	212	4	(	(	PUNCT
ejpam-6480	212	5	3.8	3.8	NUM
ejpam-6480	212	6	)	)	PUNCT
ejpam-6480	212	7	holds	hold	VERB
ejpam-6480	212	8	.	.	PUNCT
ejpam-6480	213	1	using	use	VERB
ejpam-6480	213	2	(	(	PUNCT
ejpam-6480	213	3	2.2	2.2	NUM
ejpam-6480	213	4	)	)	PUNCT
ejpam-6480	213	5	in	in	ADP
ejpam-6480	213	6	(	(	PUNCT
ejpam-6480	213	7	3.8	3.8	NUM
ejpam-6480	213	8	)	)	PUNCT
ejpam-6480	213	9	,	,	PUNCT
ejpam-6480	213	10	we	we	PRON
ejpam-6480	213	11	get	get	VERB
ejpam-6480	213	12	c	c	PROPN
ejpam-6480	213	13	∫	∫	PROPN
ejpam-6480	213	14	t2	t2	PROPN
ejpam-6480	213	15	t1	t1	NOUN
ejpam-6480	213	16	f2−α(x)dx	f2−α(x)dx	VERB
ejpam-6480	213	17	=	=	SYM
ejpam-6480	213	18	(	(	PUNCT
ejpam-6480	213	19	1	1	NUM
ejpam-6480	213	20	+	+	NUM
ejpam-6480	213	21	kt2	kt2	NOUN
ejpam-6480	213	22	)	)	PUNCT
ejpam-6480	213	23	2−α	2−α	PROPN
ejpam-6480	214	1	f2−α	f2−α	PROPN
ejpam-6480	214	2	(	(	PUNCT
ejpam-6480	214	3	t2)−	t2)−	NOUN
ejpam-6480	214	4	(	(	PUNCT
ejpam-6480	214	5	1	1	NUM
ejpam-6480	214	6	+	+	CCONJ
ejpam-6480	214	7	kt1	kt1	PROPN
ejpam-6480	214	8	)	)	PUNCT
ejpam-6480	214	9	2−α	2−α	PROPN
ejpam-6480	215	1	f2−α	f2−α	PROPN
ejpam-6480	215	2	(	(	PUNCT
ejpam-6480	215	3	t1)−	t1)−	NOUN
ejpam-6480	215	4	1	1	NUM
ejpam-6480	215	5	.	.	PUNCT
ejpam-6480	215	6	differentiating	differentiate	VERB
ejpam-6480	215	7	with	with	ADP
ejpam-6480	215	8	respect	respect	NOUN
ejpam-6480	215	9	to	to	ADP
ejpam-6480	215	10	t2	t2	NOUN
ejpam-6480	215	11	,	,	PUNCT
ejpam-6480	215	12	keeping	keep	VERB
ejpam-6480	215	13	t1	t1	NUM
ejpam-6480	215	14	fixed	fix	VERB
ejpam-6480	215	15	f′(t2	f′(t2	NOUN
ejpam-6480	215	16	)	)	PUNCT
ejpam-6480	215	17	f(t2	f(t2	NOUN
ejpam-6480	215	18	)	)	PUNCT
ejpam-6480	215	19	=	=	PUNCT
ejpam-6480	215	20	(	(	PUNCT
ejpam-6480	215	21	c−k	c−k	NOUN
ejpam-6480	215	22	2−α	2−α	NUM
ejpam-6480	215	23	)	)	PUNCT
ejpam-6480	215	24	(	(	PUNCT
ejpam-6480	215	25	1	1	NUM
ejpam-6480	215	26	1+kt2	1+kt2	NUM
ejpam-6480	215	27	)	)	PUNCT
ejpam-6480	215	28	.	.	PUNCT
ejpam-6480	216	1	similarly	similarly	ADV
ejpam-6480	216	2	differentiating	differentiate	VERB
ejpam-6480	216	3	with	with	ADP
ejpam-6480	216	4	respect	respect	NOUN
ejpam-6480	216	5	to	to	ADP
ejpam-6480	216	6	t1	t1	NOUN
ejpam-6480	216	7	,	,	PUNCT
ejpam-6480	216	8	keeping	keep	VERB
ejpam-6480	216	9	t2	t2	NOUN
ejpam-6480	216	10	fixed	fix	VERB
ejpam-6480	216	11	f′(t1	f′(t1	PROPN
ejpam-6480	216	12	)	)	PUNCT
ejpam-6480	216	13	f(t1	f(t1	NOUN
ejpam-6480	216	14	)	)	PUNCT
ejpam-6480	216	15	=	=	SYM
ejpam-6480	216	16	(	(	PUNCT
ejpam-6480	216	17	c−k	c−k	NOUN
ejpam-6480	216	18	2−α	2−α	NUM
ejpam-6480	216	19	)	)	PUNCT
ejpam-6480	216	20	(	(	PUNCT
ejpam-6480	216	21	1	1	NUM
ejpam-6480	216	22	1+kt1	1+kt1	NUM
ejpam-6480	216	23	)	)	PUNCT
ejpam-6480	216	24	.	.	PUNCT
ejpam-6480	217	1	generally	generally	ADV
ejpam-6480	217	2	,	,	PUNCT
ejpam-6480	217	3	f′(ti	f′(ti	NOUN
ejpam-6480	217	4	)	)	PUNCT
ejpam-6480	217	5	f(ti	f(ti	NOUN
ejpam-6480	217	6	)	)	PUNCT
ejpam-6480	218	1	=	=	PUNCT
ejpam-6480	218	2	(	(	PUNCT
ejpam-6480	218	3	c−k	c−k	NOUN
ejpam-6480	218	4	2−α	2−α	NUM
ejpam-6480	218	5	)	)	PUNCT
ejpam-6480	218	6	(	(	PUNCT
ejpam-6480	218	7	1	1	NUM
ejpam-6480	218	8	1+kti	1+kti	NUM
ejpam-6480	218	9	)	)	PUNCT
ejpam-6480	218	10	,	,	PUNCT
ejpam-6480	218	11	i	i	PRON
ejpam-6480	218	12	=	=	NOUN
ejpam-6480	218	13	1	1	NUM
ejpam-6480	218	14	,	,	PUNCT
ejpam-6480	218	15	2	2	NUM
ejpam-6480	218	16	.	.	PUNCT
ejpam-6480	219	1	this	this	PRON
ejpam-6480	219	2	gives	give	VERB
ejpam-6480	219	3	d	d	PROPN
ejpam-6480	219	4	dt	dt	NOUN
ejpam-6480	219	5	log	log	NOUN
ejpam-6480	219	6	f	f	PROPN
ejpam-6480	219	7	(	(	PUNCT
ejpam-6480	219	8	ti	ti	NOUN
ejpam-6480	219	9	)	)	PUNCT
ejpam-6480	219	10	=	=	SYM
ejpam-6480	219	11	(	(	PUNCT
ejpam-6480	219	12	c−	c−	X
ejpam-6480	219	13	k	k	PROPN
ejpam-6480	219	14	2−	2−	NUM
ejpam-6480	219	15	α	α	NOUN
ejpam-6480	219	16	)	)	PUNCT
ejpam-6480	219	17	(	(	PUNCT
ejpam-6480	219	18	1	1	NUM
ejpam-6480	219	19	1	1	NUM
ejpam-6480	219	20	+	+	NUM
ejpam-6480	219	21	kti	kti	PROPN
ejpam-6480	219	22	)	)	PUNCT
ejpam-6480	219	23	,	,	PUNCT
ejpam-6480	219	24	i	i	PRON
ejpam-6480	219	25	=	=	NOUN
ejpam-6480	219	26	1	1	NUM
ejpam-6480	219	27	,	,	PUNCT
ejpam-6480	219	28	2	2	NUM
ejpam-6480	219	29	(	(	PUNCT
ejpam-6480	219	30	3.10	3.10	NUM
ejpam-6480	219	31	)	)	PUNCT
ejpam-6480	219	32	(	(	PUNCT
ejpam-6480	219	33	3.10	3.10	NUM
ejpam-6480	219	34	)	)	PUNCT
ejpam-6480	219	35	clearly	clearly	ADV
ejpam-6480	219	36	shows	show	VERB
ejpam-6480	219	37	that	that	SCONJ
ejpam-6480	219	38	the	the	DET
ejpam-6480	219	39	underlying	underlie	VERB
ejpam-6480	219	40	distribution	distribution	NOUN
ejpam-6480	219	41	is	be	AUX
ejpam-6480	219	42	exponential	exponential	ADJ
ejpam-6480	219	43	if	if	SCONJ
ejpam-6480	219	44	k	k	PROPN
ejpam-6480	219	45	=	=	SYM
ejpam-6480	219	46	0	0	NUM
ejpam-6480	219	47	,	,	PUNCT
ejpam-6480	219	48	pareto	pareto	ADJ
ejpam-6480	219	49	distribution	distribution	NOUN
ejpam-6480	219	50	for	for	ADP
ejpam-6480	219	51	k	k	PROPN
ejpam-6480	219	52	>	>	X
ejpam-6480	219	53	0	0	PUNCT
ejpam-6480	220	1	and	and	CCONJ
ejpam-6480	220	2	finite	finite	VERB
ejpam-6480	220	3	rage	rage	NOUN
ejpam-6480	220	4	distribution	distribution	NOUN
ejpam-6480	220	5	for	for	ADP
ejpam-6480	220	6	k	k	X
ejpam-6480	220	7	<	<	X
ejpam-6480	220	8	0	0	X
ejpam-6480	220	9	.	.	PUNCT
ejpam-6480	221	1	hence	hence	ADV
ejpam-6480	221	2	the	the	DET
ejpam-6480	221	3	theorem	theorem	NOUN
ejpam-6480	221	4	is	be	AUX
ejpam-6480	221	5	proved	prove	VERB
ejpam-6480	221	6	.	.	PUNCT
ejpam-6480	222	1	4	4	X
ejpam-6480	222	2	.	.	X
ejpam-6480	222	3	some	some	DET
ejpam-6480	222	4	inequalities	inequality	NOUN
ejpam-6480	222	5	and	and	CCONJ
ejpam-6480	222	6	stochastic	stochastic	ADJ
ejpam-6480	222	7	comparison	comparison	NOUN
ejpam-6480	222	8	:	:	PUNCT
ejpam-6480	222	9	theorem	theorem	NOUN
ejpam-6480	222	10	4.1	4.1	NUM
ejpam-6480	222	11	.	.	PUNCT
ejpam-6480	223	1	let	let	VERB
ejpam-6480	223	2	x	x	PRON
ejpam-6480	223	3	be	be	AUX
ejpam-6480	223	4	an	an	DET
ejpam-6480	223	5	absolutely	absolutely	ADV
ejpam-6480	223	6	continuous	continuous	ADJ
ejpam-6480	223	7	random	random	ADJ
ejpam-6480	223	8	variable	variable	ADJ
ejpam-6480	223	9	density	density	NOUN
ejpam-6480	223	10	function	function	VERB
ejpam-6480	223	11	f(x	f(x	PROPN
ejpam-6480	223	12	)	)	PUNCT
ejpam-6480	223	13	and	and	CCONJ
ejpam-6480	223	14	distribution	distribution	NOUN
ejpam-6480	223	15	function	function	NOUN
ejpam-6480	223	16	f(x	f(x	PROPN
ejpam-6480	223	17	)	)	PUNCT
ejpam-6480	223	18	,	,	PUNCT
ejpam-6480	223	19	then	then	ADV
ejpam-6480	223	20	for	for	ADP
ejpam-6480	223	21	α	α	PROPN
ejpam-6480	223	22	>	>	X
ejpam-6480	223	23	1(α	1(α	NUM
ejpam-6480	223	24	<	<	X
ejpam-6480	223	25	1	1	NUM
ejpam-6480	223	26	)	)	PUNCT
ejpam-6480	223	27	,	,	PUNCT
ejpam-6480	223	28	then	then	ADV
ejpam-6480	223	29	kα	kα	X
ejpam-6480	223	30	(	(	PUNCT
ejpam-6480	223	31	x	x	X
ejpam-6480	223	32	;	;	PUNCT
ejpam-6480	223	33	t1	t1	NOUN
ejpam-6480	223	34	,	,	PUNCT
ejpam-6480	223	35	t2	t2	NOUN
ejpam-6480	223	36	)	)	PUNCT
ejpam-6480	223	37	is	be	AUX
ejpam-6480	223	38	increasing	increase	VERB
ejpam-6480	223	39	(	(	PUNCT
ejpam-6480	223	40	decreasing	decrease	VERB
ejpam-6480	223	41	)	)	PUNCT
ejpam-6480	223	42	in	in	ADP
ejpam-6480	223	43	t2	t2	PROPN
ejpam-6480	223	44	if	if	SCONJ
ejpam-6480	223	45	f	f	PROPN
ejpam-6480	223	46	(	(	PUNCT
ejpam-6480	223	47	t1	t1	NOUN
ejpam-6480	223	48	)	)	PUNCT
ejpam-6480	223	49	=	=	SYM
ejpam-6480	224	1	0	0	NUM
ejpam-6480	224	2	proof	proof	NOUN
ejpam-6480	224	3	:	:	PUNCT
ejpam-6480	224	4	kα	kα	PROPN
ejpam-6480	224	5	(	(	PUNCT
ejpam-6480	224	6	x	x	X
ejpam-6480	224	7	;	;	PUNCT
ejpam-6480	224	8	t1	t1	NOUN
ejpam-6480	224	9	,	,	PUNCT
ejpam-6480	224	10	t2	t2	NOUN
ejpam-6480	224	11	)	)	PUNCT
ejpam-6480	224	12	=	=	SYM
ejpam-6480	224	13	1	1	NUM
ejpam-6480	224	14	(	(	PUNCT
ejpam-6480	224	15	α−1	α−1	NOUN
ejpam-6480	224	16	)	)	PUNCT
ejpam-6480	225	1	[	[	X
ejpam-6480	225	2	∫	∫	X
ejpam-6480	225	3	t2	t2	PROPN
ejpam-6480	225	4	t1	t1	PROPN
ejpam-6480	225	5	(	(	PUNCT
ejpam-6480	225	6	f(x	f(x	PROPN
ejpam-6480	225	7	)	)	PUNCT
ejpam-6480	225	8	f(t2)−f(t1	f(t2)−f(t1	PROPN
ejpam-6480	225	9	)	)	PUNCT
ejpam-6480	225	10	)	)	PUNCT
ejpam-6480	225	11	2−α	2−α	NUM
ejpam-6480	226	1	dx−	dx−	NUM
ejpam-6480	226	2	1	1	X
ejpam-6480	226	3	]	]	PUNCT
ejpam-6480	226	4	for	for	ADP
ejpam-6480	226	5	f	f	PROPN
ejpam-6480	226	6	(	(	PUNCT
ejpam-6480	226	7	t1	t1	NOUN
ejpam-6480	226	8	)	)	PUNCT
ejpam-6480	226	9	=	=	SYM
ejpam-6480	226	10	0	0	NUM
ejpam-6480	226	11	,	,	PUNCT
ejpam-6480	226	12	we	we	PRON
ejpam-6480	226	13	have	have	VERB
ejpam-6480	226	14	kα	kα	VERB
ejpam-6480	226	15	(	(	PUNCT
ejpam-6480	226	16	x	x	X
ejpam-6480	226	17	;	;	PUNCT
ejpam-6480	226	18	t1	t1	NOUN
ejpam-6480	226	19	,	,	PUNCT
ejpam-6480	226	20	t2	t2	NOUN
ejpam-6480	226	21	)	)	PUNCT
ejpam-6480	226	22	=	=	SYM
ejpam-6480	226	23	1	1	NUM
ejpam-6480	226	24	(	(	PUNCT
ejpam-6480	226	25	α−1	α−1	NOUN
ejpam-6480	226	26	)	)	PUNCT
ejpam-6480	227	1	[	[	X
ejpam-6480	227	2	∫	∫	X
ejpam-6480	227	3	t2	t2	PROPN
ejpam-6480	227	4	t1	t1	PROPN
ejpam-6480	227	5	(	(	PUNCT
ejpam-6480	227	6	f(x	f(x	PROPN
ejpam-6480	227	7	)	)	PUNCT
ejpam-6480	227	8	f(t2	f(t2	NOUN
ejpam-6480	227	9	)	)	PUNCT
ejpam-6480	227	10	)	)	PUNCT
ejpam-6480	227	11	2−α	2−α	NUM
ejpam-6480	228	1	dx−	dx−	NUM
ejpam-6480	228	2	1	1	X
ejpam-6480	228	3	]	]	PUNCT
ejpam-6480	228	4	differentiating	differentiate	VERB
ejpam-6480	228	5	with	with	ADP
ejpam-6480	228	6	respect	respect	NOUN
ejpam-6480	228	7	t2	t2	NOUN
ejpam-6480	228	8	,	,	PUNCT
ejpam-6480	228	9	we	we	PRON
ejpam-6480	228	10	get	get	VERB
ejpam-6480	228	11	k′	k′	PROPN
ejpam-6480	228	12	α	α	PROPN
ejpam-6480	228	13	(	(	PUNCT
ejpam-6480	228	14	x	x	NOUN
ejpam-6480	228	15	;	;	PUNCT
ejpam-6480	228	16	t1	t1	NOUN
ejpam-6480	228	17	,	,	PUNCT
ejpam-6480	228	18	t2	t2	NOUN
ejpam-6480	228	19	)	)	PUNCT
ejpam-6480	228	20	=	=	SYM
ejpam-6480	228	21	f(t2	f(t2	NOUN
ejpam-6480	228	22	)	)	PUNCT
ejpam-6480	228	23	f3−α(t2	f3−α(t2	NOUN
ejpam-6480	228	24	)	)	PUNCT
ejpam-6480	228	25	[	[	PUNCT
ejpam-6480	228	26	f1−α	f1−α	PROPN
ejpam-6480	228	27	(	(	PUNCT
ejpam-6480	228	28	t2	t2	PROPN
ejpam-6480	228	29	)	)	PUNCT
ejpam-6480	228	30	f	f	PROPN
ejpam-6480	228	31	(	(	PUNCT
ejpam-6480	228	32	t2)−	t2)−	NOUN
ejpam-6480	228	33	(	(	PUNCT
ejpam-6480	228	34	2−	2−	NUM
ejpam-6480	228	35	α	α	NOUN
ejpam-6480	228	36	)	)	PUNCT
ejpam-6480	228	37	∫	∫	PROPN
ejpam-6480	228	38	t2	t2	PROPN
ejpam-6480	228	39	t1	t1	PROPN
ejpam-6480	228	40	f2−α(x)dx	f2−α(x)dx	VERB
ejpam-6480	228	41	]	]	PUNCT
ejpam-6480	228	42	define	define	NOUN
ejpam-6480	228	43	k(t2	k(t2	NOUN
ejpam-6480	228	44	)	)	PUNCT
ejpam-6480	228	45	=	=	SYM
ejpam-6480	228	46	f1−α	f1−α	PROPN
ejpam-6480	228	47	(	(	PUNCT
ejpam-6480	228	48	t2	t2	PROPN
ejpam-6480	228	49	)	)	PUNCT
ejpam-6480	228	50	f	f	PROPN
ejpam-6480	228	51	(	(	PUNCT
ejpam-6480	228	52	t2)−	t2)−	NOUN
ejpam-6480	228	53	(	(	PUNCT
ejpam-6480	228	54	2−	2−	NUM
ejpam-6480	228	55	α	α	NOUN
ejpam-6480	228	56	)	)	PUNCT
ejpam-6480	228	57	∫	∫	PROPN
ejpam-6480	228	58	t2	t2	PROPN
ejpam-6480	228	59	t1	t1	PROPN
ejpam-6480	228	60	f2−α(x)dx	f2−α(x)dx	NOUN
ejpam-6480	228	61	differentiating	differentiate	VERB
ejpam-6480	228	62	again	again	ADV
ejpam-6480	228	63	with	with	ADP
ejpam-6480	228	64	respect	respect	NOUN
ejpam-6480	228	65	t2	t2	NOUN
ejpam-6480	228	66	,	,	PUNCT
ejpam-6480	228	67	we	we	PRON
ejpam-6480	228	68	have	have	VERB
ejpam-6480	228	69	k′	k′	PROPN
ejpam-6480	228	70	(	(	PUNCT
ejpam-6480	228	71	t2	t2	PROPN
ejpam-6480	228	72	)	)	PUNCT
ejpam-6480	228	73	=	=	PUNCT
ejpam-6480	228	74	(	(	PUNCT
ejpam-6480	228	75	α−	α−	ADP
ejpam-6480	228	76	1)f−α	1)f−α	NUM
ejpam-6480	228	77	(	(	PUNCT
ejpam-6480	228	78	t2	t2	PROPN
ejpam-6480	228	79	)	)	PUNCT
ejpam-6480	228	80	(	(	PUNCT
ejpam-6480	228	81	f2	f2	X
ejpam-6480	228	82	(	(	PUNCT
ejpam-6480	228	83	t2)−	t2)−	NOUN
ejpam-6480	228	84	f	f	X
ejpam-6480	228	85	(	(	PUNCT
ejpam-6480	228	86	t2	t2	PROPN
ejpam-6480	228	87	)	)	PUNCT
ejpam-6480	228	88	f	f	PROPN
ejpam-6480	229	1	′	′	NUM
ejpam-6480	229	2	(	(	PUNCT
ejpam-6480	229	3	t2	t2	NOUN
ejpam-6480	229	4	)	)	PUNCT
ejpam-6480	229	5	.	.	PUNCT
ejpam-6480	230	1	if	if	SCONJ
ejpam-6480	230	2	α	α	PROPN
ejpam-6480	230	3	>	>	X
ejpam-6480	230	4	1	1	NUM
ejpam-6480	230	5	,	,	PUNCT
ejpam-6480	230	6	then	then	ADV
ejpam-6480	230	7	k′	k′	PROPN
ejpam-6480	230	8	(	(	PUNCT
ejpam-6480	230	9	t2	t2	PROPN
ejpam-6480	230	10	)	)	PUNCT
ejpam-6480	230	11	≥	≥	NOUN
ejpam-6480	230	12	0	0	NUM
ejpam-6480	230	13	,	,	PUNCT
ejpam-6480	230	14	which	which	PRON
ejpam-6480	230	15	in	in	ADP
ejpam-6480	230	16	turns	turn	NOUN
ejpam-6480	230	17	gives	give	VERB
ejpam-6480	230	18	that	that	SCONJ
ejpam-6480	230	19	kα	kα	PROPN
ejpam-6480	230	20	(	(	PUNCT
ejpam-6480	230	21	x	x	X
ejpam-6480	230	22	;	;	PUNCT
ejpam-6480	230	23	t1	t1	NOUN
ejpam-6480	230	24	,	,	PUNCT
ejpam-6480	230	25	t2	t2	NOUN
ejpam-6480	230	26	)	)	PUNCT
ejpam-6480	230	27	is	be	AUX
ejpam-6480	230	28	an	an	DET
ejpam-6480	230	29	increasing	increase	VERB
ejpam-6480	230	30	function	function	NOUN
ejpam-6480	230	31	of	of	ADP
ejpam-6480	230	32	t2	t2	NOUN
ejpam-6480	230	33	.	.	PUNCT
ejpam-6480	231	1	if	if	SCONJ
ejpam-6480	231	2	α	α	PRON
ejpam-6480	231	3	<	<	X
ejpam-6480	231	4	1	1	NUM
ejpam-6480	231	5	,	,	PUNCT
ejpam-6480	231	6	then	then	ADV
ejpam-6480	231	7	k′	k′	PROPN
ejpam-6480	231	8	(	(	PUNCT
ejpam-6480	231	9	t2	t2	PROPN
ejpam-6480	231	10	)	)	PUNCT
ejpam-6480	231	11	≤	≤	NOUN
ejpam-6480	231	12	0	0	NUM
ejpam-6480	231	13	,	,	PUNCT
ejpam-6480	231	14	which	which	PRON
ejpam-6480	231	15	in	in	ADP
ejpam-6480	231	16	turns	turn	NOUN
ejpam-6480	231	17	gives	give	VERB
ejpam-6480	231	18	that	that	SCONJ
ejpam-6480	231	19	kα	kα	PROPN
ejpam-6480	231	20	(	(	PUNCT
ejpam-6480	231	21	x	x	X
ejpam-6480	231	22	;	;	PUNCT
ejpam-6480	231	23	t1	t1	NOUN
ejpam-6480	231	24	,	,	PUNCT
ejpam-6480	231	25	t2	t2	NOUN
ejpam-6480	231	26	)	)	PUNCT
ejpam-6480	231	27	is	be	AUX
ejpam-6480	231	28	an	an	DET
ejpam-6480	231	29	decreasing	decrease	VERB
ejpam-6480	231	30	function	function	NOUN
ejpam-6480	231	31	of	of	ADP
ejpam-6480	231	32	t2	t2	PROPN
ejpam-6480	231	33	.	.	PUNCT
ejpam-6480	232	1	j.	j.	PROPN
ejpam-6480	232	2	g.	g.	PROPN
ejpam-6480	232	3	dar	dar	PROPN
ejpam-6480	232	4	,	,	PUNCT
ejpam-6480	232	5	s.	s.	PROPN
ejpam-6480	232	6	m.	m.	PROPN
ejpam-6480	232	7	a.	a.	PROPN
ejpam-6480	232	8	alsheikh	alsheikh	PROPN
ejpam-6480	232	9	,	,	PUNCT
ejpam-6480	232	10	p.	p.	PROPN
ejpam-6480	232	11	jadhav	jadhav	PROPN
ejpam-6480	232	12	/	/	SYM
ejpam-6480	232	13	eur	eur	PROPN
ejpam-6480	232	14	.	.	PUNCT
ejpam-6480	233	1	j.	j.	PROPN
ejpam-6480	233	2	pure	pure	PROPN
ejpam-6480	233	3	appl	appl	PROPN
ejpam-6480	233	4	.	.	PROPN
ejpam-6480	233	5	math	math	PROPN
ejpam-6480	233	6	,	,	PUNCT
ejpam-6480	233	7	18	18	NUM
ejpam-6480	233	8	(	(	PUNCT
ejpam-6480	233	9	4	4	NUM
ejpam-6480	233	10	)	)	PUNCT
ejpam-6480	233	11	(	(	PUNCT
ejpam-6480	233	12	2025	2025	NUM
ejpam-6480	233	13	)	)	PUNCT
ejpam-6480	233	14	,	,	PUNCT
ejpam-6480	233	15	6480	6480	NUM
ejpam-6480	233	16	12	12	NUM
ejpam-6480	233	17	of	of	ADP
ejpam-6480	233	18	14	14	NUM
ejpam-6480	233	19	theorem	theorem	VERB
ejpam-6480	233	20	4.2	4.2	NUM
ejpam-6480	233	21	.	.	PUNCT
ejpam-6480	234	1	for	for	ADP
ejpam-6480	234	2	an	an	DET
ejpam-6480	234	3	absolutely	absolutely	ADV
ejpam-6480	234	4	continuous	continuous	ADJ
ejpam-6480	234	5	random	random	ADJ
ejpam-6480	234	6	variable	variable	NOUN
ejpam-6480	234	7	x	x	INTJ
ejpam-6480	234	8	,	,	PUNCT
ejpam-6480	234	9	if	if	SCONJ
ejpam-6480	234	10	kα	kα	PROPN
ejpam-6480	234	11	(	(	PUNCT
ejpam-6480	234	12	x	x	NOUN
ejpam-6480	234	13	;	;	PUNCT
ejpam-6480	234	14	t1	t1	NOUN
ejpam-6480	234	15	,	,	PUNCT
ejpam-6480	234	16	t2	t2	NOUN
ejpam-6480	234	17	)	)	PUNCT
ejpam-6480	234	18	is	be	AUX
ejpam-6480	234	19	increasing	increase	VERB
ejpam-6480	234	20	(	(	PUNCT
ejpam-6480	234	21	decreasing	decrease	VERB
ejpam-6480	234	22	)	)	PUNCT
ejpam-6480	234	23	in	in	ADP
ejpam-6480	234	24	t1	t1	NOUN
ejpam-6480	234	25	for	for	ADP
ejpam-6480	234	26	fixed	fix	VERB
ejpam-6480	234	27	t2	t2	NOUN
ejpam-6480	234	28	,	,	PUNCT
ejpam-6480	234	29	then	then	ADV
ejpam-6480	234	30	h1	h1	PROPN
ejpam-6480	234	31	(	(	PUNCT
ejpam-6480	234	32	t1	t1	PROPN
ejpam-6480	234	33	,	,	PUNCT
ejpam-6480	234	34	t2	t2	NOUN
ejpam-6480	234	35	)	)	PUNCT
ejpam-6480	234	36	≤	≤	NOUN
ejpam-6480	234	37	(	(	PUNCT
ejpam-6480	234	38	≥	≥	NUM
ejpam-6480	234	39	)	)	PUNCT
ejpam-6480	235	1	[	[	X
ejpam-6480	235	2	(	(	PUNCT
ejpam-6480	235	3	(	(	PUNCT
ejpam-6480	235	4	2−	2−	NUM
ejpam-6480	235	5	α)(α−	α)(α−	NOUN
ejpam-6480	235	6	1)kα	1)kα	PROPN
ejpam-6480	235	7	(	(	PUNCT
ejpam-6480	235	8	x	x	NOUN
ejpam-6480	235	9	;	;	PUNCT
ejpam-6480	235	10	t1	t1	NOUN
ejpam-6480	235	11	,	,	PUNCT
ejpam-6480	235	12	t2	t2	NOUN
ejpam-6480	235	13	)	)	PUNCT
ejpam-6480	235	14	)	)	PUNCT
ejpam-6480	235	15	]	]	PUNCT
ejpam-6480	236	1	1	1	NUM
ejpam-6480	236	2	1−α	1−α	NUM
ejpam-6480	236	3	for	for	ADP
ejpam-6480	236	4	α	α	PROPN
ejpam-6480	236	5	>	>	X
ejpam-6480	236	6	1	1	NUM
ejpam-6480	236	7	h1	h1	NOUN
ejpam-6480	236	8	(	(	PUNCT
ejpam-6480	236	9	t1	t1	NOUN
ejpam-6480	236	10	,	,	PUNCT
ejpam-6480	236	11	t2	t2	PROPN
ejpam-6480	236	12	)	)	PUNCT
ejpam-6480	236	13	≥	≥	NOUN
ejpam-6480	236	14	(	(	PUNCT
ejpam-6480	236	15	≤	≤	NUM
ejpam-6480	236	16	)	)	PUNCT
ejpam-6480	237	1	[	[	X
ejpam-6480	237	2	(	(	PUNCT
ejpam-6480	237	3	(	(	PUNCT
ejpam-6480	237	4	2−	2−	NUM
ejpam-6480	237	5	α)(α−	α)(α−	NOUN
ejpam-6480	237	6	1)kα	1)kα	PROPN
ejpam-6480	237	7	(	(	PUNCT
ejpam-6480	237	8	x	x	NOUN
ejpam-6480	237	9	;	;	PUNCT
ejpam-6480	237	10	t1	t1	NOUN
ejpam-6480	237	11	,	,	PUNCT
ejpam-6480	237	12	t2	t2	NOUN
ejpam-6480	237	13	)	)	PUNCT
ejpam-6480	237	14	)	)	PUNCT
ejpam-6480	237	15	]	]	PUNCT
ejpam-6480	238	1	1	1	NUM
ejpam-6480	238	2	1−α	1−α	NUM
ejpam-6480	238	3	for	for	ADP
ejpam-6480	238	4	α	α	PROPN
ejpam-6480	238	5	<	<	X
ejpam-6480	238	6	1	1	NUM
ejpam-6480	238	7	.	.	PUNCT
ejpam-6480	239	1	proof	proof	NOUN
ejpam-6480	239	2	:	:	PUNCT
ejpam-6480	239	3	we	we	PRON
ejpam-6480	239	4	know	know	VERB
ejpam-6480	239	5	that	that	SCONJ
ejpam-6480	239	6	(	(	PUNCT
ejpam-6480	239	7	α−	α−	ADP
ejpam-6480	239	8	1	1	NUM
ejpam-6480	239	9	)	)	PUNCT
ejpam-6480	239	10	∂	∂	NOUN
ejpam-6480	239	11	∂t1	∂t1	NOUN
ejpam-6480	239	12	kα	kα	PROPN
ejpam-6480	239	13	(	(	PUNCT
ejpam-6480	239	14	x	x	NOUN
ejpam-6480	239	15	;	;	PUNCT
ejpam-6480	239	16	t1	t1	NOUN
ejpam-6480	239	17	,	,	PUNCT
ejpam-6480	239	18	t2	t2	NOUN
ejpam-6480	239	19	)	)	PUNCT
ejpam-6480	239	20	=	=	PUNCT
ejpam-6480	240	1	−h2−α	−h2−α	PROPN
ejpam-6480	240	2	1	1	NUM
ejpam-6480	240	3	(	(	PUNCT
ejpam-6480	240	4	t1	t1	NOUN
ejpam-6480	240	5	,	,	PUNCT
ejpam-6480	240	6	t2	t2	NOUN
ejpam-6480	240	7	)	)	PUNCT
ejpam-6480	240	8	+	+	CCONJ
ejpam-6480	240	9	(	(	PUNCT
ejpam-6480	240	10	2−	2−	NUM
ejpam-6480	240	11	α)(α−	α)(α−	NOUN
ejpam-6480	240	12	1)h1	1)h1	PROPN
ejpam-6480	240	13	(	(	PUNCT
ejpam-6480	240	14	t1	t1	PROPN
ejpam-6480	240	15	,	,	PUNCT
ejpam-6480	240	16	t2)kα	t2)kα	PROPN
ejpam-6480	240	17	(	(	PUNCT
ejpam-6480	240	18	x	x	NOUN
ejpam-6480	240	19	;	;	PUNCT
ejpam-6480	240	20	t1	t1	NOUN
ejpam-6480	240	21	,	,	PUNCT
ejpam-6480	240	22	t2	t2	NOUN
ejpam-6480	240	23	)	)	PUNCT
ejpam-6480	240	24	if	if	SCONJ
ejpam-6480	240	25	kα	kα	PROPN
ejpam-6480	240	26	(	(	PUNCT
ejpam-6480	240	27	x	x	NOUN
ejpam-6480	240	28	;	;	PUNCT
ejpam-6480	240	29	t1	t1	NOUN
ejpam-6480	240	30	,	,	PUNCT
ejpam-6480	240	31	t2	t2	NOUN
ejpam-6480	240	32	)	)	PUNCT
ejpam-6480	240	33	is	be	AUX
ejpam-6480	240	34	increasing	increase	VERB
ejpam-6480	240	35	(	(	PUNCT
ejpam-6480	240	36	decreasing	decrease	VERB
ejpam-6480	240	37	)	)	PUNCT
ejpam-6480	240	38	in	in	ADP
ejpam-6480	240	39	t1	t1	NOUN
ejpam-6480	240	40	for	for	ADP
ejpam-6480	240	41	fixed	fix	VERB
ejpam-6480	240	42	t2	t2	NOUN
ejpam-6480	240	43	,	,	PUNCT
ejpam-6480	240	44	then	then	ADV
ejpam-6480	240	45	−h2−α	−h2−α	PROPN
ejpam-6480	240	46	1	1	NUM
ejpam-6480	240	47	(	(	PUNCT
ejpam-6480	240	48	t1	t1	NOUN
ejpam-6480	240	49	,	,	PUNCT
ejpam-6480	240	50	t2	t2	NOUN
ejpam-6480	240	51	)	)	PUNCT
ejpam-6480	240	52	+	+	CCONJ
ejpam-6480	240	53	(	(	PUNCT
ejpam-6480	240	54	2−	2−	NUM
ejpam-6480	240	55	α)(α−	α)(α−	NOUN
ejpam-6480	240	56	1)h1	1)h1	PROPN
ejpam-6480	240	57	(	(	PUNCT
ejpam-6480	240	58	t1	t1	PROPN
ejpam-6480	240	59	,	,	PUNCT
ejpam-6480	240	60	t2)kα	t2)kα	PROPN
ejpam-6480	240	61	(	(	PUNCT
ejpam-6480	240	62	x	x	NOUN
ejpam-6480	240	63	;	;	PUNCT
ejpam-6480	240	64	t1	t1	NOUN
ejpam-6480	240	65	,	,	PUNCT
ejpam-6480	240	66	t2	t2	PROPN
ejpam-6480	240	67	)	)	PUNCT
ejpam-6480	240	68	≥	≥	NUM
ejpam-6480	240	69	(	(	PUNCT
ejpam-6480	240	70	≤)0	≤)0	VERB
ejpam-6480	240	71	h2−α	h2−α	PROPN
ejpam-6480	240	72	1	1	NUM
ejpam-6480	240	73	(	(	PUNCT
ejpam-6480	240	74	t1	t1	NOUN
ejpam-6480	240	75	,	,	PUNCT
ejpam-6480	240	76	t2	t2	NOUN
ejpam-6480	240	77	)	)	PUNCT
ejpam-6480	240	78	≤	≤	NOUN
ejpam-6480	240	79	(	(	PUNCT
ejpam-6480	240	80	≥)(2−	≥)(2−	PROPN
ejpam-6480	240	81	α)(α−	α)(α−	PRON
ejpam-6480	240	82	1)h1	1)h1	PROPN
ejpam-6480	240	83	(	(	PUNCT
ejpam-6480	240	84	t1	t1	PROPN
ejpam-6480	240	85	,	,	PUNCT
ejpam-6480	240	86	t2)kα	t2)kα	PROPN
ejpam-6480	240	87	(	(	PUNCT
ejpam-6480	240	88	x	x	NOUN
ejpam-6480	240	89	;	;	PUNCT
ejpam-6480	240	90	t1	t1	NOUN
ejpam-6480	240	91	,	,	PUNCT
ejpam-6480	240	92	t2	t2	NOUN
ejpam-6480	240	93	)	)	PUNCT
ejpam-6480	240	94	h1−α	h1−α	PROPN
ejpam-6480	240	95	1	1	NUM
ejpam-6480	240	96	(	(	PUNCT
ejpam-6480	240	97	t1	t1	NOUN
ejpam-6480	240	98	,	,	PUNCT
ejpam-6480	240	99	t2	t2	NOUN
ejpam-6480	240	100	)	)	PUNCT
ejpam-6480	240	101	≤	≤	NOUN
ejpam-6480	240	102	(	(	PUNCT
ejpam-6480	240	103	≥)(2−	≥)(2−	PROPN
ejpam-6480	240	104	α)(α−	α)(α−	PRON
ejpam-6480	240	105	1)kα	1)kα	PROPN
ejpam-6480	240	106	(	(	PUNCT
ejpam-6480	240	107	x	x	NOUN
ejpam-6480	240	108	;	;	PUNCT
ejpam-6480	240	109	t1	t1	NOUN
ejpam-6480	240	110	,	,	PUNCT
ejpam-6480	240	111	t2	t2	NOUN
ejpam-6480	240	112	)	)	PUNCT
ejpam-6480	240	113	for	for	ADP
ejpam-6480	240	114	α	α	PROPN
ejpam-6480	240	115	>	>	X
ejpam-6480	240	116	1	1	NUM
ejpam-6480	240	117	h1	h1	NOUN
ejpam-6480	240	118	(	(	PUNCT
ejpam-6480	240	119	t1	t1	NOUN
ejpam-6480	240	120	,	,	PUNCT
ejpam-6480	240	121	t2	t2	NOUN
ejpam-6480	240	122	)	)	PUNCT
ejpam-6480	240	123	≤	≤	NOUN
ejpam-6480	240	124	(	(	PUNCT
ejpam-6480	240	125	≥	≥	NUM
ejpam-6480	240	126	)	)	PUNCT
ejpam-6480	241	1	[	[	X
ejpam-6480	241	2	(	(	PUNCT
ejpam-6480	241	3	(	(	PUNCT
ejpam-6480	241	4	2−	2−	NUM
ejpam-6480	241	5	α)(α−	α)(α−	NOUN
ejpam-6480	241	6	1)kα	1)kα	PROPN
ejpam-6480	241	7	(	(	PUNCT
ejpam-6480	241	8	x	x	NOUN
ejpam-6480	241	9	;	;	PUNCT
ejpam-6480	241	10	t1	t1	NOUN
ejpam-6480	241	11	,	,	PUNCT
ejpam-6480	241	12	t2	t2	NOUN
ejpam-6480	241	13	)	)	PUNCT
ejpam-6480	241	14	)	)	PUNCT
ejpam-6480	241	15	]	]	PUNCT
ejpam-6480	242	1	1	1	NUM
ejpam-6480	242	2	1−α	1−α	NUM
ejpam-6480	242	3	for	for	ADP
ejpam-6480	242	4	α	α	PROPN
ejpam-6480	242	5	<	<	X
ejpam-6480	242	6	1	1	NUM
ejpam-6480	242	7	h1	h1	NOUN
ejpam-6480	242	8	(	(	PUNCT
ejpam-6480	242	9	t1	t1	NOUN
ejpam-6480	242	10	,	,	PUNCT
ejpam-6480	242	11	t2	t2	PROPN
ejpam-6480	242	12	)	)	PUNCT
ejpam-6480	242	13	≥	≥	NOUN
ejpam-6480	242	14	(	(	PUNCT
ejpam-6480	242	15	≤	≤	NUM
ejpam-6480	242	16	)	)	PUNCT
ejpam-6480	243	1	[	[	X
ejpam-6480	243	2	(	(	PUNCT
ejpam-6480	243	3	(	(	PUNCT
ejpam-6480	243	4	2−	2−	NUM
ejpam-6480	243	5	α)(α−	α)(α−	NOUN
ejpam-6480	243	6	1)kα	1)kα	PROPN
ejpam-6480	243	7	(	(	PUNCT
ejpam-6480	243	8	x	x	NOUN
ejpam-6480	243	9	;	;	PUNCT
ejpam-6480	243	10	t1	t1	NOUN
ejpam-6480	243	11	,	,	PUNCT
ejpam-6480	243	12	t2	t2	NOUN
ejpam-6480	243	13	)	)	PUNCT
ejpam-6480	243	14	)	)	PUNCT
ejpam-6480	243	15	]	]	PUNCT
ejpam-6480	243	16	1	1	NUM
ejpam-6480	243	17	1−α	1−α	NUM
ejpam-6480	243	18	theorem	theorem	VERB
ejpam-6480	243	19	4.3	4.3	NUM
ejpam-6480	243	20	.	.	PUNCT
ejpam-6480	244	1	for	for	ADP
ejpam-6480	244	2	an	an	DET
ejpam-6480	244	3	absolutely	absolutely	ADV
ejpam-6480	244	4	continuous	continuous	ADJ
ejpam-6480	244	5	random	random	ADJ
ejpam-6480	244	6	variable	variable	NOUN
ejpam-6480	244	7	x	x	INTJ
ejpam-6480	244	8	,	,	PUNCT
ejpam-6480	244	9	if	if	SCONJ
ejpam-6480	244	10	kα	kα	PROPN
ejpam-6480	244	11	(	(	PUNCT
ejpam-6480	244	12	x	x	NOUN
ejpam-6480	244	13	;	;	PUNCT
ejpam-6480	244	14	t1	t1	NOUN
ejpam-6480	244	15	,	,	PUNCT
ejpam-6480	244	16	t2	t2	NOUN
ejpam-6480	244	17	)	)	PUNCT
ejpam-6480	244	18	is	be	AUX
ejpam-6480	244	19	increasing	increase	VERB
ejpam-6480	244	20	(	(	PUNCT
ejpam-6480	244	21	decreasing	decrease	VERB
ejpam-6480	244	22	)	)	PUNCT
ejpam-6480	244	23	in	in	ADP
ejpam-6480	244	24	t2	t2	PROPN
ejpam-6480	244	25	for	for	ADP
ejpam-6480	244	26	fixed	fix	VERB
ejpam-6480	244	27	t1	t1	PROPN
ejpam-6480	244	28	,	,	PUNCT
ejpam-6480	244	29	then	then	ADV
ejpam-6480	244	30	h2	h2	PROPN
ejpam-6480	244	31	(	(	PUNCT
ejpam-6480	244	32	t1	t1	PROPN
ejpam-6480	244	33	,	,	PUNCT
ejpam-6480	244	34	t2	t2	NOUN
ejpam-6480	244	35	)	)	PUNCT
ejpam-6480	244	36	≤	≤	NOUN
ejpam-6480	244	37	(	(	PUNCT
ejpam-6480	244	38	≥	≥	NUM
ejpam-6480	244	39	)	)	PUNCT
ejpam-6480	245	1	[	[	X
ejpam-6480	245	2	(	(	PUNCT
ejpam-6480	245	3	(	(	PUNCT
ejpam-6480	245	4	2−	2−	NUM
ejpam-6480	245	5	α)(α−	α)(α−	NOUN
ejpam-6480	245	6	1)kα	1)kα	PROPN
ejpam-6480	245	7	(	(	PUNCT
ejpam-6480	245	8	x	x	NOUN
ejpam-6480	245	9	;	;	PUNCT
ejpam-6480	245	10	t1	t1	NOUN
ejpam-6480	245	11	,	,	PUNCT
ejpam-6480	245	12	t2	t2	NOUN
ejpam-6480	245	13	)	)	PUNCT
ejpam-6480	245	14	)	)	PUNCT
ejpam-6480	245	15	]	]	PUNCT
ejpam-6480	246	1	1	1	NUM
ejpam-6480	246	2	1−α	1−α	NUM
ejpam-6480	246	3	for	for	ADP
ejpam-6480	246	4	α	α	PROPN
ejpam-6480	246	5	>	>	X
ejpam-6480	246	6	1	1	NUM
ejpam-6480	246	7	h2	h2	NOUN
ejpam-6480	246	8	(	(	PUNCT
ejpam-6480	246	9	t1	t1	NOUN
ejpam-6480	246	10	,	,	PUNCT
ejpam-6480	246	11	t2	t2	PROPN
ejpam-6480	246	12	)	)	PUNCT
ejpam-6480	246	13	≥	≥	NOUN
ejpam-6480	246	14	(	(	PUNCT
ejpam-6480	246	15	≤	≤	NUM
ejpam-6480	246	16	)	)	PUNCT
ejpam-6480	247	1	[	[	X
ejpam-6480	247	2	(	(	PUNCT
ejpam-6480	247	3	(	(	PUNCT
ejpam-6480	247	4	2−	2−	NUM
ejpam-6480	247	5	α)(α−	α)(α−	NOUN
ejpam-6480	247	6	1)kα	1)kα	PROPN
ejpam-6480	247	7	(	(	PUNCT
ejpam-6480	247	8	x	x	NOUN
ejpam-6480	247	9	;	;	PUNCT
ejpam-6480	247	10	t1	t1	NOUN
ejpam-6480	247	11	,	,	PUNCT
ejpam-6480	247	12	t2	t2	NOUN
ejpam-6480	247	13	)	)	PUNCT
ejpam-6480	247	14	)	)	PUNCT
ejpam-6480	247	15	]	]	PUNCT
ejpam-6480	248	1	1	1	NUM
ejpam-6480	248	2	1−α	1−α	NUM
ejpam-6480	248	3	for	for	ADP
ejpam-6480	248	4	α	α	PROPN
ejpam-6480	248	5	<	<	X
ejpam-6480	248	6	1	1	NUM
ejpam-6480	248	7	.	.	PUNCT
ejpam-6480	249	1	proof	proof	NOUN
ejpam-6480	249	2	:	:	PUNCT
ejpam-6480	249	3	the	the	DET
ejpam-6480	249	4	proof	proof	NOUN
ejpam-6480	249	5	follows	follow	VERB
ejpam-6480	249	6	under	under	ADP
ejpam-6480	249	7	similar	similar	ADJ
ejpam-6480	249	8	lines	line	NOUN
ejpam-6480	249	9	as	as	ADP
ejpam-6480	249	10	in	in	ADP
ejpam-6480	249	11	theorem	theorem	ADJ
ejpam-6480	249	12	4.2	4.2	NUM
ejpam-6480	249	13	.	.	PUNCT
ejpam-6480	250	1	let	let	VERB
ejpam-6480	250	2	x	x	PRON
ejpam-6480	250	3	and	and	CCONJ
ejpam-6480	250	4	y	y	PROPN
ejpam-6480	250	5	be	be	AUX
ejpam-6480	250	6	two	two	NUM
ejpam-6480	250	7	random	random	ADJ
ejpam-6480	250	8	variables	variable	NOUN
ejpam-6480	250	9	.	.	PUNCT
ejpam-6480	251	1	also	also	ADV
ejpam-6480	251	2	,	,	PUNCT
ejpam-6480	251	3	the	the	DET
ejpam-6480	251	4	distribution	distribution	NOUN
ejpam-6480	251	5	function	function	NOUN
ejpam-6480	251	6	and	and	CCONJ
ejpam-6480	251	7	density	density	NOUN
ejpam-6480	251	8	function	function	NOUN
ejpam-6480	251	9	of	of	ADP
ejpam-6480	251	10	x	x	SYM
ejpam-6480	251	11	are	be	AUX
ejpam-6480	251	12	indicated	indicate	VERB
ejpam-6480	251	13	by	by	ADP
ejpam-6480	251	14	f	f	PROPN
ejpam-6480	251	15	(	(	PUNCT
ejpam-6480	251	16	x	x	NOUN
ejpam-6480	251	17	)	)	PUNCT
ejpam-6480	251	18	and	and	CCONJ
ejpam-6480	251	19	f(x	f(x	PROPN
ejpam-6480	251	20	)	)	PUNCT
ejpam-6480	251	21	and	and	CCONJ
ejpam-6480	251	22	those	those	PRON
ejpam-6480	251	23	of	of	ADP
ejpam-6480	251	24	y	y	PROPN
ejpam-6480	251	25	are	be	AUX
ejpam-6480	251	26	denoted	denote	VERB
ejpam-6480	251	27	by	by	ADP
ejpam-6480	251	28	g(x	g(x	NOUN
ejpam-6480	251	29	)	)	PUNCT
ejpam-6480	251	30	and	and	CCONJ
ejpam-6480	251	31	g(x	g(x	NOUN
ejpam-6480	251	32	)	)	PUNCT
ejpam-6480	251	33	respectively	respectively	ADV
ejpam-6480	251	34	,	,	PUNCT
ejpam-6480	251	35	then	then	ADV
ejpam-6480	251	36	x	x	PUNCT
ejpam-6480	251	37	is	be	AUX
ejpam-6480	251	38	said	say	VERB
ejpam-6480	251	39	to	to	PART
ejpam-6480	251	40	be	be	AUX
ejpam-6480	251	41	less	less	ADJ
ejpam-6480	251	42	than	than	ADP
ejpam-6480	251	43	or	or	CCONJ
ejpam-6480	251	44	equal	equal	ADJ
ejpam-6480	251	45	to	to	ADP
ejpam-6480	251	46	y	y	PROPN
ejpam-6480	251	47	in	in	ADP
ejpam-6480	251	48	likelihood	likelihood	NOUN
ejpam-6480	251	49	ratio	ratio	NOUN
ejpam-6480	251	50	ordering	ordering	NOUN
ejpam-6480	251	51	,	,	PUNCT
ejpam-6480	251	52	if	if	SCONJ
ejpam-6480	251	53	f	f	PROPN
ejpam-6480	251	54	(	(	PUNCT
ejpam-6480	251	55	x	x	NOUN
ejpam-6480	251	56	)	)	PUNCT
ejpam-6480	251	57	≥	≥	NOUN
ejpam-6480	251	58	g(x	g(x	NOUN
ejpam-6480	251	59	)	)	PUNCT
ejpam-6480	251	60	,	,	PUNCT
ejpam-6480	251	61	x	x	X
ejpam-6480	251	62	≥	≥	NOUN
ejpam-6480	251	63	0	0	NUM
ejpam-6480	251	64	.	.	PUNCT
ejpam-6480	252	1	we	we	PRON
ejpam-6480	252	2	write	write	VERB
ejpam-6480	252	3	x	x	PUNCT
ejpam-6480	252	4	≤st	≤st	ADJ
ejpam-6480	252	5	y	y	PROPN
ejpam-6480	252	6	.	.	PUNCT
ejpam-6480	253	1	theorem	theorem	VERB
ejpam-6480	253	2	4.4	4.4	NUM
ejpam-6480	253	3	.	.	PUNCT
ejpam-6480	254	1	let	let	VERB
ejpam-6480	254	2	x	x	PRON
ejpam-6480	254	3	and	and	CCONJ
ejpam-6480	254	4	y	y	PROPN
ejpam-6480	254	5	be	be	AUX
ejpam-6480	254	6	an	an	DET
ejpam-6480	254	7	absolutely	absolutely	ADV
ejpam-6480	254	8	continuous	continuous	ADJ
ejpam-6480	254	9	random	random	ADJ
ejpam-6480	254	10	variable	variable	ADJ
ejpam-6480	254	11	density	density	NOUN
ejpam-6480	254	12	function	function	VERB
ejpam-6480	254	13	with	with	ADP
ejpam-6480	254	14	cdf	cdf	PROPN
ejpam-6480	254	15	f(x	f(x	PROPN
ejpam-6480	254	16	)	)	PUNCT
ejpam-6480	254	17	and	and	CCONJ
ejpam-6480	254	18	g(x	g(x	NOUN
ejpam-6480	254	19	)	)	PUNCT
ejpam-6480	254	20	respectively	respectively	ADV
ejpam-6480	254	21	.	.	PUNCT
ejpam-6480	255	1	if	if	SCONJ
ejpam-6480	255	2	x	x	PRON
ejpam-6480	255	3	≤st	≤st	VERB
ejpam-6480	255	4	y	y	NOUN
ejpam-6480	255	5	for	for	ADP
ejpam-6480	255	6	all	all	DET
ejpam-6480	255	7	t1	t1	NOUN
ejpam-6480	255	8	,	,	PUNCT
ejpam-6480	255	9	t2	t2	NOUN
ejpam-6480	255	10	≥	≥	NUM
ejpam-6480	255	11	0	0	NUM
ejpam-6480	255	12	,	,	PUNCT
ejpam-6480	255	13	then	then	ADV
ejpam-6480	255	14	and	and	CCONJ
ejpam-6480	255	15	distribution	distribution	NOUN
ejpam-6480	255	16	function	function	NOUN
ejpam-6480	255	17	f(x	f(x	PROPN
ejpam-6480	255	18	)	)	PUNCT
ejpam-6480	255	19	,	,	PUNCT
ejpam-6480	255	20	then	then	ADV
ejpam-6480	255	21	for	for	ADP
ejpam-6480	255	22	α	α	PROPN
ejpam-6480	255	23	>	>	X
ejpam-6480	255	24	1(0	1(0	PROPN
ejpam-6480	255	25	<	<	X
ejpam-6480	255	26	α	α	X
ejpam-6480	255	27	<	<	X
ejpam-6480	255	28	1	1	NUM
ejpam-6480	255	29	)	)	PUNCT
ejpam-6480	255	30	,	,	PUNCT
ejpam-6480	255	31	then	then	ADV
ejpam-6480	255	32	kα	kα	X
ejpam-6480	255	33	(	(	PUNCT
ejpam-6480	255	34	x	x	X
ejpam-6480	255	35	;	;	PUNCT
ejpam-6480	255	36	t1	t1	NOUN
ejpam-6480	255	37	,	,	PUNCT
ejpam-6480	255	38	t2	t2	PROPN
ejpam-6480	255	39	)	)	PUNCT
ejpam-6480	255	40	≥	≥	NOUN
ejpam-6480	255	41	(	(	PUNCT
ejpam-6480	255	42	≤)kα	≤)kα	PROPN
ejpam-6480	255	43	(	(	PUNCT
ejpam-6480	255	44	y	y	PROPN
ejpam-6480	255	45	;	;	PUNCT
ejpam-6480	255	46	t1	t1	NOUN
ejpam-6480	255	47	,	,	PUNCT
ejpam-6480	255	48	t2	t2	NOUN
ejpam-6480	255	49	)	)	PUNCT
ejpam-6480	255	50	for	for	ADP
ejpam-6480	255	51	α	α	PROPN
ejpam-6480	255	52	>	>	X
ejpam-6480	255	53	1	1	NUM
ejpam-6480	255	54	and	and	CCONJ
ejpam-6480	255	55	for	for	ADP
ejpam-6480	255	56	proof	proof	NOUN
ejpam-6480	255	57	:	:	PUNCT
ejpam-6480	255	58	since	since	SCONJ
ejpam-6480	255	59	x	x	PART
ejpam-6480	255	60	≤st	≤st	ADJ
ejpam-6480	255	61	y	y	NOUN
ejpam-6480	255	62	,	,	PUNCT
ejpam-6480	255	63	therefore	therefore	ADV
ejpam-6480	255	64	1	1	NUM
ejpam-6480	255	65	(	(	PUNCT
ejpam-6480	255	66	α−	α−	ADP
ejpam-6480	255	67	1	1	NUM
ejpam-6480	255	68	)	)	PUNCT
ejpam-6480	256	1	[	[	X
ejpam-6480	256	2	∫	∫	X
ejpam-6480	256	3	t2	t2	PROPN
ejpam-6480	256	4	t1	t1	PROPN
ejpam-6480	256	5	(	(	PUNCT
ejpam-6480	256	6	f(x	f(x	PROPN
ejpam-6480	256	7	)	)	PUNCT
ejpam-6480	256	8	f	f	PROPN
ejpam-6480	256	9	(	(	PUNCT
ejpam-6480	256	10	t2)−	t2)−	NOUN
ejpam-6480	256	11	f	f	X
ejpam-6480	256	12	(	(	PUNCT
ejpam-6480	256	13	t1	t1	PROPN
ejpam-6480	256	14	)	)	PUNCT
ejpam-6480	256	15	)	)	PUNCT
ejpam-6480	256	16	2−α	2−α	NUM
ejpam-6480	257	1	dx−	dx−	NUM
ejpam-6480	257	2	1	1	X
ejpam-6480	257	3	]	]	PUNCT
ejpam-6480	257	4	≥	≥	NUM
ejpam-6480	257	5	1	1	NUM
ejpam-6480	257	6	(	(	PUNCT
ejpam-6480	257	7	α−	α−	ADP
ejpam-6480	257	8	1	1	NUM
ejpam-6480	257	9	)	)	PUNCT
ejpam-6480	258	1	[	[	X
ejpam-6480	258	2	∫	∫	X
ejpam-6480	258	3	t2	t2	PROPN
ejpam-6480	258	4	t1	t1	NOUN
ejpam-6480	258	5	(	(	PUNCT
ejpam-6480	258	6	g(x	g(x	NOUN
ejpam-6480	258	7	)	)	PUNCT
ejpam-6480	258	8	g	g	NOUN
ejpam-6480	258	9	(	(	PUNCT
ejpam-6480	258	10	t2)−g	t2)−g	X
ejpam-6480	258	11	(	(	PUNCT
ejpam-6480	258	12	t1	t1	NOUN
ejpam-6480	258	13	)	)	PUNCT
ejpam-6480	258	14	)	)	PUNCT
ejpam-6480	258	15	2−α	2−α	NUM
ejpam-6480	259	1	dx−	dx−	NUM
ejpam-6480	259	2	1	1	X
ejpam-6480	259	3	]	]	PUNCT
ejpam-6480	259	4	thus	thus	ADV
ejpam-6480	259	5	for	for	ADP
ejpam-6480	259	6	α	α	PROPN
ejpam-6480	259	7	>	>	X
ejpam-6480	259	8	1	1	NUM
ejpam-6480	259	9	,	,	PUNCT
ejpam-6480	259	10	we	we	PRON
ejpam-6480	259	11	have	have	VERB
ejpam-6480	259	12	kα	kα	VERB
ejpam-6480	259	13	(	(	PUNCT
ejpam-6480	259	14	x	x	X
ejpam-6480	259	15	;	;	PUNCT
ejpam-6480	259	16	t1	t1	NOUN
ejpam-6480	259	17	,	,	PUNCT
ejpam-6480	259	18	t2	t2	PROPN
ejpam-6480	259	19	)	)	PUNCT
ejpam-6480	259	20	≥	≥	NOUN
ejpam-6480	259	21	kα	kα	PROPN
ejpam-6480	259	22	(	(	PUNCT
ejpam-6480	259	23	y	y	NOUN
ejpam-6480	259	24	;	;	PUNCT
ejpam-6480	259	25	t1	t1	NOUN
ejpam-6480	259	26	,	,	PUNCT
ejpam-6480	259	27	t2	t2	NOUN
ejpam-6480	259	28	)	)	PUNCT
ejpam-6480	259	29	and	and	CCONJ
ejpam-6480	259	30	for	for	ADP
ejpam-6480	259	31	0	0	NUM
ejpam-6480	259	32	<	<	X
ejpam-6480	259	33	α	α	X
ejpam-6480	259	34	<	<	X
ejpam-6480	259	35	1	1	NUM
ejpam-6480	259	36	,	,	PUNCT
ejpam-6480	259	37	it	it	PRON
ejpam-6480	259	38	is	be	AUX
ejpam-6480	260	1	obvious	obvious	ADJ
ejpam-6480	260	2	kα	kα	X
ejpam-6480	260	3	(	(	PUNCT
ejpam-6480	260	4	x	x	NOUN
ejpam-6480	260	5	;	;	PUNCT
ejpam-6480	260	6	t1	t1	NOUN
ejpam-6480	260	7	,	,	PUNCT
ejpam-6480	260	8	t2	t2	NOUN
ejpam-6480	260	9	)	)	PUNCT
ejpam-6480	260	10	≤	≤	PUNCT
ejpam-6480	261	1	kα	kα	PROPN
ejpam-6480	261	2	(	(	PUNCT
ejpam-6480	261	3	y	y	NOUN
ejpam-6480	261	4	;	;	PUNCT
ejpam-6480	261	5	t1	t1	NOUN
ejpam-6480	261	6	,	,	PUNCT
ejpam-6480	261	7	t2	t2	PROPN
ejpam-6480	261	8	)	)	PUNCT
ejpam-6480	261	9	j.	j.	PROPN
ejpam-6480	261	10	g.	g.	PROPN
ejpam-6480	261	11	dar	dar	PROPN
ejpam-6480	261	12	,	,	PUNCT
ejpam-6480	261	13	s.	s.	PROPN
ejpam-6480	261	14	m.	m.	PROPN
ejpam-6480	261	15	a.	a.	PROPN
ejpam-6480	261	16	alsheikh	alsheikh	PROPN
ejpam-6480	261	17	,	,	PUNCT
ejpam-6480	261	18	p.	p.	PROPN
ejpam-6480	261	19	jadhav	jadhav	PROPN
ejpam-6480	261	20	/	/	SYM
ejpam-6480	261	21	eur	eur	PROPN
ejpam-6480	261	22	.	.	PUNCT
ejpam-6480	262	1	j.	j.	PROPN
ejpam-6480	262	2	pure	pure	PROPN
ejpam-6480	262	3	appl	appl	PROPN
ejpam-6480	262	4	.	.	PROPN
ejpam-6480	262	5	math	math	PROPN
ejpam-6480	262	6	,	,	PUNCT
ejpam-6480	262	7	18	18	NUM
ejpam-6480	262	8	(	(	PUNCT
ejpam-6480	262	9	4	4	NUM
ejpam-6480	262	10	)	)	PUNCT
ejpam-6480	262	11	(	(	PUNCT
ejpam-6480	262	12	2025	2025	NUM
ejpam-6480	262	13	)	)	PUNCT
ejpam-6480	262	14	,	,	PUNCT
ejpam-6480	262	15	6480	6480	NUM
ejpam-6480	262	16	13	13	NUM
ejpam-6480	262	17	of	of	ADP
ejpam-6480	262	18	14	14	NUM
ejpam-6480	262	19	5	5	NUM
ejpam-6480	262	20	.	.	PUNCT
ejpam-6480	263	1	conclusion	conclusion	NOUN
ejpam-6480	263	2	:	:	PUNCT
ejpam-6480	263	3	generalized	generalized	ADJ
ejpam-6480	263	4	interval	interval	NOUN
ejpam-6480	263	5	entropy	entropy	NOUN
ejpam-6480	263	6	plays	play	VERB
ejpam-6480	263	7	a	a	DET
ejpam-6480	263	8	critical	critical	ADJ
ejpam-6480	263	9	role	role	NOUN
ejpam-6480	263	10	in	in	ADP
ejpam-6480	263	11	information	information	NOUN
ejpam-6480	263	12	theory	theory	NOUN
ejpam-6480	263	13	,	,	PUNCT
ejpam-6480	263	14	reliability	reliability	NOUN
ejpam-6480	263	15	modeling	modeling	NOUN
ejpam-6480	263	16	and	and	CCONJ
ejpam-6480	263	17	survival	survival	NOUN
ejpam-6480	263	18	analysis	analysis	NOUN
ejpam-6480	263	19	by	by	ADP
ejpam-6480	263	20	quantifying	quantify	VERB
ejpam-6480	263	21	the	the	DET
ejpam-6480	263	22	uncertainty	uncertainty	NOUN
ejpam-6480	263	23	associated	associate	VERB
ejpam-6480	263	24	with	with	ADP
ejpam-6480	263	25	a	a	DET
ejpam-6480	263	26	system	system	NOUN
ejpam-6480	263	27	’s	’s	PART
ejpam-6480	263	28	lifetime	lifetime	NOUN
ejpam-6480	263	29	,	,	PUNCT
ejpam-6480	263	30	particularly	particularly	ADV
ejpam-6480	263	31	when	when	SCONJ
ejpam-6480	263	32	it	it	PRON
ejpam-6480	263	33	has	have	AUX
ejpam-6480	263	34	already	already	ADV
ejpam-6480	263	35	survived	survive	VERB
ejpam-6480	263	36	between	between	ADP
ejpam-6480	263	37	two	two	NUM
ejpam-6480	263	38	time	time	NOUN
ejpam-6480	263	39	points	point	NOUN
ejpam-6480	263	40	.	.	PUNCT
ejpam-6480	264	1	the	the	DET
ejpam-6480	264	2	measure	measure	NOUN
ejpam-6480	264	3	is	be	AUX
ejpam-6480	264	4	useful	useful	ADJ
ejpam-6480	264	5	in	in	ADP
ejpam-6480	264	6	characterizing	characterize	VERB
ejpam-6480	264	7	different	different	ADJ
ejpam-6480	264	8	lifetime	lifetime	NOUN
ejpam-6480	264	9	distributions	distribution	NOUN
ejpam-6480	264	10	and	and	CCONJ
ejpam-6480	264	11	establishing	establish	VERB
ejpam-6480	264	12	relationships	relationship	NOUN
ejpam-6480	264	13	with	with	ADP
ejpam-6480	264	14	reliability	reliability	NOUN
ejpam-6480	264	15	measures	measure	NOUN
ejpam-6480	264	16	such	such	ADJ
ejpam-6480	264	17	as	as	ADP
ejpam-6480	264	18	survival	survival	NOUN
ejpam-6480	264	19	functions	function	NOUN
ejpam-6480	264	20	and	and	CCONJ
ejpam-6480	264	21	hazard	hazard	NOUN
ejpam-6480	264	22	rates	rate	NOUN
ejpam-6480	264	23	.	.	PUNCT
ejpam-6480	265	1	additionally	additionally	ADV
ejpam-6480	265	2	,	,	PUNCT
ejpam-6480	265	3	the	the	DET
ejpam-6480	265	4	connection	connection	NOUN
ejpam-6480	265	5	between	between	ADP
ejpam-6480	265	6	generalized	generalized	ADJ
ejpam-6480	265	7	interval	interval	NOUN
ejpam-6480	265	8	entropy	entropy	NOUN
ejpam-6480	265	9	and	and	CCONJ
ejpam-6480	265	10	stochastic	stochastic	ADJ
ejpam-6480	265	11	ordering	ordering	NOUN
ejpam-6480	265	12	provides	provide	VERB
ejpam-6480	265	13	a	a	DET
ejpam-6480	265	14	powerful	powerful	ADJ
ejpam-6480	265	15	tool	tool	NOUN
ejpam-6480	265	16	for	for	ADP
ejpam-6480	265	17	comparing	compare	VERB
ejpam-6480	265	18	different	different	ADJ
ejpam-6480	265	19	lifetime	lifetime	NOUN
ejpam-6480	265	20	distributions	distribution	NOUN
ejpam-6480	265	21	.	.	PUNCT
ejpam-6480	266	1	overall	overall	ADV
ejpam-6480	266	2	,	,	PUNCT
ejpam-6480	266	3	the	the	DET
ejpam-6480	266	4	application	application	NOUN
ejpam-6480	266	5	of	of	ADP
ejpam-6480	266	6	generalized	generalized	ADJ
ejpam-6480	266	7	interval	interval	NOUN
ejpam-6480	266	8	entropy	entropy	NOUN
ejpam-6480	266	9	in	in	ADP
ejpam-6480	266	10	the	the	DET
ejpam-6480	266	11	context	context	NOUN
ejpam-6480	266	12	of	of	ADP
ejpam-6480	266	13	doubly	doubly	ADV
ejpam-6480	266	14	truncated	truncate	VERB
ejpam-6480	266	15	random	random	ADJ
ejpam-6480	266	16	variables	variable	NOUN
ejpam-6480	266	17	and	and	CCONJ
ejpam-6480	266	18	its	its	PRON
ejpam-6480	266	19	generalization	generalization	NOUN
ejpam-6480	266	20	of	of	ADP
ejpam-6480	266	21	previous	previous	ADJ
ejpam-6480	266	22	results	result	NOUN
ejpam-6480	266	23	represents	represent	VERB
ejpam-6480	266	24	an	an	DET
ejpam-6480	266	25	important	important	ADJ
ejpam-6480	266	26	advancement	advancement	NOUN
ejpam-6480	266	27	in	in	ADP
ejpam-6480	266	28	understanding	understanding	NOUN
ejpam-6480	266	29	and	and	CCONJ
ejpam-6480	266	30	modeling	model	VERB
ejpam-6480	266	31	the	the	DET
ejpam-6480	266	32	uncertainty	uncertainty	NOUN
ejpam-6480	266	33	inherent	inherent	ADJ
ejpam-6480	266	34	in	in	ADP
ejpam-6480	266	35	lifetime	lifetime	NOUN
ejpam-6480	266	36	distributions	distribution	NOUN
ejpam-6480	266	37	.	.	PUNCT
ejpam-6480	267	1	these	these	DET
ejpam-6480	267	2	developments	development	NOUN
ejpam-6480	267	3	have	have	VERB
ejpam-6480	267	4	important	important	ADJ
ejpam-6480	267	5	implications	implication	NOUN
ejpam-6480	267	6	for	for	ADP
ejpam-6480	267	7	reliability	reliability	NOUN
ejpam-6480	267	8	engineering	engineering	NOUN
ejpam-6480	267	9	,	,	PUNCT
ejpam-6480	267	10	survival	survival	NOUN
ejpam-6480	267	11	analysis	analysis	NOUN
ejpam-6480	267	12	,	,	PUNCT
ejpam-6480	267	13	risk	risk	NOUN
ejpam-6480	267	14	management	management	NOUN
ejpam-6480	267	15	,	,	PUNCT
ejpam-6480	267	16	and	and	CCONJ
ejpam-6480	267	17	other	other	ADJ
ejpam-6480	267	18	fields	field	NOUN
ejpam-6480	267	19	where	where	SCONJ
ejpam-6480	267	20	the	the	DET
ejpam-6480	267	21	timing	timing	NOUN
ejpam-6480	267	22	of	of	ADP
ejpam-6480	267	23	events	event	NOUN
ejpam-6480	267	24	plays	play	VERB
ejpam-6480	267	25	a	a	DET
ejpam-6480	267	26	crucial	crucial	ADJ
ejpam-6480	267	27	role	role	NOUN
ejpam-6480	267	28	.	.	PUNCT
ejpam-6480	268	1	conflict	conflict	NOUN
ejpam-6480	268	2	of	of	ADP
ejpam-6480	268	3	interest	interest	NOUN
ejpam-6480	268	4	:	:	PUNCT
ejpam-6480	268	5	the	the	DET
ejpam-6480	268	6	authors	author	NOUN
ejpam-6480	268	7	declare	declare	VERB
ejpam-6480	268	8	that	that	SCONJ
ejpam-6480	268	9	they	they	PRON
ejpam-6480	268	10	have	have	VERB
ejpam-6480	268	11	no	no	DET
ejpam-6480	268	12	conflict	conflict	NOUN
ejpam-6480	268	13	of	of	ADP
ejpam-6480	268	14	interest	interest	NOUN
ejpam-6480	268	15	references	reference	NOUN
ejpam-6480	268	16	[	[	X
ejpam-6480	268	17	1	1	NUM
ejpam-6480	268	18	]	]	PUNCT
ejpam-6480	268	19	ce	ce	PROPN
ejpam-6480	268	20	shannon	shannon	PROPN
ejpam-6480	268	21	.	.	PUNCT
ejpam-6480	269	1	a	a	DET
ejpam-6480	269	2	mathematical	mathematical	ADJ
ejpam-6480	269	3	theoryof	theoryof	NOUN
ejpam-6480	269	4	communication	communication	NOUN
ejpam-6480	269	5	,	,	PUNCT
ejpam-6480	269	6	bell	bell	NOUN
ejpam-6480	269	7	system	system	NOUN
ejpam-6480	269	8	tech	tech	NOUN
ejpam-6480	269	9	.	.	PUNCT
ejpam-6480	270	1	j	j	PROPN
ejpam-6480	270	2	,	,	PUNCT
ejpam-6480	270	3	27:379–423	27:379–423	NUM
ejpam-6480	270	4	,	,	PUNCT
ejpam-6480	270	5	1948	1948	NUM
ejpam-6480	270	6	.	.	PUNCT
ejpam-6480	271	1	[	[	X
ejpam-6480	271	2	2	2	X
ejpam-6480	271	3	]	]	X
ejpam-6480	271	4	sm	sm	PROPN
ejpam-6480	271	5	sunoj	sunoj	PROPN
ejpam-6480	271	6	,	,	PUNCT
ejpam-6480	271	7	pg	pg	PRON
ejpam-6480	271	8	sankaran	sankaran	VERB
ejpam-6480	271	9	,	,	PUNCT
ejpam-6480	271	10	and	and	CCONJ
ejpam-6480	271	11	ss	ss	PROPN
ejpam-6480	271	12	maya	maya	PROPN
ejpam-6480	271	13	.	.	PUNCT
ejpam-6480	272	1	characterizations	characterization	NOUN
ejpam-6480	272	2	of	of	ADP
ejpam-6480	272	3	life	life	NOUN
ejpam-6480	272	4	distributions	distribution	NOUN
ejpam-6480	272	5	using	use	VERB
ejpam-6480	272	6	conditional	conditional	ADJ
ejpam-6480	272	7	expectations	expectation	NOUN
ejpam-6480	272	8	of	of	ADP
ejpam-6480	272	9	doubly	doubly	ADV
ejpam-6480	272	10	(	(	PUNCT
ejpam-6480	272	11	interval	interval	NOUN
ejpam-6480	272	12	)	)	PUNCT
ejpam-6480	272	13	truncated	truncate	VERB
ejpam-6480	272	14	random	random	ADJ
ejpam-6480	272	15	variables	variable	NOUN
ejpam-6480	272	16	.	.	PUNCT
ejpam-6480	273	1	communications	communication	NOUN
ejpam-6480	273	2	in	in	ADP
ejpam-6480	273	3	statistics	statistic	NOUN
ejpam-6480	273	4	-	-	PUNCT
ejpam-6480	273	5	theory	theory	NOUN
ejpam-6480	273	6	and	and	CCONJ
ejpam-6480	273	7	methods	method	NOUN
ejpam-6480	273	8	,	,	PUNCT
ejpam-6480	273	9	38(9):1441–1452	38(9):1441–1452	NUM
ejpam-6480	273	10	,	,	PUNCT
ejpam-6480	273	11	2009	2009	NUM
ejpam-6480	273	12	.	.	PUNCT
ejpam-6480	274	1	[	[	X
ejpam-6480	274	2	3	3	NUM
ejpam-6480	274	3	]	]	PUNCT
ejpam-6480	274	4	am	be	AUX
ejpam-6480	274	5	mathai	mathai	PROPN
ejpam-6480	274	6	and	and	CCONJ
ejpam-6480	274	7	hans	hans	PROPN
ejpam-6480	274	8	j	j	PROPN
ejpam-6480	274	9	haubold	haubold	PROPN
ejpam-6480	274	10	.	.	PUNCT
ejpam-6480	275	1	pathway	pathway	NOUN
ejpam-6480	275	2	model	model	PROPN
ejpam-6480	275	3	,	,	PUNCT
ejpam-6480	275	4	superstatistics	superstatistic	NOUN
ejpam-6480	275	5	,	,	PUNCT
ejpam-6480	275	6	tsallis	tsallis	PROPN
ejpam-6480	275	7	statistics	statistic	NOUN
ejpam-6480	275	8	,	,	PUNCT
ejpam-6480	275	9	and	and	CCONJ
ejpam-6480	275	10	a	a	DET
ejpam-6480	275	11	generalized	generalized	ADJ
ejpam-6480	275	12	measure	measure	NOUN
ejpam-6480	275	13	of	of	ADP
ejpam-6480	275	14	entropy	entropy	PROPN
ejpam-6480	275	15	.	.	PUNCT
ejpam-6480	276	1	physica	physica	VERB
ejpam-6480	276	2	a	a	DET
ejpam-6480	276	3	:	:	PUNCT
ejpam-6480	276	4	statistical	statistical	ADJ
ejpam-6480	276	5	mechanics	mechanic	NOUN
ejpam-6480	276	6	and	and	CCONJ
ejpam-6480	276	7	its	its	PRON
ejpam-6480	276	8	applications	application	NOUN
ejpam-6480	276	9	,	,	PUNCT
ejpam-6480	276	10	375(1):110–122	375(1):110–122	NUM
ejpam-6480	276	11	,	,	PUNCT
ejpam-6480	276	12	2007	2007	NUM
ejpam-6480	276	13	.	.	PUNCT
ejpam-6480	277	1	[	[	X
ejpam-6480	277	2	4	4	X
ejpam-6480	277	3	]	]	X
ejpam-6480	277	4	nader	nader	PROPN
ejpam-6480	277	5	ebrahimi	ebrahimi	PROPN
ejpam-6480	277	6	.	.	PUNCT
ejpam-6480	278	1	how	how	SCONJ
ejpam-6480	278	2	to	to	PART
ejpam-6480	278	3	measure	measure	VERB
ejpam-6480	278	4	uncertainty	uncertainty	NOUN
ejpam-6480	278	5	in	in	ADP
ejpam-6480	278	6	the	the	DET
ejpam-6480	278	7	residual	residual	ADJ
ejpam-6480	278	8	life	life	NOUN
ejpam-6480	278	9	time	time	NOUN
ejpam-6480	278	10	distribution	distribution	NOUN
ejpam-6480	278	11	.	.	PUNCT
ejpam-6480	279	1	sankhyā	sankhyā	NOUN
ejpam-6480	279	2	:	:	PUNCT
ejpam-6480	279	3	the	the	DET
ejpam-6480	279	4	indian	indian	PROPN
ejpam-6480	279	5	journal	journal	PROPN
ejpam-6480	279	6	of	of	ADP
ejpam-6480	279	7	statistics	statistic	NOUN
ejpam-6480	279	8	,	,	PUNCT
ejpam-6480	279	9	series	series	PROPN
ejpam-6480	279	10	a	a	NOUN
ejpam-6480	279	11	,	,	PUNCT
ejpam-6480	279	12	pages	page	NOUN
ejpam-6480	279	13	48–56	48–56	NUM
ejpam-6480	279	14	,	,	PUNCT
ejpam-6480	279	15	1996	1996	NUM
ejpam-6480	279	16	.	.	PUNCT
ejpam-6480	280	1	[	[	X
ejpam-6480	280	2	5	5	NUM
ejpam-6480	280	3	]	]	PUNCT
ejpam-6480	280	4	felix	felix	NOUN
ejpam-6480	280	5	belzunce	belzunce	ADV
ejpam-6480	280	6	,	,	PUNCT
ejpam-6480	280	7	jorge	jorge	PROPN
ejpam-6480	280	8	navarro	navarro	PROPN
ejpam-6480	280	9	,	,	PUNCT
ejpam-6480	280	10	josé	josé	PROPN
ejpam-6480	280	11	m	m	PROPN
ejpam-6480	280	12	ruiz	ruiz	NOUN
ejpam-6480	280	13	,	,	PUNCT
ejpam-6480	280	14	and	and	CCONJ
ejpam-6480	280	15	yolanda	yolanda	PROPN
ejpam-6480	280	16	del	del	PROPN
ejpam-6480	280	17	aguila	aguila	PROPN
ejpam-6480	280	18	.	.	PUNCT
ejpam-6480	281	1	some	some	DET
ejpam-6480	281	2	results	result	NOUN
ejpam-6480	281	3	on	on	ADP
ejpam-6480	281	4	residual	residual	ADJ
ejpam-6480	281	5	entropy	entropy	NOUN
ejpam-6480	281	6	function	function	NOUN
ejpam-6480	281	7	.	.	PUNCT
ejpam-6480	282	1	metrika	metrika	NOUN
ejpam-6480	282	2	,	,	PUNCT
ejpam-6480	282	3	59(2):147–161	59(2):147–161	NUM
ejpam-6480	282	4	,	,	PUNCT
ejpam-6480	282	5	2004	2004	NUM
ejpam-6480	282	6	.	.	PUNCT
ejpam-6480	283	1	[	[	X
ejpam-6480	283	2	6	6	NUM
ejpam-6480	283	3	]	]	X
ejpam-6480	283	4	majid	majid	PROPN
ejpam-6480	283	5	asadi	asadi	PROPN
ejpam-6480	283	6	,	,	PUNCT
ejpam-6480	283	7	nader	nader	PROPN
ejpam-6480	283	8	ebrahimi	ebrahimi	PROPN
ejpam-6480	283	9	,	,	PUNCT
ejpam-6480	283	10	and	and	CCONJ
ejpam-6480	283	11	ehsan	ehsan	PROPN
ejpam-6480	283	12	s	s	PROPN
ejpam-6480	283	13	soofi	soofi	ADJ
ejpam-6480	283	14	.	.	PUNCT
ejpam-6480	284	1	dynamic	dynamic	ADJ
ejpam-6480	284	2	generalized	generalize	VERB
ejpam-6480	284	3	information	information	NOUN
ejpam-6480	284	4	measures	measure	NOUN
ejpam-6480	284	5	.	.	PUNCT
ejpam-6480	285	1	statistics	statistic	NOUN
ejpam-6480	285	2	&	&	CCONJ
ejpam-6480	285	3	probability	probability	NOUN
ejpam-6480	285	4	letters	letter	NOUN
ejpam-6480	285	5	,	,	PUNCT
ejpam-6480	285	6	71(1):85–98	71(1):85–98	NUM
ejpam-6480	285	7	,	,	PUNCT
ejpam-6480	285	8	2005	2005	NUM
ejpam-6480	285	9	.	.	PUNCT
ejpam-6480	286	1	[	[	X
ejpam-6480	286	2	7	7	X
ejpam-6480	286	3	]	]	X
ejpam-6480	286	4	mirza	mirza	PROPN
ejpam-6480	286	5	abdul	abdul	PROPN
ejpam-6480	286	6	khalique	khalique	PROPN
ejpam-6480	286	7	baig	baig	PROPN
ejpam-6480	286	8	and	and	CCONJ
ejpam-6480	286	9	javid	javid	PROPN
ejpam-6480	286	10	gani	gani	PROPN
ejpam-6480	286	11	dar	dar	PROPN
ejpam-6480	286	12	.	.	PUNCT
ejpam-6480	286	13	generalized	generalize	VERB
ejpam-6480	286	14	residual	residual	ADJ
ejpam-6480	286	15	entropy	entropy	NOUN
ejpam-6480	286	16	function	function	NOUN
ejpam-6480	286	17	and	and	CCONJ
ejpam-6480	286	18	its	its	PRON
ejpam-6480	286	19	applications	application	NOUN
ejpam-6480	286	20	.	.	PUNCT
ejpam-6480	287	1	european	european	ADJ
ejpam-6480	287	2	journal	journal	PROPN
ejpam-6480	287	3	of	of	ADP
ejpam-6480	287	4	pure	pure	ADJ
ejpam-6480	287	5	and	and	CCONJ
ejpam-6480	287	6	applied	applied	ADJ
ejpam-6480	287	7	mathematics	mathematic	NOUN
ejpam-6480	287	8	,	,	PUNCT
ejpam-6480	287	9	1(4	1(4	NUM
ejpam-6480	287	10	)	)	PUNCT
ejpam-6480	287	11	,	,	PUNCT
ejpam-6480	287	12	2008	2008	NUM
ejpam-6480	287	13	.	.	PUNCT
ejpam-6480	288	1	[	[	X
ejpam-6480	288	2	8	8	NUM
ejpam-6480	288	3	]	]	X
ejpam-6480	288	4	anant	anant	PROPN
ejpam-6480	288	5	hegde	hegde	PROPN
ejpam-6480	288	6	,	,	PUNCT
ejpam-6480	288	7	tian	tian	ADJ
ejpam-6480	288	8	lan	lan	PROPN
ejpam-6480	288	9	,	,	PUNCT
ejpam-6480	288	10	and	and	CCONJ
ejpam-6480	288	11	deniz	deniz	PROPN
ejpam-6480	288	12	erdogmus	erdogmus	PROPN
ejpam-6480	288	13	.	.	PUNCT
ejpam-6480	289	1	order	order	NOUN
ejpam-6480	289	2	statistics	statistic	NOUN
ejpam-6480	289	3	based	base	VERB
ejpam-6480	289	4	estimator	estimator	NOUN
ejpam-6480	289	5	for	for	ADP
ejpam-6480	289	6	renyi	renyi	PROPN
ejpam-6480	289	7	’s	’s	PART
ejpam-6480	289	8	entropy	entropy	NOUN
ejpam-6480	289	9	.	.	PUNCT
ejpam-6480	290	1	in	in	ADP
ejpam-6480	290	2	2005	2005	NUM
ejpam-6480	290	3	ieee	ieee	NOUN
ejpam-6480	290	4	workshop	workshop	NOUN
ejpam-6480	290	5	on	on	ADP
ejpam-6480	290	6	machine	machine	NOUN
ejpam-6480	290	7	learning	learn	VERB
ejpam-6480	290	8	for	for	ADP
ejpam-6480	290	9	signal	signal	ADJ
ejpam-6480	290	10	processing	processing	NOUN
ejpam-6480	290	11	,	,	PUNCT
ejpam-6480	290	12	pages	page	NOUN
ejpam-6480	290	13	335–339	335–339	NUM
ejpam-6480	290	14	.	.	PUNCT
ejpam-6480	291	1	ieee	ieee	NOUN
ejpam-6480	291	2	,	,	PUNCT
ejpam-6480	291	3	2005	2005	NUM
ejpam-6480	291	4	.	.	PUNCT
ejpam-6480	292	1	[	[	X
ejpam-6480	292	2	9	9	NUM
ejpam-6480	292	3	]	]	X
ejpam-6480	292	4	g	g	PROPN
ejpam-6480	292	5	rajesh	rajesh	PROPN
ejpam-6480	292	6	and	and	CCONJ
ejpam-6480	292	7	kr	kr	PROPN
ejpam-6480	292	8	muraleedharan	muraleedharan	PROPN
ejpam-6480	292	9	nair	nair	PROPN
ejpam-6480	292	10	.	.	PUNCT
ejpam-6480	293	1	characterization	characterization	NOUN
ejpam-6480	293	2	of	of	ADP
ejpam-6480	293	3	probability	probability	NOUN
ejpam-6480	293	4	distributions	distribution	NOUN
ejpam-6480	293	5	using	use	VERB
ejpam-6480	293	6	the	the	DET
ejpam-6480	293	7	residual	residual	ADJ
ejpam-6480	293	8	entropy	entropy	NOUN
ejpam-6480	293	9	function	function	NOUN
ejpam-6480	293	10	.	.	PUNCT
ejpam-6480	294	1	phd	phd	NOUN
ejpam-6480	294	2	thesis	thesis	PROPN
ejpam-6480	294	3	,	,	PUNCT
ejpam-6480	294	4	cochin	cochin	PROPN
ejpam-6480	294	5	university	university	PROPN
ejpam-6480	294	6	of	of	ADP
ejpam-6480	294	7	science	science	NOUN
ejpam-6480	294	8	and	and	CCONJ
ejpam-6480	294	9	technology	technology	NOUN
ejpam-6480	294	10	,	,	PUNCT
ejpam-6480	294	11	2001	2001	NUM
ejpam-6480	294	12	.	.	PUNCT
ejpam-6480	295	1	[	[	X
ejpam-6480	295	2	10	10	NUM
ejpam-6480	295	3	]	]	X
ejpam-6480	295	4	majid	majid	PROPN
ejpam-6480	295	5	asadi	asadi	PROPN
ejpam-6480	295	6	and	and	CCONJ
ejpam-6480	295	7	nader	nader	PROPN
ejpam-6480	295	8	ebrahimi	ebrahimi	PROPN
ejpam-6480	295	9	.	.	PUNCT
ejpam-6480	296	1	residual	residual	ADJ
ejpam-6480	296	2	entropy	entropy	NOUN
ejpam-6480	296	3	and	and	CCONJ
ejpam-6480	296	4	its	its	PRON
ejpam-6480	296	5	characterizations	characterization	NOUN
ejpam-6480	296	6	in	in	ADP
ejpam-6480	296	7	j.	j.	PROPN
ejpam-6480	296	8	g.	g.	PROPN
ejpam-6480	296	9	dar	dar	PROPN
ejpam-6480	296	10	,	,	PUNCT
ejpam-6480	296	11	s.	s.	PROPN
ejpam-6480	296	12	m.	m.	PROPN
ejpam-6480	296	13	a.	a.	PROPN
ejpam-6480	296	14	alsheikh	alsheikh	PROPN
ejpam-6480	296	15	,	,	PUNCT
ejpam-6480	296	16	p.	p.	PROPN
ejpam-6480	296	17	jadhav	jadhav	PROPN
ejpam-6480	296	18	/	/	SYM
ejpam-6480	296	19	eur	eur	PROPN
ejpam-6480	296	20	.	.	PUNCT
ejpam-6480	297	1	j.	j.	PROPN
ejpam-6480	297	2	pure	pure	PROPN
ejpam-6480	297	3	appl	appl	PROPN
ejpam-6480	297	4	.	.	PROPN
ejpam-6480	297	5	math	math	PROPN
ejpam-6480	297	6	,	,	PUNCT
ejpam-6480	297	7	18	18	NUM
ejpam-6480	297	8	(	(	PUNCT
ejpam-6480	297	9	4	4	NUM
ejpam-6480	297	10	)	)	PUNCT
ejpam-6480	297	11	(	(	PUNCT
ejpam-6480	297	12	2025	2025	NUM
ejpam-6480	297	13	)	)	PUNCT
ejpam-6480	297	14	,	,	PUNCT
ejpam-6480	297	15	6480	6480	NUM
ejpam-6480	297	16	14	14	NUM
ejpam-6480	297	17	of	of	ADP
ejpam-6480	297	18	14	14	NUM
ejpam-6480	297	19	terms	term	NOUN
ejpam-6480	297	20	of	of	ADP
ejpam-6480	297	21	hazard	hazard	NOUN
ejpam-6480	297	22	function	function	NOUN
ejpam-6480	297	23	and	and	CCONJ
ejpam-6480	297	24	mean	mean	VERB
ejpam-6480	297	25	residual	residual	ADJ
ejpam-6480	297	26	life	life	NOUN
ejpam-6480	297	27	function	function	NOUN
ejpam-6480	297	28	.	.	PUNCT
ejpam-6480	298	1	statistics	statistic	NOUN
ejpam-6480	298	2	&	&	CCONJ
ejpam-6480	298	3	probability	probability	NOUN
ejpam-6480	298	4	letters	letter	NOUN
ejpam-6480	298	5	,	,	PUNCT
ejpam-6480	298	6	49(3):263–269	49(3):263–269	PROPN
ejpam-6480	298	7	,	,	PUNCT
ejpam-6480	298	8	2000	2000	NUM
ejpam-6480	298	9	.	.	PUNCT
ejpam-6480	299	1	[	[	X
ejpam-6480	299	2	11	11	NUM
ejpam-6480	299	3	]	]	X
ejpam-6480	299	4	antonio	antonio	PROPN
ejpam-6480	299	5	di	di	PROPN
ejpam-6480	299	6	crescenzo	crescenzo	PROPN
ejpam-6480	299	7	and	and	CCONJ
ejpam-6480	299	8	maria	maria	PROPN
ejpam-6480	299	9	longobardi	longobardi	PROPN
ejpam-6480	299	10	.	.	PUNCT
ejpam-6480	300	1	entropy	entropy	PROPN
ejpam-6480	300	2	-	-	PUNCT
ejpam-6480	300	3	based	base	VERB
ejpam-6480	300	4	measure	measure	NOUN
ejpam-6480	300	5	of	of	ADP
ejpam-6480	300	6	uncertainty	uncertainty	NOUN
ejpam-6480	300	7	in	in	ADP
ejpam-6480	300	8	past	past	ADJ
ejpam-6480	300	9	lifetime	lifetime	NOUN
ejpam-6480	300	10	distributions	distribution	NOUN
ejpam-6480	300	11	.	.	PUNCT
ejpam-6480	301	1	journal	journal	NOUN
ejpam-6480	301	2	of	of	ADP
ejpam-6480	301	3	applied	apply	VERB
ejpam-6480	301	4	probability	probability	NOUN
ejpam-6480	301	5	,	,	PUNCT
ejpam-6480	301	6	39(2):434–440	39(2):434–440	PROPN
ejpam-6480	301	7	,	,	PUNCT
ejpam-6480	301	8	2002	2002	NUM
ejpam-6480	301	9	.	.	PUNCT
ejpam-6480	302	1	[	[	X
ejpam-6480	302	2	12	12	NUM
ejpam-6480	302	3	]	]	X
ejpam-6480	302	4	antonio	antonio	PROPN
ejpam-6480	302	5	di	di	PROPN
ejpam-6480	302	6	crescenzo	crescenzo	PROPN
ejpam-6480	302	7	and	and	CCONJ
ejpam-6480	302	8	maria	maria	PROPN
ejpam-6480	302	9	longobardi	longobardi	PROPN
ejpam-6480	302	10	.	.	PUNCT
ejpam-6480	303	1	a	a	DET
ejpam-6480	303	2	measure	measure	NOUN
ejpam-6480	303	3	of	of	ADP
ejpam-6480	303	4	discrimination	discrimination	NOUN
ejpam-6480	303	5	between	between	ADP
ejpam-6480	303	6	past	past	ADJ
ejpam-6480	303	7	lifetime	lifetime	NOUN
ejpam-6480	303	8	distributions	distribution	NOUN
ejpam-6480	303	9	.	.	PUNCT
ejpam-6480	304	1	statistics	statistic	NOUN
ejpam-6480	304	2	&	&	CCONJ
ejpam-6480	304	3	probability	probability	NOUN
ejpam-6480	304	4	letters	letter	NOUN
ejpam-6480	304	5	,	,	PUNCT
ejpam-6480	304	6	67(2):173–182	67(2):173–182	NOUN
ejpam-6480	304	7	,	,	PUNCT
ejpam-6480	304	8	2004	2004	NUM
ejpam-6480	304	9	.	.	PUNCT
ejpam-6480	305	1	[	[	X
ejpam-6480	305	2	13	13	NUM
ejpam-6480	305	3	]	]	X
ejpam-6480	305	4	asok	asok	NOUN
ejpam-6480	305	5	k	k	PROPN
ejpam-6480	305	6	nanda	nanda	PROPN
ejpam-6480	305	7	and	and	CCONJ
ejpam-6480	305	8	prasanta	prasanta	ADJ
ejpam-6480	305	9	paul	paul	PROPN
ejpam-6480	305	10	.	.	PUNCT
ejpam-6480	306	1	some	some	DET
ejpam-6480	306	2	properties	property	NOUN
ejpam-6480	306	3	of	of	ADP
ejpam-6480	306	4	past	past	ADJ
ejpam-6480	306	5	entropy	entropy	NOUN
ejpam-6480	306	6	and	and	CCONJ
ejpam-6480	306	7	their	their	PRON
ejpam-6480	306	8	applications	application	NOUN
ejpam-6480	306	9	.	.	PUNCT
ejpam-6480	307	1	metrika	metrika	NOUN
ejpam-6480	307	2	,	,	PUNCT
ejpam-6480	307	3	64(1):47–61	64(1):47–61	NUM
ejpam-6480	307	4	,	,	PUNCT
ejpam-6480	307	5	2006	2006	NUM
ejpam-6480	307	6	.	.	PUNCT
ejpam-6480	308	1	[	[	X
ejpam-6480	308	2	14	14	NUM
ejpam-6480	308	3	]	]	X
ejpam-6480	308	4	nader	nader	PROPN
ejpam-6480	308	5	ebrahimi	ebrahimi	PROPN
ejpam-6480	308	6	and	and	CCONJ
ejpam-6480	308	7	franco	franco	PROPN
ejpam-6480	308	8	pellerey	pellerey	PROPN
ejpam-6480	308	9	.	.	PUNCT
ejpam-6480	309	1	new	new	ADJ
ejpam-6480	309	2	partial	partial	ADJ
ejpam-6480	309	3	ordering	ordering	NOUN
ejpam-6480	309	4	of	of	ADP
ejpam-6480	309	5	survival	survival	NOUN
ejpam-6480	309	6	functions	function	NOUN
ejpam-6480	309	7	based	base	VERB
ejpam-6480	309	8	on	on	ADP
ejpam-6480	309	9	the	the	DET
ejpam-6480	309	10	notion	notion	NOUN
ejpam-6480	309	11	of	of	ADP
ejpam-6480	309	12	uncertainty	uncertainty	NOUN
ejpam-6480	309	13	.	.	PUNCT
ejpam-6480	310	1	journal	journal	PROPN
ejpam-6480	310	2	of	of	ADP
ejpam-6480	310	3	applied	apply	VERB
ejpam-6480	310	4	probability	probability	NOUN
ejpam-6480	310	5	,	,	PUNCT
ejpam-6480	310	6	32(1):202–211	32(1):202–211	PROPN
ejpam-6480	310	7	,	,	PUNCT
ejpam-6480	310	8	1995	1995	NUM
ejpam-6480	310	9	.	.	PUNCT
ejpam-6480	311	1	[	[	X
ejpam-6480	311	2	15	15	NUM
ejpam-6480	311	3	]	]	X
ejpam-6480	311	4	f	f	PROPN
ejpam-6480	311	5	misagh	misagh	PROPN
ejpam-6480	311	6	and	and	CCONJ
ejpam-6480	311	7	gh	gh	PROPN
ejpam-6480	311	8	yari	yari	PROPN
ejpam-6480	311	9	.	.	PUNCT
ejpam-6480	312	1	on	on	ADP
ejpam-6480	312	2	weighted	weight	VERB
ejpam-6480	312	3	interval	interval	NOUN
ejpam-6480	312	4	entropy	entropy	NOUN
ejpam-6480	312	5	.	.	PUNCT
ejpam-6480	313	1	statistics	statistic	NOUN
ejpam-6480	313	2	&	&	CCONJ
ejpam-6480	313	3	probability	probability	NOUN
ejpam-6480	313	4	letters	letter	NOUN
ejpam-6480	313	5	,	,	PUNCT
ejpam-6480	313	6	81(2):188–194	81(2):188–194	PROPN
ejpam-6480	313	7	,	,	PUNCT
ejpam-6480	313	8	2011	2011	NUM
ejpam-6480	313	9	.	.	PUNCT
ejpam-6480	314	1	[	[	X
ejpam-6480	314	2	16	16	NUM
ejpam-6480	314	3	]	]	PUNCT
ejpam-6480	314	4	fakhroddin	fakhroddin	ADV
ejpam-6480	314	5	misagh	misagh	NOUN
ejpam-6480	314	6	and	and	CCONJ
ejpam-6480	314	7	gholamhossein	gholamhossein	ADJ
ejpam-6480	314	8	yari	yari	NOUN
ejpam-6480	314	9	.	.	PUNCT
ejpam-6480	315	1	interval	interval	NOUN
ejpam-6480	315	2	entropy	entropy	NOUN
ejpam-6480	315	3	and	and	CCONJ
ejpam-6480	315	4	informative	informative	ADJ
ejpam-6480	315	5	distance	distance	NOUN
ejpam-6480	315	6	.	.	PUNCT
ejpam-6480	316	1	entropy	entropy	PROPN
ejpam-6480	316	2	,	,	PUNCT
ejpam-6480	316	3	14(3):480–490	14(3):480–490	NUM
ejpam-6480	316	4	,	,	PUNCT
ejpam-6480	316	5	2012	2012	NUM
ejpam-6480	316	6	.	.	PUNCT
ejpam-6480	317	1	[	[	X
ejpam-6480	317	2	17	17	NUM
ejpam-6480	317	3	]	]	X
ejpam-6480	317	4	suchandan	suchandan	PROPN
ejpam-6480	317	5	kayal	kayal	PROPN
ejpam-6480	317	6	and	and	CCONJ
ejpam-6480	317	7	rajesh	rajesh	PROPN
ejpam-6480	317	8	moharana	moharana	PROPN
ejpam-6480	317	9	.	.	PUNCT
ejpam-6480	318	1	some	some	DET
ejpam-6480	318	2	results	result	VERB
ejpam-6480	318	3	on	on	ADP
ejpam-6480	318	4	a	a	DET
ejpam-6480	318	5	doubly	doubly	ADV
ejpam-6480	318	6	truncated	truncated	ADJ
ejpam-6480	318	7	generalized	generalized	ADJ
ejpam-6480	318	8	discrimination	discrimination	NOUN
ejpam-6480	318	9	measure	measure	NOUN
ejpam-6480	318	10	.	.	PUNCT
ejpam-6480	319	1	applications	application	NOUN
ejpam-6480	319	2	of	of	ADP
ejpam-6480	319	3	mathematics	mathematic	NOUN
ejpam-6480	319	4	,	,	PUNCT
ejpam-6480	319	5	61(5):585–605	61(5):585–605	PROPN
ejpam-6480	319	6	,	,	PUNCT
ejpam-6480	319	7	2016	2016	NUM
ejpam-6480	319	8	.	.	PUNCT
ejpam-6480	320	1	[	[	X
ejpam-6480	320	2	18	18	NUM
ejpam-6480	320	3	]	]	PUNCT
ejpam-6480	320	4	chanchal	chanchal	ADJ
ejpam-6480	320	5	kundu	kundu	NOUN
ejpam-6480	320	6	.	.	PUNCT
ejpam-6480	321	1	on	on	ADP
ejpam-6480	321	2	weighted	weight	VERB
ejpam-6480	321	3	measure	measure	NOUN
ejpam-6480	321	4	of	of	ADP
ejpam-6480	321	5	inaccuracy	inaccuracy	NOUN
ejpam-6480	321	6	for	for	ADP
ejpam-6480	321	7	doubly	doubly	ADV
ejpam-6480	321	8	truncated	truncate	VERB
ejpam-6480	321	9	random	random	ADJ
ejpam-6480	321	10	variables	variable	NOUN
ejpam-6480	321	11	.	.	PUNCT
ejpam-6480	322	1	communications	communication	NOUN
ejpam-6480	322	2	in	in	ADP
ejpam-6480	322	3	statistics	statistic	NOUN
ejpam-6480	322	4	-	-	PUNCT
ejpam-6480	322	5	theory	theory	NOUN
ejpam-6480	322	6	and	and	CCONJ
ejpam-6480	322	7	methods	method	NOUN
ejpam-6480	322	8	,	,	PUNCT
ejpam-6480	322	9	46(7):3135–3147	46(7):3135–3147	NUM
ejpam-6480	322	10	,	,	PUNCT
ejpam-6480	322	11	2017	2017	NUM
ejpam-6480	322	12	.	.	PUNCT
ejpam-6480	323	1	[	[	X
ejpam-6480	323	2	19	19	NUM
ejpam-6480	323	3	]	]	PUNCT
ejpam-6480	323	4	samira	samira	PROPN
ejpam-6480	323	5	jalayeri	jalayeri	PROPN
ejpam-6480	323	6	,	,	PUNCT
ejpam-6480	323	7	gr	gr	PRON
ejpam-6480	323	8	mohtashami	mohtashami	NOUN
ejpam-6480	323	9	borzadaran	borzadaran	NOUN
ejpam-6480	323	10	,	,	PUNCT
ejpam-6480	323	11	and	and	CCONJ
ejpam-6480	323	12	m	m	PROPN
ejpam-6480	323	13	khorashadizadeh	khorashadizadeh	NOUN
ejpam-6480	323	14	.	.	PUNCT
ejpam-6480	324	1	some	some	DET
ejpam-6480	324	2	properties	property	NOUN
ejpam-6480	324	3	of	of	ADP
ejpam-6480	324	4	tsallis	tsallis	PROPN
ejpam-6480	324	5	entropy	entropy	PROPN
ejpam-6480	324	6	based	base	VERB
ejpam-6480	324	7	on	on	ADP
ejpam-6480	324	8	a	a	DET
ejpam-6480	324	9	doubly	doubly	ADV
ejpam-6480	324	10	truncated	truncated	ADJ
ejpam-6480	324	11	(	(	PUNCT
ejpam-6480	324	12	interval	interval	NOUN
ejpam-6480	324	13	)	)	PUNCT
ejpam-6480	324	14	random	random	ADJ
ejpam-6480	324	15	variable	variable	NOUN
ejpam-6480	324	16	.	.	PUNCT
ejpam-6480	325	1	reliability	reliability	NOUN
ejpam-6480	325	2	:	:	PUNCT
ejpam-6480	325	3	theory	theory	NOUN
ejpam-6480	325	4	&	&	CCONJ
ejpam-6480	325	5	applications	application	NOUN
ejpam-6480	325	6	,	,	PUNCT
ejpam-6480	325	7	19(1	19(1	NUM
ejpam-6480	325	8	(	(	PUNCT
ejpam-6480	325	9	77)):448–464	77)):448–464	PROPN
ejpam-6480	325	10	,	,	PUNCT
ejpam-6480	325	11	2024	2024	NUM
ejpam-6480	325	12	.	.	PUNCT
ejpam-6480	326	1	[	[	X
ejpam-6480	326	2	20	20	NUM
ejpam-6480	326	3	]	]	PUNCT
ejpam-6480	326	4	vikas	vikas	PROPN
ejpam-6480	326	5	kumar	kumar	PROPN
ejpam-6480	326	6	and	and	CCONJ
ejpam-6480	326	7	nirdesh	nirdesh	PROPN
ejpam-6480	326	8	singh	singh	PROPN
ejpam-6480	326	9	.	.	PUNCT
ejpam-6480	327	1	characterization	characterization	NOUN
ejpam-6480	327	2	of	of	ADP
ejpam-6480	327	3	lifetime	lifetime	NOUN
ejpam-6480	327	4	distribution	distribution	NOUN
ejpam-6480	327	5	based	base	VERB
ejpam-6480	327	6	on	on	ADP
ejpam-6480	327	7	generalized	generalized	ADJ
ejpam-6480	327	8	interval	interval	NOUN
ejpam-6480	327	9	entropy	entropy	NOUN
ejpam-6480	327	10	.	.	PUNCT
ejpam-6480	328	1	statistics	statistic	NOUN
ejpam-6480	328	2	,	,	PUNCT
ejpam-6480	328	3	optimization	optimization	NOUN
ejpam-6480	328	4	&	&	CCONJ
ejpam-6480	328	5	information	information	PROPN
ejpam-6480	328	6	computing	computing	PROPN
ejpam-6480	328	7	,	,	PUNCT
ejpam-6480	328	8	6(4):547–559	6(4):547–559	NOUN
ejpam-6480	328	9	,	,	PUNCT
ejpam-6480	328	10	2018	2018	NUM
ejpam-6480	328	11	.	.	PUNCT
ejpam-6480	329	1	[	[	X
ejpam-6480	329	2	21	21	NUM
ejpam-6480	329	3	]	]	AUX
ejpam-6480	329	4	rebecca	rebecca	VERB
ejpam-6480	329	5	a	a	DET
ejpam-6480	329	6	betensky	betensky	NOUN
ejpam-6480	329	7	and	and	CCONJ
ejpam-6480	329	8	emily	emily	PROPN
ejpam-6480	329	9	c	c	PROPN
ejpam-6480	329	10	martin	martin	PROPN
ejpam-6480	329	11	.	.	PUNCT
ejpam-6480	330	1	commentary	commentary	NOUN
ejpam-6480	330	2	:	:	PUNCT
ejpam-6480	330	3	failure	failure	NOUN
ejpam-6480	330	4	-	-	PUNCT
ejpam-6480	330	5	rate	rate	NOUN
ejpam-6480	330	6	functions	function	NOUN
ejpam-6480	330	7	for	for	ADP
ejpam-6480	330	8	doubly	doubly	ADV
ejpam-6480	330	9	-	-	PUNCT
ejpam-6480	330	10	truncated	truncate	VERB
ejpam-6480	330	11	random	random	ADJ
ejpam-6480	330	12	variables	variable	NOUN
ejpam-6480	330	13	.	.	PUNCT
ejpam-6480	331	1	ieee	ieee	NOUN
ejpam-6480	331	2	transactions	transaction	NOUN
ejpam-6480	331	3	on	on	ADP
ejpam-6480	331	4	reliability	reliability	NOUN
ejpam-6480	331	5	,	,	PUNCT
ejpam-6480	331	6	52(1):7–8	52(1):7–8	NOUN
ejpam-6480	331	7	,	,	PUNCT
ejpam-6480	331	8	2003	2003	NUM
ejpam-6480	331	9	.	.	PUNCT
ejpam-6480	332	1	[	[	X
ejpam-6480	332	2	22	22	NUM
ejpam-6480	332	3	]	]	PUNCT
ejpam-6480	332	4	vikas	vikas	PROPN
ejpam-6480	332	5	kumar	kumar	PROPN
ejpam-6480	332	6	and	and	CCONJ
ejpam-6480	332	7	nirdesh	nirdesh	PROPN
ejpam-6480	332	8	singh	singh	PROPN
ejpam-6480	332	9	.	.	PUNCT
ejpam-6480	333	1	characterization	characterization	NOUN
ejpam-6480	333	2	of	of	ADP
ejpam-6480	333	3	lifetime	lifetime	NOUN
ejpam-6480	333	4	distribution	distribution	NOUN
ejpam-6480	333	5	based	base	VERB
ejpam-6480	333	6	on	on	ADP
ejpam-6480	333	7	generalized	generalized	ADJ
ejpam-6480	333	8	interval	interval	NOUN
ejpam-6480	333	9	entropy	entropy	NOUN
ejpam-6480	333	10	.	.	PUNCT
ejpam-6480	334	1	statistics	statistic	NOUN
ejpam-6480	334	2	,	,	PUNCT
ejpam-6480	334	3	optimization	optimization	NOUN
ejpam-6480	334	4	&	&	CCONJ
ejpam-6480	334	5	information	information	PROPN
ejpam-6480	334	6	computing	computing	PROPN
ejpam-6480	334	7	,	,	PUNCT
ejpam-6480	334	8	6(4):547–559	6(4):547–559	NOUN
ejpam-6480	334	9	,	,	PUNCT
ejpam-6480	334	10	2018	2018	NUM
ejpam-6480	334	11	.	.	PUNCT
ejpam-6480	335	1	[	[	X
ejpam-6480	335	2	23	23	NUM
ejpam-6480	335	3	]	]	X
ejpam-6480	335	4	vaishali	vaishali	PROPN
ejpam-6480	335	5	manish	manish	PROPN
ejpam-6480	335	6	joshi	joshi	PROPN
ejpam-6480	335	7	and	and	CCONJ
ejpam-6480	335	8	javid	javid	PROPN
ejpam-6480	335	9	dar	dar	PROPN
ejpam-6480	335	10	.	.	PUNCT
ejpam-6480	336	1	some	some	DET
ejpam-6480	336	2	results	result	NOUN
ejpam-6480	336	3	on	on	ADP
ejpam-6480	336	4	mathai	mathai	PROPN
ejpam-6480	336	5	-	-	PUNCT
ejpam-6480	336	6	haubold	haubold	ADJ
ejpam-6480	336	7	fuzzy	fuzzy	ADJ
ejpam-6480	336	8	entropy	entropy	NOUN
ejpam-6480	336	9	.	.	PUNCT
ejpam-6480	337	1	european	european	PROPN
ejpam-6480	337	2	journal	journal	PROPN
ejpam-6480	337	3	of	of	ADP
ejpam-6480	337	4	pure	pure	ADJ
ejpam-6480	337	5	and	and	CCONJ
ejpam-6480	337	6	applied	applied	ADJ
ejpam-6480	337	7	mathematics	mathematic	NOUN
ejpam-6480	337	8	,	,	PUNCT
ejpam-6480	337	9	17(3):2349–2360	17(3):2349–2360	NUM
ejpam-6480	337	10	,	,	PUNCT
ejpam-6480	337	11	2024	2024	NUM
ejpam-6480	337	12	.	.	PUNCT
ejpam-6480	338	1	[	[	X
ejpam-6480	338	2	24	24	NUM
ejpam-6480	338	3	]	]	X
ejpam-6480	338	4	oindrali	oindrali	ADJ
ejpam-6480	338	5	das	das	PROPN
ejpam-6480	338	6	,	,	PUNCT
ejpam-6480	338	7	siddhartha	siddhartha	PROPN
ejpam-6480	338	8	chakraborty	chakraborty	PROPN
ejpam-6480	338	9	,	,	PUNCT
ejpam-6480	338	10	and	and	CCONJ
ejpam-6480	338	11	biswabrata	biswabrata	ADJ
ejpam-6480	338	12	pradhan	pradhan	NOUN
ejpam-6480	338	13	.	.	PUNCT
ejpam-6480	339	1	on	on	ADP
ejpam-6480	339	2	mathai	mathai	PROPN
ejpam-6480	339	3	–	–	PUNCT
ejpam-6480	339	4	haubold	haubold	PROPN
ejpam-6480	339	5	past	past	PROPN
ejpam-6480	339	6	entropy	entropy	PROPN
ejpam-6480	339	7	measure	measure	NOUN
ejpam-6480	339	8	.	.	PUNCT
ejpam-6480	340	1	journal	journal	NOUN
ejpam-6480	340	2	of	of	ADP
ejpam-6480	340	3	the	the	DET
ejpam-6480	340	4	indian	indian	ADJ
ejpam-6480	340	5	society	society	NOUN
ejpam-6480	340	6	for	for	ADP
ejpam-6480	340	7	probability	probability	NOUN
ejpam-6480	340	8	and	and	CCONJ
ejpam-6480	340	9	statistics	statistic	NOUN
ejpam-6480	340	10	,	,	PUNCT
ejpam-6480	340	11	25(1):327–342	25(1):327–342	PROPN
ejpam-6480	340	12	,	,	PUNCT
ejpam-6480	340	13	2024	2024	NUM
ejpam-6480	340	14	.	.	PUNCT
ejpam-6480	341	1	[	[	X
ejpam-6480	341	2	25	25	NUM
ejpam-6480	341	3	]	]	X
ejpam-6480	341	4	javid	javid	PROPN
ejpam-6480	341	5	gani	gani	PROPN
ejpam-6480	341	6	dar	dar	PROPN
ejpam-6480	341	7	and	and	CCONJ
ejpam-6480	341	8	bander	bander	PROPN
ejpam-6480	341	9	al	al	PROPN
ejpam-6480	341	10	-	-	PUNCT
ejpam-6480	341	11	zahrani	zahrani	PROPN
ejpam-6480	341	12	.	.	PUNCT
ejpam-6480	342	1	on	on	ADP
ejpam-6480	342	2	some	some	DET
ejpam-6480	342	3	characterization	characterization	NOUN
ejpam-6480	342	4	results	result	NOUN
ejpam-6480	342	5	of	of	ADP
ejpam-6480	342	6	life	life	NOUN
ejpam-6480	342	7	time	time	NOUN
ejpam-6480	342	8	distributions	distribution	NOUN
ejpam-6480	342	9	using	use	VERB
ejpam-6480	342	10	mathai	mathai	PROPN
ejpam-6480	342	11	–	–	PUNCT
ejpam-6480	342	12	haubold	haubold	ADJ
ejpam-6480	342	13	residual	residual	ADJ
ejpam-6480	342	14	entropy	entropy	NOUN
ejpam-6480	342	15	.	.	PUNCT
ejpam-6480	343	1	iosr	iosr	ADJ
ejpam-6480	343	2	journal	journal	PROPN
ejpam-6480	343	3	of	of	ADP
ejpam-6480	343	4	mathematics	mathematics	PROPN
ejpam-6480	343	5	,	,	PUNCT
ejpam-6480	343	6	3:56–60	3:56–60	NUM
ejpam-6480	343	7	,	,	PUNCT
ejpam-6480	343	8	2013	2013	NUM
ejpam-6480	343	9	.	.	PUNCT
ejpam-6480	344	1	introduction	introduction	NOUN
ejpam-6480	344	2	mathai	mathai	PROPN
ejpam-6480	344	3	-	-	PUNCT
ejpam-6480	344	4	haubold	haubold	PROPN
ejpam-6480	344	5	interval	interval	NOUN
ejpam-6480	344	6	entropy	entropy	VERB
ejpam-6480	344	7	some	some	DET
ejpam-6480	344	8	characterization	characterization	NOUN
ejpam-6480	344	9	results	result	VERB
ejpam-6480	344	10	:	:	PUNCT
ejpam-6480	344	11	some	some	DET
ejpam-6480	344	12	inequalities	inequality	NOUN
ejpam-6480	344	13	and	and	CCONJ
ejpam-6480	344	14	stochastic	stochastic	ADJ
ejpam-6480	344	15	comparison	comparison	NOUN
ejpam-6480	344	16	:	:	PUNCT
ejpam-6480	344	17	conclusion	conclusion	NOUN
ejpam-6480	344	18	:	:	PUNCT