id	sid	tid	token	lemma	pos
cana-6157	1	1	communications	communication	NOUN
cana-6157	1	2	on	on	ADP
cana-6157	1	3	applied	apply	VERB
cana-6157	1	4	nonlinear	nonlinear	ADJ
cana-6157	1	5	analysis	analysis	NOUN
cana-6157	1	6	issn	issn	NOUN
cana-6157	1	7	:	:	PUNCT
cana-6157	1	8	1074	1074	NUM
cana-6157	1	9	-	-	PUNCT
cana-6157	1	10	133x	133x	NUM
cana-6157	1	11	vol	vol	VERB
cana-6157	1	12	32	32	NUM
cana-6157	1	13	no	no	NOUN
cana-6157	1	14	.	.	PUNCT
cana-6157	2	1	10s	10	NOUN
cana-6157	2	2	(	(	PUNCT
cana-6157	2	3	2025	2025	NUM
cana-6157	2	4	)	)	PUNCT
cana-6157	2	5	3480	3480	NUM
cana-6157	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	2	7	modeling	modeling	NOUN
cana-6157	2	8	and	and	CCONJ
cana-6157	2	9	fitting	fit	VERB
cana-6157	2	10	the	the	DET
cana-6157	2	11	alpha	alpha	NOUN
cana-6157	2	12	-	-	PUNCT
cana-6157	2	13	power	power	NOUN
cana-6157	2	14	transformed	transform	VERB
cana-6157	2	15	extended	extend	VERB
cana-6157	2	16	exponential	exponential	ADJ
cana-6157	2	17	distribution	distribution	NOUN
cana-6157	2	18	for	for	ADP
cana-6157	2	19	competing	compete	VERB
cana-6157	2	20	risks	risk	NOUN
cana-6157	2	21	:	:	PUNCT
cana-6157	2	22	methods	method	NOUN
cana-6157	2	23	and	and	CCONJ
cana-6157	2	24	applications	application	NOUN
cana-6157	2	25	asma	asma	PROPN
cana-6157	2	26	bouaziz	bouaziz	PROPN
cana-6157	2	27	and	and	CCONJ
cana-6157	2	28	nacira	nacira	PROPN
cana-6157	2	29	seddik	seddik	VERB
cana-6157	2	30	-	-	PUNCT
cana-6157	2	31	ameur	ameur	NOUN
cana-6157	2	32	laps	lap	VERB
cana-6157	2	33	laboratory	laboratory	NOUN
cana-6157	2	34	,	,	PUNCT
cana-6157	2	35	badji	badji	PROPN
cana-6157	2	36	-	-	PUNCT
cana-6157	2	37	mokhtar	mokhtar	PROPN
cana-6157	2	38	university	university	PROPN
cana-6157	2	39	,	,	PUNCT
cana-6157	2	40	box	box	PROPN
cana-6157	2	41	12	12	NUM
cana-6157	2	42	,	,	PUNCT
cana-6157	2	43	annaba	annaba	PROPN
cana-6157	2	44	,	,	PUNCT
cana-6157	2	45	23000	23000	NUM
cana-6157	2	46	,	,	PUNCT
cana-6157	2	47	algeria	algeria	PROPN
cana-6157	2	48	.	.	PUNCT
cana-6157	3	1	asma.bouaziz@univ-annaba.dz	asma.bouaziz@univ-annaba.dz	NOUN
cana-6157	3	2	,	,	PUNCT
cana-6157	3	3	naciraseddik@yahoo.fr	naciraseddik@yahoo.fr	PROPN
cana-6157	3	4	article	article	NOUN
cana-6157	3	5	history	history	NOUN
cana-6157	3	6	:	:	PUNCT
cana-6157	3	7	received	receive	VERB
cana-6157	3	8	:	:	PUNCT
cana-6157	3	9	03	03	NUM
cana-6157	3	10	-	-	SYM
cana-6157	3	11	01	01	NUM
cana-6157	3	12	-	-	PUNCT
cana-6157	3	13	2025	2025	NUM
cana-6157	3	14	revised	revise	VERB
cana-6157	3	15	:	:	PUNCT
cana-6157	3	16	25	25	NUM
cana-6157	3	17	-	-	PUNCT
cana-6157	3	18	04	04	NUM
cana-6157	3	19	-	-	PUNCT
cana-6157	3	20	2025	2025	NUM
cana-6157	3	21	accepted	accept	VERB
cana-6157	3	22	:	:	PUNCT
cana-6157	3	23	05	05	NUM
cana-6157	3	24	-	-	PUNCT
cana-6157	3	25	05	05	NUM
cana-6157	3	26	-	-	PUNCT
cana-6157	3	27	2025	2025	NUM
cana-6157	3	28	abstract	abstract	NOUN
cana-6157	3	29	:	:	PUNCT
cana-6157	3	30	survival	survival	NOUN
cana-6157	3	31	analysis	analysis	NOUN
cana-6157	3	32	concerns	concern	VERB
cana-6157	3	33	the	the	DET
cana-6157	3	34	modeling	modeling	NOUN
cana-6157	3	35	of	of	ADP
cana-6157	3	36	time	time	NOUN
cana-6157	3	37	-	-	PUNCT
cana-6157	3	38	to	to	ADP
cana-6157	3	39	-	-	PUNCT
cana-6157	3	40	event	event	NOUN
cana-6157	3	41	data	datum	NOUN
cana-6157	3	42	,	,	PUNCT
cana-6157	3	43	especially	especially	ADV
cana-6157	3	44	when	when	SCONJ
cana-6157	3	45	the	the	DET
cana-6157	3	46	event	event	NOUN
cana-6157	3	47	of	of	ADP
cana-6157	3	48	interest	interest	NOUN
cana-6157	3	49	can	can	AUX
cana-6157	3	50	occur	occur	VERB
cana-6157	3	51	due	due	ADJ
cana-6157	3	52	to	to	ADP
cana-6157	3	53	multiple	multiple	ADJ
cana-6157	3	54	,	,	PUNCT
cana-6157	3	55	mutually	mutually	ADV
cana-6157	3	56	exclusive	exclusive	ADJ
cana-6157	3	57	causes	cause	NOUN
cana-6157	3	58	.	.	PUNCT
cana-6157	4	1	in	in	ADP
cana-6157	4	2	such	such	ADJ
cana-6157	4	3	contexts	contexts	NOUN
cana-6157	4	4	,	,	PUNCT
cana-6157	4	5	competing	compete	VERB
cana-6157	4	6	risks	risk	NOUN
cana-6157	4	7	models	model	NOUN
cana-6157	4	8	are	be	AUX
cana-6157	4	9	essential	essential	ADJ
cana-6157	4	10	,	,	PUNCT
cana-6157	4	11	whether	whether	SCONJ
cana-6157	4	12	in	in	ADP
cana-6157	4	13	reliability	reliability	NOUN
cana-6157	4	14	engineering	engineering	NOUN
cana-6157	4	15	-	-	PUNCT
cana-6157	4	16	where	where	SCONJ
cana-6157	4	17	components	component	NOUN
cana-6157	4	18	may	may	AUX
cana-6157	4	19	fail	fail	VERB
cana-6157	4	20	for	for	ADP
cana-6157	4	21	different	different	ADJ
cana-6157	4	22	reasons	reason	NOUN
cana-6157	4	23	-	-	PUNCT
cana-6157	4	24	or	or	CCONJ
cana-6157	4	25	in	in	ADP
cana-6157	4	26	medical	medical	ADJ
cana-6157	4	27	research	research	NOUN
cana-6157	4	28	-	-	PUNCT
cana-6157	4	29	where	where	SCONJ
cana-6157	4	30	patients	patient	NOUN
cana-6157	4	31	may	may	AUX
cana-6157	4	32	die	die	VERB
cana-6157	4	33	from	from	ADP
cana-6157	4	34	various	various	ADJ
cana-6157	4	35	causes	cause	NOUN
cana-6157	4	36	.	.	PUNCT
cana-6157	5	1	the	the	DET
cana-6157	5	2	alpha	alpha	NOUN
cana-6157	5	3	-	-	PUNCT
cana-6157	5	4	power	power	NOUN
cana-6157	5	5	transformed	transform	VERB
cana-6157	5	6	extended	extend	VERB
cana-6157	5	7	exponential	exponential	NOUN
cana-6157	5	8	(	(	PUNCT
cana-6157	5	9	aptee	aptee	ADJ
cana-6157	5	10	)	)	PUNCT
cana-6157	5	11	distribution	distribution	NOUN
cana-6157	5	12	,	,	PUNCT
cana-6157	5	13	defined	define	VERB
cana-6157	5	14	through	through	ADP
cana-6157	5	15	the	the	DET
cana-6157	5	16	transformation	transformation	NOUN
cana-6157	5	17	of	of	ADP
cana-6157	5	18	the	the	DET
cana-6157	5	19	extended	extended	ADJ
cana-6157	5	20	exponential	exponential	ADJ
cana-6157	5	21	distribution	distribution	NOUN
cana-6157	5	22	,	,	PUNCT
cana-6157	5	23	offers	offer	VERB
cana-6157	5	24	a	a	DET
cana-6157	5	25	highly	highly	ADV
cana-6157	5	26	flexible	flexible	ADJ
cana-6157	5	27	framework	framework	NOUN
cana-6157	5	28	for	for	ADP
cana-6157	5	29	modeling	model	VERB
cana-6157	5	30	competing	compete	VERB
cana-6157	5	31	risks	risk	NOUN
cana-6157	5	32	.	.	PUNCT
cana-6157	6	1	it	it	PRON
cana-6157	6	2	encompasses	encompass	VERB
cana-6157	6	3	several	several	ADJ
cana-6157	6	4	classical	classical	ADJ
cana-6157	6	5	distributions	distribution	NOUN
cana-6157	6	6	as	as	ADP
cana-6157	6	7	special	special	ADJ
cana-6157	6	8	cases	case	NOUN
cana-6157	6	9	and	and	CCONJ
cana-6157	6	10	accommodates	accommodate	VERB
cana-6157	6	11	various	various	ADJ
cana-6157	6	12	hazard	hazard	NOUN
cana-6157	6	13	rate	rate	NOUN
cana-6157	6	14	shapes	shape	NOUN
cana-6157	6	15	including	include	VERB
cana-6157	6	16	increasing	increase	VERB
cana-6157	6	17	,	,	PUNCT
cana-6157	6	18	decreasing	decrease	VERB
cana-6157	6	19	,	,	PUNCT
cana-6157	6	20	constant	constant	ADJ
cana-6157	6	21	,	,	PUNCT
cana-6157	6	22	bathtub	bathtub	PROPN
cana-6157	6	23	,	,	PUNCT
cana-6157	6	24	and	and	CCONJ
cana-6157	6	25	upside	upside	ADV
cana-6157	6	26	-	-	PUNCT
cana-6157	6	27	down	down	ADP
cana-6157	6	28	bathtub	bathtub	NOUN
cana-6157	6	29	forms	form	NOUN
cana-6157	6	30	.	.	PUNCT
cana-6157	7	1	in	in	ADP
cana-6157	7	2	this	this	DET
cana-6157	7	3	study	study	NOUN
cana-6157	7	4	,	,	PUNCT
cana-6157	7	5	we	we	PRON
cana-6157	7	6	estimate	estimate	VERB
cana-6157	7	7	the	the	DET
cana-6157	7	8	parameters	parameter	NOUN
cana-6157	7	9	of	of	ADP
cana-6157	7	10	the	the	DET
cana-6157	7	11	aptee	aptee	NOUN
cana-6157	7	12	model	model	NOUN
cana-6157	7	13	using	use	VERB
cana-6157	7	14	multiple	multiple	ADJ
cana-6157	7	15	estimation	estimation	NOUN
cana-6157	7	16	techniques	technique	NOUN
cana-6157	7	17	such	such	ADJ
cana-6157	7	18	as	as	ADP
cana-6157	7	19	maximum	maximum	ADJ
cana-6157	7	20	likelihood	likelihood	NOUN
cana-6157	7	21	,	,	PUNCT
cana-6157	7	22	kolmogorov	kolmogorov	PROPN
cana-6157	7	23	-	-	PUNCT
cana-6157	7	24	smirnov	smirnov	NOUN
cana-6157	7	25	,	,	PUNCT
cana-6157	7	26	anderson	anderson	PROPN
cana-6157	7	27	-	-	PUNCT
cana-6157	7	28	darling	darling	PROPN
cana-6157	7	29	,	,	PUNCT
cana-6157	7	30	and	and	CCONJ
cana-6157	7	31	cramer	cramer	PROPN
cana-6157	7	32	-	-	PUNCT
cana-6157	7	33	von	von	PROPN
cana-6157	7	34	mises	mises	PROPN
cana-6157	7	35	methods	method	NOUN
cana-6157	7	36	.	.	PUNCT
cana-6157	8	1	furthermore	furthermore	ADV
cana-6157	8	2	,	,	PUNCT
cana-6157	8	3	we	we	PRON
cana-6157	8	4	introduce	introduce	VERB
cana-6157	8	5	a	a	DET
cana-6157	8	6	modified	modified	ADJ
cana-6157	8	7	chi	chi	ADJ
cana-6157	8	8	-	-	PUNCT
cana-6157	8	9	square	square	NOUN
cana-6157	8	10	goodness	goodness	NOUN
cana-6157	8	11	-	-	PUNCT
cana-6157	8	12	of	of	ADP
cana-6157	8	13	-	-	PUNCT
cana-6157	8	14	fit	fit	NOUN
cana-6157	8	15	statistic	statistic	NOUN
cana-6157	8	16	that	that	PRON
cana-6157	8	17	recovers	recover	VERB
cana-6157	8	18	information	information	NOUN
cana-6157	8	19	typically	typically	ADV
cana-6157	8	20	lost	lose	VERB
cana-6157	8	21	through	through	ADP
cana-6157	8	22	data	datum	NOUN
cana-6157	8	23	grouping	grouping	NOUN
cana-6157	8	24	and	and	CCONJ
cana-6157	8	25	enhances	enhance	VERB
cana-6157	8	26	the	the	DET
cana-6157	8	27	model	model	NOUN
cana-6157	8	28	selection	selection	NOUN
cana-6157	8	29	process	process	NOUN
cana-6157	8	30	.	.	PUNCT
cana-6157	9	1	we	we	PRON
cana-6157	9	2	also	also	ADV
cana-6157	9	3	conduct	conduct	VERB
cana-6157	9	4	comprehensive	comprehensive	ADJ
cana-6157	9	5	model	model	NOUN
cana-6157	9	6	diagnostics	diagnostic	NOUN
cana-6157	9	7	,	,	PUNCT
cana-6157	9	8	including	include	VERB
cana-6157	9	9	cox	cox	PROPN
cana-6157	9	10	-	-	PUNCT
cana-6157	9	11	snell	snell	PROPN
cana-6157	9	12	residual	residual	ADJ
cana-6157	9	13	analysis	analysis	NOUN
cana-6157	9	14	,	,	PUNCT
cana-6157	9	15	q	q	ADJ
cana-6157	9	16	-	-	PUNCT
cana-6157	9	17	q	q	NOUN
cana-6157	9	18	plots	plot	NOUN
cana-6157	9	19	,	,	PUNCT
cana-6157	9	20	and	and	CCONJ
cana-6157	9	21	hazard	hazard	NOUN
cana-6157	9	22	rate	rate	NOUN
cana-6157	9	23	comparisons	comparison	NOUN
cana-6157	9	24	,	,	PUNCT
cana-6157	9	25	to	to	PART
cana-6157	9	26	evaluate	evaluate	VERB
cana-6157	9	27	the	the	DET
cana-6157	9	28	adequacy	adequacy	NOUN
cana-6157	9	29	and	and	CCONJ
cana-6157	9	30	robustness	robustness	NOUN
cana-6157	9	31	of	of	ADP
cana-6157	9	32	the	the	DET
cana-6157	9	33	fitted	fit	VERB
cana-6157	9	34	model	model	NOUN
cana-6157	9	35	.	.	PUNCT
cana-6157	10	1	the	the	DET
cana-6157	10	2	proposed	propose	VERB
cana-6157	10	3	methodology	methodology	NOUN
cana-6157	10	4	is	be	AUX
cana-6157	10	5	validated	validate	VERB
cana-6157	10	6	through	through	ADP
cana-6157	10	7	extensive	extensive	ADJ
cana-6157	10	8	simulation	simulation	NOUN
cana-6157	10	9	studies	study	NOUN
cana-6157	10	10	and	and	CCONJ
cana-6157	10	11	an	an	DET
cana-6157	10	12	application	application	NOUN
cana-6157	10	13	to	to	ADP
cana-6157	10	14	real	real	ADJ
cana-6157	10	15	-	-	PUNCT
cana-6157	10	16	world	world	NOUN
cana-6157	10	17	medical	medical	ADJ
cana-6157	10	18	data	datum	NOUN
cana-6157	10	19	,	,	PUNCT
cana-6157	10	20	demonstrating	demonstrate	VERB
cana-6157	10	21	the	the	DET
cana-6157	10	22	practical	practical	ADJ
cana-6157	10	23	effectiveness	effectiveness	NOUN
cana-6157	10	24	of	of	ADP
cana-6157	10	25	the	the	DET
cana-6157	10	26	aptee	aptee	NOUN
cana-6157	10	27	model	model	NOUN
cana-6157	10	28	in	in	ADP
cana-6157	10	29	survival	survival	NOUN
cana-6157	10	30	and	and	CCONJ
cana-6157	10	31	reliability	reliability	NOUN
cana-6157	10	32	analysis	analysis	NOUN
cana-6157	10	33	.	.	PUNCT
cana-6157	11	1	keywords	keyword	NOUN
cana-6157	11	2	:	:	PUNCT
cana-6157	11	3	aptee	aptee	ADJ
cana-6157	11	4	distribution	distribution	NOUN
cana-6157	11	5	,	,	PUNCT
cana-6157	11	6	competing	compete	VERB
cana-6157	11	7	risks	risk	NOUN
cana-6157	11	8	,	,	PUNCT
cana-6157	11	9	survival	survival	NOUN
cana-6157	11	10	analysis	analysis	NOUN
cana-6157	11	11	,	,	PUNCT
cana-6157	11	12	estimation	estimation	NOUN
cana-6157	11	13	methods	method	NOUN
cana-6157	11	14	,	,	PUNCT
cana-6157	11	15	modified	modify	VERB
cana-6157	11	16	chi	chi	ADJ
cana-6157	11	17	-	-	PUNCT
cana-6157	11	18	square	square	ADJ
cana-6157	11	19	test	test	NOUN
cana-6157	11	20	.	.	PUNCT
cana-6157	12	1	ams	am	NOUN
cana-6157	12	2	classification	classification	NOUN
cana-6157	12	3	:	:	PUNCT
cana-6157	12	4	62g10	62g10	NUM
cana-6157	12	5	-	-	NOUN
cana-6157	12	6	62n05	62n05	NUM
cana-6157	12	7	-	-	PUNCT
cana-6157	12	8	62f12	62f12	NUM
cana-6157	12	9	.	.	PUNCT
cana-6157	13	1	i.introduction	i.introduction	NOUN
cana-6157	13	2	in	in	ADP
cana-6157	13	3	survival	survival	NOUN
cana-6157	13	4	and	and	CCONJ
cana-6157	13	5	reliability	reliability	NOUN
cana-6157	13	6	studies	study	NOUN
cana-6157	13	7	,	,	PUNCT
cana-6157	13	8	the	the	DET
cana-6157	13	9	event	event	NOUN
cana-6157	13	10	of	of	ADP
cana-6157	13	11	interest	interest	NOUN
cana-6157	13	12	-	-	PUNCT
cana-6157	13	13	such	such	ADJ
cana-6157	13	14	as	as	ADP
cana-6157	13	15	failure	failure	NOUN
cana-6157	13	16	or	or	CCONJ
cana-6157	13	17	death	death	NOUN
cana-6157	13	18	-	-	PUNCT
cana-6157	13	19	often	often	ADV
cana-6157	13	20	occurs	occur	VERB
cana-6157	13	21	due	due	ADJ
cana-6157	13	22	to	to	ADP
cana-6157	13	23	multiple	multiple	ADJ
cana-6157	13	24	competing	compete	VERB
cana-6157	13	25	causes	cause	NOUN
cana-6157	13	26	.	.	PUNCT
cana-6157	14	1	for	for	ADP
cana-6157	14	2	instance	instance	NOUN
cana-6157	14	3	,	,	PUNCT
cana-6157	14	4	patients	patient	NOUN
cana-6157	14	5	in	in	ADP
cana-6157	14	6	clinical	clinical	ADJ
cana-6157	14	7	trials	trial	NOUN
cana-6157	14	8	may	may	AUX
cana-6157	14	9	suffer	suffer	VERB
cana-6157	14	10	from	from	ADP
cana-6157	14	11	several	several	ADJ
cana-6157	14	12	health	health	NOUN
cana-6157	14	13	conditions	condition	NOUN
cana-6157	14	14	,	,	PUNCT
cana-6157	14	15	each	each	PRON
cana-6157	14	16	potentially	potentially	ADV
cana-6157	14	17	leading	lead	VERB
cana-6157	14	18	to	to	ADP
cana-6157	14	19	death	death	NOUN
cana-6157	14	20	,	,	PUNCT
cana-6157	14	21	while	while	SCONJ
cana-6157	14	22	mechanical	mechanical	ADJ
cana-6157	14	23	systems	system	NOUN
cana-6157	14	24	may	may	AUX
cana-6157	14	25	fail	fail	VERB
cana-6157	14	26	due	due	ADP
cana-6157	14	27	to	to	ADP
cana-6157	14	28	various	various	ADJ
cana-6157	14	29	distinct	distinct	ADJ
cana-6157	14	30	causes	cause	NOUN
cana-6157	14	31	under	under	ADP
cana-6157	14	32	diverse	diverse	ADJ
cana-6157	14	33	operational	operational	ADJ
cana-6157	14	34	conditions	condition	NOUN
cana-6157	14	35	.	.	PUNCT
cana-6157	15	1	in	in	ADP
cana-6157	15	2	such	such	ADJ
cana-6157	15	3	scenarios	scenario	NOUN
cana-6157	15	4	,	,	PUNCT
cana-6157	15	5	conventional	conventional	ADJ
cana-6157	15	6	single	single	ADJ
cana-6157	15	7	-	-	PUNCT
cana-6157	15	8	risk	risk	NOUN
cana-6157	15	9	models	model	NOUN
cana-6157	15	10	are	be	AUX
cana-6157	15	11	inadequate	inadequate	ADJ
cana-6157	15	12	,	,	PUNCT
cana-6157	15	13	making	make	VERB
cana-6157	15	14	competing	compete	VERB
cana-6157	15	15	risks	risk	NOUN
cana-6157	15	16	models	model	NOUN
cana-6157	15	17	essential	essential	ADJ
cana-6157	15	18	for	for	ADP
cana-6157	15	19	accurate	accurate	ADJ
cana-6157	15	20	analysis	analysis	NOUN
cana-6157	15	21	.	.	PUNCT
cana-6157	16	1	motivation	motivation	NOUN
cana-6157	16	2	:	:	PUNCT
cana-6157	16	3	in	in	ADP
cana-6157	16	4	presence	presence	NOUN
cana-6157	16	5	of	of	ADP
cana-6157	16	6	different	different	ADJ
cana-6157	16	7	risks	risk	NOUN
cana-6157	16	8	of	of	ADP
cana-6157	16	9	failure	failure	NOUN
cana-6157	16	10	,	,	PUNCT
cana-6157	16	11	researchers	researcher	NOUN
cana-6157	16	12	used	use	VERB
cana-6157	16	13	the	the	DET
cana-6157	16	14	proportional	proportional	ADJ
cana-6157	16	15	hazard	hazard	NOUN
cana-6157	16	16	models	model	NOUN
cana-6157	16	17	of	of	ADP
cana-6157	16	18	cox	cox	PROPN
cana-6157	16	19	such	such	ADJ
cana-6157	16	20	ph	ph	ADJ
cana-6157	16	21	-	-	ADJ
cana-6157	16	22	exponential	exponential	ADJ
cana-6157	16	23	and	and	CCONJ
cana-6157	16	24	ph	ph	NOUN
cana-6157	16	25	-	-	PUNCT
cana-6157	16	26	weibull	weibull	NOUN
cana-6157	16	27	,	,	PUNCT
cana-6157	16	28	accelerated	accelerate	VERB
cana-6157	16	29	failure	failure	NOUN
cana-6157	16	30	times	time	NOUN
cana-6157	16	31	(	(	PUNCT
cana-6157	16	32	aft	aft	NOUN
cana-6157	16	33	)	)	PUNCT
cana-6157	16	34	or	or	CCONJ
cana-6157	16	35	regression	regression	NOUN
cana-6157	16	36	models	model	NOUN
cana-6157	16	37	which	which	PRON
cana-6157	16	38	take	take	VERB
cana-6157	16	39	into	into	ADP
cana-6157	16	40	account	account	NOUN
cana-6157	16	41	several	several	ADJ
cana-6157	16	42	causes	cause	NOUN
cana-6157	16	43	of	of	ADP
cana-6157	16	44	failures	failure	NOUN
cana-6157	16	45	.	.	PUNCT
cana-6157	17	1	however	however	ADV
cana-6157	17	2	,	,	PUNCT
cana-6157	17	3	these	these	DET
cana-6157	17	4	lifetime	lifetime	NOUN
cana-6157	17	5	distributions	distribution	NOUN
cana-6157	17	6	frequently	frequently	ADV
cana-6157	17	7	lack	lack	VERB
cana-6157	17	8	the	the	DET
cana-6157	17	9	flexibility	flexibility	NOUN
cana-6157	17	10	to	to	PART
cana-6157	17	11	capture	capture	VERB
cana-6157	17	12	the	the	DET
cana-6157	17	13	full	full	ADJ
cana-6157	17	14	spectrum	spectrum	NOUN
cana-6157	17	15	of	of	ADP
cana-6157	17	16	hazard	hazard	NOUN
cana-6157	17	17	rate	rate	NOUN
cana-6157	17	18	behaviors	behavior	NOUN
cana-6157	17	19	observed	observe	VERB
cana-6157	17	20	in	in	ADP
cana-6157	17	21	practice	practice	NOUN
cana-6157	17	22	.	.	PUNCT
cana-6157	18	1	this	this	DET
cana-6157	18	2	limitation	limitation	NOUN
cana-6157	18	3	has	have	AUX
cana-6157	18	4	spurred	spur	VERB
cana-6157	18	5	recent	recent	ADJ
cana-6157	18	6	research	research	NOUN
cana-6157	18	7	into	into	ADP
cana-6157	18	8	more	more	ADV
cana-6157	18	9	adaptable	adaptable	ADJ
cana-6157	18	10	models	model	NOUN
cana-6157	18	11	.	.	PUNCT
cana-6157	19	1	we	we	PRON
cana-6157	19	2	can	can	AUX
cana-6157	19	3	cite	cite	VERB
cana-6157	19	4	for	for	ADP
cana-6157	19	5	example	example	NOUN
cana-6157	19	6	the	the	DET
cana-6157	19	7	competing	compete	VERB
cana-6157	19	8	risks	risk	NOUN
cana-6157	19	9	model	model	NOUN
cana-6157	19	10	of	of	ADP
cana-6157	19	11	bertholon	bertholon	NOUN
cana-6157	19	12	which	which	PRON
cana-6157	19	13	represents	represent	VERB
cana-6157	19	14	the	the	DET
cana-6157	19	15	minimum	minimum	NOUN
cana-6157	19	16	between	between	ADP
cana-6157	19	17	an	an	DET
cana-6157	19	18	exponential	exponential	NOUN
cana-6157	19	19	and	and	CCONJ
cana-6157	19	20	weibull	weibull	NOUN
cana-6157	19	21	distributions	distribution	NOUN
cana-6157	19	22	(	(	PUNCT
cana-6157	19	23	bertholon	bertholon	NOUN
cana-6157	19	24	et	et	PROPN
cana-6157	19	25	al	al	PROPN
cana-6157	19	26	.	.	PROPN
cana-6157	19	27	,	,	PUNCT
cana-6157	19	28	2004	2004	NUM
cana-6157	19	29	;	;	PUNCT
cana-6157	19	30	chouia	chouia	PROPN
cana-6157	19	31	and	and	CCONJ
cana-6157	19	32	seddik	seddik	NOUN
cana-6157	19	33	-	-	PUNCT
cana-6157	19	34	ameur	ameur	NOUN
cana-6157	19	35	,	,	PUNCT
cana-6157	19	36	2014	2014	NUM
cana-6157	19	37	;	;	PUNCT
cana-6157	19	38	chouia	chouia	PROPN
cana-6157	19	39	and	and	CCONJ
cana-6157	19	40	seddik	seddik	NOUN
cana-6157	19	41	-	-	PUNCT
cana-6157	19	42	ameur	ameur	NOUN
cana-6157	19	43	,	,	PUNCT
cana-6157	19	44	2017	2017	NUM
cana-6157	19	45	)	)	PUNCT
cana-6157	19	46	,	,	PUNCT
cana-6157	19	47	the	the	DET
cana-6157	19	48	accelerated	accelerated	ADJ
cana-6157	19	49	failure	failure	NOUN
cana-6157	19	50	time	time	NOUN
cana-6157	19	51	and	and	CCONJ
cana-6157	19	52	proportional	proportional	ADJ
cana-6157	19	53	hazard	hazard	NOUN
cana-6157	19	54	weibull	weibull	PROPN
cana-6157	19	55	extension	extension	NOUN
cana-6157	19	56	models	model	NOUN
cana-6157	19	57	which	which	PRON
cana-6157	19	58	describe	describe	VERB
cana-6157	19	59	the	the	DET
cana-6157	19	60	effect	effect	NOUN
cana-6157	19	61	of	of	ADP
cana-6157	19	62	covariates	covariate	NOUN
cana-6157	19	63	on	on	ADP
cana-6157	19	64	the	the	DET
cana-6157	19	65	hazard	hazard	NOUN
cana-6157	19	66	and	and	CCONJ
cana-6157	19	67	survival	survival	NOUN
cana-6157	19	68	functions	function	NOUN
cana-6157	19	69	respectively	respectively	ADV
cana-6157	19	70	(	(	PUNCT
cana-6157	19	71	seddik	seddik	NOUN
cana-6157	19	72	-	-	PUNCT
cana-6157	19	73	ameur	ameur	NOUN
cana-6157	19	74	and	and	CCONJ
cana-6157	19	75	treidi	treidi	NOUN
cana-6157	19	76	,	,	PUNCT
cana-6157	19	77	2017	2017	NUM
cana-6157	19	78	)	)	PUNCT
cana-6157	19	79	and	and	CCONJ
cana-6157	19	80	the	the	DET
cana-6157	19	81	bi	bi	ADJ
cana-6157	19	82	-	-	ADJ
cana-6157	19	83	weibull	weibull	ADJ
cana-6157	19	84	distribution	distribution	NOUN
cana-6157	19	85	which	which	PRON
cana-6157	19	86	is	be	AUX
cana-6157	19	87	the	the	DET
cana-6157	19	88	minimum	minimum	NOUN
cana-6157	19	89	between	between	ADP
cana-6157	19	90	two	two	NUM
cana-6157	19	91	weibull	weibull	PROPN
cana-6157	19	92	distributions	distribution	NOUN
cana-6157	19	93	mailto:naciraseddik@yahoo.fr	mailto:naciraseddik@yahoo.fr	PROPN
cana-6157	19	94	communications	communication	NOUN
cana-6157	19	95	on	on	ADP
cana-6157	19	96	applied	apply	VERB
cana-6157	19	97	nonlinear	nonlinear	ADJ
cana-6157	19	98	analysis	analysis	NOUN
cana-6157	19	99	issn	issn	NOUN
cana-6157	19	100	:	:	PUNCT
cana-6157	19	101	1074	1074	NUM
cana-6157	19	102	-	-	PUNCT
cana-6157	19	103	133x	133x	NUM
cana-6157	19	104	vol	vol	VERB
cana-6157	19	105	32	32	NUM
cana-6157	19	106	no	no	NOUN
cana-6157	19	107	.	.	PUNCT
cana-6157	20	1	10s	10	NOUN
cana-6157	20	2	(	(	PUNCT
cana-6157	20	3	2025	2025	NUM
cana-6157	20	4	)	)	PUNCT
cana-6157	20	5	3481	3481	NUM
cana-6157	21	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	21	2	(	(	PUNCT
cana-6157	21	3	bouaziz	bouaziz	NOUN
cana-6157	21	4	et	et	PROPN
cana-6157	21	5	al	al	PROPN
cana-6157	21	6	.	.	PROPN
cana-6157	21	7	,	,	PUNCT
cana-6157	21	8	2025	2025	NUM
cana-6157	21	9	)	)	PUNCT
cana-6157	21	10	.	.	PUNCT
cana-6157	22	1	the	the	DET
cana-6157	22	2	alpha	alpha	NOUN
cana-6157	22	3	-	-	PUNCT
cana-6157	22	4	power	power	NOUN
cana-6157	22	5	transformed	transform	VERB
cana-6157	22	6	extended	extend	VERB
cana-6157	22	7	exponential	exponential	NOUN
cana-6157	22	8	(	(	PUNCT
cana-6157	22	9	aptee	aptee	ADJ
cana-6157	22	10	)	)	PUNCT
cana-6157	22	11	distribution	distribution	NOUN
cana-6157	22	12	,	,	PUNCT
cana-6157	22	13	introduced	introduce	VERB
cana-6157	22	14	by	by	ADP
cana-6157	22	15	alghamedi	alghamedi	PROPN
cana-6157	22	16	et	et	PROPN
cana-6157	22	17	al	al	PROPN
cana-6157	22	18	.	.	PROPN
cana-6157	22	19	,	,	PUNCT
cana-6157	22	20	(	(	PUNCT
cana-6157	22	21	2019	2019	NUM
cana-6157	22	22	)	)	PUNCT
cana-6157	22	23	,	,	PUNCT
cana-6157	22	24	extends	extend	VERB
cana-6157	22	25	the	the	DET
cana-6157	22	26	classical	classical	ADJ
cana-6157	22	27	extended	extended	ADJ
cana-6157	22	28	exponential	exponential	ADJ
cana-6157	22	29	distribution	distribution	NOUN
cana-6157	22	30	proposed	propose	VERB
cana-6157	22	31	by	by	ADP
cana-6157	22	32	nadarajah	nadarajah	PROPN
cana-6157	22	33	and	and	CCONJ
cana-6157	22	34	haghighi	haghighi	PROPN
cana-6157	22	35	(	(	PUNCT
cana-6157	22	36	2011	2011	NUM
cana-6157	22	37	)	)	PUNCT
cana-6157	22	38	and	and	CCONJ
cana-6157	22	39	encompasses	encompass	VERB
cana-6157	22	40	the	the	DET
cana-6157	22	41	alpha	alpha	NOUN
cana-6157	22	42	-	-	PUNCT
cana-6157	22	43	power	power	NOUN
cana-6157	22	44	exponential	exponential	ADJ
cana-6157	22	45	distribution	distribution	NOUN
cana-6157	22	46	by	by	ADP
cana-6157	22	47	mahdavi	mahdavi	NOUN
cana-6157	22	48	and	and	CCONJ
cana-6157	22	49	kundu	kundu	NOUN
cana-6157	22	50	(	(	PUNCT
cana-6157	22	51	2016	2016	NUM
cana-6157	22	52	)	)	PUNCT
cana-6157	22	53	as	as	ADP
cana-6157	22	54	a	a	DET
cana-6157	22	55	special	special	ADJ
cana-6157	22	56	case	case	NOUN
cana-6157	22	57	.	.	PUNCT
cana-6157	23	1	its	its	PRON
cana-6157	23	2	unique	unique	ADJ
cana-6157	23	3	structure	structure	NOUN
cana-6157	23	4	allows	allow	VERB
cana-6157	23	5	it	it	PRON
cana-6157	23	6	to	to	PART
cana-6157	23	7	model	model	VERB
cana-6157	23	8	a	a	DET
cana-6157	23	9	wide	wide	ADJ
cana-6157	23	10	variety	variety	NOUN
cana-6157	23	11	of	of	ADP
cana-6157	23	12	hazard	hazard	NOUN
cana-6157	23	13	functions	function	NOUN
cana-6157	23	14	-	-	PUNCT
cana-6157	23	15	whether	whether	SCONJ
cana-6157	23	16	increasing	increase	VERB
cana-6157	23	17	,	,	PUNCT
cana-6157	23	18	decreasing	decrease	VERB
cana-6157	23	19	,	,	PUNCT
cana-6157	23	20	constant	constant	ADJ
cana-6157	23	21	,	,	PUNCT
cana-6157	23	22	bathtub	bathtub	NOUN
cana-6157	23	23	-	-	PUNCT
cana-6157	23	24	shaped	shape	VERB
cana-6157	23	25	,	,	PUNCT
cana-6157	23	26	or	or	CCONJ
cana-6157	23	27	upside	upside	ADV
cana-6157	23	28	-	-	PUNCT
cana-6157	23	29	down	down	ADP
cana-6157	23	30	bathtub	bathtub	NOUN
cana-6157	23	31	-	-	PUNCT
cana-6157	23	32	shaped	shape	VERB
cana-6157	23	33	-	-	PUNCT
cana-6157	23	34	making	make	VERB
cana-6157	23	35	it	it	PRON
cana-6157	23	36	highly	highly	ADV
cana-6157	23	37	applicable	applicable	ADJ
cana-6157	23	38	in	in	ADP
cana-6157	23	39	both	both	PRON
cana-6157	23	40	reliability	reliability	NOUN
cana-6157	23	41	engineering	engineering	NOUN
cana-6157	23	42	and	and	CCONJ
cana-6157	23	43	biomedical	biomedical	ADJ
cana-6157	23	44	research	research	NOUN
cana-6157	23	45	.	.	PUNCT
cana-6157	24	1	the	the	DET
cana-6157	24	2	original	original	ADJ
cana-6157	24	3	development	development	NOUN
cana-6157	24	4	of	of	ADP
cana-6157	24	5	the	the	DET
cana-6157	24	6	aptee	aptee	ADJ
cana-6157	24	7	distribution	distribution	NOUN
cana-6157	24	8	includes	include	VERB
cana-6157	24	9	comprehensive	comprehensive	ADJ
cana-6157	24	10	statistical	statistical	ADJ
cana-6157	24	11	properties	property	NOUN
cana-6157	24	12	such	such	ADJ
cana-6157	24	13	as	as	ADP
cana-6157	24	14	its	its	PRON
cana-6157	24	15	moments	moment	NOUN
cana-6157	24	16	,	,	PUNCT
cana-6157	24	17	quantiles	quantile	NOUN
cana-6157	24	18	,	,	PUNCT
cana-6157	24	19	stochastic	stochastic	ADJ
cana-6157	24	20	orderings	ordering	NOUN
cana-6157	24	21	,	,	PUNCT
cana-6157	24	22	bonferroni	bonferroni	NOUN
cana-6157	24	23	and	and	CCONJ
cana-6157	24	24	lorenz	lorenz	PROPN
cana-6157	24	25	curves	curve	NOUN
cana-6157	24	26	,	,	PUNCT
cana-6157	24	27	stress	stress	NOUN
cana-6157	24	28	-	-	PUNCT
cana-6157	24	29	strength	strength	NOUN
cana-6157	24	30	reliability	reliability	NOUN
cana-6157	24	31	,	,	PUNCT
cana-6157	24	32	and	and	CCONJ
cana-6157	24	33	order	order	NOUN
cana-6157	24	34	statistics	statistic	NOUN
cana-6157	24	35	.	.	PUNCT
cana-6157	25	1	maximum	maximum	ADJ
cana-6157	25	2	likelihood	likelihood	NOUN
cana-6157	25	3	estimators	estimator	NOUN
cana-6157	25	4	for	for	ADP
cana-6157	25	5	its	its	PRON
cana-6157	25	6	three	three	NUM
cana-6157	25	7	parameters	parameter	NOUN
cana-6157	25	8	were	be	AUX
cana-6157	25	9	also	also	ADV
cana-6157	25	10	derived	derive	VERB
cana-6157	25	11	and	and	CCONJ
cana-6157	25	12	their	their	PRON
cana-6157	25	13	performance	performance	NOUN
cana-6157	25	14	evaluated	evaluate	VERB
cana-6157	25	15	via	via	ADP
cana-6157	25	16	simulation	simulation	NOUN
cana-6157	25	17	studies	study	NOUN
cana-6157	25	18	focusing	focus	VERB
cana-6157	25	19	on	on	ADP
cana-6157	25	20	bias	bias	NOUN
cana-6157	25	21	and	and	CCONJ
cana-6157	25	22	mean	mean	VERB
cana-6157	25	23	squared	square	VERB
cana-6157	25	24	error	error	NOUN
cana-6157	25	25	.	.	PUNCT
cana-6157	26	1	building	build	VERB
cana-6157	26	2	on	on	ADP
cana-6157	26	3	this	this	DET
cana-6157	26	4	foundation	foundation	NOUN
cana-6157	26	5	,	,	PUNCT
cana-6157	26	6	our	our	PRON
cana-6157	26	7	study	study	NOUN
cana-6157	26	8	contributes	contribute	VERB
cana-6157	26	9	several	several	ADJ
cana-6157	26	10	advancements	advancement	NOUN
cana-6157	26	11	:	:	PUNCT
cana-6157	26	12	we	we	PRON
cana-6157	26	13	investigate	investigate	VERB
cana-6157	26	14	four	four	NUM
cana-6157	26	15	parameter	parameter	NOUN
cana-6157	26	16	estimation	estimation	NOUN
cana-6157	26	17	methods	method	NOUN
cana-6157	26	18	for	for	ADP
cana-6157	26	19	the	the	DET
cana-6157	26	20	aptee	aptee	ADJ
cana-6157	26	21	distribution	distribution	NOUN
cana-6157	26	22	:	:	PUNCT
cana-6157	26	23	maximum	maximum	ADJ
cana-6157	26	24	likelihood	likelihood	NOUN
cana-6157	26	25	estimation	estimation	NOUN
cana-6157	26	26	(	(	PUNCT
cana-6157	26	27	mle	mle	PROPN
cana-6157	26	28	)	)	PUNCT
cana-6157	26	29	,	,	PUNCT
cana-6157	26	30	kolmogorov	kolmogorov	PROPN
cana-6157	26	31	-	-	PUNCT
cana-6157	26	32	smirnov	smirnov	NOUN
cana-6157	26	33	,	,	PUNCT
cana-6157	26	34	anderson	anderson	PROPN
cana-6157	26	35	-	-	PUNCT
cana-6157	26	36	darling	darling	PROPN
cana-6157	26	37	,	,	PUNCT
cana-6157	26	38	and	and	CCONJ
cana-6157	26	39	cramer	cramer	PROPN
cana-6157	26	40	-	-	PUNCT
cana-6157	26	41	von	von	PROPN
cana-6157	26	42	mises	mises	PROPN
cana-6157	26	43	methods	method	NOUN
cana-6157	26	44	.	.	PUNCT
cana-6157	27	1	we	we	PRON
cana-6157	27	2	propose	propose	VERB
cana-6157	27	3	a	a	DET
cana-6157	27	4	modified	modified	ADJ
cana-6157	27	5	chi	chi	ADJ
cana-6157	27	6	-	-	PUNCT
cana-6157	27	7	square	square	NOUN
cana-6157	27	8	goodness	goodness	NOUN
cana-6157	27	9	-	-	PUNCT
cana-6157	27	10	of	of	ADP
cana-6157	27	11	-	-	PUNCT
cana-6157	27	12	fit	fit	ADJ
cana-6157	27	13	statistic	statistic	NOUN
cana-6157	27	14	designed	design	VERB
cana-6157	27	15	for	for	ADP
cana-6157	27	16	grouped	group	VERB
cana-6157	27	17	data	data	NOUN
cana-6157	27	18	scenarios	scenario	NOUN
cana-6157	27	19	,	,	PUNCT
cana-6157	27	20	which	which	PRON
cana-6157	27	21	retains	retain	VERB
cana-6157	27	22	information	information	NOUN
cana-6157	27	23	typically	typically	ADV
cana-6157	27	24	lost	lose	VERB
cana-6157	27	25	during	during	ADP
cana-6157	27	26	discretization	discretization	NOUN
cana-6157	27	27	and	and	CCONJ
cana-6157	27	28	improves	improve	VERB
cana-6157	27	29	model	model	NOUN
cana-6157	27	30	discrimination	discrimination	NOUN
cana-6157	27	31	.	.	PUNCT
cana-6157	28	1	we	we	PRON
cana-6157	28	2	perform	perform	VERB
cana-6157	28	3	in	in	ADP
cana-6157	28	4	-	-	PUNCT
cana-6157	28	5	depth	depth	NOUN
cana-6157	28	6	model	model	NOUN
cana-6157	28	7	diagnostics	diagnostic	NOUN
cana-6157	28	8	employing	employ	VERB
cana-6157	28	9	cox	cox	PROPN
cana-6157	28	10	-	-	PUNCT
cana-6157	28	11	snell	snell	PROPN
cana-6157	28	12	residuals	residual	NOUN
cana-6157	28	13	,	,	PUNCT
cana-6157	28	14	q	q	ADJ
cana-6157	28	15	-	-	PUNCT
cana-6157	28	16	q	q	NOUN
cana-6157	28	17	plots	plot	NOUN
cana-6157	28	18	,	,	PUNCT
cana-6157	28	19	and	and	CCONJ
cana-6157	28	20	comparisons	comparison	NOUN
cana-6157	28	21	between	between	ADP
cana-6157	28	22	empirical	empirical	ADJ
cana-6157	28	23	and	and	CCONJ
cana-6157	28	24	theoretical	theoretical	ADJ
cana-6157	28	25	hazard	hazard	NOUN
cana-6157	28	26	functions	function	NOUN
cana-6157	28	27	to	to	PART
cana-6157	28	28	assess	assess	VERB
cana-6157	28	29	the	the	DET
cana-6157	28	30	adequacy	adequacy	NOUN
cana-6157	28	31	of	of	ADP
cana-6157	28	32	the	the	DET
cana-6157	28	33	model	model	NOUN
cana-6157	28	34	.	.	PUNCT
cana-6157	29	1	we	we	PRON
cana-6157	29	2	validate	validate	VERB
cana-6157	29	3	the	the	DET
cana-6157	29	4	overall	overall	ADJ
cana-6157	29	5	methodology	methodology	NOUN
cana-6157	29	6	through	through	ADP
cana-6157	29	7	extensive	extensive	ADJ
cana-6157	29	8	simulation	simulation	NOUN
cana-6157	29	9	studies	study	NOUN
cana-6157	29	10	and	and	CCONJ
cana-6157	29	11	an	an	DET
cana-6157	29	12	application	application	NOUN
cana-6157	29	13	to	to	ADP
cana-6157	29	14	a	a	DET
cana-6157	29	15	real	real	ADJ
cana-6157	29	16	-	-	PUNCT
cana-6157	29	17	world	world	NOUN
cana-6157	29	18	medical	medical	ADJ
cana-6157	29	19	dataset	dataset	NOUN
cana-6157	29	20	involving	involve	VERB
cana-6157	29	21	competing	compete	VERB
cana-6157	29	22	risks	risk	NOUN
cana-6157	29	23	.	.	PUNCT
cana-6157	30	1	our	our	PRON
cana-6157	30	2	analysis	analysis	NOUN
cana-6157	30	3	confirms	confirm	VERB
cana-6157	30	4	that	that	SCONJ
cana-6157	30	5	the	the	DET
cana-6157	30	6	aptee	aptee	ADJ
cana-6157	30	7	distribution	distribution	NOUN
cana-6157	30	8	outperforms	outperform	VERB
cana-6157	30	9	traditional	traditional	ADJ
cana-6157	30	10	models	model	NOUN
cana-6157	30	11	such	such	ADJ
cana-6157	30	12	as	as	ADP
cana-6157	30	13	the	the	DET
cana-6157	30	14	weibull	weibull	NOUN
cana-6157	30	15	,	,	PUNCT
cana-6157	30	16	generalized	generalized	ADJ
cana-6157	30	17	exponential	exponential	NOUN
cana-6157	30	18	(	(	PUNCT
cana-6157	30	19	ge	ge	PROPN
cana-6157	30	20	)	)	PUNCT
cana-6157	30	21	,	,	PUNCT
cana-6157	30	22	and	and	CCONJ
cana-6157	30	23	exponentiated	exponentiate	VERB
cana-6157	30	24	nadarajah	nadarajah	PROPN
cana-6157	30	25	-	-	PUNCT
cana-6157	30	26	haghighi	haghighi	PROPN
cana-6157	30	27	(	(	PUNCT
cana-6157	30	28	enh	enh	NOUN
cana-6157	30	29	)	)	PUNCT
cana-6157	30	30	distributions	distribution	NOUN
cana-6157	30	31	in	in	ADP
cana-6157	30	32	terms	term	NOUN
cana-6157	30	33	of	of	ADP
cana-6157	30	34	both	both	CCONJ
cana-6157	30	35	fit	fit	ADJ
cana-6157	30	36	and	and	CCONJ
cana-6157	30	37	flexibility	flexibility	NOUN
cana-6157	30	38	.	.	PUNCT
cana-6157	31	1	structure	structure	NOUN
cana-6157	31	2	of	of	ADP
cana-6157	31	3	the	the	DET
cana-6157	31	4	paper	paper	NOUN
cana-6157	31	5	:	:	PUNCT
cana-6157	31	6	the	the	DET
cana-6157	31	7	remainder	remainder	NOUN
cana-6157	31	8	of	of	ADP
cana-6157	31	9	this	this	DET
cana-6157	31	10	paper	paper	NOUN
cana-6157	31	11	is	be	AUX
cana-6157	31	12	organized	organize	VERB
cana-6157	31	13	as	as	SCONJ
cana-6157	31	14	follows	follow	VERB
cana-6157	31	15	:	:	PUNCT
cana-6157	31	16	•	•	NUM
cana-6157	31	17	section	section	NOUN
cana-6157	31	18	2	2	NUM
cana-6157	31	19	introduces	introduce	VERB
cana-6157	31	20	the	the	DET
cana-6157	31	21	aptee	aptee	ADJ
cana-6157	31	22	distribution	distribution	NOUN
cana-6157	31	23	and	and	CCONJ
cana-6157	31	24	outlines	outline	VERB
cana-6157	31	25	its	its	PRON
cana-6157	31	26	key	key	ADJ
cana-6157	31	27	properties	property	NOUN
cana-6157	31	28	.	.	PUNCT
cana-6157	32	1	•	•	NUM
cana-6157	32	2	section	section	NOUN
cana-6157	32	3	3	3	NUM
cana-6157	32	4	details	detail	NOUN
cana-6157	32	5	the	the	DET
cana-6157	32	6	parameter	parameter	NOUN
cana-6157	32	7	estimation	estimation	NOUN
cana-6157	32	8	methods	method	NOUN
cana-6157	32	9	employed	employ	VERB
cana-6157	32	10	in	in	ADP
cana-6157	32	11	this	this	DET
cana-6157	32	12	study	study	NOUN
cana-6157	32	13	.	.	PUNCT
cana-6157	33	1	•	•	NUM
cana-6157	33	2	section	section	NOUN
cana-6157	33	3	4	4	NUM
cana-6157	33	4	presents	present	VERB
cana-6157	33	5	the	the	DET
cana-6157	33	6	modified	modified	ADJ
cana-6157	33	7	chi	chi	ADJ
cana-6157	33	8	-	-	PUNCT
cana-6157	33	9	square	square	NOUN
cana-6157	33	10	goodness	goodness	NOUN
cana-6157	33	11	-	-	PUNCT
cana-6157	33	12	of	of	ADP
cana-6157	33	13	-	-	PUNCT
cana-6157	33	14	fit	fit	ADJ
cana-6157	33	15	test	test	NOUN
cana-6157	33	16	tailored	tailor	VERB
cana-6157	33	17	for	for	ADP
cana-6157	33	18	grouped	group	VERB
cana-6157	33	19	data	datum	NOUN
cana-6157	33	20	.	.	PUNCT
cana-6157	34	1	•	•	NUM
cana-6157	34	2	section	section	NOUN
cana-6157	34	3	5	5	NUM
cana-6157	34	4	offers	offer	VERB
cana-6157	34	5	a	a	DET
cana-6157	34	6	simulation	simulation	NOUN
cana-6157	34	7	study	study	NOUN
cana-6157	34	8	to	to	PART
cana-6157	34	9	assess	assess	VERB
cana-6157	34	10	estimation	estimation	NOUN
cana-6157	34	11	accuracy	accuracy	NOUN
cana-6157	34	12	and	and	CCONJ
cana-6157	34	13	test	test	NOUN
cana-6157	34	14	performance	performance	NOUN
cana-6157	34	15	.	.	PUNCT
cana-6157	35	1	•	•	NUM
cana-6157	35	2	section	section	NOUN
cana-6157	35	3	6	6	NUM
cana-6157	35	4	applies	apply	VERB
cana-6157	35	5	the	the	DET
cana-6157	35	6	aptee	aptee	ADJ
cana-6157	35	7	model	model	NOUN
cana-6157	35	8	to	to	ADP
cana-6157	35	9	a	a	DET
cana-6157	35	10	real	real	ADJ
cana-6157	35	11	-	-	PUNCT
cana-6157	35	12	world	world	NOUN
cana-6157	35	13	medical	medical	ADJ
cana-6157	35	14	dataset	dataset	NOUN
cana-6157	35	15	involving	involve	VERB
cana-6157	35	16	competing	compete	VERB
cana-6157	35	17	risks	risk	NOUN
cana-6157	35	18	.	.	PUNCT
cana-6157	36	1	•	•	NUM
cana-6157	36	2	section	section	NOUN
cana-6157	36	3	7	7	NUM
cana-6157	36	4	discusses	discuss	VERB
cana-6157	36	5	model	model	NOUN
cana-6157	36	6	diagnostics	diagnostic	NOUN
cana-6157	36	7	and	and	CCONJ
cana-6157	36	8	residual	residual	ADJ
cana-6157	36	9	analysis	analysis	NOUN
cana-6157	36	10	for	for	ADP
cana-6157	36	11	validating	validate	VERB
cana-6157	36	12	the	the	DET
cana-6157	36	13	model	model	NOUN
cana-6157	36	14	fit	fit	PROPN
cana-6157	36	15	.	.	PUNCT
cana-6157	37	1	•	•	NUM
cana-6157	37	2	section	section	NOUN
cana-6157	37	3	8	8	NUM
cana-6157	37	4	concludes	conclude	VERB
cana-6157	37	5	the	the	DET
cana-6157	37	6	paper	paper	NOUN
cana-6157	37	7	with	with	ADP
cana-6157	37	8	key	key	ADJ
cana-6157	37	9	findings	finding	NOUN
cana-6157	37	10	and	and	CCONJ
cana-6157	37	11	suggestions	suggestion	NOUN
cana-6157	37	12	for	for	ADP
cana-6157	37	13	future	future	ADJ
cana-6157	37	14	research	research	NOUN
cana-6157	37	15	.	.	PUNCT
cana-6157	38	1	ii	ii	PROPN
cana-6157	38	2	.	.	PUNCT
cana-6157	39	1	the	the	DET
cana-6157	39	2	alpha	alpha	NOUN
cana-6157	39	3	-	-	PUNCT
cana-6157	39	4	power	power	NOUN
cana-6157	39	5	transformed	transform	VERB
cana-6157	39	6	extended	extend	VERB
cana-6157	39	7	exponential	exponential	NOUN
cana-6157	39	8	(	(	PUNCT
cana-6157	39	9	aptee	aptee	NOUN
cana-6157	39	10	)	)	PUNCT
cana-6157	39	11	distribution	distribution	NOUN
cana-6157	39	12	(	(	PUNCT
cana-6157	39	13	competing	compete	VERB
cana-6157	39	14	risks	risk	NOUN
cana-6157	39	15	aptee	aptee	VERB
cana-6157	39	16	distribution	distribution	NOUN
cana-6157	39	17	)	)	PUNCT
cana-6157	39	18	in	in	ADP
cana-6157	39	19	this	this	DET
cana-6157	39	20	section	section	NOUN
cana-6157	39	21	,	,	PUNCT
cana-6157	39	22	we	we	PRON
cana-6157	39	23	present	present	VERB
cana-6157	39	24	the	the	DET
cana-6157	39	25	alpha	alpha	NOUN
cana-6157	39	26	-	-	PUNCT
cana-6157	39	27	power	power	NOUN
cana-6157	39	28	transformed	transform	VERB
cana-6157	39	29	extended	extend	VERB
cana-6157	39	30	exponential	exponential	NOUN
cana-6157	39	31	(	(	PUNCT
cana-6157	39	32	aptee	aptee	ADJ
cana-6157	39	33	)	)	PUNCT
cana-6157	39	34	distribution	distribution	NOUN
cana-6157	39	35	,	,	PUNCT
cana-6157	39	36	a	a	DET
cana-6157	39	37	flexible	flexible	ADJ
cana-6157	39	38	lifetime	lifetime	NOUN
cana-6157	39	39	model	model	NOUN
cana-6157	39	40	particularly	particularly	ADV
cana-6157	39	41	well	well	ADV
cana-6157	39	42	-	-	PUNCT
cana-6157	39	43	suited	suited	ADJ
cana-6157	39	44	for	for	ADP
cana-6157	39	45	analyzing	analyze	VERB
cana-6157	39	46	competing	compete	VERB
cana-6157	39	47	risks	risk	NOUN
cana-6157	39	48	data	datum	NOUN
cana-6157	39	49	.	.	PUNCT
cana-6157	40	1	the	the	DET
cana-6157	40	2	cumulative	cumulative	ADJ
cana-6157	40	3	distribution	distribution	NOUN
cana-6157	40	4	function	function	NOUN
cana-6157	40	5	(	(	PUNCT
cana-6157	40	6	cdf	cdf	PROPN
cana-6157	40	7	)	)	PUNCT
cana-6157	40	8	of	of	ADP
cana-6157	40	9	the	the	DET
cana-6157	40	10	aptee	aptee	ADJ
cana-6157	40	11	distribution	distribution	NOUN
cana-6157	40	12	is	be	AUX
cana-6157	40	13	defined	define	VERB
cana-6157	40	14	as	as	ADP
cana-6157	40	15	:	:	PUNCT
cana-6157	40	16	𝐹(𝑡	𝐹(𝑡	NUM
cana-6157	40	17	)	)	PUNCT
cana-6157	40	18	=	=	PUNCT
cana-6157	40	19	𝛼	𝛼	SYM
cana-6157	40	20	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	NUM
cana-6157	40	21	)	)	PUNCT
cana-6157	40	22	−1	−1	NOUN
cana-6157	40	23	𝛼−1	𝛼−1	NUM
cana-6157	40	24	,	,	PUNCT
cana-6157	40	25	𝑡	𝑡	X
cana-6157	40	26	>	>	X
cana-6157	40	27	0(1	0(1	NUM
cana-6157	40	28	)	)	PUNCT
cana-6157	40	29	where	where	SCONJ
cana-6157	40	30	𝛼	𝛼	X
cana-6157	40	31	>	>	X
cana-6157	40	32	0	0	PROPN
cana-6157	40	33	,	,	PUNCT
cana-6157	40	34	𝛼	𝛼	PROPN
cana-6157	40	35	≠	≠	PROPN
cana-6157	40	36	1	1	NUM
cana-6157	40	37	,	,	PUNCT
cana-6157	40	38	𝜆	𝜆	ADJ
cana-6157	40	39	>	>	X
cana-6157	40	40	0	0	NUM
cana-6157	40	41	,	,	PUNCT
cana-6157	40	42	𝑎𝑛𝑑𝛽	𝑎𝑛𝑑𝛽	VERB
cana-6157	40	43	>	>	X
cana-6157	40	44	0are	0are	PUNCT
cana-6157	40	45	the	the	DET
cana-6157	40	46	shape	shape	NOUN
cana-6157	40	47	and	and	CCONJ
cana-6157	40	48	scale	scale	NOUN
cana-6157	40	49	parameters	parameter	NOUN
cana-6157	40	50	.	.	PUNCT
cana-6157	41	1	the	the	DET
cana-6157	41	2	corresponding	corresponding	ADJ
cana-6157	41	3	probability	probability	NOUN
cana-6157	41	4	density	density	NOUN
cana-6157	41	5	function	function	NOUN
cana-6157	41	6	(	(	PUNCT
cana-6157	41	7	pdf	pdf	NOUN
cana-6157	41	8	)	)	PUNCT
cana-6157	41	9	is	be	AUX
cana-6157	41	10	given	give	VERB
cana-6157	41	11	by	by	ADP
cana-6157	41	12	:	:	PUNCT
cana-6157	41	13	𝑓(𝑡	𝑓(𝑡	PROPN
cana-6157	41	14	)	)	PUNCT
cana-6157	41	15	=	=	SYM
cana-6157	41	16	𝑙𝑜𝑔(𝛼	𝑙𝑜𝑔(𝛼	PROPN
cana-6157	41	17	)	)	PUNCT
cana-6157	42	1	𝛼−1	𝛼−1	PRON
cana-6157	42	2	 	 	SPACE
cana-6157	42	3	𝛽𝜆(1	𝛽𝜆(1	PROPN
cana-6157	42	4	+	+	CCONJ
cana-6157	42	5	𝜆𝑡)𝛽−1	𝜆𝑡)𝛽−1	X
cana-6157	42	6	𝑒𝑥𝑝(1	𝑒𝑥𝑝(1	NOUN
cana-6157	42	7	−	−	PROPN
cana-6157	42	8	(	(	PUNCT
cana-6157	42	9	1	1	NUM
cana-6157	42	10	+	+	CCONJ
cana-6157	42	11	𝜆𝑡)𝛽	𝜆𝑡)𝛽	NOUN
cana-6157	42	12	)	)	PUNCT
cana-6157	42	13	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	NOUN
cana-6157	42	14	)	)	PUNCT
cana-6157	42	15	𝛽)(2	𝛽)(2	NOUN
cana-6157	42	16	)	)	PUNCT
cana-6157	42	17	hereafter	hereafter	ADV
cana-6157	42	18	,	,	PUNCT
cana-6157	42	19	arandomvariabletthatfollowsthedistributionin(1)isdenotedbyt~	arandomvariabletthatfollowsthedistributionin(1)isdenotedbyt~	PROPN
cana-6157	42	20	aptee(α	aptee(α	PROPN
cana-6157	42	21	,	,	PUNCT
cana-6157	42	22	β	β	X
cana-6157	42	23	,	,	PUNCT
cana-6157	42	24	λ	λ	PROPN
cana-6157	42	25	)	)	PUNCT
cana-6157	42	26	.	.	PUNCT
cana-6157	43	1	1	1	NUM
cana-6157	43	2	.5	.5	NUM
cana-6157	43	3	communications	communication	NOUN
cana-6157	43	4	on	on	ADP
cana-6157	43	5	applied	apply	VERB
cana-6157	43	6	nonlinear	nonlinear	ADJ
cana-6157	43	7	analysis	analysis	NOUN
cana-6157	43	8	issn	issn	NOUN
cana-6157	43	9	:	:	PUNCT
cana-6157	43	10	1074	1074	NUM
cana-6157	43	11	-	-	PUNCT
cana-6157	43	12	133x	133x	NUM
cana-6157	43	13	vol	vol	VERB
cana-6157	43	14	32	32	NUM
cana-6157	43	15	no	no	NOUN
cana-6157	43	16	.	.	PUNCT
cana-6157	44	1	10s	10	NOUN
cana-6157	44	2	(	(	PUNCT
cana-6157	44	3	2025	2025	NUM
cana-6157	44	4	)	)	PUNCT
cana-6157	44	5	3482	3482	NUM
cana-6157	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	44	7	figure	figure	NOUN
cana-6157	44	8	1	1	NUM
cana-6157	44	9	:	:	PUNCT
cana-6157	44	10	plotsofaptee(0.5,2,1)curve(1),aptee(2,2,1)curve(2),aptee(2,0.5,2)curve	plotsofaptee(0.5,2,1)curve(1),aptee(2,2,1)curve(2),aptee(2,0.5,2)curve	PROPN
cana-6157	44	11	(	(	PUNCT
cana-6157	44	12	3)andaptee(2,0.5,1)curve(4	3)andaptee(2,0.5,1)curve(4	NUM
cana-6157	44	13	)	)	PUNCT
cana-6157	44	14	.	.	PUNCT
cana-6157	45	1	special	special	ADJ
cana-6157	45	2	cases	case	NOUN
cana-6157	45	3	the	the	DET
cana-6157	45	4	aptee	aptee	ADJ
cana-6157	45	5	distribution	distribution	NOUN
cana-6157	45	6	includes	include	VERB
cana-6157	45	7	several	several	ADJ
cana-6157	45	8	well	well	ADV
cana-6157	45	9	-	-	PUNCT
cana-6157	45	10	known	know	VERB
cana-6157	45	11	lifetime	lifetime	NOUN
cana-6157	45	12	models	model	NOUN
cana-6157	45	13	as	as	ADP
cana-6157	45	14	special	special	ADJ
cana-6157	45	15	cases	case	NOUN
cana-6157	45	16	:	:	PUNCT
cana-6157	45	17	when	when	SCONJ
cana-6157	45	18	β=	β=	NOUN
cana-6157	45	19	1	1	NUM
cana-6157	45	20	,	,	PUNCT
cana-6157	45	21	the	the	DET
cana-6157	45	22	aptee	aptee	NOUN
cana-6157	45	23	reduces	reduce	VERB
cana-6157	45	24	to	to	ADP
cana-6157	45	25	the	the	DET
cana-6157	45	26	alpha	alpha	NOUN
cana-6157	45	27	power	power	NOUN
cana-6157	45	28	exponential	exponential	NOUN
cana-6157	45	29	(	(	PUNCT
cana-6157	45	30	ape	ape	NOUN
cana-6157	45	31	)	)	PUNCT
cana-6157	45	32	distribution	distribution	NOUN
cana-6157	45	33	(	(	PUNCT
cana-6157	45	34	mahdavi2016	mahdavi2016	PROPN
cana-6157	45	35	)	)	PUNCT
cana-6157	45	36	.	.	PUNCT
cana-6157	46	1	when	when	SCONJ
cana-6157	46	2	α=	α=	NOUN
cana-6157	46	3	1	1	NUM
cana-6157	46	4	,	,	PUNCT
cana-6157	46	5	it	it	PRON
cana-6157	46	6	simplifies	simplify	VERB
cana-6157	46	7	to	to	ADP
cana-6157	46	8	the	the	DET
cana-6157	46	9	extended	extend	VERB
cana-6157	46	10	exponential	exponential	NOUN
cana-6157	46	11	(	(	PUNCT
cana-6157	46	12	ee	ee	NOUN
cana-6157	46	13	)	)	PUNCT
cana-6157	46	14	distribution	distribution	NOUN
cana-6157	46	15	(	(	PUNCT
cana-6157	46	16	nadarajah2011	nadarajah2011	PROPN
cana-6157	46	17	)	)	PUNCT
cana-6157	46	18	.	.	PUNCT
cana-6157	47	1	when	when	SCONJ
cana-6157	47	2	α=1	α=1	X
cana-6157	47	3	and	and	CCONJ
cana-6157	47	4	β=1	β=1	ADP
cana-6157	47	5	,	,	PUNCT
cana-6157	47	6	it	it	PRON
cana-6157	47	7	reduces	reduce	VERB
cana-6157	47	8	further	far	ADV
cana-6157	47	9	to	to	ADP
cana-6157	47	10	the	the	DET
cana-6157	47	11	classical	classical	ADJ
cana-6157	47	12	exponential	exponential	ADJ
cana-6157	47	13	distribution	distribution	NOUN
cana-6157	47	14	.	.	PUNCT
cana-6157	48	1	i.survival	i.survival	ADJ
cana-6157	48	2	and	and	CCONJ
cana-6157	48	3	hazard	hazard	NOUN
cana-6157	48	4	rate	rate	NOUN
cana-6157	48	5	functions	function	NOUN
cana-6157	48	6	the	the	DET
cana-6157	48	7	survival	survival	NOUN
cana-6157	48	8	function	function	PROPN
cana-6157	48	9	s(t	s(t	PROPN
cana-6157	48	10	)	)	PUNCT
cana-6157	48	11	of	of	ADP
cana-6157	48	12	the	the	DET
cana-6157	48	13	aptee	aptee	ADJ
cana-6157	48	14	distribution	distribution	NOUN
cana-6157	48	15	is	be	AUX
cana-6157	48	16	derived	derive	VERB
cana-6157	48	17	as	as	ADP
cana-6157	48	18	:	:	PUNCT
cana-6157	48	19	𝑆(𝑡	𝑆(𝑡	ADJ
cana-6157	48	20	)	)	PUNCT
cana-6157	48	21	=	=	SYM
cana-6157	48	22	𝛼−𝛼	𝛼−𝛼	NUM
cana-6157	48	23	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	NUM
cana-6157	48	24	)	)	PUNCT
cana-6157	49	1	𝛼−1	𝛼−1	PRON
cana-6157	49	2	(	(	PUNCT
cana-6157	49	3	3	3	X
cana-6157	49	4	)	)	PUNCT
cana-6157	49	5	the	the	DET
cana-6157	49	6	hazard	hazard	NOUN
cana-6157	49	7	rate	rate	NOUN
cana-6157	49	8	function	function	NOUN
cana-6157	49	9	,	,	PUNCT
cana-6157	49	10	which	which	PRON
cana-6157	49	11	describes	describe	VERB
cana-6157	49	12	the	the	DET
cana-6157	49	13	instantaneous	instantaneous	ADJ
cana-6157	49	14	risk	risk	NOUN
cana-6157	49	15	of	of	ADP
cana-6157	49	16	failure	failure	NOUN
cana-6157	49	17	at	at	ADP
cana-6157	49	18	time	time	NOUN
cana-6157	49	19	t	t	PROPN
cana-6157	49	20	,	,	PUNCT
cana-6157	49	21	is	be	AUX
cana-6157	49	22	given	give	VERB
cana-6157	49	23	by	by	ADP
cana-6157	49	24	:	:	PUNCT
cana-6157	49	25	ℎ(𝑡	ℎ(𝑡	PROPN
cana-6157	49	26	)	)	PUNCT
cana-6157	49	27	=	=	VERB
cana-6157	50	1	𝛽𝜆	𝛽𝜆	NOUN
cana-6157	50	2	𝑙𝑜𝑔(𝛼)(1+𝜆𝑡)𝛽−1	𝑙𝑜𝑔(𝛼)(1+𝜆𝑡)𝛽−1	NUM
cana-6157	50	3	𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽)𝛼	𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽)𝛼	PROPN
cana-6157	50	4	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	NUM
cana-6157	50	5	)	)	PUNCT
cana-6157	50	6	𝛼	𝛼	PROPN
cana-6157	50	7	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	1−𝑒𝑥𝑝(1−(1+𝜆𝑡)𝛽	NUM
cana-6157	50	8	)	)	PUNCT
cana-6157	50	9	−1	−1	NOUN
cana-6157	50	10	(	(	PUNCT
cana-6157	50	11	4	4	NUM
cana-6157	50	12	)	)	PUNCT
cana-6157	50	13	0	0	NUM
cana-6157	51	1	.0	.0	NUM
cana-6157	51	2	communications	communication	NOUN
cana-6157	51	3	on	on	ADP
cana-6157	51	4	applied	apply	VERB
cana-6157	51	5	nonlinear	nonlinear	ADJ
cana-6157	51	6	analysis	analysis	NOUN
cana-6157	51	7	issn	issn	NOUN
cana-6157	51	8	:	:	PUNCT
cana-6157	51	9	1074	1074	NUM
cana-6157	51	10	-	-	PUNCT
cana-6157	51	11	133x	133x	NUM
cana-6157	51	12	vol	vol	VERB
cana-6157	51	13	32	32	NUM
cana-6157	51	14	no	no	NOUN
cana-6157	51	15	.	.	PUNCT
cana-6157	52	1	10s	10	NOUN
cana-6157	52	2	(	(	PUNCT
cana-6157	52	3	2025	2025	NUM
cana-6157	52	4	)	)	PUNCT
cana-6157	52	5	3483	3483	NUM
cana-6157	52	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	52	7	figure	figure	NOUN
cana-6157	52	8	2	2	NUM
cana-6157	52	9	:	:	PUNCT
cana-6157	52	10	plots	plot	NOUN
cana-6157	52	11	for	for	ADP
cana-6157	52	12	the	the	DET
cana-6157	52	13	hazard	hazard	NOUN
cana-6157	52	14	functions	function	NOUN
cana-6157	52	15	for	for	ADP
cana-6157	52	16	aptee(0.5,2,1	aptee(0.5,2,1	NOUN
cana-6157	52	17	)	)	PUNCT
cana-6157	52	18	(	(	PUNCT
cana-6157	52	19	solid	solid	ADJ
cana-6157	52	20	line	line	NOUN
cana-6157	52	21	)	)	PUNCT
cana-6157	52	22	and	and	CCONJ
cana-6157	52	23	aptee(2,2,1	aptee(2,2,1	PROPN
cana-6157	52	24	)	)	PUNCT
cana-6157	52	25	(	(	PUNCT
cana-6157	52	26	dashed	dash	VERB
cana-6157	52	27	line	line	NOUN
cana-6157	52	28	)	)	PUNCT
cana-6157	52	29	and	and	CCONJ
cana-6157	52	30	for	for	ADP
cana-6157	52	31	aptee(2,0.5,2	aptee(2,0.5,2	NOUN
cana-6157	52	32	)	)	PUNCT
cana-6157	52	33	(	(	PUNCT
cana-6157	52	34	solid	solid	ADJ
cana-6157	52	35	line	line	NOUN
cana-6157	52	36	)	)	PUNCT
cana-6157	52	37	and	and	CCONJ
cana-6157	52	38	aptee(2,0.5,1	aptee(2,0.5,1	NOUN
cana-6157	52	39	)	)	PUNCT
cana-6157	52	40	(	(	PUNCT
cana-6157	52	41	dashed	dash	VERB
cana-6157	52	42	line	line	NOUN
cana-6157	52	43	)	)	PUNCT
cana-6157	52	44	.	.	PUNCT
cana-6157	53	1	ii	ii	PROPN
cana-6157	53	2	.	.	PUNCT
cana-6157	53	3	shape	shape	NOUN
cana-6157	53	4	properties	property	NOUN
cana-6157	53	5	the	the	DET
cana-6157	53	6	aptee	aptee	ADJ
cana-6157	53	7	distribution	distribution	NOUN
cana-6157	53	8	is	be	AUX
cana-6157	53	9	highly	highly	ADV
cana-6157	53	10	flexible	flexible	ADJ
cana-6157	53	11	and	and	CCONJ
cana-6157	53	12	capable	capable	ADJ
cana-6157	53	13	of	of	ADP
cana-6157	53	14	modeling	model	VERB
cana-6157	53	15	a	a	DET
cana-6157	53	16	variety	variety	NOUN
cana-6157	53	17	of	of	ADP
cana-6157	53	18	hazard	hazard	NOUN
cana-6157	53	19	rate	rate	NOUN
cana-6157	53	20	shapes	shape	NOUN
cana-6157	53	21	,	,	PUNCT
cana-6157	53	22	including	include	VERB
cana-6157	53	23	:	:	PUNCT
cana-6157	53	24	•	•	NUM
cana-6157	53	25	constant	constant	ADJ
cana-6157	53	26	•	•	NOUN
cana-6157	53	27	increasing	increase	VERB
cana-6157	53	28	•	•	ADV
cana-6157	53	29	decreasing	decrease	VERB
cana-6157	53	30	•	•	NOUN
cana-6157	53	31	bathtub	bathtub	ADV
cana-6157	53	32	-	-	PUNCT
cana-6157	53	33	shaped	shape	VERB
cana-6157	53	34	•	•	NOUN
cana-6157	53	35	upside	upside	ADV
cana-6157	53	36	-	-	PUNCT
cana-6157	53	37	down	down	ADP
cana-6157	53	38	bathtub	bathtub	NOUN
cana-6157	53	39	this	this	PRON
cana-6157	53	40	makes	make	VERB
cana-6157	53	41	the	the	DET
cana-6157	53	42	aptee	aptee	NOUN
cana-6157	53	43	a	a	DET
cana-6157	53	44	robust	robust	ADJ
cana-6157	53	45	candidate	candidate	NOUN
cana-6157	53	46	for	for	ADP
cana-6157	53	47	modeling	model	VERB
cana-6157	53	48	lifetime	lifetime	NOUN
cana-6157	53	49	data	datum	NOUN
cana-6157	53	50	in	in	ADP
cana-6157	53	51	both	both	CCONJ
cana-6157	53	52	medical	medical	ADJ
cana-6157	53	53	and	and	CCONJ
cana-6157	53	54	reliability	reliability	NOUN
cana-6157	53	55	applications	application	NOUN
cana-6157	53	56	where	where	SCONJ
cana-6157	53	57	the	the	DET
cana-6157	53	58	hazard	hazard	NOUN
cana-6157	53	59	rate	rate	NOUN
cana-6157	53	60	is	be	AUX
cana-6157	53	61	not	not	PART
cana-6157	53	62	monotonic	monotonic	ADJ
cana-6157	53	63	.	.	PUNCT
cana-6157	53	64	iii	iii	PROPN
cana-6157	53	65	.	.	PROPN
cana-6157	53	66	parameter	parameter	PROPN
cana-6157	53	67	estimation	estimation	NOUN
cana-6157	53	68	methods	method	NOUN
cana-6157	53	69	let	let	VERB
cana-6157	53	70	us	we	PRON
cana-6157	53	71	consider	consider	VERB
cana-6157	53	72	a	a	DET
cana-6157	53	73	random	random	ADJ
cana-6157	53	74	sample	sample	NOUN
cana-6157	53	75	of	of	ADP
cana-6157	53	76	observations	observation	NOUN
cana-6157	53	77	(	(	PUNCT
cana-6157	53	78	t₁	t₁	NOUN
cana-6157	53	79	,	,	PUNCT
cana-6157	53	80	t₂	t₂	NOUN
cana-6157	53	81	,	,	PUNCT
cana-6157	53	82	...	...	PUNCT
cana-6157	53	83	,	,	PUNCT
cana-6157	53	84	𝑡𝑛)from	𝑡𝑛)from	ADP
cana-6157	53	85	aptee	aptee	PROPN
cana-6157	53	86	(	(	PUNCT
cana-6157	53	87	α	α	X
cana-6157	53	88	,	,	PUNCT
cana-6157	53	89	β	β	X
cana-6157	53	90	,	,	PUNCT
cana-6157	53	91	λ	λ	PROPN
cana-6157	53	92	)	)	PUNCT
cana-6157	53	93	with	with	ADP
cana-6157	53	94	unknown	unknown	ADJ
cana-6157	53	95	parameters	parameter	NOUN
cana-6157	53	96	.	.	PUNCT
cana-6157	54	1	in	in	ADP
cana-6157	54	2	this	this	DET
cana-6157	54	3	section	section	NOUN
cana-6157	54	4	,	,	PUNCT
cana-6157	54	5	we	we	PRON
cana-6157	54	6	propose	propose	VERB
cana-6157	54	7	different	different	ADJ
cana-6157	54	8	estimation	estimation	NOUN
cana-6157	54	9	methods	method	NOUN
cana-6157	54	10	to	to	PART
cana-6157	54	11	evaluate	evaluate	VERB
cana-6157	54	12	their	their	PRON
cana-6157	54	13	values	value	NOUN
cana-6157	54	14	.	.	PUNCT
cana-6157	55	1	i.maximum	i.maximum	ADJ
cana-6157	55	2	likelihood	likelihood	NOUN
cana-6157	55	3	estimation	estimation	NOUN
cana-6157	55	4	method	method	NOUN
cana-6157	55	5	because	because	SCONJ
cana-6157	55	6	of	of	ADP
cana-6157	55	7	their	their	PRON
cana-6157	55	8	nice	nice	ADJ
cana-6157	55	9	properties	property	NOUN
cana-6157	55	10	namely	namely	ADV
cana-6157	55	11	the	the	DET
cana-6157	55	12	consistency	consistency	NOUN
cana-6157	55	13	and	and	CCONJ
cana-6157	55	14	the	the	DET
cana-6157	55	15	asymptomatic	asymptomatic	ADJ
cana-6157	55	16	normality	normality	NOUN
cana-6157	55	17	,	,	PUNCT
cana-6157	55	18	the	the	DET
cana-6157	55	19	maximum	maximum	ADJ
cana-6157	55	20	likelihood	likelihood	NOUN
cana-6157	55	21	estimators	estimator	NOUN
cana-6157	55	22	are	be	AUX
cana-6157	55	23	generally	generally	ADV
cana-6157	55	24	required	require	VERB
cana-6157	55	25	.	.	PUNCT
cana-6157	56	1	the	the	DET
cana-6157	56	2	likelihood	likelihood	NOUN
cana-6157	56	3	function	function	NOUN
cana-6157	56	4	is	be	AUX
cana-6157	56	5	:	:	PUNCT
cana-6157	56	6	(	(	PUNCT
cana-6157	56	7	𝑡1	𝑡1	NOUN
cana-6157	56	8	,	,	PUNCT
cana-6157	56	9	𝑡2	𝑡2	PROPN
cana-6157	56	10	,	,	PUNCT
cana-6157	56	11	…	…	PUNCT
cana-6157	56	12	,	,	PUNCT
cana-6157	56	13	𝑡𝑛)𝑓𝑟𝑜𝑚𝐴𝑃𝑇𝐸𝐸(𝛼	𝑡𝑛)𝑓𝑟𝑜𝑚𝐴𝑃𝑇𝐸𝐸(𝛼	NOUN
cana-6157	56	14	,	,	PUNCT
cana-6157	56	15	𝛽	𝛽	NOUN
cana-6157	56	16	,	,	PUNCT
cana-6157	56	17	𝜆	𝜆	NOUN
cana-6157	56	18	)	)	PUNCT
cana-6157	56	19	𝑙(𝛼	𝑙(𝛼	PROPN
cana-6157	56	20	,	,	PUNCT
cana-6157	56	21	𝛽	𝛽	NOUN
cana-6157	56	22	,	,	PUNCT
cana-6157	56	23	𝜆\𝑡	𝜆\𝑡	X
cana-6157	56	24	)	)	PUNCT
cana-6157	56	25	=	=	SYM
cana-6157	56	26	∏𝑓(𝑡𝑖	∏𝑓(𝑡𝑖	NOUN
cana-6157	56	27	)	)	PUNCT
cana-6157	56	28	𝑛	𝑛	NOUN
cana-6157	56	29	𝑖=1	𝑖=1	PUNCT
cana-6157	57	1	=	=	SYM
cana-6157	57	2	∏	∏	NUM
cana-6157	57	3	𝑙𝑜𝑔	𝑙𝑜𝑔	NOUN
cana-6157	57	4	𝛼	𝛼	X
cana-6157	57	5	𝛼	𝛼	NOUN
cana-6157	57	6	−	−	PROPN
cana-6157	57	7	1	1	NUM
cana-6157	57	8	𝛽𝜆(1	𝛽𝜆(1	NOUN
cana-6157	57	9	+	+	NOUN
cana-6157	57	10	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	57	11	)	)	PUNCT
cana-6157	57	12	𝛽−1	𝛽−1	PROPN
cana-6157	57	13	𝑒𝑥𝑝(1	𝑒𝑥𝑝(1	NOUN
cana-6157	57	14	−	−	PROPN
cana-6157	57	15	(	(	PUNCT
cana-6157	57	16	1	1	NUM
cana-6157	57	17	+	+	NUM
cana-6157	57	18	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	57	19	)	)	PUNCT
cana-6157	57	20	𝛽	𝛽	NOUN
cana-6157	57	21	)	)	PUNCT
cana-6157	57	22	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NUM
cana-6157	57	23	)	)	PUNCT
cana-6157	57	24	𝛽	𝛽	NOUN
cana-6157	57	25	)	)	PUNCT
cana-6157	57	26	𝑛	𝑛	PRON
cana-6157	57	27	𝑖=1	𝑖=1	PUNCT
cana-6157	57	28	by	by	ADP
cana-6157	57	29	differentiating	differentiate	VERB
cana-6157	57	30	equation	equation	NOUN
cana-6157	57	31	with	with	ADP
cana-6157	57	32	respect	respect	NOUN
cana-6157	57	33	to	to	ADP
cana-6157	57	34	α	α	PRON
cana-6157	57	35	,	,	PUNCT
cana-6157	57	36	β	β	X
cana-6157	57	37	and	and	CCONJ
cana-6157	57	38	λ	λ	PROPN
cana-6157	57	39	,	,	PUNCT
cana-6157	57	40	respectively	respectively	ADV
cana-6157	57	41	,	,	PUNCT
cana-6157	57	42	and	and	CCONJ
cana-6157	57	43	equating	equate	VERB
cana-6157	57	44	to	to	ADP
cana-6157	57	45	zero	zero	NUM
cana-6157	57	46	,	,	PUNCT
cana-6157	57	47	we	we	PRON
cana-6157	57	48	have	have	VERB
cana-6157	57	49	𝜕	𝜕	NOUN
cana-6157	57	50	𝑙𝑜𝑔	𝑙𝑜𝑔	PROPN
cana-6157	57	51	𝑙(𝛼,𝛽,𝜆\𝑡	𝑙(𝛼,𝛽,𝜆\𝑡	NOUN
cana-6157	57	52	)	)	PUNCT
cana-6157	57	53	𝜕𝛼	𝜕𝛼	NOUN
cana-6157	57	54	=	=	SYM
cana-6157	57	55	𝑛	𝑛	PRON
cana-6157	57	56	𝛼	𝛼	PROPN
cana-6157	57	57	𝑙𝑜𝑔(𝛼	𝑙𝑜𝑔(𝛼	PROPN
cana-6157	57	58	)	)	PUNCT
cana-6157	57	59	−	−	NOUN
cana-6157	57	60	𝑛	𝑛	PRON
cana-6157	57	61	𝛼−1	𝛼−1	NOUN
cana-6157	57	62	+	+	NOUN
cana-6157	57	63	∑	∑	PROPN
cana-6157	57	64	(	(	PUNCT
cana-6157	57	65	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NOUN
cana-6157	57	66	)	)	PUNCT
cana-6157	57	67	𝛽))𝑛	𝛽))𝑛	NOUN
cana-6157	57	68	𝑖=1	𝑖=1	PROPN
cana-6157	57	69	𝛼	𝛼	PROPN
cana-6157	57	70	(	(	PUNCT
cana-6157	57	71	5	5	NUM
cana-6157	57	72	)	)	PUNCT
cana-6157	57	73	∂𝑙𝑜𝑔𝑙(α	∂𝑙𝑜𝑔𝑙(α	PROPN
cana-6157	57	74	,	,	PUNCT
cana-6157	57	75	β	β	X
cana-6157	57	76	,	,	PUNCT
cana-6157	57	77	λ\𝑡	λ\𝑡	NOUN
cana-6157	57	78	)	)	PUNCT
cana-6157	58	1	∂β	∂β	PROPN
cana-6157	58	2	=	=	PUNCT
cana-6157	58	3	𝑛	𝑛	PROPN
cana-6157	58	4	β	β	NOUN
cana-6157	58	5	+	+	CCONJ
cana-6157	58	6	∑	∑	ADP
cana-6157	58	7	𝑙𝑜𝑔(1	𝑙𝑜𝑔(1	NOUN
cana-6157	58	8	+	+	CCONJ
cana-6157	58	9	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	58	10	)	)	PUNCT
cana-6157	58	11	𝑛	𝑛	PRON
cana-6157	58	12	𝑖=1	𝑖=1	PROPN
cana-6157	59	1	−∑	−∑	PROPN
cana-6157	59	2	(	(	PUNCT
cana-6157	59	3	1	1	NUM
cana-6157	59	4	+	+	NUM
cana-6157	59	5	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	59	6	)	)	PUNCT
cana-6157	59	7	β𝑙𝑜𝑔(1	β𝑙𝑜𝑔(1	PUNCT
cana-6157	60	1	+	+	CCONJ
cana-6157	60	2	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	60	3	)	)	PUNCT
cana-6157	60	4	𝑛	𝑛	PRON
cana-6157	60	5	𝑖=1	𝑖=1	PUNCT
cana-6157	61	1	+	+	CCONJ
cana-6157	61	2	𝑙𝑜𝑔(α)∑	𝑙𝑜𝑔(α)∑	NOUN
cana-6157	61	3	(	(	PUNCT
cana-6157	61	4	1	1	NUM
cana-6157	61	5	+	+	NUM
cana-6157	61	6	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	61	7	)	)	PUNCT
cana-6157	61	8	β𝑙𝑜𝑔(1	β𝑙𝑜𝑔(1	PUNCT
cana-6157	62	1	+	+	ADP
cana-6157	62	2	𝑛	𝑛	DET
cana-6157	62	3	𝑖=1	𝑖=1	PROPN
cana-6157	62	4	λ𝑡𝑖)𝑒𝑥𝑝(1	λ𝑡𝑖)𝑒𝑥𝑝(1	SYM
cana-6157	62	5	−	−	PROPN
cana-6157	62	6	(	(	PUNCT
cana-6157	62	7	1	1	NUM
cana-6157	62	8	+	+	NUM
cana-6157	62	9	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	62	10	)	)	PUNCT
cana-6157	62	11	β	β	X
cana-6157	62	12	)	)	PUNCT
cana-6157	62	13	 	 	SPACE
cana-6157	62	14	(	(	PUNCT
cana-6157	62	15	6	6	NUM
cana-6157	62	16	)	)	PUNCT
cana-6157	62	17	communications	communication	NOUN
cana-6157	62	18	on	on	ADP
cana-6157	62	19	applied	apply	VERB
cana-6157	62	20	nonlinear	nonlinear	ADJ
cana-6157	62	21	analysis	analysis	NOUN
cana-6157	62	22	issn	issn	NOUN
cana-6157	62	23	:	:	PUNCT
cana-6157	62	24	1074	1074	NUM
cana-6157	62	25	-	-	PUNCT
cana-6157	62	26	133x	133x	NUM
cana-6157	62	27	vol	vol	VERB
cana-6157	62	28	32	32	NUM
cana-6157	62	29	no	no	NOUN
cana-6157	62	30	.	.	PUNCT
cana-6157	63	1	10s	10	NOUN
cana-6157	63	2	(	(	PUNCT
cana-6157	63	3	2025	2025	NUM
cana-6157	63	4	)	)	PUNCT
cana-6157	63	5	3484	3484	NUM
cana-6157	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	63	7	and	and	CCONJ
cana-6157	63	8	∂𝑙𝑜𝑔𝑙(α	∂𝑙𝑜𝑔𝑙(α	PROPN
cana-6157	63	9	,	,	PUNCT
cana-6157	63	10	β	β	X
cana-6157	63	11	,	,	PUNCT
cana-6157	63	12	λ\𝑡	λ\𝑡	VERB
cana-6157	63	13	)	)	PUNCT
cana-6157	63	14	∂λ	∂λ	PROPN
cana-6157	63	15	=	=	SYM
cana-6157	63	16	𝑛	𝑛	PRON
cana-6157	63	17	λ	λ	PROPN
cana-6157	63	18	+	+	CCONJ
cana-6157	63	19	(	(	PUNCT
cana-6157	63	20	β	β	NOUN
cana-6157	63	21	−	−	NUM
cana-6157	63	22	1)∑	1)∑	NUM
cana-6157	63	23	𝑡𝑖	𝑡𝑖	NOUN
cana-6157	63	24	(	(	PUNCT
cana-6157	63	25	1	1	NUM
cana-6157	63	26	+	+	NUM
cana-6157	63	27	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	63	28	)	)	PUNCT
cana-6157	63	29	𝑛	𝑛	PRON
cana-6157	63	30	𝑖=1	𝑖=1	PUNCT
cana-6157	64	1	−	−	PROPN
cana-6157	65	1	β∑𝑡𝑖(1	β∑𝑡𝑖(1	PUNCT
cana-6157	66	1	+	+	NUM
cana-6157	66	2	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	66	3	)	)	PUNCT
cana-6157	66	4	β−1	β−1	PUNCT
cana-6157	67	1	𝑛	𝑛	PRON
cana-6157	67	2	𝑖=1	𝑖=1	PUNCT
cana-6157	68	1	+	+	NOUN
cana-6157	68	2	𝑙𝑜𝑔(α)∑	𝑙𝑜𝑔(α)∑	NOUN
cana-6157	68	3	β𝑡𝑖(1	β𝑡𝑖(1	VERB
cana-6157	68	4	+	+	CCONJ
cana-6157	68	5	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	68	6	)	)	PUNCT
cana-6157	68	7	β−1𝑒𝑥𝑝(1	β−1𝑒𝑥𝑝(1	VERB
cana-6157	68	8	−	−	PROPN
cana-6157	69	1	(	(	PUNCT
cana-6157	69	2	1	1	NUM
cana-6157	69	3	+	+	NUM
cana-6157	69	4	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	69	5	)	)	PUNCT
cana-6157	69	6	β)𝑛	β)𝑛	PUNCT
cana-6157	70	1	𝑖=1	𝑖=1	PUNCT
cana-6157	70	2	(	(	PUNCT
cana-6157	70	3	7	7	X
cana-6157	70	4	)	)	PUNCT
cana-6157	70	5	ii	ii	PROPN
cana-6157	70	6	.	.	PUNCT
cana-6157	71	1	kolmogorov	kolmogorov	PROPN
cana-6157	71	2	-	-	PUNCT
cana-6157	71	3	smirnov	smirnov	PROPN
cana-6157	71	4	estimation	estimation	NOUN
cana-6157	71	5	method	method	VERB
cana-6157	71	6	another	another	DET
cana-6157	71	7	classical	classical	ADJ
cana-6157	71	8	method	method	NOUN
cana-6157	71	9	to	to	PART
cana-6157	71	10	calculate	calculate	VERB
cana-6157	71	11	the	the	DET
cana-6157	71	12	unknown	unknown	ADJ
cana-6157	71	13	parameters	parameter	NOUN
cana-6157	71	14	is	be	AUX
cana-6157	71	15	given	give	VERB
cana-6157	71	16	by	by	ADP
cana-6157	71	17	maximizing	maximize	VERB
cana-6157	71	18	the	the	DET
cana-6157	71	19	kolmogorovsmirnov	kolmogorovsmirnov	ADJ
cana-6157	71	20	statistic	statistic	NOUN
cana-6157	71	21	𝐷𝑛	𝐷𝑛	NOUN
cana-6157	71	22	with	with	ADP
cana-6157	71	23	respect	respect	NOUN
cana-6157	71	24	to	to	ADP
cana-6157	71	25	the	the	DET
cana-6157	71	26	unknown	unknown	ADJ
cana-6157	71	27	parameters	parameter	NOUN
cana-6157	71	28	.	.	PUNCT
cana-6157	72	1	𝐷𝑛	𝐷𝑛	NOUN
cana-6157	72	2	=	=	PUNCT
cana-6157	72	3	𝑚𝑎𝑥[𝐷	𝑚𝑎𝑥[𝐷	NUM
cana-6157	72	4	+	+	ADV
cana-6157	72	5	;	;	PUNCT
cana-6157	72	6	𝐷−	𝐷−	PROPN
cana-6157	72	7	]	]	PUNCT
cana-6157	72	8	𝐷+	𝐷+	X
cana-6157	72	9	=	=	SYM
cana-6157	72	10	𝑚𝑎𝑥	𝑚𝑎𝑥	PRON
cana-6157	72	11	1≤𝑖≤𝑛	1≤𝑖≤𝑛	NUM
cana-6157	72	12	[	[	X
cana-6157	72	13	(	(	PUNCT
cana-6157	72	14	𝑖	𝑖	NOUN
cana-6157	72	15	𝑛	𝑛	NOUN
cana-6157	72	16	)	)	PUNCT
cana-6157	72	17	−	−	PROPN
cana-6157	72	18	𝐹(𝑡(𝑖	𝐹(𝑡(𝑖	NUM
cana-6157	72	19	)	)	PUNCT
cana-6157	72	20	)	)	PUNCT
cana-6157	72	21	]	]	PUNCT
cana-6157	72	22	    	    	SPACE
cana-6157	72	23	;	;	PUNCT
cana-6157	72	24	   	   	SPACE
cana-6157	72	25	𝐷−	𝐷−	VERB
cana-6157	72	26	=	=	PUNCT
cana-6157	72	27	𝑚𝑎𝑥	𝑚𝑎𝑥	PRON
cana-6157	72	28	1≤𝑖≤𝑛	1≤𝑖≤𝑛	NUM
cana-6157	72	29	[	[	X
cana-6157	72	30	𝐹(𝑡(𝑖	𝐹(𝑡(𝑖	NUM
cana-6157	72	31	)	)	PUNCT
cana-6157	72	32	)	)	PUNCT
cana-6157	73	1	−	−	PROPN
cana-6157	73	2	(	(	PUNCT
cana-6157	73	3	𝑖	𝑖	SYM
cana-6157	73	4	−	−	PROPN
cana-6157	73	5	1	1	NUM
cana-6157	73	6	𝑛	𝑛	PROPN
cana-6157	73	7	)	)	PUNCT
cana-6157	73	8	]	]	PUNCT
cana-6157	73	9	𝐷+	𝐷+	X
cana-6157	73	10	=	=	SYM
cana-6157	73	11	𝑀𝑎𝑥{1≤𝑖≤𝑛	𝑀𝑎𝑥{1≤𝑖≤𝑛	X
cana-6157	73	12	}	}	PUNCT
cana-6157	73	13	[	[	X
cana-6157	73	14	(	(	PUNCT
cana-6157	73	15	𝑖	𝑖	NOUN
cana-6157	73	16	𝑛	𝑛	NOUN
cana-6157	73	17	)	)	PUNCT
cana-6157	73	18	−	−	PROPN
cana-6157	73	19	𝛼	𝛼	NUM
cana-6157	73	20	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NUM
cana-6157	73	21	)	)	PUNCT
cana-6157	73	22	𝛽	𝛽	NOUN
cana-6157	73	23	)	)	PUNCT
cana-6157	73	24	−1	−1	NOUN
cana-6157	74	1	𝛼−1	𝛼−1	NOUN
cana-6157	74	2	]	]	PUNCT
cana-6157	74	3	(	(	PUNCT
cana-6157	74	4	8)	8)	NUM
cana-6157	74	5	and	and	CCONJ
cana-6157	74	6	𝐷−	𝐷−	NOUN
cana-6157	74	7	=	=	SYM
cana-6157	74	8	𝑀𝑎𝑥{1≤𝑖≤𝑛	𝑀𝑎𝑥{1≤𝑖≤𝑛	X
cana-6157	74	9	}	}	PUNCT
cana-6157	74	10	[	[	PUNCT
cana-6157	74	11	𝛼	𝛼	NOUN
cana-6157	74	12	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NUM
cana-6157	74	13	)	)	PUNCT
cana-6157	74	14	𝛽	𝛽	NOUN
cana-6157	74	15	)	)	PUNCT
cana-6157	74	16	−1	−1	NOUN
cana-6157	75	1	𝛼−1	𝛼−1	ADV
cana-6157	75	2	−	−	PROPN
cana-6157	76	1	(	(	PUNCT
cana-6157	76	2	𝑖−1	𝑖−1	NOUN
cana-6157	76	3	𝑛	𝑛	PROPN
cana-6157	76	4	)	)	PUNCT
cana-6157	76	5	]	]	X
cana-6157	76	6	(	(	PUNCT
cana-6157	76	7	9	9	X
cana-6157	76	8	)	)	PUNCT
cana-6157	76	9	iii	iii	PROPN
cana-6157	76	10	.	.	PUNCT
cana-6157	77	1	cramer	cramer	PROPN
cana-6157	77	2	-	-	PUNCT
cana-6157	77	3	von	von	PROPN
cana-6157	77	4	-	-	PUNCT
cana-6157	77	5	mises	mises	PROPN
cana-6157	77	6	estimation	estimation	NOUN
cana-6157	77	7	method	method	VERB
cana-6157	77	8	the	the	DET
cana-6157	77	9	cramer	cramer	PROPN
cana-6157	77	10	-	-	PUNCT
cana-6157	77	11	von	von	PROPN
cana-6157	77	12	-	-	PUNCT
cana-6157	77	13	mises	mises	PROPN
cana-6157	77	14	cvm	cvm	PROPN
cana-6157	77	15	method	method	PROPN
cana-6157	77	16	estimation	estimation	NOUN
cana-6157	77	17	consists	consist	VERB
cana-6157	77	18	in	in	ADP
cana-6157	77	19	minimizing	minimize	VERB
cana-6157	77	20	the	the	DET
cana-6157	77	21	following	follow	VERB
cana-6157	77	22	function	function	NOUN
cana-6157	77	23	with	with	ADP
cana-6157	77	24	respect	respect	NOUN
cana-6157	77	25	to	to	ADP
cana-6157	77	26	the	the	DET
cana-6157	77	27	unknown	unknown	ADJ
cana-6157	77	28	parameters	parameter	NOUN
cana-6157	77	29	.	.	PUNCT
cana-6157	78	1	this	this	DET
cana-6157	78	2	method	method	NOUN
cana-6157	78	3	is	be	AUX
cana-6157	78	4	shown	show	VERB
cana-6157	78	5	to	to	PART
cana-6157	78	6	give	give	VERB
cana-6157	78	7	the	the	DET
cana-6157	78	8	smaller	small	ADJ
cana-6157	78	9	bias	bias	NOUN
cana-6157	78	10	estimators	estimator	NOUN
cana-6157	78	11	than	than	ADP
cana-6157	78	12	the	the	DET
cana-6157	78	13	other	other	ADJ
cana-6157	78	14	minimum	minimum	ADJ
cana-6157	78	15	distance	distance	NOUN
cana-6157	78	16	estimators	estimator	NOUN
cana-6157	78	17	.	.	PUNCT
cana-6157	79	1	𝑊𝑛	𝑊𝑛	ADP
cana-6157	79	2	2	2	NUM
cana-6157	79	3	=	=	SYM
cana-6157	79	4	∑[𝐹(𝑡𝑖	∑[𝐹(𝑡𝑖	NOUN
cana-6157	79	5	)	)	PUNCT
cana-6157	79	6	−	−	PROPN
cana-6157	79	7	2𝑖	2𝑖	NOUN
cana-6157	79	8	−	−	PROPN
cana-6157	79	9	1	1	NUM
cana-6157	79	10	2𝑛	2𝑛	PROPN
cana-6157	79	11	]	]	PUNCT
cana-6157	80	1	2𝑛	2𝑛	PROPN
cana-6157	80	2	𝑖=1	𝑖=1	PUNCT
cana-6157	81	1	+	+	PUNCT
cana-6157	81	2	1	1	NUM
cana-6157	81	3	12𝑛	12𝑛	NUM
cana-6157	81	4	so	so	ADV
cana-6157	81	5	,	,	PUNCT
cana-6157	81	6	for	for	ADP
cana-6157	81	7	aptee	aptee	NOUN
cana-6157	81	8	(	(	PUNCT
cana-6157	81	9	α	α	X
cana-6157	81	10	,	,	PUNCT
cana-6157	81	11	β	β	X
cana-6157	81	12	,	,	PUNCT
cana-6157	81	13	λ	λ	NOUN
cana-6157	81	14	)	)	PUNCT
cana-6157	81	15	distribution	distribution	NOUN
cana-6157	81	16	,	,	PUNCT
cana-6157	81	17	we	we	PRON
cana-6157	81	18	obtain	obtain	VERB
cana-6157	81	19	𝑊𝑛	𝑊𝑛	PROPN
cana-6157	81	20	2	2	NUM
cana-6157	81	21	=	=	SYM
cana-6157	81	22	∑	∑	PUNCT
cana-6157	81	23	[	[	PUNCT
cana-6157	81	24	𝛼	𝛼	NOUN
cana-6157	81	25	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NUM
cana-6157	81	26	)	)	PUNCT
cana-6157	81	27	𝛽	𝛽	NOUN
cana-6157	81	28	)	)	PUNCT
cana-6157	81	29	−1	−1	NOUN
cana-6157	82	1	𝛼−1	𝛼−1	PRON
cana-6157	82	2	−	−	PROPN
cana-6157	82	3	2𝑖−1	2𝑖−1	NUM
cana-6157	82	4	2𝑛	2𝑛	PROPN
cana-6157	82	5	]	]	PUNCT
cana-6157	82	6	2	2	NUM
cana-6157	82	7	𝑛	𝑛	PRON
cana-6157	82	8	𝑖=1	𝑖=1	PUNCT
cana-6157	82	9	+	+	CCONJ
cana-6157	82	10	1	1	NUM
cana-6157	82	11	12𝑛	12𝑛	NUM
cana-6157	82	12	(	(	PUNCT
cana-6157	82	13	10	10	NUM
cana-6157	82	14	)	)	PUNCT
cana-6157	82	15	as	as	ADV
cana-6157	82	16	all	all	DET
cana-6157	82	17	the	the	DET
cana-6157	82	18	analytical	analytical	ADJ
cana-6157	82	19	forms	form	NOUN
cana-6157	82	20	of	of	ADP
cana-6157	82	21	the	the	DET
cana-6157	82	22	estimators	estimator	NOUN
cana-6157	82	23	can	can	AUX
cana-6157	82	24	not	not	PART
cana-6157	82	25	be	be	AUX
cana-6157	82	26	given	give	VERB
cana-6157	82	27	,	,	PUNCT
cana-6157	82	28	so	so	SCONJ
cana-6157	82	29	we	we	PRON
cana-6157	82	30	use	use	VERB
cana-6157	82	31	numerical	numerical	ADJ
cana-6157	82	32	methods	method	NOUN
cana-6157	82	33	to	to	PART
cana-6157	82	34	calculate	calculate	VERB
cana-6157	82	35	the	the	DET
cana-6157	82	36	corresponding	corresponding	ADJ
cana-6157	82	37	values	value	NOUN
cana-6157	82	38	.	.	PUNCT
cana-6157	83	1	vii	vii	PROPN
cana-6157	83	2	.	.	PROPN
cana-6157	83	3	anderson	anderson	PROPN
cana-6157	83	4	-	-	PUNCT
cana-6157	83	5	darling	darling	NOUN
cana-6157	83	6	estimation	estimation	NOUN
cana-6157	83	7	this	this	DET
cana-6157	83	8	method	method	NOUN
cana-6157	83	9	is	be	AUX
cana-6157	83	10	based	base	VERB
cana-6157	83	11	on	on	ADP
cana-6157	83	12	the	the	DET
cana-6157	83	13	well	well	ADV
cana-6157	83	14	-	-	PUNCT
cana-6157	83	15	known	know	VERB
cana-6157	83	16	anderson	anderson	PROPN
cana-6157	83	17	-	-	PUNCT
cana-6157	83	18	darling	darling	NOUN
cana-6157	83	19	statistic	statistic	NOUN
cana-6157	83	20	𝐴𝑛	𝐴𝑛	PROPN
cana-6157	83	21	2	2	NUM
cana-6157	83	22	.	.	PUNCT
cana-6157	84	1	these	these	DET
cana-6157	84	2	estimators	estimator	NOUN
cana-6157	84	3	are	be	AUX
cana-6157	84	4	derived	derive	VERB
cana-6157	84	5	from	from	ADP
cana-6157	84	6	the	the	DET
cana-6157	84	7	minimum	minimum	NOUN
cana-6157	84	8	of	of	ADP
cana-6157	84	9	𝐴𝑛	𝐴𝑛	PROPN
cana-6157	84	10	2	2	NUM
cana-6157	84	11	with	with	ADP
cana-6157	84	12	respect	respect	NOUN
cana-6157	84	13	to	to	ADP
cana-6157	84	14	the	the	DET
cana-6157	84	15	unknown	unknown	ADJ
cana-6157	84	16	parameters	parameter	NOUN
cana-6157	84	17	.	.	PUNCT
cana-6157	85	1	𝐴𝑛	𝐴𝑛	NOUN
cana-6157	85	2	2	2	NUM
cana-6157	85	3	=	=	SYM
cana-6157	85	4	−𝑛	−𝑛	NOUN
cana-6157	85	5	−	−	PROPN
cana-6157	85	6	1	1	NUM
cana-6157	85	7	𝑛	𝑛	PROPN
cana-6157	85	8	{	{	PUNCT
cana-6157	85	9	∑(2𝑖	∑(2𝑖	PROPN
cana-6157	85	10	−	−	NOUN
cana-6157	85	11	1	1	X
cana-6157	85	12	)	)	PUNCT
cana-6157	85	13	[	[	X
cana-6157	85	14	𝑙𝑛𝐹(𝑡(𝑖	𝑙𝑛𝐹(𝑡(𝑖	NUM
cana-6157	85	15	)	)	PUNCT
cana-6157	85	16	)	)	PUNCT
cana-6157	86	1	+	+	CCONJ
cana-6157	86	2	𝑙𝑛	𝑙𝑛	NOUN
cana-6157	86	3	(	(	PUNCT
cana-6157	86	4	1	1	NUM
cana-6157	86	5	−	−	PROPN
cana-6157	86	6	𝐹(𝑡(𝑛+1−𝑖	𝐹(𝑡(𝑛+1−𝑖	NOUN
cana-6157	86	7	)	)	PUNCT
cana-6157	86	8	)	)	PUNCT
cana-6157	86	9	)	)	PUNCT
cana-6157	86	10	]	]	PUNCT
cana-6157	86	11	𝑛	𝑛	PRON
cana-6157	86	12	𝑖=1	𝑖=1	PUNCT
cana-6157	86	13	}	}	PUNCT
cana-6157	86	14	communications	communication	NOUN
cana-6157	86	15	on	on	ADP
cana-6157	86	16	applied	apply	VERB
cana-6157	86	17	nonlinear	nonlinear	ADJ
cana-6157	86	18	analysis	analysis	NOUN
cana-6157	86	19	issn	issn	NOUN
cana-6157	86	20	:	:	PUNCT
cana-6157	86	21	1074	1074	NUM
cana-6157	86	22	-	-	PUNCT
cana-6157	86	23	133x	133x	NUM
cana-6157	86	24	vol	vol	VERB
cana-6157	86	25	32	32	NUM
cana-6157	86	26	no	no	NOUN
cana-6157	86	27	.	.	PUNCT
cana-6157	87	1	10s	10	NOUN
cana-6157	87	2	(	(	PUNCT
cana-6157	87	3	2025	2025	NUM
cana-6157	87	4	)	)	PUNCT
cana-6157	87	5	3485	3485	NUM
cana-6157	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	87	7	takes	take	VERB
cana-6157	87	8	the	the	DET
cana-6157	87	9	following	follow	VERB
cana-6157	87	10	formula	formula	NOUN
cana-6157	87	11	for	for	ADP
cana-6157	87	12	the	the	DET
cana-6157	87	13	competing	compete	VERB
cana-6157	87	14	risks	risk	NOUN
cana-6157	87	15	model	model	NOUN
cana-6157	87	16	of	of	ADP
cana-6157	87	17	aptee	aptee	NOUN
cana-6157	87	18	𝐴𝑛	𝐴𝑛	PROPN
cana-6157	87	19	2	2	NUM
cana-6157	87	20	=	=	SYM
cana-6157	87	21	−𝑛	−𝑛	NOUN
cana-6157	87	22	−	−	PROPN
cana-6157	87	23	1	1	NUM
cana-6157	87	24	𝑛	𝑛	PROPN
cana-6157	88	1	[	[	X
cana-6157	88	2	∑	∑	INTJ
cana-6157	88	3	(	(	PUNCT
cana-6157	88	4	2𝑖	2𝑖	NOUN
cana-6157	88	5	−	−	NOUN
cana-6157	88	6	1	1	X
cana-6157	88	7	)	)	PUNCT
cana-6157	88	8	[	[	X
cana-6157	88	9	𝑙𝑛	𝑙𝑛	X
cana-6157	88	10	(	(	PUNCT
cana-6157	88	11	𝛼	𝛼	NOUN
cana-6157	88	12	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NUM
cana-6157	88	13	)	)	PUNCT
cana-6157	88	14	𝛽	𝛽	NOUN
cana-6157	88	15	)	)	PUNCT
cana-6157	88	16	−1	−1	NOUN
cana-6157	88	17	𝛼−1	𝛼−1	NOUN
cana-6157	88	18	)	)	PUNCT
cana-6157	88	19	]	]	X
cana-6157	88	20	𝑛	𝑛	PRON
cana-6157	88	21	𝑖=1	𝑖=1	PUNCT
cana-6157	89	1	+	+	NUM
cana-6157	89	2	𝑙𝑛	𝑙𝑛	NOUN
cana-6157	89	3	(	(	PUNCT
cana-6157	89	4	1	1	NUM
cana-6157	89	5	−	−	PROPN
cana-6157	89	6	𝛼	𝛼	NUM
cana-6157	89	7	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑛+1−𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑛+1−𝑖	NUM
cana-6157	89	8	)	)	PUNCT
cana-6157	89	9	𝛽	𝛽	NOUN
cana-6157	89	10	)	)	PUNCT
cana-6157	89	11	−1	−1	NOUN
cana-6157	89	12	𝛼−1	𝛼−1	NOUN
cana-6157	89	13	)	)	PUNCT
cana-6157	89	14	]	]	X
cana-6157	89	15	(	(	PUNCT
cana-6157	89	16	11	11	NUM
cana-6157	89	17	)	)	PUNCT
cana-6157	89	18	vii	vii	PROPN
cana-6157	89	19	.	.	PROPN
cana-6157	89	20	modified	modify	VERB
cana-6157	89	21	statistic	statistic	ADJ
cana-6157	89	22	test	test	NOUN
cana-6157	89	23	for	for	ADP
cana-6157	89	24	aptee	aptee	ADJ
cana-6157	89	25	distribution	distribution	NOUN
cana-6157	89	26	in	in	ADP
cana-6157	89	27	this	this	DET
cana-6157	89	28	section	section	NOUN
cana-6157	89	29	,	,	PUNCT
cana-6157	89	30	we	we	PRON
cana-6157	89	31	propose	propose	VERB
cana-6157	89	32	to	to	PART
cana-6157	89	33	construct	construct	VERB
cana-6157	89	34	a	a	DET
cana-6157	89	35	new	new	ADJ
cana-6157	89	36	chi	chi	ADJ
cana-6157	89	37	-	-	PUNCT
cana-6157	89	38	square	square	ADJ
cana-6157	89	39	statistic	statistic	NOUN
cana-6157	89	40	test	test	NOUN
cana-6157	89	41	y²	y²	NOUN
cana-6157	89	42	for	for	ADP
cana-6157	89	43	fitting	fit	VERB
cana-6157	89	44	the	the	DET
cana-6157	89	45	aptee	aptee	ADJ
cana-6157	89	46	distribution	distribution	NOUN
cana-6157	89	47	using	use	VERB
cana-6157	89	48	the	the	DET
cana-6157	89	49	approach	approach	NOUN
cana-6157	89	50	of	of	ADP
cana-6157	89	51	nikulin	nikulin	NOUN
cana-6157	89	52	,	,	PUNCT
cana-6157	89	53	rao	rao	NOUN
cana-6157	89	54	and	and	CCONJ
cana-6157	89	55	robson	robson	NOUN
cana-6157	89	56	(	(	PUNCT
cana-6157	89	57	1973	1973	NUM
cana-6157	89	58	,	,	PUNCT
cana-6157	89	59	1974	1974	NUM
cana-6157	89	60	)	)	PUNCT
cana-6157	89	61	.	.	PUNCT
cana-6157	90	1	based	base	VERB
cana-6157	90	2	on	on	ADP
cana-6157	90	3	initial	initial	ADJ
cana-6157	90	4	data	datum	NOUN
cana-6157	90	5	,	,	PUNCT
cana-6157	90	6	this	this	DET
cana-6157	90	7	statistic	statistic	NOUN
cana-6157	90	8	recovers	recover	VERB
cana-6157	90	9	the	the	DET
cana-6157	90	10	information	information	NOUN
cana-6157	90	11	lost	lose	VERB
cana-6157	90	12	in	in	ADP
cana-6157	90	13	regrouping	regrouping	ADJ
cana-6157	90	14	data	datum	NOUN
cana-6157	90	15	.	.	PUNCT
cana-6157	91	1	this	this	DET
cana-6157	91	2	statistic	statistic	ADJ
cana-6157	91	3	permit	permit	NOUN
cana-6157	91	4	to	to	ADP
cana-6157	91	5	practitioners	practitioner	NOUN
cana-6157	91	6	to	to	PART
cana-6157	91	7	check	check	VERB
cana-6157	91	8	the	the	DET
cana-6157	91	9	validity	validity	NOUN
cana-6157	91	10	of	of	ADP
cana-6157	91	11	this	this	DET
cana-6157	91	12	distribution	distribution	NOUN
cana-6157	91	13	without	without	ADP
cana-6157	91	14	regarding	regard	VERB
cana-6157	91	15	the	the	DET
cana-6157	91	16	possible	possible	ADJ
cana-6157	91	17	competitors	competitor	NOUN
cana-6157	91	18	.	.	PUNCT
cana-6157	92	1	i.criteria	i.criteria	NUM
cana-6157	92	2	test	test	NOUN
cana-6157	92	3	for	for	ADP
cana-6157	92	4	testing	test	VERB
cana-6157	92	5	the	the	DET
cana-6157	92	6	null	null	ADJ
cana-6157	92	7	hypothesis	hypothesis	NOUN
cana-6157	92	8	𝐻0	𝐻0	NOUN
cana-6157	92	9	that	that	SCONJ
cana-6157	92	10	the	the	DET
cana-6157	92	11	sample	sample	NOUN
cana-6157	92	12	𝑇	𝑇	PROPN
cana-6157	92	13	=	=	SYM
cana-6157	92	14	(	(	PUNCT
cana-6157	92	15	𝑡1	𝑡1	PROPN
cana-6157	92	16	,	,	PUNCT
cana-6157	92	17	…	…	PUNCT
cana-6157	92	18	,	,	PUNCT
cana-6157	92	19	𝑡2	𝑡2	ADJ
cana-6157	92	20	)	)	PUNCT
cana-6157	92	21	𝑇of	𝑇of	PROPN
cana-6157	92	22	n	n	PRON
cana-6157	92	23	independent	independent	ADJ
cana-6157	92	24	and	and	CCONJ
cana-6157	92	25	identically	identically	ADV
cana-6157	92	26	distribution	distribution	NOUN
cana-6157	92	27	random	random	ADJ
cana-6157	92	28	variables	variable	NOUN
cana-6157	92	29	comes	come	VERB
cana-6157	92	30	from	from	ADP
cana-6157	92	31	a	a	DET
cana-6157	92	32	population	population	NOUN
cana-6157	92	33	with	with	ADP
cana-6157	92	34	𝐹(θ)distribution	𝐹(θ)distribution	NOUN
cana-6157	92	35	with	with	ADP
cana-6157	92	36	unknown	unknown	ADJ
cana-6157	92	37	parameters	parameter	NOUN
cana-6157	92	38	vector	vector	NOUN
cana-6157	92	39	𝜃	𝜃	NOUN
cana-6157	92	40	=	=	PUNCT
cana-6157	92	41	(	(	PUNCT
cana-6157	92	42	𝜃1	𝜃1	PROPN
cana-6157	92	43	,	,	PUNCT
cana-6157	92	44	𝜃2	𝜃2	PROPN
cana-6157	92	45	,	,	PUNCT
cana-6157	92	46	.	.	PUNCT
cana-6157	92	47	.	.	PUNCT
cana-6157	93	1	,	,	PUNCT
cana-6157	93	2	𝜃𝑠	𝜃𝑠	AUX
cana-6157	93	3	)	)	PUNCT
cana-6157	93	4	𝑇the	𝑇the	PROPN
cana-6157	93	5	authors	author	NOUN
cana-6157	93	6	proposed	propose	VERB
cana-6157	93	7	a	a	DET
cana-6157	93	8	modified	modify	VERB
cana-6157	93	9	pearson	pearson	NOUN
cana-6157	93	10	statistic	statistic	PROPN
cana-6157	93	11	y²	y²	PROPN
cana-6157	93	12	defined	define	VERB
cana-6157	93	13	by	by	ADP
cana-6157	93	14	a	a	DET
cana-6157	93	15	sum	sum	NOUN
cana-6157	93	16	of	of	ADP
cana-6157	93	17	the	the	DET
cana-6157	93	18	pearson	pearson	PROPN
cana-6157	93	19	statistic	statistic	NOUN
cana-6157	93	20	𝑋𝑛	𝑋𝑛	PROPN
cana-6157	93	21	2	2	NUM
cana-6157	93	22	and	and	CCONJ
cana-6157	93	23	a	a	DET
cana-6157	93	24	quadratic	quadratic	ADJ
cana-6157	93	25	form	form	NOUN
cana-6157	93	26	:	:	PUNCT
cana-6157	94	1	𝑌𝑛	𝑌𝑛	PROPN
cana-6157	94	2	2(	2(	NUM
cana-6157	94	3	�	�	PROPN
cana-6157	94	4	̂	̂	NUM
cana-6157	94	5	�	�	NOUN
cana-6157	94	6	)	)	PUNCT
cana-6157	94	7	=	=	SYM
cana-6157	94	8	𝑋𝑛	𝑋𝑛	PROPN
cana-6157	94	9	2(	2(	NUM
cana-6157	94	10	�	�	PROPN
cana-6157	94	11	̂	̂	NUM
cana-6157	94	12	�	�	NOUN
cana-6157	94	13	)	)	PUNCT
cana-6157	94	14	+	+	CCONJ
cana-6157	94	15	1	1	NUM
cana-6157	94	16	𝑛	𝑛	DET
cana-6157	94	17	𝐿𝑇(	𝐿𝑇(	PROPN
cana-6157	94	18	�	�	PROPN
cana-6157	94	19	̂	̂	NOUN
cana-6157	94	20	�	�	NOUN
cana-6157	94	21	)	)	PUNCT
cana-6157	94	22	(	(	PUNCT
cana-6157	94	23	𝐼(	𝐼(	PROPN
cana-6157	94	24	�	�	PROPN
cana-6157	94	25	̂	̂	NUM
cana-6157	94	26	�	�	PROPN
cana-6157	94	27	)	)	PUNCT
cana-6157	94	28	−	−	PROPN
cana-6157	94	29	𝐽(	𝐽(	X
cana-6157	94	30	�	�	PROPN
cana-6157	94	31	̂	̂	NOUN
cana-6157	94	32	�	�	NOUN
cana-6157	94	33	)	)	PUNCT
cana-6157	94	34	)	)	PUNCT
cana-6157	94	35	−1	−1	NOUN
cana-6157	94	36	𝐿(	𝐿(	PROPN
cana-6157	94	37	�	�	PROPN
cana-6157	94	38	̂	̂	NOUN
cana-6157	94	39	�	�	PROPN
cana-6157	94	40	)	)	PUNCT
cana-6157	94	41	(	(	PUNCT
cana-6157	94	42	12	12	NUM
cana-6157	94	43	)	)	PUNCT
cana-6157	94	44	we	we	PRON
cana-6157	94	45	grouped	group	VERB
cana-6157	94	46	data	datum	NOUN
cana-6157	94	47	into	into	ADP
cana-6157	94	48	r	r	NOUN
cana-6157	94	49	classes	class	NOUN
cana-6157	94	50	δj(j	δj(j	NOUN
cana-6157	94	51	=	=	NOUN
cana-6157	94	52	1	1	NUM
cana-6157	94	53	,	,	PUNCT
cana-6157	94	54	…	…	PUNCT
cana-6157	94	55	,	,	PUNCT
cana-6157	94	56	r	r	X
cana-6157	94	57	)	)	PUNCT
cana-6157	94	58	such	such	ADJ
cana-6157	94	59	δj	δj	ADJ
cana-6157	94	60	∩	∩	NOUN
cana-6157	94	61	δi	δi	NOUN
cana-6157	94	62	=	=	PROPN
cana-6157	94	63	φ	φ	NOUN
cana-6157	94	64	for	for	ADP
cana-6157	94	65	any	any	DET
cana-6157	94	66	j≠i	j≠i	NOUN
cana-6157	94	67	.	.	PUNCT
cana-6157	95	1	the	the	DET
cana-6157	95	2	vector	vector	NOUN
cana-6157	95	3	𝜐	𝜐	PROPN
cana-6157	95	4	=	=	PRON
cana-6157	95	5	(	(	PUNCT
cana-6157	95	6	𝜐1	𝜐1	NOUN
cana-6157	95	7	,	,	PUNCT
cana-6157	95	8	…	…	PUNCT
cana-6157	95	9	,	,	PUNCT
cana-6157	95	10	𝜐𝑟	𝜐𝑟	NOUN
cana-6157	95	11	)	)	PUNCT
cana-6157	95	12	𝑇reprents	𝑇reprent	VERB
cana-6157	95	13	the	the	DET
cana-6157	95	14	frequencies	frequency	NOUN
cana-6157	95	15	of	of	ADP
cana-6157	95	16	these	these	DET
cana-6157	95	17	classes	class	NOUN
cana-6157	95	18	,	,	PUNCT
cana-6157	95	19	s	s	VERB
cana-6157	95	20	the	the	DET
cana-6157	95	21	number	number	NOUN
cana-6157	95	22	of	of	ADP
cana-6157	95	23	estimated	estimate	VERB
cana-6157	95	24	parameters	parameter	NOUN
cana-6157	95	25	,	,	PUNCT
cana-6157	95	26	i(θ	i(θ	PROPN
cana-6157	95	27	)	)	PUNCT
cana-6157	95	28	and	and	CCONJ
cana-6157	95	29	j(θ	j(θ	PROPN
cana-6157	95	30	)	)	PUNCT
cana-6157	95	31	are	be	AUX
cana-6157	95	32	the	the	DET
cana-6157	95	33	estimated	estimate	VERB
cana-6157	95	34	information	information	NOUN
cana-6157	95	35	matrices	matrix	NOUN
cana-6157	95	36	on	on	ADP
cana-6157	95	37	non	non	ADJ
cana-6157	95	38	-	-	ADJ
cana-6157	95	39	grouped	grouped	ADJ
cana-6157	95	40	and	and	CCONJ
cana-6157	95	41	grouped	group	VERB
cana-6157	95	42	data	datum	NOUN
cana-6157	95	43	,	,	PUNCT
cana-6157	95	44	and	and	CCONJ
cana-6157	95	45	:	:	PUNCT
cana-6157	95	46	𝑋𝑛(𝜃	𝑋𝑛(𝜃	X
cana-6157	95	47	)	)	PUNCT
cana-6157	95	48	=	=	SYM
cana-6157	95	49	(	(	PUNCT
cana-6157	95	50	𝜐1−𝑛𝑝1(𝜃	𝜐1−𝑛𝑝1(𝜃	NOUN
cana-6157	95	51	)	)	PUNCT
cana-6157	95	52	√𝑛𝑝1(𝜃	√𝑛𝑝1(𝜃	ADJ
cana-6157	95	53	)	)	PUNCT
cana-6157	95	54	,	,	PUNCT
cana-6157	95	55	…	…	PUNCT
cana-6157	95	56	,	,	PUNCT
cana-6157	95	57	𝜐𝑟−𝑛𝑝𝑟(𝜃	𝜐𝑟−𝑛𝑝𝑟(𝜃	NOUN
cana-6157	95	58	)	)	PUNCT
cana-6157	95	59	√𝑛𝑝𝑟(𝜃	√𝑛𝑝𝑟(𝜃	PROPN
cana-6157	95	60	)	)	PUNCT
cana-6157	95	61	)	)	PUNCT
cana-6157	96	1	𝑇	𝑇	PROPN
cana-6157	96	2	     	     	SPACE
cana-6157	96	3	;	;	PUNCT
cana-6157	96	4	  	  	SPACE
cana-6157	96	5	\	\	NOUN
cana-6157	96	6	   	   	SPACE
cana-6157	96	7	𝐿(𝜃	𝐿(𝜃	PROPN
cana-6157	96	8	)	)	PUNCT
cana-6157	96	9	=	=	SYM
cana-6157	96	10	(	(	PUNCT
cana-6157	96	11	𝐿1	𝐿1	PROPN
cana-6157	96	12	,	,	PUNCT
cana-6157	96	13	…	…	PUNCT
cana-6157	96	14	,	,	PUNCT
cana-6157	96	15	𝐿𝑖	𝐿𝑖	PROPN
cana-6157	96	16	)	)	PUNCT
cana-6157	96	17	𝑇	𝑇	PROPN
cana-6157	96	18	;	;	PUNCT
cana-6157	96	19	      	      	SPACE
cana-6157	96	20	(	(	PUNCT
cana-6157	96	21	13	13	NUM
cana-6157	96	22	)	)	PUNCT
cana-6157	96	23	  	  	SPACE
cana-6157	96	24	𝐿𝑖(𝜃	𝐿𝑖(𝜃	NOUN
cana-6157	96	25	)	)	PUNCT
cana-6157	96	26	=	=	NOUN
cana-6157	96	27	∑	∑	PUNCT
cana-6157	96	28	𝜐𝑗	𝜐𝑗	VERB
cana-6157	96	29	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	96	30	𝜕𝑃𝑗	𝜕𝑃𝑗	NOUN
cana-6157	96	31	𝜕𝜃𝑖	𝜕𝜃𝑖	NOUN
cana-6157	96	32	(	(	PUNCT
cana-6157	96	33	𝜃	𝜃	X
cana-6157	96	34	)	)	PUNCT
cana-6157	96	35	𝑟	𝑟	NOUN
cana-6157	96	36	𝑗=1	𝑗=1	SYM
cana-6157	96	37	   	   	SPACE
cana-6157	96	38	𝑖	𝑖	SYM
cana-6157	97	1	=	=	NOUN
cana-6157	97	2	1	1	NUM
cana-6157	97	3	,	,	PUNCT
cana-6157	97	4	…	…	PUNCT
cana-6157	97	5	𝑠	𝑠	INTJ
cana-6157	97	6	and	and	CCONJ
cana-6157	97	7	𝑃(𝜃	𝑃(𝜃	NOUN
cana-6157	97	8	)	)	PUNCT
cana-6157	97	9	=	=	SYM
cana-6157	97	10	(	(	PUNCT
cana-6157	97	11	𝑃1(𝜃	𝑃1(𝜃	PROPN
cana-6157	97	12	)	)	PUNCT
cana-6157	97	13	,	,	PUNCT
cana-6157	97	14	𝑃2(𝜃	𝑃2(𝜃	PROPN
cana-6157	97	15	)	)	PUNCT
cana-6157	97	16	,	,	PUNCT
cana-6157	97	17	…	…	PUNCT
cana-6157	97	18	,	,	PUNCT
cana-6157	97	19	𝑃𝑟(𝜃	𝑃𝑟(𝜃	PROPN
cana-6157	97	20	)	)	PUNCT
cana-6157	97	21	)	)	PUNCT
cana-6157	98	1	𝑇	𝑇	PROPN
cana-6157	98	2	  	  	SPACE
cana-6157	98	3	𝑊ℎ𝑒𝑟𝑒𝑃𝑗(𝜃	𝑊ℎ𝑒𝑟𝑒𝑃𝑗(𝜃	NOUN
cana-6157	98	4	)	)	PUNCT
cana-6157	98	5	=	=	SYM
cana-6157	98	6	∫	∫	PROPN
cana-6157	99	1	𝑓(𝑡	𝑓(𝑡	PROPN
cana-6157	99	2	;	;	PUNCT
cana-6157	99	3	𝜃)𝑑𝑡	𝜃)𝑑𝑡	PROPN
cana-6157	99	4	𝛥𝑗	𝛥𝑗	PROPN
cana-6157	99	5	    	    	SPACE
cana-6157	99	6	𝑗	𝑗	NOUN
cana-6157	99	7	=	=	ADJ
cana-6157	99	8	1	1	NUM
cana-6157	99	9	,	,	PUNCT
cana-6157	99	10	…	…	PUNCT
cana-6157	99	11	,	,	PUNCT
cana-6157	99	12	𝑟	𝑟	X
cana-6157	99	13	𝐽(𝜃	𝐽(𝜃	NOUN
cana-6157	99	14	)	)	PUNCT
cana-6157	99	15	=	=	NOUN
cana-6157	99	16	𝐵(𝜃)𝑇	𝐵(𝜃)𝑇	X
cana-6157	99	17	.	.	PUNCT
cana-6157	100	1	𝐵(𝜃	𝐵(𝜃	NUM
cana-6157	100	2	)	)	PUNCT
cana-6157	100	3	,	,	PUNCT
cana-6157	100	4	    	    	SPACE
cana-6157	100	5	with	with	ADP
cana-6157	100	6	        	        	SPACE
cana-6157	100	7	𝑏𝑗𝑖(𝜃	𝑏𝑗𝑖(𝜃	PROPN
cana-6157	100	8	)	)	PUNCT
cana-6157	100	9	=	=	PUNCT
cana-6157	100	10	1	1	NUM
cana-6157	100	11	√𝑃𝑗	√𝑃𝑗	PROPN
cana-6157	100	12	.	.	PUNCT
cana-6157	101	1	𝜕𝑃𝑗(𝜃	𝜕𝑃𝑗(𝜃	ADJ
cana-6157	101	2	)	)	PUNCT
cana-6157	101	3	𝜕𝜃𝑖	𝜕𝜃𝑖	PUNCT
cana-6157	101	4	;	;	PUNCT
cana-6157	101	5	    	    	SPACE
cana-6157	101	6	𝑗	𝑗	PROPN
cana-6157	101	7	=	=	ADJ
cana-6157	101	8	1	1	NUM
cana-6157	101	9	,	,	PUNCT
cana-6157	101	10	…	…	PUNCT
cana-6157	101	11	,	,	PUNCT
cana-6157	101	12	𝑟	𝑟	NOUN
cana-6157	101	13	;	;	PUNCT
cana-6157	101	14	 	 	SPACE
cana-6157	101	15	𝑖	𝑖	SYM
cana-6157	101	16	=	=	NOUN
cana-6157	101	17	1	1	NUM
cana-6157	101	18	,	,	PUNCT
cana-6157	101	19	…	…	PUNCT
cana-6157	101	20	,	,	PUNCT
cana-6157	101	21	𝑠	𝑠	PROPN
cana-6157	101	22	under	under	ADP
cana-6157	101	23	𝐻0	𝐻0	PROPN
cana-6157	101	24	the	the	DET
cana-6157	101	25	statistic	statistic	ADJ
cana-6157	101	26	𝑌2	𝑌2	NOUN
cana-6157	101	27	follows	follow	VERB
cana-6157	101	28	the	the	DET
cana-6157	101	29	chi	chi	ADJ
cana-6157	101	30	-	-	PUNCT
cana-6157	101	31	square	square	ADJ
cana-6157	101	32	distribution	distribution	NOUN
cana-6157	101	33	with	with	ADP
cana-6157	101	34	r-1	r-1	ADJ
cana-6157	101	35	degrees	degree	NOUN
cana-6157	101	36	of	of	ADP
cana-6157	101	37	freedom	freedom	NOUN
cana-6157	101	38	.	.	PUNCT
cana-6157	102	1	construction	construction	NOUN
cana-6157	102	2	of	of	ADP
cana-6157	102	3	statistic	statistic	ADJ
cana-6157	102	4	test	test	NOUN
cana-6157	102	5	for	for	ADP
cana-6157	102	6	aptee	aptee	ADJ
cana-6157	102	7	distribution	distribution	NOUN
cana-6157	102	8	to	to	PART
cana-6157	102	9	verify	verify	VERB
cana-6157	102	10	if	if	SCONJ
cana-6157	102	11	the	the	DET
cana-6157	102	12	sample	sample	NOUN
cana-6157	102	13	𝑇	𝑇	PROPN
cana-6157	102	14	=	=	SYM
cana-6157	102	15	(	(	PUNCT
cana-6157	102	16	𝑡1	𝑡1	PROPN
cana-6157	102	17	,	,	PUNCT
cana-6157	102	18	…	…	PUNCT
cana-6157	102	19	,	,	PUNCT
cana-6157	102	20	𝑡𝑛	𝑡𝑛	NOUN
cana-6157	102	21	)	)	PUNCT
cana-6157	102	22	𝑇belongs	𝑇belong	NOUN
cana-6157	102	23	to	to	ADP
cana-6157	102	24	the	the	DET
cana-6157	102	25	aptee	aptee	ADJ
cana-6157	102	26	distribution	distribution	NOUN
cana-6157	102	27	faptee(t	faptee(t	PROPN
cana-6157	102	28	;	;	PUNCT
cana-6157	102	29	θ	θ	PROPN
cana-6157	102	30	):	):	PUNCT
cana-6157	102	31	𝑃(𝑇𝑗	𝑃(𝑇𝑗	NOUN
cana-6157	102	32	≤	≤	NUM
cana-6157	102	33	𝑡	𝑡	PROPN
cana-6157	102	34	∣∣	∣∣	PROPN
cana-6157	102	35	𝐻0	𝐻0	PROPN
cana-6157	102	36	)	)	PUNCT
cana-6157	102	37	=	=	SYM
cana-6157	102	38	𝐹𝐴𝑃𝑇𝐸𝐸(𝑡	𝐹𝐴𝑃𝑇𝐸𝐸(𝑡	NOUN
cana-6157	102	39	;	;	PUNCT
cana-6157	102	40	𝜃	𝜃	X
cana-6157	102	41	)	)	PUNCT
cana-6157	102	42	,	,	PUNCT
cana-6157	102	43	   	   	SPACE
cana-6157	102	44	𝑡	𝑡	PROPN
cana-6157	102	45	≥	≥	NOUN
cana-6157	102	46	0	0	NUM
cana-6157	102	47	,	,	PUNCT
cana-6157	102	48	       	       	SPACE
cana-6157	102	49	with	with	ADP
cana-6157	102	50	              	              	SPACE
cana-6157	102	51	𝜃	𝜃	NOUN
cana-6157	102	52	=	=	PUNCT
cana-6157	102	53	(	(	PUNCT
cana-6157	102	54	𝛼	𝛼	PROPN
cana-6157	102	55	,	,	PUNCT
cana-6157	102	56	𝛽	𝛽	NOUN
cana-6157	102	57	,	,	PUNCT
cana-6157	102	58	𝜆)𝑇	𝜆)𝑇	X
cana-6157	102	59	,	,	PUNCT
cana-6157	102	60	firstly	firstly	ADV
cana-6157	102	61	,	,	PUNCT
cana-6157	102	62	we	we	PRON
cana-6157	102	63	calculate	calculate	VERB
cana-6157	102	64	the	the	DET
cana-6157	102	65	ml	ml	NOUN
cana-6157	102	66	estimators	estimator	NOUN
cana-6157	102	67	of	of	ADP
cana-6157	102	68	the	the	DET
cana-6157	102	69	unknown	unknown	ADJ
cana-6157	102	70	parameters	parameter	NOUN
cana-6157	102	71	.	.	PUNCT
cana-6157	103	1	for	for	ADP
cana-6157	103	2	this	this	DET
cana-6157	103	3	statistic	statistic	NOUN
cana-6157	103	4	,	,	PUNCT
cana-6157	103	5	the	the	DET
cana-6157	103	6	r	r	NOUN
cana-6157	103	7	grouped	group	VERB
cana-6157	103	8	classes	class	NOUN
cana-6157	103	9	δ	δ	PROPN
cana-6157	103	10	 	 	SPACE
cana-6157	103	11	𝑗	𝑗	VERB
cana-6157	103	12	   	   	SPACE
cana-6157	103	13	must	must	AUX
cana-6157	103	14	be	be	AUX
cana-6157	103	15	equiprobable	equiprobable	ADJ
cana-6157	103	16	which	which	PRON
cana-6157	103	17	means	mean	VERB
cana-6157	103	18	p1	p1	NOUN
cana-6157	103	19	=	=	NOUN
cana-6157	103	20	p2	p2	PROPN
cana-6157	103	21	=	=	SYM
cana-6157	103	22	⋯	⋯	NOUN
cana-6157	103	23	=	=	NOUN
cana-6157	103	24	pr	pr	NOUN
cana-6157	103	25	=	=	SYM
cana-6157	103	26	1	1	NUM
cana-6157	103	27	r	r	NOUN
cana-6157	103	28	.	.	PUNCT
cana-6157	104	1	in	in	ADP
cana-6157	104	2	this	this	DET
cana-6157	104	3	case	case	NOUN
cana-6157	104	4	the	the	DET
cana-6157	104	5	limits	limit	NOUN
cana-6157	104	6	𝑎𝑗	𝑎𝑗	ADP
cana-6157	104	7	   	   	SPACE
cana-6157	104	8	of	of	ADP
cana-6157	104	9	the	the	DET
cana-6157	104	10	classes	class	NOUN
cana-6157	104	11	  	  	SPACE
cana-6157	104	12	δ	δ	PROPN
cana-6157	104	13	 	 	SPACE
cana-6157	104	14	j	j	PROPN
cana-6157	105	1	=	=	PUNCT
cana-6157	106	1	[	[	AUX
cana-6157	106	2	aj−1	aj−1	NOUN
cana-6157	106	3	   	   	SPACE
cana-6157	106	4	,	,	PUNCT
cana-6157	106	5	aj	aj	PROPN
cana-6157	106	6	 	 	SPACE
cana-6157	106	7	[	[	PUNCT
cana-6157	106	8	are	be	AUX
cana-6157	106	9	obtained	obtain	VERB
cana-6157	106	10	by	by	ADP
cana-6157	106	11	:	:	PUNCT
cana-6157	106	12	communications	communication	NOUN
cana-6157	106	13	on	on	ADP
cana-6157	106	14	applied	apply	VERB
cana-6157	106	15	nonlinear	nonlinear	ADJ
cana-6157	106	16	analysis	analysis	NOUN
cana-6157	106	17	issn	issn	NOUN
cana-6157	106	18	:	:	PUNCT
cana-6157	106	19	1074	1074	NUM
cana-6157	106	20	-	-	PUNCT
cana-6157	106	21	133x	133x	NUM
cana-6157	106	22	vol	vol	VERB
cana-6157	106	23	32	32	NUM
cana-6157	106	24	no	no	NOUN
cana-6157	106	25	.	.	PUNCT
cana-6157	107	1	10s	10	NOUN
cana-6157	107	2	(	(	PUNCT
cana-6157	107	3	2025	2025	NUM
cana-6157	107	4	)	)	PUNCT
cana-6157	107	5	3486	3486	NUM
cana-6157	107	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	107	7	𝑎𝑗	𝑎𝑗	PROPN
cana-6157	107	8	=	=	PUNCT
cana-6157	107	9	𝐹𝐴𝑃𝑇𝐸𝐸	𝐹𝐴𝑃𝑇𝐸𝐸	PROPN
cana-6157	107	10	−1	−1	NOUN
cana-6157	107	11	(	(	PUNCT
cana-6157	107	12	𝑗	𝑗	NOUN
cana-6157	107	13	𝑟	𝑟	NOUN
cana-6157	107	14	)	)	PUNCT
cana-6157	107	15	=	=	PUNCT
cana-6157	108	1	[	[	X
cana-6157	108	2	𝑙𝑜𝑔	𝑙𝑜𝑔	X
cana-6157	108	3	(	(	PUNCT
cana-6157	108	4	1	1	NUM
cana-6157	108	5	−	−	NOUN
cana-6157	108	6	{	{	PUNCT
cana-6157	108	7	𝑙𝑜𝑔[(𝛼−1	𝑙𝑜𝑔[(𝛼−1	NOUN
cana-6157	108	8	)	)	PUNCT
cana-6157	108	9	]	]	PUNCT
cana-6157	108	10	(	(	PUNCT
cana-6157	108	11	𝑗	𝑗	INTJ
cana-6157	108	12	𝑟	𝑟	NOUN
cana-6157	108	13	)	)	PUNCT
cana-6157	108	14	+1	+1	PROPN
cana-6157	108	15	𝑙𝑜𝑔(𝛼	𝑙𝑜𝑔(𝛼	PROPN
cana-6157	108	16	)	)	PUNCT
cana-6157	108	17	}	}	PUNCT
cana-6157	108	18	1	1	NUM
cana-6157	108	19	𝛽	𝛽	NOUN
cana-6157	108	20	)	)	PUNCT
cana-6157	108	21	]	]	PUNCT
cana-6157	109	1	−	−	PROPN
cana-6157	109	2	1	1	NUM
cana-6157	109	3	𝜆	𝜆	X
cana-6157	109	4	                        	                        	SPACE
cana-6157	109	5	𝑗	𝑗	NOUN
cana-6157	109	6	=	=	ADJ
cana-6157	109	7	1	1	NUM
cana-6157	109	8	,	,	PUNCT
cana-6157	109	9	…	…	PUNCT
cana-6157	109	10	,	,	PUNCT
cana-6157	109	11	𝑟	𝑟	X
cana-6157	109	12	−	−	PROPN
cana-6157	109	13	1(14	1(14	NUM
cana-6157	109	14	)	)	PUNCT
cana-6157	109	15	and	and	CCONJ
cana-6157	109	16	𝑃𝑗(	𝑃𝑗(	PART
cana-6157	109	17	�	�	NOUN
cana-6157	109	18	̂	̂	VERB
cana-6157	109	19	�	�	NOUN
cana-6157	109	20	)	)	PUNCT
cana-6157	109	21	=	=	PUNCT
cana-6157	109	22	(	(	PUNCT
cana-6157	109	23	𝛼	𝛼	NOUN
cana-6157	109	24	1−𝑒𝑥𝑝(1−(1+𝜆𝑎𝑗	1−𝑒𝑥𝑝(1−(1+𝜆𝑎𝑗	NUM
cana-6157	109	25	)	)	PUNCT
cana-6157	109	26	𝛽	𝛽	NOUN
cana-6157	109	27	)	)	PUNCT
cana-6157	109	28	−1	−1	NOUN
cana-6157	109	29	𝛼−1	𝛼−1	NOUN
cana-6157	109	30	)	)	PUNCT
cana-6157	109	31	−	−	PROPN
cana-6157	110	1	(	(	PUNCT
cana-6157	110	2	𝛼	𝛼	PROPN
cana-6157	110	3	1−𝑒𝑥𝑝(1−(1+𝜆𝑎𝑗−1	1−𝑒𝑥𝑝(1−(1+𝜆𝑎𝑗−1	PROPN
cana-6157	110	4	)	)	PUNCT
cana-6157	110	5	𝛽	𝛽	NOUN
cana-6157	110	6	)	)	PUNCT
cana-6157	110	7	−1	−1	NOUN
cana-6157	110	8	𝛼−1	𝛼−1	NOUN
cana-6157	110	9	)	)	PUNCT
cana-6157	110	10	       	       	SPACE
cana-6157	110	11	with	with	ADP
cana-6157	110	12	𝑗	𝑗	PROPN
cana-6157	110	13	=	=	SYM
cana-6157	110	14	1	1	NUM
cana-6157	110	15	,	,	PUNCT
cana-6157	110	16	…	…	PUNCT
cana-6157	110	17	.	.	PUNCT
cana-6157	111	1	,	,	PUNCT
cana-6157	111	2	𝑟(15	𝑟(15	NOUN
cana-6157	111	3	)	)	PUNCT
cana-6157	111	4	to	to	PART
cana-6157	111	5	provide	provide	VERB
cana-6157	111	6	the	the	DET
cana-6157	111	7	criteria	criterion	NOUN
cana-6157	111	8	statistic	statistic	VERB
cana-6157	111	9	𝑌2for	𝑌2for	PROPN
cana-6157	111	10	fitting	fit	VERB
cana-6157	111	11	the	the	DET
cana-6157	111	12	𝐹𝐴𝑃𝑇𝐸𝐸(𝑡	𝐹𝐴𝑃𝑇𝐸𝐸(𝑡	NOUN
cana-6157	111	13	;	;	PUNCT
cana-6157	111	14	𝜃	𝜃	X
cana-6157	111	15	)	)	PUNCT
cana-6157	111	16	 	 	SPACE
cana-6157	111	17	distribution	distribution	NOUN
cana-6157	111	18	,	,	PUNCT
cana-6157	111	19	we	we	PRON
cana-6157	111	20	need	need	VERB
cana-6157	111	21	both	both	PRON
cana-6157	111	22	of	of	ADP
cana-6157	111	23	the	the	DET
cana-6157	111	24	estimated	estimate	VERB
cana-6157	111	25	information	information	NOUN
cana-6157	111	26	estimation	estimation	NOUN
cana-6157	111	27	matrices	matrix	NOUN
cana-6157	111	28	𝐽(θ̂)𝑎𝑛𝑑𝐼(θ̂	𝐽(θ̂)𝑎𝑛𝑑𝐼(θ̂	NOUN
cana-6157	111	29	)	)	PUNCT
cana-6157	111	30	for	for	ADP
cana-6157	111	31	grouped	group	VERB
cana-6157	111	32	and	and	CCONJ
cana-6157	111	33	non	non	ADJ
cana-6157	111	34	-	-	ADJ
cana-6157	111	35	grouped	group	VERB
cana-6157	111	36	data	datum	NOUN
cana-6157	111	37	.	.	PUNCT
cana-6157	112	1	ii	ii	PROPN
cana-6157	112	2	.	.	PUNCT
cana-6157	113	1	estimated	estimate	VERB
cana-6157	113	2	information	information	NOUN
cana-6157	113	3	matrix	matrix	NOUN
cana-6157	113	4	𝑱(	𝑱(	X
cana-6157	113	5	�	�	PROPN
cana-6157	113	6	̂	̂	VERB
cana-6157	113	7	�	�	PROPN
cana-6157	113	8	)	)	PUNCT
cana-6157	113	9	the	the	DET
cana-6157	113	10	components	component	NOUN
cana-6157	113	11	of	of	ADP
cana-6157	113	12	the	the	DET
cana-6157	113	13	estimated	estimate	VERB
cana-6157	113	14	symmetric	symmetric	ADJ
cana-6157	113	15	matrix	matrix	NOUN
cana-6157	113	16	𝐽(	𝐽(	X
cana-6157	113	17	�	�	PROPN
cana-6157	113	18	̂	̂	NOUN
cana-6157	113	19	�	�	PROPN
cana-6157	113	20	)for	)for	PUNCT
cana-6157	113	21	the	the	DET
cana-6157	113	22	grouped	group	VERB
cana-6157	113	23	data	data	PROPN
cana-6157	113	24	𝐽11(	𝐽11(	PROPN
cana-6157	113	25	�	�	PROPN
cana-6157	113	26	̂	̂	NOUN
cana-6157	113	27	�	�	NOUN
cana-6157	113	28	)	)	PUNCT
cana-6157	114	1	=	=	NOUN
cana-6157	114	2	∑	∑	PROPN
cana-6157	114	3	1	1	NUM
cana-6157	114	4	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	114	5	(	(	PUNCT
cana-6157	114	6	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	114	7	𝜕	𝜕	PROPN
cana-6157	114	8	�	�	PROPN
cana-6157	114	9	̂	̂	NUM
cana-6157	114	10	�	�	PROPN
cana-6157	114	11	)	)	PUNCT
cana-6157	114	12	2𝑟	2𝑟	PROPN
cana-6157	114	13	𝑗=1	𝑗=1	PROPN
cana-6157	114	14	;	;	PUNCT
cana-6157	114	15	𝐽22(	𝐽22(	NUM
cana-6157	114	16	�	�	NOUN
cana-6157	114	17	̂	̂	SYM
cana-6157	114	18	�	�	NOUN
cana-6157	114	19	)	)	PUNCT
cana-6157	115	1	=	=	NOUN
cana-6157	115	2	∑	∑	PROPN
cana-6157	115	3	1	1	NUM
cana-6157	115	4	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	115	5	(	(	PUNCT
cana-6157	115	6	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	115	7	𝜕	𝜕	PROPN
cana-6157	115	8	�	�	PROPN
cana-6157	115	9	̂	̂	NUM
cana-6157	115	10	�	�	PROPN
cana-6157	115	11	)	)	PUNCT
cana-6157	115	12	2𝑟	2𝑟	PROPN
cana-6157	115	13	𝑗=1	𝑗=1	PART
cana-6157	115	14	𝐽33(	𝐽33(	PROPN
cana-6157	115	15	�	�	PROPN
cana-6157	115	16	̂	̂	NOUN
cana-6157	115	17	�	�	NOUN
cana-6157	115	18	)	)	PUNCT
cana-6157	115	19	=	=	PUNCT
cana-6157	115	20	∑	∑	PUNCT
cana-6157	115	21	1	1	NUM
cana-6157	115	22	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	115	23	(	(	PUNCT
cana-6157	115	24	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	115	25	𝜕	𝜕	PROPN
cana-6157	115	26	�	�	PROPN
cana-6157	115	27	̂	̂	NUM
cana-6157	115	28	�	�	PROPN
cana-6157	115	29	)	)	PUNCT
cana-6157	115	30	2𝑟	2𝑟	NUM
cana-6157	115	31	𝑗=1	𝑗=1	PUNCT
cana-6157	115	32	𝐽12	𝐽12	PUNCT
cana-6157	116	1	=	=	PUNCT
cana-6157	116	2	𝐽21	𝐽21	NOUN
cana-6157	116	3	=	=	SYM
cana-6157	116	4	∑	∑	PROPN
cana-6157	116	5	1	1	NUM
cana-6157	116	6	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	116	7	(	(	PUNCT
cana-6157	116	8	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	9	𝜕	𝜕	PROPN
cana-6157	116	10	�	�	PROPN
cana-6157	116	11	̂	̂	NUM
cana-6157	116	12	�	�	PROPN
cana-6157	116	13	)	)	PUNCT
cana-6157	116	14	(	(	PUNCT
cana-6157	116	15	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	16	𝜕	𝜕	PROPN
cana-6157	116	17	�	�	PROPN
cana-6157	116	18	̂	̂	NUM
cana-6157	116	19	�	�	PROPN
cana-6157	116	20	)	)	PUNCT
cana-6157	116	21	𝑟	𝑟	NOUN
cana-6157	116	22	𝑗=1	𝑗=1	NOUN
cana-6157	116	23	;	;	PUNCT
cana-6157	116	24	𝐽13	𝐽13	PROPN
cana-6157	116	25	=	=	SYM
cana-6157	116	26	𝐽31	𝐽31	PROPN
cana-6157	116	27	=	=	SYM
cana-6157	116	28	∑	∑	PROPN
cana-6157	116	29	1	1	NUM
cana-6157	116	30	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	116	31	(	(	PUNCT
cana-6157	116	32	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	33	𝜕	𝜕	PROPN
cana-6157	116	34	�	�	PROPN
cana-6157	116	35	̂	̂	NUM
cana-6157	116	36	�	�	PROPN
cana-6157	116	37	)	)	PUNCT
cana-6157	116	38	(	(	PUNCT
cana-6157	116	39	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	40	𝜕	𝜕	PROPN
cana-6157	116	41	�	�	PROPN
cana-6157	116	42	̂	̂	NUM
cana-6157	116	43	�	�	PROPN
cana-6157	116	44	)	)	PUNCT
cana-6157	116	45	𝑟	𝑟	NOUN
cana-6157	116	46	𝑗=1	𝑗=1	PUNCT
cana-6157	116	47	𝐽23	𝐽23	PROPN
cana-6157	116	48	=	=	PUNCT
cana-6157	116	49	𝐽32	𝐽32	PUNCT
cana-6157	116	50	=	=	SYM
cana-6157	116	51	∑	∑	PROPN
cana-6157	116	52	1	1	NUM
cana-6157	116	53	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	116	54	(	(	PUNCT
cana-6157	116	55	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	56	𝜕	𝜕	PROPN
cana-6157	116	57	�	�	PROPN
cana-6157	116	58	̂	̂	NUM
cana-6157	116	59	�	�	PROPN
cana-6157	116	60	)	)	PUNCT
cana-6157	116	61	(	(	PUNCT
cana-6157	116	62	𝜕𝑃𝑗	𝜕𝑃𝑗	PROPN
cana-6157	116	63	𝜕	𝜕	PROPN
cana-6157	116	64	�	�	PROPN
cana-6157	116	65	̂	̂	NUM
cana-6157	116	66	�	�	PROPN
cana-6157	116	67	)	)	PUNCT
cana-6157	116	68	𝑟	𝑟	NOUN
cana-6157	116	69	𝑗=1	𝑗=1	PROPN
cana-6157	116	70	can	can	AUX
cana-6157	116	71	be	be	AUX
cana-6157	116	72	derived	derive	VERB
cana-6157	116	73	from	from	ADP
cana-6157	116	74	the	the	DET
cana-6157	116	75	following	follow	VERB
cana-6157	116	76	partial	partial	ADJ
cana-6157	116	77	derivatives	derivative	NOUN
cana-6157	116	78	𝜕𝑃𝑗(	𝜕𝑃𝑗(	NUM
cana-6157	116	79	�	�	NOUN
cana-6157	116	80	̂	̂	SYM
cana-6157	116	81	�	�	PROPN
cana-6157	116	82	)	)	PUNCT
cana-6157	116	83	𝜕	𝜕	PROPN
cana-6157	116	84	�	�	PROPN
cana-6157	116	85	̂	̂	NUM
cana-6157	116	86	�	�	NOUN
cana-6157	116	87	=	=	SYM
cana-6157	116	88	(	(	PUNCT
cana-6157	116	89	𝑙𝑛	𝑙𝑛	X
cana-6157	116	90	�	�	PROPN
cana-6157	116	91	̂	̂	PROPN
cana-6157	116	92	�	�	PROPN
cana-6157	116	93	(	(	PUNCT
cana-6157	116	94	1	1	NUM
cana-6157	116	95	−	−	NOUN
cana-6157	116	96	𝑒𝑥𝑝	𝑒𝑥𝑝	INTJ
cana-6157	116	97	(	(	PUNCT
cana-6157	116	98	1	1	NUM
cana-6157	116	99	−	−	PROPN
cana-6157	116	100	(	(	PUNCT
cana-6157	116	101	1	1	NUM
cana-6157	116	102	+	+	NUM
cana-6157	116	103	�	�	PROPN
cana-6157	116	104	̂	̂	NOUN
cana-6157	116	105	�	�	NOUN
cana-6157	116	106	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	116	107	)	)	PUNCT
cana-6157	116	108	�	�	PROPN
cana-6157	116	109	̂	̂	PROPN
cana-6157	116	110	�	�	PROPN
cana-6157	116	111	)	)	PUNCT
cana-6157	116	112	)	)	PUNCT
cana-6157	117	1	(	(	PUNCT
cana-6157	117	2	𝛼	𝛼	PROPN
cana-6157	117	3	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	117	4	�	�	SYM
cana-6157	117	5	̂	̂	NOUN
cana-6157	117	6	�	�	NOUN
cana-6157	117	7	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	117	8	)	)	PUNCT
cana-6157	117	9	�	�	PROPN
cana-6157	117	10	̂	̂	PROPN
cana-6157	117	11	�	�	PROPN
cana-6157	117	12	)	)	PUNCT
cana-6157	117	13	̂	̂	X
cana-6157	117	14	−1	−1	NOUN
cana-6157	117	15	)	)	PUNCT
cana-6157	117	16	)	)	PUNCT
cana-6157	117	17	(	(	PUNCT
cana-6157	117	18	�	�	NOUN
cana-6157	117	19	̂	̂	SYM
cana-6157	117	20	�	�	NOUN
cana-6157	117	21	−	−	PROPN
cana-6157	117	22	1)2	1)2	NUM
cana-6157	117	23	−	−	PROPN
cana-6157	117	24	(	(	PUNCT
cana-6157	117	25	𝑙𝑛	𝑙𝑛	X
cana-6157	117	26	�	�	PROPN
cana-6157	117	27	̂	̂	PROPN
cana-6157	117	28	�	�	PROPN
cana-6157	117	29	(1−𝑒𝑥𝑝(1−(1+	(1−𝑒𝑥𝑝(1−(1+	SYM
cana-6157	117	30	�	�	PROPN
cana-6157	117	31	̂	̂	NOUN
cana-6157	117	32	�	�	NOUN
cana-6157	117	33	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	117	34	)	)	PUNCT
cana-6157	117	35	�	�	PROPN
cana-6157	117	36	̂	̂	NUM
cana-6157	117	37	�	�	PROPN
cana-6157	117	38	)	)	PUNCT
cana-6157	117	39	)	)	PUNCT
cana-6157	118	1	(	(	PUNCT
cana-6157	118	2	𝛼	𝛼	PROPN
cana-6157	118	3	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	118	4	�	�	SYM
cana-6157	118	5	̂	̂	NOUN
cana-6157	118	6	�	�	NOUN
cana-6157	118	7	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	118	8	)	)	PUNCT
cana-6157	118	9	�	�	PROPN
cana-6157	118	10	̂	̂	SYM
cana-6157	118	11	�	�	PROPN
cana-6157	118	12	)	)	PUNCT
cana-6157	118	13	̂	̂	X
cana-6157	118	14	−1	−1	NOUN
cana-6157	118	15	)	)	PUNCT
cana-6157	118	16	)	)	PUNCT
cana-6157	118	17	(	(	PUNCT
cana-6157	118	18	�	�	NOUN
cana-6157	118	19	̂	̂	SYM
cana-6157	118	20	�	�	NOUN
cana-6157	118	21	−1)2	−1)2	X
cana-6157	118	22	(	(	PUNCT
cana-6157	118	23	16	16	NUM
cana-6157	118	24	)	)	PUNCT
cana-6157	118	25	𝜕𝑃𝑗(	𝜕𝑃𝑗(	NUM
cana-6157	118	26	�	�	NOUN
cana-6157	118	27	̂	̂	SYM
cana-6157	118	28	�	�	PROPN
cana-6157	118	29	)	)	PUNCT
cana-6157	118	30	𝜕	𝜕	PROPN
cana-6157	118	31	�	�	PROPN
cana-6157	118	32	̂	̂	NUM
cana-6157	118	33	�	�	NOUN
cana-6157	118	34	=	=	SYM
cana-6157	118	35	(	(	PUNCT
cana-6157	118	36	(	(	PUNCT
cana-6157	118	37	1+	1+	NUM
cana-6157	118	38	�	�	NOUN
cana-6157	118	39	̂	̂	NUM
cana-6157	118	40	�	�	NOUN
cana-6157	118	41	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	42	)	)	PUNCT
cana-6157	118	43	�	�	PROPN
cana-6157	118	44	̂	̂	VERB
cana-6157	118	45	�	�	PROPN
cana-6157	118	46	𝑙𝑛(1+	𝑙𝑛(1+	SYM
cana-6157	118	47	�	�	PROPN
cana-6157	118	48	̂	̂	NUM
cana-6157	118	49	�	�	NOUN
cana-6157	118	50	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	51	)	)	PUNCT
cana-6157	118	52	(	(	PUNCT
cana-6157	118	53	𝛼	𝛼	PROPN
cana-6157	118	54	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	118	55	�	�	SYM
cana-6157	118	56	̂	̂	NOUN
cana-6157	118	57	�	�	NOUN
cana-6157	118	58	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	59	)	)	PUNCT
cana-6157	118	60	�	�	PROPN
cana-6157	118	61	̂	̂	PROPN
cana-6157	118	62	�	�	PROPN
cana-6157	118	63	)	)	PUNCT
cana-6157	118	64	̂	̂	X
cana-6157	118	65	)	)	PUNCT
cana-6157	118	66	(	(	PUNCT
cana-6157	118	67	−𝑒𝑥𝑝(1−(1+	−𝑒𝑥𝑝(1−(1+	PROPN
cana-6157	118	68	�	�	PROPN
cana-6157	118	69	̂	̂	PROPN
cana-6157	118	70	�	�	PROPN
cana-6157	118	71	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	72	)	)	PUNCT
cana-6157	118	73	�	�	PROPN
cana-6157	118	74	̂	̂	PROPN
cana-6157	118	75	�	�	PROPN
cana-6157	118	76	)	)	PUNCT
cana-6157	118	77	)	)	PUNCT
cana-6157	118	78	)	)	PUNCT
cana-6157	118	79	(	(	PUNCT
cana-6157	118	80	�	�	NOUN
cana-6157	118	81	̂	̂	SYM
cana-6157	118	82	�	�	NOUN
cana-6157	118	83	−1)2	−1)2	X
cana-6157	118	84	(	(	PUNCT
cana-6157	118	85	(	(	PUNCT
cana-6157	118	86	1+	1+	NUM
cana-6157	118	87	�	�	NOUN
cana-6157	118	88	̂	̂	SYM
cana-6157	118	89	�	�	NOUN
cana-6157	118	90	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	118	91	)	)	PUNCT
cana-6157	118	92	�	�	PROPN
cana-6157	118	93	̂	̂	VERB
cana-6157	118	94	�	�	PROPN
cana-6157	118	95	𝑙𝑛(1+	𝑙𝑛(1+	SYM
cana-6157	118	96	�	�	PROPN
cana-6157	118	97	̂	̂	NUM
cana-6157	118	98	�	�	NOUN
cana-6157	118	99	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	118	100	)	)	PUNCT
cana-6157	118	101	(	(	PUNCT
cana-6157	118	102	𝛼	𝛼	PROPN
cana-6157	118	103	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	118	104	�	�	SYM
cana-6157	118	105	̂	̂	NOUN
cana-6157	118	106	�	�	NOUN
cana-6157	118	107	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	118	108	)	)	PUNCT
cana-6157	118	109	�	�	PROPN
cana-6157	118	110	̂	̂	SYM
cana-6157	118	111	�	�	PROPN
cana-6157	118	112	)	)	PUNCT
cana-6157	118	113	̂	̂	X
cana-6157	118	114	)	)	PUNCT
cana-6157	118	115	(	(	PUNCT
cana-6157	118	116	−𝑒𝑥𝑝(1−(1+	−𝑒𝑥𝑝(1−(1+	PROPN
cana-6157	118	117	�	�	PROPN
cana-6157	118	118	̂	̂	PROPN
cana-6157	118	119	�	�	PROPN
cana-6157	118	120	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	118	121	)	)	PUNCT
cana-6157	118	122	�	�	PROPN
cana-6157	118	123	̂	̂	NUM
cana-6157	118	124	�	�	PROPN
cana-6157	118	125	)	)	PUNCT
cana-6157	118	126	)	)	PUNCT
cana-6157	118	127	)	)	PUNCT
cana-6157	118	128	(	(	PUNCT
cana-6157	118	129	�	�	NOUN
cana-6157	118	130	̂	̂	SYM
cana-6157	118	131	�	�	NOUN
cana-6157	118	132	−1)2	−1)2	X
cana-6157	118	133	(	(	PUNCT
cana-6157	118	134	17	17	NUM
cana-6157	118	135	)	)	PUNCT
cana-6157	118	136	𝜕𝑃𝑗(	𝜕𝑃𝑗(	NUM
cana-6157	118	137	�	�	NOUN
cana-6157	118	138	̂	̂	SYM
cana-6157	118	139	�	�	PROPN
cana-6157	118	140	)	)	PUNCT
cana-6157	118	141	𝜕	𝜕	PROPN
cana-6157	118	142	�	�	PROPN
cana-6157	118	143	̂̂	̂̂	NOUN
cana-6157	118	144	�	�	NOUN
cana-6157	118	145	=	=	SYM
cana-6157	118	146	(	(	PUNCT
cana-6157	118	147	�	�	PROPN
cana-6157	118	148	̂	̂	VERB
cana-6157	118	149	�	�	PROPN
cana-6157	118	150	𝑎𝑗(1+	𝑎𝑗(1+	NOUN
cana-6157	118	151	�	�	PROPN
cana-6157	118	152	̂	̂	NOUN
cana-6157	118	153	�	�	NOUN
cana-6157	118	154	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	155	)	)	PUNCT
cana-6157	118	156	𝛽−1̂	𝛽−1̂	NOUN
cana-6157	118	157	(	(	PUNCT
cana-6157	118	158	𝛼	𝛼	PROPN
cana-6157	118	159	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	118	160	�	�	SYM
cana-6157	118	161	̂	̂	NOUN
cana-6157	118	162	�	�	NOUN
cana-6157	118	163	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	164	)	)	PUNCT
cana-6157	118	165	�	�	PROPN
cana-6157	118	166	̂	̂	PROPN
cana-6157	118	167	�	�	PROPN
cana-6157	118	168	)	)	PUNCT
cana-6157	118	169	̂	̂	X
cana-6157	118	170	)	)	PUNCT
cana-6157	118	171	(	(	PUNCT
cana-6157	118	172	−𝑒𝑥𝑝(1−(1+	−𝑒𝑥𝑝(1−(1+	PROPN
cana-6157	118	173	�	�	PROPN
cana-6157	118	174	̂	̂	PROPN
cana-6157	118	175	�	�	PROPN
cana-6157	118	176	𝑎𝑗	𝑎𝑗	NOUN
cana-6157	118	177	)	)	PUNCT
cana-6157	118	178	�	�	PROPN
cana-6157	118	179	̂	̂	PROPN
cana-6157	118	180	�	�	PROPN
cana-6157	118	181	)	)	PUNCT
cana-6157	118	182	)	)	PUNCT
cana-6157	118	183	)	)	PUNCT
cana-6157	118	184	(	(	PUNCT
cana-6157	118	185	�	�	NOUN
cana-6157	118	186	̂	̂	SYM
cana-6157	118	187	�	�	NOUN
cana-6157	118	188	−1)2	−1)2	X
cana-6157	118	189	communications	communication	NOUN
cana-6157	118	190	on	on	ADP
cana-6157	118	191	applied	apply	VERB
cana-6157	118	192	nonlinear	nonlinear	ADJ
cana-6157	118	193	analysis	analysis	NOUN
cana-6157	118	194	issn	issn	NOUN
cana-6157	118	195	:	:	PUNCT
cana-6157	118	196	1074	1074	NUM
cana-6157	118	197	-	-	PUNCT
cana-6157	118	198	133x	133x	NUM
cana-6157	118	199	vol	vol	VERB
cana-6157	118	200	32	32	NUM
cana-6157	118	201	no	no	NOUN
cana-6157	118	202	.	.	PUNCT
cana-6157	119	1	10s	10	NOUN
cana-6157	119	2	(	(	PUNCT
cana-6157	119	3	2025	2025	NUM
cana-6157	119	4	)	)	PUNCT
cana-6157	119	5	3487	3487	NUM
cana-6157	119	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	119	7	−	−	PROPN
cana-6157	119	8	(	(	PUNCT
cana-6157	119	9	�	�	PROPN
cana-6157	119	10	̂	̂	SYM
cana-6157	119	11	�	�	NOUN
cana-6157	119	12	𝑎𝑗−1(1+	𝑎𝑗−1(1+	ADP
cana-6157	119	13	�	�	PROPN
cana-6157	119	14	̂	̂	SYM
cana-6157	119	15	�	�	NOUN
cana-6157	119	16	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	119	17	)	)	PUNCT
cana-6157	119	18	𝛽−1̂	𝛽−1̂	NOUN
cana-6157	119	19	(	(	PUNCT
cana-6157	119	20	𝛼	𝛼	PROPN
cana-6157	119	21	1−𝑒𝑥𝑝(1−(1+	1−𝑒𝑥𝑝(1−(1+	NUM
cana-6157	119	22	�	�	SYM
cana-6157	119	23	̂	̂	NOUN
cana-6157	119	24	�	�	NOUN
cana-6157	119	25	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	119	26	)	)	PUNCT
cana-6157	119	27	�	�	PROPN
cana-6157	119	28	̂	̂	SYM
cana-6157	119	29	�	�	PROPN
cana-6157	119	30	)	)	PUNCT
cana-6157	119	31	̂	̂	X
cana-6157	119	32	)	)	PUNCT
cana-6157	119	33	(	(	PUNCT
cana-6157	119	34	−𝑒𝑥𝑝(1−(1+	−𝑒𝑥𝑝(1−(1+	PROPN
cana-6157	119	35	�	�	PROPN
cana-6157	119	36	̂	̂	PROPN
cana-6157	119	37	�	�	PROPN
cana-6157	119	38	𝑎𝑗−1	𝑎𝑗−1	PROPN
cana-6157	119	39	)	)	PUNCT
cana-6157	119	40	�	�	PROPN
cana-6157	119	41	̂	̂	NUM
cana-6157	119	42	�	�	PROPN
cana-6157	119	43	)	)	PUNCT
cana-6157	119	44	)	)	PUNCT
cana-6157	119	45	)	)	PUNCT
cana-6157	120	1	(	(	PUNCT
cana-6157	120	2	�	�	NOUN
cana-6157	120	3	̂	̂	SYM
cana-6157	120	4	�	�	NOUN
cana-6157	120	5	−1)2	−1)2	X
cana-6157	120	6	(	(	PUNCT
cana-6157	120	7	18	18	NUM
cana-6157	120	8	)	)	PUNCT
cana-6157	120	9	and	and	CCONJ
cana-6157	120	10	the	the	DET
cana-6157	120	11	vector	vector	NOUN
cana-6157	120	12	𝐿(θ̂	𝐿(θ̂	NUM
cana-6157	120	13	)	)	PUNCT
cana-6157	120	14	=	=	PUNCT
cana-6157	120	15	(	(	PUNCT
cana-6157	120	16	l1	l1	PROPN
cana-6157	120	17	,	,	PUNCT
cana-6157	120	18	l2	l2	NOUN
cana-6157	120	19	,	,	PUNCT
cana-6157	120	20	l3	l3	PROPN
cana-6157	120	21	)	)	PUNCT
cana-6157	120	22	t	t	PROPN
cana-6157	120	23	is	be	AUX
cana-6157	120	24	given	give	VERB
cana-6157	120	25	by	by	ADP
cana-6157	120	26	:	:	PUNCT
cana-6157	120	27	𝐿1(	𝐿1(	PROPN
cana-6157	120	28	�	�	PROPN
cana-6157	120	29	̂	̂	NUM
cana-6157	120	30	�	�	NOUN
cana-6157	120	31	)	)	PUNCT
cana-6157	120	32	=	=	PUNCT
cana-6157	120	33	∑	∑	PUNCT
cana-6157	120	34	𝜐𝑗	𝜐𝑗	VERB
cana-6157	120	35	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	120	36	𝜕𝑃𝑗	𝜕𝑃𝑗	ADJ
cana-6157	120	37	𝜕	𝜕	PROPN
cana-6157	120	38	�	�	PROPN
cana-6157	120	39	̂	̂	SYM
cana-6157	120	40	�	�	PROPN
cana-6157	120	41	(	(	PUNCT
cana-6157	120	42	�	�	PROPN
cana-6157	120	43	̂	̂	SYM
cana-6157	120	44	�	�	NOUN
cana-6157	120	45	)	)	PUNCT
cana-6157	120	46	𝑗	𝑗	PROPN
cana-6157	120	47	;	;	PUNCT
cana-6157	120	48	𝐿2(	𝐿2(	PROPN
cana-6157	120	49	�	�	PROPN
cana-6157	120	50	̂	̂	NUM
cana-6157	120	51	�	�	NOUN
cana-6157	120	52	)	)	PUNCT
cana-6157	120	53	=	=	PUNCT
cana-6157	120	54	∑	∑	PUNCT
cana-6157	120	55	𝜐𝑗	𝜐𝑗	VERB
cana-6157	120	56	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	120	57	𝜕𝑃𝑗	𝜕𝑃𝑗	ADJ
cana-6157	120	58	𝜕	𝜕	PROPN
cana-6157	120	59	�	�	PROPN
cana-6157	120	60	̂̂	̂̂	NOUN
cana-6157	120	61	�	�	PROPN
cana-6157	120	62	(	(	PUNCT
cana-6157	120	63	�	�	PROPN
cana-6157	120	64	̂	̂	SYM
cana-6157	120	65	�	�	NOUN
cana-6157	120	66	)	)	PUNCT
cana-6157	120	67	𝑗	𝑗	PROPN
cana-6157	120	68	;	;	PUNCT
cana-6157	120	69	 	 	SPACE
cana-6157	120	70	𝐿3(	𝐿3(	NOUN
cana-6157	120	71	�	�	NOUN
cana-6157	120	72	̂	̂	NOUN
cana-6157	120	73	�	�	NOUN
cana-6157	120	74	)	)	PUNCT
cana-6157	120	75	=	=	NOUN
cana-6157	120	76	∑	∑	PUNCT
cana-6157	120	77	𝜐𝑗	𝜐𝑗	VERB
cana-6157	120	78	𝑃𝑗	𝑃𝑗	PROPN
cana-6157	120	79	𝜕𝑃𝑗	𝜕𝑃𝑗	ADJ
cana-6157	120	80	𝜕	𝜕	PROPN
cana-6157	120	81	�	�	PROPN
cana-6157	120	82	̂	̂	SYM
cana-6157	120	83	�	�	PROPN
cana-6157	120	84	(	(	PUNCT
cana-6157	120	85	𝜃	𝜃	NOUN
cana-6157	120	86	)	)	PUNCT
cana-6157	120	87	𝑗	𝑗	PROPN
cana-6157	120	88	iii	iii	PROPN
cana-6157	120	89	.	.	PUNCT
cana-6157	121	1	fisher	fisher	PROPN
cana-6157	121	2	information	information	NOUN
cana-6157	121	3	matrix	matrix	NOUN
cana-6157	121	4	𝑰(	𝑰(	VERB
cana-6157	121	5	�	�	PROPN
cana-6157	121	6	̂	̂	NUM
cana-6157	121	7	�	�	NOUN
cana-6157	121	8	)	)	PUNCT
cana-6157	121	9	the	the	DET
cana-6157	121	10	elements	element	NOUN
cana-6157	121	11	of	of	ADP
cana-6157	121	12	the	the	DET
cana-6157	121	13	fisher	fisher	NOUN
cana-6157	121	14	's	's	PART
cana-6157	121	15	information	information	NOUN
cana-6157	121	16	matrix	matrix	NOUN
cana-6157	121	17	on	on	ADP
cana-6157	121	18	initial	initial	ADJ
cana-6157	121	19	data	datum	NOUN
cana-6157	121	20	,	,	PUNCT
cana-6157	121	21	𝐼(	𝐼(	PROPN
cana-6157	121	22	�	�	PROPN
cana-6157	121	23	̂	̂	NUM
cana-6157	121	24	�	�	PROPN
cana-6157	121	25	)	)	PUNCT
cana-6157	121	26	3∗3	3∗3	NUM
cana-6157	121	27	for	for	ADP
cana-6157	121	28	the	the	DET
cana-6157	121	29	aptee	aptee	ADJ
cana-6157	121	30	distribution	distribution	NOUN
cana-6157	121	31	are	be	AUX
cana-6157	121	32	obtained	obtain	VERB
cana-6157	121	33	as	as	SCONJ
cana-6157	121	34	follows	follow	VERB
cana-6157	121	35	:	:	PUNCT
cana-6157	122	1	𝐼𝛼𝛼	𝐼𝛼𝛼	PROPN
cana-6157	122	2	=	=	PUNCT
cana-6157	122	3	−	−	PROPN
cana-6157	122	4	(	(	PUNCT
cana-6157	122	5	(	(	PUNCT
cana-6157	122	6	𝑛(𝑙𝑜𝑔(𝛼)+1	𝑛(𝑙𝑜𝑔(𝛼)+1	NOUN
cana-6157	122	7	)	)	PUNCT
cana-6157	122	8	)	)	PUNCT
cana-6157	122	9	(	(	PUNCT
cana-6157	122	10	𝛼𝑙𝑜𝑔(𝛼	𝛼𝑙𝑜𝑔(𝛼	NOUN
cana-6157	122	11	)	)	PUNCT
cana-6157	122	12	)	)	PUNCT
cana-6157	122	13	2	2	NUM
cana-6157	122	14	)	)	PUNCT
cana-6157	122	15	−	−	PROPN
cana-6157	122	16	(	(	PUNCT
cana-6157	122	17	𝑛/((𝛼	𝑛/((𝛼	NOUN
cana-6157	122	18	−	−	PROPN
cana-6157	122	19	1	1	NUM
cana-6157	122	20	)	)	PUNCT
cana-6157	122	21	2	2	NUM
cana-6157	122	22	)	)	PUNCT
cana-6157	122	23	)	)	PUNCT
cana-6157	123	1	+	+	CCONJ
cana-6157	123	2	(	(	PUNCT
cana-6157	123	3	(	(	PUNCT
cana-6157	123	4	∑	∑	X
cana-6157	123	5	(	(	PUNCT
cana-6157	123	6	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	1−𝑒𝑥𝑝(1−(1+𝜆𝑡𝑖	NOUN
cana-6157	123	7	)	)	PUNCT
cana-6157	123	8	𝛽))𝑛	𝛽))𝑛	NOUN
cana-6157	123	9	𝑖=1	𝑖=1	PROPN
cana-6157	123	10	)	)	PUNCT
cana-6157	123	11	𝛼2	𝛼2	PROPN
cana-6157	123	12	)	)	PUNCT
cana-6157	123	13	(	(	PUNCT
cana-6157	123	14	19	19	NUM
cana-6157	123	15	)	)	PUNCT
cana-6157	123	16	𝐼ββ	𝐼ββ	PROPN
cana-6157	123	17	=	=	SYM
cana-6157	124	1	−	−	PROPN
cana-6157	124	2	(	(	PUNCT
cana-6157	124	3	𝑛	𝑛	PROPN
cana-6157	124	4	β2	β2	PROPN
cana-6157	124	5	)	)	PUNCT
cana-6157	124	6	−∑(1	−∑(1	PROPN
cana-6157	125	1	+	+	NUM
cana-6157	125	2	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	125	3	)	)	PUNCT
cana-6157	126	1	β	β	X
cana-6157	126	2	𝑛	𝑛	X
cana-6157	126	3	𝑖=1	𝑖=1	PUNCT
cana-6157	127	1	[	[	X
cana-6157	127	2	𝑙𝑜𝑔(1	𝑙𝑜𝑔(1	X
cana-6157	127	3	+	+	X
cana-6157	127	4	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	127	5	)	)	PUNCT
cana-6157	127	6	]	]	PUNCT
cana-6157	127	7	2	2	NUM
cana-6157	127	8	+	+	NOUN
cana-6157	127	9	𝑙𝑜𝑔(α)∑	𝑙𝑜𝑔(α)∑	NOUN
cana-6157	127	10	λ𝑡𝑖[𝑙𝑜𝑔(1	λ𝑡𝑖[𝑙𝑜𝑔(1	AUX
cana-6157	128	1	+	+	CCONJ
cana-6157	128	2	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	128	3	)	)	PUNCT
cana-6157	128	4	]	]	PUNCT
cana-6157	128	5	2𝑒𝑥𝑝(1	2𝑒𝑥𝑝(1	NUM
cana-6157	128	6	−	−	NOUN
cana-6157	128	7	(	(	PUNCT
cana-6157	128	8	1	1	NUM
cana-6157	128	9	+	+	NUM
cana-6157	128	10	λ𝑡𝑖	λ𝑡𝑖	NOUN
cana-6157	128	11	)	)	PUNCT
cana-6157	128	12	β)(1	β)(1	PUNCT
cana-6157	129	1	+	+	CCONJ
cana-6157	129	2	λ𝑡𝑖	λ𝑡𝑖	INTJ
cana-6157	129	3	)	)	PUNCT
cana-6157	129	4	𝑛	𝑛	PRON
cana-6157	129	5	𝑖=1	𝑖=1	PROPN
cana-6157	129	6	(	(	PUNCT
cana-6157	129	7	20	20	NUM
cana-6157	129	8	)	)	PUNCT
cana-6157	129	9	𝐼𝜆𝜆	𝐼𝜆𝜆	NOUN
cana-6157	129	10	=	=	SYM
cana-6157	129	11	−	−	PROPN
cana-6157	129	12	(	(	PUNCT
cana-6157	129	13	𝑛	𝑛	DET
cana-6157	129	14	𝜆2	𝜆2	NOUN
cana-6157	129	15	)	)	PUNCT
cana-6157	130	1	+	+	CCONJ
cana-6157	130	2	(	(	PUNCT
cana-6157	130	3	𝛽	𝛽	NOUN
cana-6157	130	4	−	−	PROPN
cana-6157	130	5	1)∑	1)∑	NUM
cana-6157	130	6	(	(	PUNCT
cana-6157	130	7	𝑡𝑖	𝑡𝑖	NOUN
cana-6157	130	8	2	2	NUM
cana-6157	130	9	(	(	PUNCT
cana-6157	130	10	1	1	NUM
cana-6157	130	11	+	+	NUM
cana-6157	130	12	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	130	13	)	)	PUNCT
cana-6157	130	14	2	2	NUM
cana-6157	130	15	)	)	PUNCT
cana-6157	130	16	𝑛	𝑛	PRON
cana-6157	130	17	𝑖=1	𝑖=1	PROPN
cana-6157	130	18	−	−	PROPN
cana-6157	131	1	𝛽(𝛽	𝛽(𝛽	NOUN
cana-6157	131	2	−	−	PROPN
cana-6157	131	3	1)∑𝑡𝑖	1)∑𝑡𝑖	NUM
cana-6157	131	4	2(1	2(1	NUM
cana-6157	131	5	+	+	NUM
cana-6157	131	6	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	131	7	)	)	PUNCT
cana-6157	131	8	𝛽−2	𝛽−2	PROPN
cana-6157	131	9	𝑛	𝑛	PRON
cana-6157	131	10	𝑖=1	𝑖=1	PROPN
cana-6157	131	11	−𝛽𝑙𝑜𝑔(𝛼)∑	−𝛽𝑙𝑜𝑔(𝛼)∑	PROPN
cana-6157	131	12	𝑡𝑖	𝑡𝑖	NOUN
cana-6157	131	13	2𝑒𝑥𝑝(1	2𝑒𝑥𝑝(1	NUM
cana-6157	131	14	−	−	PROPN
cana-6157	131	15	(	(	PUNCT
cana-6157	131	16	1	1	NUM
cana-6157	131	17	+	+	NUM
cana-6157	131	18	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	131	19	)	)	PUNCT
cana-6157	131	20	𝛽)(1	𝛽)(1	NUM
cana-6157	132	1	+	+	CCONJ
cana-6157	132	2	𝜆𝑡𝑖	𝜆𝑡𝑖	X
cana-6157	132	3	)	)	PUNCT
cana-6157	132	4	𝛽−2[𝛽(1	𝛽−2[𝛽(1	PROPN
cana-6157	132	5	+	+	CCONJ
cana-6157	132	6	𝜆𝑡𝑖	𝜆𝑡𝑖	NUM
cana-6157	132	7	)	)	PUNCT
cana-6157	132	8	−	−	PROPN
cana-6157	133	1	(	(	PUNCT
cana-6157	133	2	𝛽	𝛽	NOUN
cana-6157	133	3	−	−	PROPN
cana-6157	133	4	1	1	NUM
cana-6157	133	5	)	)	PUNCT
cana-6157	133	6	]	]	PUNCT
cana-6157	134	1	𝑛	𝑛	PRON
cana-6157	134	2	𝑖=1	𝑖=1	PROPN
cana-6157	134	3	(	(	PUNCT
cana-6157	134	4	21	21	NUM
cana-6157	134	5	)	)	PUNCT
cana-6157	134	6	and	and	CCONJ
cana-6157	134	7	𝐼𝛼𝛽	𝐼𝛼𝛽	CCONJ
cana-6157	134	8	=	=	SYM
cana-6157	134	9	1	1	NUM
cana-6157	134	10	𝛼	𝛼	NOUN
cana-6157	134	11	∑	∑	PUNCT
cana-6157	134	12	𝑒𝑥𝑝(1	𝑒𝑥𝑝(1	NOUN
cana-6157	134	13	−	−	PROPN
cana-6157	134	14	(	(	PUNCT
cana-6157	134	15	1	1	NUM
cana-6157	134	16	+	+	NUM
cana-6157	134	17	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	134	18	)	)	PUNCT
cana-6157	134	19	𝛽)(1	𝛽)(1	NUM
cana-6157	135	1	+	+	CCONJ
cana-6157	135	2	𝜆𝑡𝑖	𝜆𝑡𝑖	X
cana-6157	135	3	)	)	PUNCT
cana-6157	135	4	𝛽𝑛	𝛽𝑛	PROPN
cana-6157	135	5	𝑖=1	𝑖=1	PROPN
cana-6157	135	6	𝑙𝑜𝑔(1	𝑙𝑜𝑔(1	NOUN
cana-6157	136	1	+	+	CCONJ
cana-6157	136	2	𝜆𝑡𝑖	𝜆𝑡𝑖	X
cana-6157	136	3	)	)	PUNCT
cana-6157	136	4	(	(	PUNCT
cana-6157	136	5	22	22	NUM
cana-6157	136	6	)	)	PUNCT
cana-6157	137	1	𝐼𝛼𝜆	𝐼𝛼𝜆	PROPN
cana-6157	137	2	=	=	SYM
cana-6157	137	3	𝛽	𝛽	NOUN
cana-6157	137	4	𝛼	𝛼	ADP
cana-6157	137	5	∑	∑	PROPN
cana-6157	137	6	𝑡𝑖	𝑡𝑖	NOUN
cana-6157	137	7	𝑛	𝑛	PRON
cana-6157	137	8	𝑖=1	𝑖=1	PROPN
cana-6157	137	9	𝑒𝑥𝑝(1	𝑒𝑥𝑝(1	NOUN
cana-6157	137	10	−	−	PROPN
cana-6157	137	11	(	(	PUNCT
cana-6157	137	12	1	1	NUM
cana-6157	137	13	+	+	NUM
cana-6157	137	14	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	137	15	)	)	PUNCT
cana-6157	137	16	𝛽)(1	𝛽)(1	NUM
cana-6157	138	1	+	+	CCONJ
cana-6157	138	2	𝜆𝑡𝑖	𝜆𝑡𝑖	NOUN
cana-6157	138	3	)	)	PUNCT
cana-6157	138	4	𝛽−1(23	𝛽−1(23	NOUN
cana-6157	138	5	)	)	PUNCT
cana-6157	138	6	iβλ	iβλ	NOUN
cana-6157	138	7	=	=	SYM
cana-6157	138	8	∑	∑	PUNCT
cana-6157	138	9	ti	ti	X
cana-6157	138	10	(	(	PUNCT
cana-6157	138	11	1+λti	1+λti	NOUN
cana-6157	138	12	)	)	PUNCT
cana-6157	138	13	𝑛	𝑛	PRON
cana-6157	138	14	𝑖=1	𝑖=1	PUNCT
cana-6157	139	1	−	−	PUNCT
cana-6157	139	2	∑	∑	PUNCT
cana-6157	139	3	ti(1	ti(1	PROPN
cana-6157	139	4	+	+	ADJ
cana-6157	139	5	λti	λti	NOUN
cana-6157	139	6	)	)	PUNCT
cana-6157	139	7	β−1(βlog(1	β−1(βlog(1	PUNCT
cana-6157	140	1	+	+	NUM
cana-6157	140	2	λti	λti	NOUN
cana-6157	140	3	)	)	PUNCT
cana-6157	140	4	+	+	CCONJ
cana-6157	140	5	1	1	X
cana-6157	140	6	)	)	PUNCT
cana-6157	140	7	𝑛	𝑛	PRON
cana-6157	140	8	𝑖=1	𝑖=1	PUNCT
cana-6157	141	1	−	−	NOUN
cana-6157	141	2	log(α)∑	log(α)∑	NOUN
cana-6157	141	3	ti	ti	NOUN
cana-6157	141	4	𝑛	𝑛	PRON
cana-6157	141	5	𝑖=1	𝑖=1	PROPN
cana-6157	141	6	exp(1	exp(1	NOUN
cana-6157	141	7	−	−	PROPN
cana-6157	142	1	(	(	PUNCT
cana-6157	142	2	1	1	NUM
cana-6157	142	3	+	+	NUM
cana-6157	142	4	λti	λti	NOUN
cana-6157	142	5	)	)	PUNCT
cana-6157	142	6	β)(1	β)(1	PUNCT
cana-6157	143	1	+	+	CCONJ
cana-6157	143	2	λti	λti	NOUN
cana-6157	143	3	)	)	PUNCT
cana-6157	143	4	β−1[βti(1	β−1[βti(1	PROPN
cana-6157	143	5	+	+	CCONJ
cana-6157	143	6	λti	λti	NOUN
cana-6157	143	7	)	)	PUNCT
cana-6157	143	8	βlog(1	βlog(1	PUNCT
cana-6157	144	1	+	+	NUM
cana-6157	144	2	λti	λti	NOUN
cana-6157	144	3	)	)	PUNCT
cana-6157	144	4	−	−	PROPN
cana-6157	144	5	βlog(1	βlog(1	PUNCT
cana-6157	145	1	+	+	NUM
cana-6157	145	2	λti	λti	NOUN
cana-6157	145	3	)	)	PUNCT
cana-6157	145	4	−	−	PROPN
cana-6157	146	1	1	1	NUM
cana-6157	146	2	]	]	PUNCT
cana-6157	146	3	(	(	PUNCT
cana-6157	146	4	24	24	NUM
cana-6157	146	5	)	)	PUNCT
cana-6157	146	6	therefore	therefore	ADV
cana-6157	146	7	,	,	PUNCT
cana-6157	146	8	we	we	PRON
cana-6157	146	9	can	can	AUX
cana-6157	146	10	deduce	deduce	VERB
cana-6157	146	11	the	the	DET
cana-6157	146	12	value	value	NOUN
cana-6157	146	13	of	of	ADP
cana-6157	146	14	the	the	DET
cana-6157	146	15	test	test	NOUN
cana-6157	146	16	statistic	statistic	NOUN
cana-6157	146	17	𝑌2	𝑌2	NOUN
cana-6157	146	18	.	.	PUNCT
cana-6157	147	1	for	for	ADP
cana-6157	147	2	𝛼	𝛼	NOUN
cana-6157	147	3	level	level	NOUN
cana-6157	147	4	of	of	ADP
cana-6157	147	5	significance	significance	NOUN
cana-6157	147	6	,	,	PUNCT
cana-6157	147	7	𝐻0	𝐻0	PROPN
cana-6157	147	8	is	be	AUX
cana-6157	147	9	accepted	accept	VERB
cana-6157	147	10	if	if	SCONJ
cana-6157	147	11	yn	yn	PROPN
cana-6157	147	12	2(θ̂	2(θ̂	NUM
cana-6157	147	13	)	)	PUNCT
cana-6157	147	14	≤	≤	NUM
cana-6157	147	15	χα	χα	NOUN
cana-6157	147	16	,	,	PUNCT
cana-6157	147	17	r−1	r−1	PROPN
cana-6157	147	18	2	2	NUM
cana-6157	147	19	.	.	PUNCT
cana-6157	148	1	viii	viii	PROPN
cana-6157	148	2	.	.	PUNCT
cana-6157	149	1	simulations	simulation	NOUN
cana-6157	149	2	and	and	CCONJ
cana-6157	149	3	application	application	NOUN
cana-6157	149	4	i.	i.	NOUN
cana-6157	149	5	parameters	parameters	PROPN
cana-6157	149	6	estimation	estimation	PROPN
cana-6157	149	7	to	to	PART
cana-6157	149	8	assess	assess	VERB
cana-6157	149	9	the	the	DET
cana-6157	149	10	performance	performance	NOUN
cana-6157	149	11	of	of	ADP
cana-6157	149	12	the	the	DET
cana-6157	149	13	estimation	estimation	NOUN
cana-6157	149	14	methods	method	NOUN
cana-6157	149	15	used	use	VERB
cana-6157	149	16	,	,	PUNCT
cana-6157	149	17	we	we	PRON
cana-6157	149	18	generated	generate	VERB
cana-6157	149	19	n=10,000	n=10,000	VERB
cana-6157	149	20	samples	sample	NOUN
cana-6157	149	21	of	of	ADP
cana-6157	149	22	different	different	ADJ
cana-6157	149	23	sizes	size	NOUN
cana-6157	149	24	(	(	PUNCT
cana-6157	149	25	n=15	n=15	ADV
cana-6157	149	26	,	,	PUNCT
cana-6157	149	27	n=50	n=50	ADJ
cana-6157	149	28	,	,	PUNCT
cana-6157	149	29	n=100	n=100	PROPN
cana-6157	149	30	,	,	PUNCT
cana-6157	149	31	n=200	n=200	NUM
cana-6157	149	32	)	)	PUNCT
cana-6157	149	33	with	with	ADP
cana-6157	149	34	the	the	DET
cana-6157	149	35	parameter	parameter	NOUN
cana-6157	149	36	values	value	NOUN
cana-6157	149	37	α̂	α̂	NUM
cana-6157	150	1	=	=	SYM
cana-6157	150	2	2	2	NUM
cana-6157	150	3	,	,	PUNCT
cana-6157	150	4	β̂	β̂	PUNCT
cana-6157	150	5	=	=	SYM
cana-6157	150	6	0.5	0.5	NUM
cana-6157	150	7	;	;	PUNCT
cana-6157	150	8	λ̂	λ̂	NUM
cana-6157	151	1	=	=	SYM
cana-6157	151	2	1.5	1.5	NUM
cana-6157	151	3	,	,	PUNCT
cana-6157	151	4	,	,	PUNCT
cana-6157	151	5	from	from	ADP
cana-6157	151	6	the	the	DET
cana-6157	151	7	aptee	aptee	ADJ
cana-6157	151	8	distribution	distribution	NOUN
cana-6157	151	9	.	.	PUNCT
cana-6157	152	1	using	use	VERB
cana-6157	152	2	r	r	NOUN
cana-6157	152	3	software	software	NOUN
cana-6157	152	4	,	,	PUNCT
cana-6157	152	5	we	we	PRON
cana-6157	152	6	compute	compute	VERB
cana-6157	152	7	the	the	DET
cana-6157	152	8	values	value	NOUN
cana-6157	152	9	of	of	ADP
cana-6157	152	10	the	the	DET
cana-6157	152	11	maximum	maximum	ADJ
cana-6157	152	12	likelihood	likelihood	NOUN
cana-6157	152	13	estimates	estimate	NOUN
cana-6157	152	14	(	(	PUNCT
cana-6157	152	15	table1	table1	PROPN
cana-6157	152	16	)	)	PUNCT
cana-6157	152	17	,	,	PUNCT
cana-6157	152	18	kolmogorov	kolmogorov	ADJ
cana-6157	152	19	-	-	PUNCT
cana-6157	152	20	smirnov	smirnov	ADJ
cana-6157	152	21	estimates	estimate	NOUN
cana-6157	152	22	(	(	PUNCT
cana-6157	152	23	table	table	NOUN
cana-6157	152	24	2	2	NUM
cana-6157	152	25	)	)	PUNCT
cana-6157	152	26	,	,	PUNCT
cana-6157	152	27	the	the	DET
cana-6157	152	28	andersondarling	andersondarle	VERB
cana-6157	152	29	estimates	estimate	NOUN
cana-6157	152	30	(	(	PUNCT
cana-6157	152	31	table	table	NOUN
cana-6157	152	32	3	3	NUM
cana-6157	152	33	)	)	PUNCT
cana-6157	152	34	,	,	PUNCT
cana-6157	152	35	the	the	DET
cana-6157	152	36	cramer	cramer	PROPN
cana-6157	152	37	von	von	PROPN
cana-6157	152	38	-	-	PUNCT
cana-6157	152	39	mises	mises	PROPN
cana-6157	152	40	estimates	estimate	NOUN
cana-6157	152	41	(	(	PUNCT
cana-6157	152	42	table	table	NOUN
cana-6157	152	43	4	4	NUM
cana-6157	152	44	)	)	PUNCT
cana-6157	152	45	and	and	CCONJ
cana-6157	152	46	their	their	PRON
cana-6157	152	47	corresponding	corresponding	ADJ
cana-6157	152	48	mean	mean	ADJ
cana-6157	152	49	squared	square	VERB
cana-6157	152	50	errors	error	NOUN
cana-6157	152	51	.	.	PUNCT
cana-6157	153	1	communications	communication	NOUN
cana-6157	153	2	on	on	ADP
cana-6157	153	3	applied	apply	VERB
cana-6157	153	4	nonlinear	nonlinear	ADJ
cana-6157	153	5	analysis	analysis	NOUN
cana-6157	153	6	issn	issn	NOUN
cana-6157	153	7	:	:	PUNCT
cana-6157	153	8	1074	1074	NUM
cana-6157	153	9	-	-	PUNCT
cana-6157	153	10	133x	133x	NUM
cana-6157	153	11	vol	vol	VERB
cana-6157	153	12	32	32	NUM
cana-6157	153	13	no	no	NOUN
cana-6157	153	14	.	.	PUNCT
cana-6157	154	1	10s	10	NOUN
cana-6157	154	2	(	(	PUNCT
cana-6157	154	3	2025	2025	NUM
cana-6157	154	4	)	)	PUNCT
cana-6157	154	5	3488	3488	NUM
cana-6157	154	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	154	7	table1	table1	PROPN
cana-6157	154	8	:	:	PUNCT
cana-6157	154	9	ml	ml	ADP
cana-6157	154	10	estimators	estimator	NOUN
cana-6157	154	11	and	and	CCONJ
cana-6157	154	12	their	their	PRON
cana-6157	154	13	mean	mean	ADJ
cana-6157	154	14	squared	square	VERB
cana-6157	154	15	errors	error	NOUN
cana-6157	154	16	n=10.000	n=10.000	NUM
cana-6157	154	17	α̂	α̂	NUM
cana-6157	154	18	β̂	β̂	ADP
cana-6157	154	19	λ̂	λ̂	X
cana-6157	154	20	n=15	n=15	ADV
cana-6157	154	21	aes	aes	PROPN
cana-6157	154	22	1.88769	1.88769	NUM
cana-6157	154	23	0.45578	0.45578	NUM
cana-6157	154	24	1.47863	1.47863	NUM
cana-6157	154	25	sme	sme	NOUN
cana-6157	154	26	0.08873	0.08873	NUM
cana-6157	154	27	0.00783	0.00783	NUM
cana-6157	154	28	0.01812	0.01812	NUM
cana-6157	154	29	n=50	n=50	ADJ
cana-6157	154	30	aes	aes	PROPN
cana-6157	154	31	1.91835	1.91835	NUM
cana-6157	154	32	0.48869	0.48869	NUM
cana-6157	154	33	1.48625	1.48625	NUM
cana-6157	154	34	sme	sme	NOUN
cana-6157	154	35	0.06724	0.06724	NUM
cana-6157	154	36	0.00511	0.00511	NUM
cana-6157	154	37	0.01561	0.01561	NUM
cana-6157	154	38	n=100	n=100	NUM
cana-6157	154	39	aes	aes	VERB
cana-6157	154	40	1.95092	1.95092	NUM
cana-6157	154	41	0.50262	0.50262	NUM
cana-6157	154	42	1.48459	1.48459	NUM
cana-6157	154	43	sme	sme	NOUN
cana-6157	154	44	0.02619	0.02619	NUM
cana-6157	154	45	0.00354	0.00354	NUM
cana-6157	154	46	0.01356	0.01356	NUM
cana-6157	154	47	n=200	n=200	NUM
cana-6157	154	48	aes	aes	PROPN
cana-6157	154	49	1.98548	1.98548	NUM
cana-6157	154	50	0.50578	0.50578	NUM
cana-6157	154	51	1.49379	1.49379	NUM
cana-6157	154	52	sme	sme	NOUN
cana-6157	154	53	0.00672	0.00672	NUM
cana-6157	154	54	0.00261	0.00261	NUM
cana-6157	154	55	0.00946	0.00946	NUM
cana-6157	154	56	table2	table2	NOUN
cana-6157	154	57	:	:	PUNCT
cana-6157	155	1	ks	ks	NOUN
cana-6157	155	2	estimators	estimator	NOUN
cana-6157	155	3	for	for	ADP
cana-6157	155	4	parameters	parameter	NOUN
cana-6157	155	5	and	and	CCONJ
cana-6157	155	6	their	their	PRON
cana-6157	155	7	mean	mean	ADJ
cana-6157	155	8	square	square	ADJ
cana-6157	155	9	-	-	PUNCT
cana-6157	155	10	errors	error	NOUN
cana-6157	155	11	n=10.000	n=10.000	NUM
cana-6157	155	12	α̂	α̂	NUM
cana-6157	155	13	β̂	β̂	ADP
cana-6157	155	14	λ̂	λ̂	X
cana-6157	155	15	n=15	n=15	ADV
cana-6157	155	16	aes	aes	VERB
cana-6157	155	17	2.06512	2.06512	NUM
cana-6157	155	18	0.51193	0.51193	NUM
cana-6157	155	19	1.48082	1.48082	NUM
cana-6157	155	20	sme	sme	NOUN
cana-6157	155	21	0.06473	0.06473	NUM
cana-6157	155	22	0.01685	0.01685	NUM
cana-6157	155	23	0.00902	0.00902	NUM
cana-6157	155	24	n=50	n=50	ADJ
cana-6157	155	25	aes	aes	PROPN
cana-6157	155	26	2.04507	2.04507	NUM
cana-6157	155	27	0.50330	0.50330	NUM
cana-6157	155	28	1.48920	1.48920	NUM
cana-6157	155	29	sme	sme	NOUN
cana-6157	155	30	0.03163	0.03163	NUM
cana-6157	155	31	0.00934	0.00934	NUM
cana-6157	155	32	0.00853	0.00853	NUM
cana-6157	155	33	n=100	n=100	NUM
cana-6157	155	34	aes	aes	PROPN
cana-6157	155	35	2.01887	2.01887	NUM
cana-6157	155	36	0.50216	0.50216	NUM
cana-6157	155	37	1.49272	1.49272	NUM
cana-6157	155	38	sme	sme	NOUN
cana-6157	155	39	0.00848	0.00848	NUM
cana-6157	155	40	0.00462	0.00462	NUM
cana-6157	155	41	0.00792	0.00792	NUM
cana-6157	155	42	n=200	n=200	NUM
cana-6157	155	43	aes	aes	PROPN
cana-6157	155	44	2.00143	2.00143	NUM
cana-6157	155	45	0.50187	0.50187	NUM
cana-6157	155	46	1.49972	1.49972	NUM
cana-6157	155	47	sme	sme	NOUN
cana-6157	155	48	0.00609	0.00609	NUM
cana-6157	155	49	0.00313	0.00313	NUM
cana-6157	155	50	0.00423	0.00423	NUM
cana-6157	155	51	table3	table3	PROPN
cana-6157	155	52	:	:	PUNCT
cana-6157	155	53	cvm	cvm	NOUN
cana-6157	155	54	estimators	estimator	NOUN
cana-6157	155	55	for	for	ADP
cana-6157	155	56	parameters	parameter	NOUN
cana-6157	155	57	and	and	CCONJ
cana-6157	155	58	their	their	PRON
cana-6157	155	59	mean	mean	ADJ
cana-6157	155	60	square	square	ADJ
cana-6157	155	61	-	-	PUNCT
cana-6157	155	62	errors	error	NOUN
cana-6157	156	1	n=10.000	n=10.000	NUM
cana-6157	156	2	α̂	α̂	NUM
cana-6157	156	3	β̂	β̂	ADP
cana-6157	156	4	λ̂	λ̂	X
cana-6157	156	5	n=15	n=15	ADV
cana-6157	156	6	aes	aes	VERB
cana-6157	156	7	1.93732	1.93732	NUM
cana-6157	156	8	0.53416	0.53416	NUM
cana-6157	156	9	1.51731	1.51731	NUM
cana-6157	156	10	sme	sme	NOUN
cana-6157	156	11	0.02935	0.02935	NUM
cana-6157	156	12	0.01808	0.01808	NUM
cana-6157	156	13	0.00912	0.00912	NUM
cana-6157	156	14	n=50	n=50	ADJ
cana-6157	156	15	aes	aes	PROPN
cana-6157	156	16	1.97703	1.97703	NUM
cana-6157	156	17	0.51809	0.51809	NUM
cana-6157	156	18	1.50451	1.50451	NUM
cana-6157	156	19	sme	sme	NOUN
cana-6157	156	20	0.00514	0.00514	NUM
cana-6157	156	21	0.00911	0.00911	NUM
cana-6157	156	22	0.00853	0.00853	NUM
cana-6157	156	23	n=100	n=100	NUM
cana-6157	156	24	aes	aes	PROPN
cana-6157	156	25	1.97802	1.97802	NUM
cana-6157	156	26	0.51472	0.51472	NUM
cana-6157	156	27	1.50208	1.50208	NUM
cana-6157	156	28	sme	sme	NOUN
cana-6157	156	29	0.00288	0.00288	NUM
cana-6157	156	30	0.00551	0.00551	NUM
cana-6157	156	31	0.00825	0.00825	NUM
cana-6157	156	32	n=200	n=200	NUM
cana-6157	156	33	aes	aes	PROPN
cana-6157	156	34	1.99525	1.99525	NUM
cana-6157	156	35	0.51014	0.51014	NUM
cana-6157	156	36	1.50127	1.50127	NUM
cana-6157	156	37	sme	sme	NOUN
cana-6157	156	38	0.00053	0.00053	NUM
cana-6157	156	39	0.00343	0.00343	NUM
cana-6157	156	40	0.00721	0.00721	NUM
cana-6157	156	41	table4	table4	NOUN
cana-6157	156	42	:	:	PUNCT
cana-6157	157	1	ad	ad	NOUN
cana-6157	157	2	estimators	estimator	NOUN
cana-6157	157	3	for	for	ADP
cana-6157	157	4	parameters	parameter	NOUN
cana-6157	157	5	and	and	CCONJ
cana-6157	157	6	their	their	PRON
cana-6157	157	7	mean	mean	ADJ
cana-6157	157	8	square	square	ADJ
cana-6157	157	9	-	-	PUNCT
cana-6157	157	10	errors	error	NOUN
cana-6157	157	11	n=10.000	n=10.000	NUM
cana-6157	157	12	α̂	α̂	NUM
cana-6157	157	13	β̂	β̂	ADP
cana-6157	157	14	λ̂	λ̂	X
cana-6157	157	15	n=15	n=15	ADV
cana-6157	157	16	aes	aes	VERB
cana-6157	157	17	2.00856	2.00856	NUM
cana-6157	157	18	0.51393	0.51393	NUM
cana-6157	157	19	1.49588	1.49588	NUM
cana-6157	157	20	sme	sme	NOUN
cana-6157	157	21	0.03439	0.03439	NUM
cana-6157	157	22	0.01578	0.01578	NUM
cana-6157	157	23	0.00916	0.00916	NUM
cana-6157	157	24	n=50	n=50	ADJ
cana-6157	157	25	aes	aes	PROPN
cana-6157	157	26	1.98429	1.98429	NUM
cana-6157	157	27	0.51354	0.51354	NUM
cana-6157	157	28	1.49510	1.49510	NUM
cana-6157	157	29	sme	sme	NOUN
cana-6157	157	30	0.02837	0.02837	NUM
cana-6157	157	31	0.00754	0.00754	NUM
cana-6157	157	32	0.00828	0.00828	NUM
cana-6157	157	33	n=100	n=100	NUM
cana-6157	157	34	aes	aes	PROPN
cana-6157	157	35	2.00514	2.00514	NUM
cana-6157	157	36	0.50690	0.50690	NUM
cana-6157	157	37	1.49510	1.49510	NUM
cana-6157	157	38	sme	sme	NOUN
cana-6157	157	39	0.01522	0.01522	NUM
cana-6157	157	40	0.00468	0.00468	NUM
cana-6157	157	41	0.00796	0.00796	NUM
cana-6157	157	42	n=200	n=200	NUM
cana-6157	157	43	aes	aes	PROPN
cana-6157	157	44	2.02087	2.02087	NUM
cana-6157	157	45	0.50548	0.50548	NUM
cana-6157	157	46	1.49116	1.49116	NUM
cana-6157	157	47	sme	sme	NOUN
cana-6157	157	48	0.00225	0.00225	NUM
cana-6157	157	49	0.00279	0.00279	NUM
cana-6157	157	50	0.00681	0.00681	NUM
cana-6157	157	51	from	from	ADP
cana-6157	157	52	numerical	numerical	ADJ
cana-6157	157	53	experiments	experiment	NOUN
cana-6157	157	54	,	,	PUNCT
cana-6157	157	55	it	it	PRON
cana-6157	157	56	is	be	AUX
cana-6157	157	57	observed	observe	VERB
cana-6157	157	58	that	that	SCONJ
cana-6157	157	59	the	the	DET
cana-6157	157	60	obtained	obtain	VERB
cana-6157	157	61	estimators	estimator	NOUN
cana-6157	157	62	are	be	AUX
cana-6157	157	63	consistent	consistent	ADJ
cana-6157	157	64	and	and	CCONJ
cana-6157	157	65	the	the	DET
cana-6157	157	66	average	average	ADJ
cana-6157	157	67	values	value	NOUN
cana-6157	157	68	of	of	ADP
cana-6157	157	69	the	the	DET
cana-6157	157	70	estimates	estimate	NOUN
cana-6157	157	71	(	(	PUNCT
cana-6157	157	72	aes	aes	NOUN
cana-6157	157	73	)	)	PUNCT
cana-6157	157	74	and	and	CCONJ
cana-6157	157	75	the	the	DET
cana-6157	157	76	average	average	ADJ
cana-6157	157	77	mean	mean	NOUN
cana-6157	157	78	squared	square	VERB
cana-6157	157	79	errors	error	NOUN
cana-6157	157	80	(	(	PUNCT
cana-6157	157	81	sme	sme	NOUN
cana-6157	157	82	)	)	PUNCT
cana-6157	157	83	decrease	decrease	NOUN
cana-6157	157	84	as	as	ADP
cana-6157	157	85	the	the	DET
cana-6157	157	86	sample	sample	NOUN
cana-6157	157	87	size	size	NOUN
cana-6157	157	88	increases	increase	NOUN
cana-6157	157	89	.	.	PUNCT
cana-6157	158	1	ii	ii	PROPN
cana-6157	158	2	.	.	PROPN
cana-6157	158	3	criteria	criteria	PROPN
cana-6157	158	4	test	test	VERB
cana-6157	158	5	to	to	PART
cana-6157	158	6	show	show	VERB
cana-6157	158	7	the	the	DET
cana-6157	158	8	practibility	practibility	NOUN
cana-6157	158	9	of	of	ADP
cana-6157	158	10	the	the	DET
cana-6157	158	11	statistic	statistic	ADJ
cana-6157	158	12	test	test	NOUN
cana-6157	158	13	provided	provide	VERB
cana-6157	158	14	in	in	ADP
cana-6157	158	15	this	this	DET
cana-6157	158	16	work	work	NOUN
cana-6157	158	17	,	,	PUNCT
cana-6157	158	18	we	we	PRON
cana-6157	158	19	test	test	VERB
cana-6157	158	20	the	the	DET
cana-6157	158	21	null	null	ADJ
cana-6157	158	22	hypothesis	hypothesis	NOUN
cana-6157	158	23	𝐻0that	𝐻0that	PRON
cana-6157	158	24	samples	sample	NOUN
cana-6157	158	25	are	be	AUX
cana-6157	158	26	drawn	draw	VERB
cana-6157	158	27	from	from	ADP
cana-6157	158	28	the	the	DET
cana-6157	158	29	aptee	aptee	ADJ
cana-6157	158	30	distribution	distribution	NOUN
cana-6157	158	31	.	.	PUNCT
cana-6157	159	1	at	at	ADP
cana-6157	159	2	this	this	DET
cana-6157	159	3	end	end	NOUN
cana-6157	159	4	,	,	PUNCT
cana-6157	159	5	the	the	DET
cana-6157	159	6	theoretical	theoretical	ADJ
cana-6157	159	7	levels	level	NOUN
cana-6157	159	8	of	of	ADP
cana-6157	159	9	significance	significance	NOUN
cana-6157	159	10	ξ=	ξ=	NOUN
cana-6157	159	11	(	(	PUNCT
cana-6157	159	12	0.01,0.05,0.1	0.01,0.05,0.1	NOUN
cana-6157	159	13	)	)	PUNCT
cana-6157	159	14	are	be	AUX
cana-6157	159	15	communications	communication	NOUN
cana-6157	159	16	on	on	ADP
cana-6157	159	17	applied	apply	VERB
cana-6157	159	18	nonlinear	nonlinear	ADJ
cana-6157	159	19	analysis	analysis	NOUN
cana-6157	159	20	issn	issn	NOUN
cana-6157	159	21	:	:	PUNCT
cana-6157	159	22	1074	1074	NUM
cana-6157	159	23	-	-	PUNCT
cana-6157	159	24	133x	133x	NUM
cana-6157	159	25	vol	vol	VERB
cana-6157	159	26	32	32	NUM
cana-6157	159	27	no	no	NOUN
cana-6157	159	28	.	.	PUNCT
cana-6157	160	1	10s	10	NOUN
cana-6157	160	2	(	(	PUNCT
cana-6157	160	3	2025	2025	NUM
cana-6157	160	4	)	)	PUNCT
cana-6157	160	5	3489	3489	NUM
cana-6157	160	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	160	7	compared	compare	VERB
cana-6157	160	8	to	to	ADP
cana-6157	160	9	those	those	PRON
cana-6157	160	10	corresponding	correspond	VERB
cana-6157	160	11	to	to	ADP
cana-6157	160	12	empirical	empirical	ADJ
cana-6157	160	13	levels	level	NOUN
cana-6157	160	14	of	of	ADP
cana-6157	160	15	significance	significance	NOUN
cana-6157	160	16	for	for	ADP
cana-6157	160	17	10.000	10.000	NUM
cana-6157	160	18	simulated	simulated	ADJ
cana-6157	160	19	samples	sample	NOUN
cana-6157	160	20	from	from	ADP
cana-6157	160	21	different	different	ADJ
cana-6157	160	22	sizes	size	NOUN
cana-6157	160	23	(	(	PUNCT
cana-6157	160	24	n=15,50,100,200	n=15,50,100,200	X
cana-6157	160	25	)	)	PUNCT
cana-6157	160	26	.	.	PUNCT
cana-6157	161	1	the	the	DET
cana-6157	161	2	results	result	NOUN
cana-6157	161	3	are	be	AUX
cana-6157	161	4	summarized	summarize	VERB
cana-6157	161	5	in	in	ADP
cana-6157	161	6	table	table	NOUN
cana-6157	161	7	5	5	NUM
cana-6157	161	8	.	.	PUNCT
cana-6157	161	9	table	table	NOUN
cana-6157	161	10	5	5	NUM
cana-6157	161	11	:	:	PUNCT
cana-6157	161	12	critical	critical	ADJ
cana-6157	161	13	chi	chi	NOUN
cana-6157	161	14	-	-	PUNCT
cana-6157	161	15	square	square	NOUN
cana-6157	161	16	and	and	CCONJ
cana-6157	161	17	their	their	PRON
cana-6157	161	18	corresponding	correspond	VERB
cana-6157	161	19	empirical	empirical	ADJ
cana-6157	161	20	values	value	NOUN
cana-6157	161	21	n	n	PRON
cana-6157	161	22	ξ=0.01	ξ=0.01	ADJ
cana-6157	161	23	ξ=0.1	ξ=0.1	ADJ
cana-6157	161	24	ξ=0.05	ξ=0.05	NOUN
cana-6157	161	25	15	15	NUM
cana-6157	161	26	0.0158	0.0158	NUM
cana-6157	161	27	0.1240	0.1240	NUM
cana-6157	161	28	0.0462	0.0462	NUM
cana-6157	161	29	50	50	NUM
cana-6157	161	30	0.0133	0.0133	NUM
cana-6157	161	31	0.1090	0.1090	NUM
cana-6157	161	32	0.0492	0.0492	NUM
cana-6157	161	33	100	100	NUM
cana-6157	161	34	0.0112	0.0112	NUM
cana-6157	161	35	0.1055	0.1055	NUM
cana-6157	161	36	0.0498	0.0498	NUM
cana-6157	161	37	200	200	NUM
cana-6157	161	38	0.0108	0.0108	NUM
cana-6157	161	39	0.1003	0.1003	NUM
cana-6157	161	40	0.5009	0.5009	NUM
cana-6157	161	41	as	as	SCONJ
cana-6157	161	42	expected	expect	VERB
cana-6157	161	43	,	,	PUNCT
cana-6157	161	44	the	the	DET
cana-6157	161	45	obtained	obtain	VERB
cana-6157	161	46	empirical	empirical	ADJ
cana-6157	161	47	values	value	NOUN
cana-6157	161	48	are	be	AUX
cana-6157	161	49	very	very	ADV
cana-6157	161	50	close	close	ADJ
cana-6157	161	51	to	to	ADP
cana-6157	161	52	their	their	PRON
cana-6157	161	53	corresponding	correspond	VERB
cana-6157	161	54	theoretical	theoretical	ADJ
cana-6157	161	55	ones	one	NOUN
cana-6157	161	56	which	which	PRON
cana-6157	161	57	implies	imply	VERB
cana-6157	161	58	the	the	DET
cana-6157	161	59	feasibility	feasibility	NOUN
cana-6157	161	60	of	of	ADP
cana-6157	161	61	the	the	DET
cana-6157	161	62	proposed	propose	VERB
cana-6157	161	63	goodness	goodness	NOUN
cana-6157	161	64	-	-	PUNCT
cana-6157	161	65	of	of	ADP
cana-6157	161	66	-	-	PUNCT
cana-6157	161	67	fit	fit	NOUN
cana-6157	161	68	test	test	NOUN
cana-6157	161	69	to	to	PART
cana-6157	161	70	validate	validate	VERB
cana-6157	161	71	the	the	DET
cana-6157	161	72	aptee	aptee	ADJ
cana-6157	161	73	distribution	distribution	NOUN
cana-6157	161	74	.	.	PUNCT
cana-6157	162	1	iii	iii	X
cana-6157	162	2	.	.	PUNCT
cana-6157	162	3	application	application	NOUN
cana-6157	162	4	in	in	ADP
cana-6157	162	5	this	this	DET
cana-6157	162	6	section	section	NOUN
cana-6157	163	1	,	,	PUNCT
cana-6157	163	2	we	we	PRON
cana-6157	163	3	applied	apply	VERB
cana-6157	163	4	the	the	DET
cana-6157	163	5	obtained	obtain	VERB
cana-6157	163	6	results	result	NOUN
cana-6157	163	7	to	to	ADP
cana-6157	163	8	a	a	DET
cana-6157	163	9	real	real	ADJ
cana-6157	163	10	dataset	dataset	NOUN
cana-6157	163	11	(	(	PUNCT
cana-6157	163	12	dataset	dataset	NOUN
cana-6157	163	13	i	i	PRON
cana-6157	163	14	)	)	PUNCT
cana-6157	163	15	representing	represent	VERB
cana-6157	163	16	the	the	DET
cana-6157	163	17	survival	survival	NOUN
cana-6157	163	18	time	time	NOUN
cana-6157	163	19	(	(	PUNCT
cana-6157	163	20	in	in	ADP
cana-6157	163	21	days	day	NOUN
cana-6157	163	22	)	)	PUNCT
cana-6157	163	23	of	of	ADP
cana-6157	163	24	72	72	NUM
cana-6157	163	25	guinea	guinea	NOUN
cana-6157	163	26	pigs	pig	NOUN
cana-6157	163	27	infected	infect	VERB
cana-6157	163	28	with	with	ADP
cana-6157	163	29	virulent	virulent	ADJ
cana-6157	163	30	tubercle	tubercle	NOUN
cana-6157	163	31	bacilli	bacilli	NOUN
cana-6157	163	32	,	,	PUNCT
cana-6157	163	33	as	as	SCONJ
cana-6157	163	34	reported	report	VERB
cana-6157	163	35	by	by	ADP
cana-6157	163	36	bjerkedal	bjerkedal	NOUN
cana-6157	163	37	(	(	PUNCT
cana-6157	163	38	1960	1960	NUM
cana-6157	163	39	)	)	PUNCT
cana-6157	163	40	.	.	PUNCT
cana-6157	164	1	the	the	DET
cana-6157	164	2	data	datum	NOUN
cana-6157	164	3	are	be	AUX
cana-6157	164	4	as	as	SCONJ
cana-6157	164	5	follows	follow	VERB
cana-6157	164	6	:	:	PUNCT
cana-6157	164	7	0.1	0.1	NUM
cana-6157	164	8	,	,	PUNCT
cana-6157	164	9	0.33	0.33	NUM
cana-6157	164	10	,	,	PUNCT
cana-6157	164	11	0.44	0.44	NUM
cana-6157	164	12	,	,	PUNCT
cana-6157	164	13	0.56	0.56	NUM
cana-6157	164	14	,	,	PUNCT
cana-6157	164	15	0.59	0.59	NUM
cana-6157	164	16	,	,	PUNCT
cana-6157	164	17	0.72	0.72	NUM
cana-6157	164	18	,	,	PUNCT
cana-6157	164	19	0.74	0.74	NUM
cana-6157	164	20	,	,	PUNCT
cana-6157	164	21	0.77	0.77	NUM
cana-6157	164	22	,	,	PUNCT
cana-6157	164	23	0.92	0.92	NUM
cana-6157	164	24	,	,	PUNCT
cana-6157	164	25	0.93	0.93	NUM
cana-6157	164	26	,	,	PUNCT
cana-6157	164	27	0.96	0.96	NUM
cana-6157	164	28	,	,	PUNCT
cana-6157	164	29	1	1	NUM
cana-6157	164	30	,	,	PUNCT
cana-6157	164	31	1	1	NUM
cana-6157	164	32	,	,	PUNCT
cana-6157	164	33	1.02	1.02	NUM
cana-6157	164	34	,	,	PUNCT
cana-6157	164	35	1.05	1.05	NUM
cana-6157	164	36	,	,	PUNCT
cana-6157	164	37	1.07	1.07	NUM
cana-6157	164	38	,	,	PUNCT
cana-6157	164	39	07	07	NUM
cana-6157	164	40	,	,	PUNCT
cana-6157	164	41	1.08	1.08	NUM
cana-6157	164	42	,	,	PUNCT
cana-6157	164	43	1.08,1.08	1.08,1.08	NUM
cana-6157	164	44	,	,	PUNCT
cana-6157	164	45	1.09	1.09	NUM
cana-6157	164	46	,	,	PUNCT
cana-6157	164	47	1.12	1.12	NUM
cana-6157	164	48	,	,	PUNCT
cana-6157	164	49	1.13	1.13	NUM
cana-6157	164	50	,	,	PUNCT
cana-6157	164	51	1.15	1.15	NUM
cana-6157	164	52	,	,	PUNCT
cana-6157	164	53	1.16	1.16	NUM
cana-6157	164	54	,	,	PUNCT
cana-6157	164	55	1.2	1.2	NUM
cana-6157	164	56	,	,	PUNCT
cana-6157	164	57	1.21	1.21	NUM
cana-6157	164	58	,	,	PUNCT
cana-6157	164	59	1.22	1.22	NUM
cana-6157	164	60	,	,	PUNCT
cana-6157	164	61	1.22	1.22	NUM
cana-6157	164	62	,	,	PUNCT
cana-6157	164	63	1.24	1.24	NUM
cana-6157	164	64	,	,	PUNCT
cana-6157	164	65	1.3	1.3	NUM
cana-6157	164	66	,	,	PUNCT
cana-6157	164	67	1.34	1.34	NUM
cana-6157	164	68	,	,	PUNCT
cana-6157	164	69	1.36	1.36	NUM
cana-6157	164	70	,	,	PUNCT
cana-6157	164	71	1.39	1.39	NUM
cana-6157	164	72	,	,	PUNCT
cana-6157	164	73	1.44	1.44	NUM
cana-6157	164	74	,	,	PUNCT
cana-6157	164	75	1.46	1.46	NUM
cana-6157	164	76	,	,	PUNCT
cana-6157	164	77	1.53,1.59	1.53,1.59	NUM
cana-6157	164	78	,	,	PUNCT
cana-6157	164	79	1.6	1.6	NUM
cana-6157	164	80	,	,	PUNCT
cana-6157	164	81	1.63	1.63	NUM
cana-6157	164	82	,	,	PUNCT
cana-6157	164	83	1.63	1.63	NUM
cana-6157	164	84	,	,	PUNCT
cana-6157	164	85	1.68	1.68	NUM
cana-6157	164	86	,	,	PUNCT
cana-6157	164	87	1.71	1.71	NUM
cana-6157	164	88	,	,	PUNCT
cana-6157	164	89	1.72	1.72	NUM
cana-6157	164	90	,	,	PUNCT
cana-6157	164	91	1.76	1.76	NUM
cana-6157	164	92	,	,	PUNCT
cana-6157	164	93	1.83	1.83	NUM
cana-6157	164	94	,	,	PUNCT
cana-6157	164	95	1.95	1.95	NUM
cana-6157	164	96	,	,	PUNCT
cana-6157	164	97	1.96	1.96	NUM
cana-6157	164	98	,	,	PUNCT
cana-6157	164	99	1.97	1.97	NUM
cana-6157	164	100	,	,	PUNCT
cana-6157	164	101	2.02	2.02	NUM
cana-6157	164	102	,	,	PUNCT
cana-6157	164	103	2.13	2.13	NUM
cana-6157	164	104	,	,	PUNCT
cana-6157	164	105	2.15	2.15	NUM
cana-6157	164	106	,	,	PUNCT
cana-6157	164	107	2.16	2.16	NUM
cana-6157	164	108	,	,	PUNCT
cana-6157	164	109	2.22	2.22	NUM
cana-6157	164	110	,	,	PUNCT
cana-6157	164	111	2.3,2.31	2.3,2.31	NUM
cana-6157	164	112	,	,	PUNCT
cana-6157	164	113	2.4	2.4	NUM
cana-6157	164	114	,	,	PUNCT
cana-6157	164	115	2.45	2.45	NUM
cana-6157	164	116	,	,	PUNCT
cana-6157	164	117	2.51	2.51	NUM
cana-6157	164	118	,	,	PUNCT
cana-6157	164	119	2.53	2.53	NUM
cana-6157	164	120	,	,	PUNCT
cana-6157	164	121	2.54	2.54	NUM
cana-6157	164	122	,	,	PUNCT
cana-6157	164	123	2.54	2.54	NUM
cana-6157	164	124	,	,	PUNCT
cana-6157	164	125	2.78	2.78	NUM
cana-6157	164	126	,	,	PUNCT
cana-6157	164	127	2.93	2.93	NUM
cana-6157	164	128	,	,	PUNCT
cana-6157	164	129	3.27	3.27	NUM
cana-6157	164	130	,	,	PUNCT
cana-6157	164	131	3.42	3.42	NUM
cana-6157	164	132	,	,	PUNCT
cana-6157	164	133	3.47	3.47	NUM
cana-6157	164	134	,	,	PUNCT
cana-6157	164	135	3.61	3.61	NUM
cana-6157	164	136	,	,	PUNCT
cana-6157	164	137	4.02	4.02	NUM
cana-6157	164	138	,	,	PUNCT
cana-6157	164	139	4.32	4.32	NUM
cana-6157	164	140	,	,	PUNCT
cana-6157	164	141	4.58	4.58	NUM
cana-6157	164	142	,	,	PUNCT
cana-6157	164	143	5.55	5.55	NUM
cana-6157	164	144	.	.	PUNCT
cana-6157	165	1	table6	table6	NOUN
cana-6157	165	2	:	:	PUNCT
cana-6157	165	3	estimated	estimate	VERB
cana-6157	165	4	values	value	NOUN
cana-6157	165	5	for	for	ADP
cana-6157	165	6	the	the	DET
cana-6157	165	7	unknown	unknown	ADJ
cana-6157	165	8	parameters	parameter	NOUN
cana-6157	165	9	of	of	ADP
cana-6157	165	10	the	the	DET
cana-6157	165	11	competing	compete	VERB
cana-6157	165	12	distribution	distribution	NOUN
cana-6157	165	13	associatedwithdataset	associatedwithdataset	NOUN
cana-6157	166	1	i	i	PRON
cana-6157	166	2	methode	methode	NOUN
cana-6157	166	3	α	α	PROPN
cana-6157	166	4	β	β	X
cana-6157	166	5	λ̂	λ̂	X
cana-6157	166	6	ad	ad	NOUN
cana-6157	166	7	1.29811	1.29811	NUM
cana-6157	166	8	0.05858	0.05858	NUM
cana-6157	166	9	1.71231	1.71231	NUM
cana-6157	166	10	cvm	cvm	NOUN
cana-6157	166	11	1.60684	1.60684	NUM
cana-6157	166	12	0.86685	0.86685	NUM
cana-6157	166	13	0.72275	0.72275	NUM
cana-6157	166	14	ks	ks	PROPN
cana-6157	166	15	1.641786	1.641786	NUM
cana-6157	166	16	0.87502	0.87502	NUM
cana-6157	166	17	1.60815	1.60815	NUM
cana-6157	166	18	mle	mle	NOUN
cana-6157	166	19	0.04398	0.04398	NUM
cana-6157	166	20	1.57090	1.57090	NUM
cana-6157	166	21	0.05153	0.05153	NUM
cana-6157	166	22	on	on	ADP
cana-6157	166	23	the	the	DET
cana-6157	166	24	other	other	ADJ
cana-6157	166	25	hand	hand	NOUN
cana-6157	166	26	,	,	PUNCT
cana-6157	166	27	we	we	PRON
cana-6157	166	28	assume	assume	VERB
cana-6157	166	29	the	the	DET
cana-6157	166	30	null	null	ADJ
cana-6157	166	31	hypothesis	hypothesis	NOUN
cana-6157	166	32	that	that	PRON
cana-6157	166	33	the	the	DET
cana-6157	166	34	dataset	dataset	NOUN
cana-6157	166	35	i	i	PRON
cana-6157	166	36	belongs	belong	VERB
cana-6157	166	37	to	to	ADP
cana-6157	166	38	the	the	DET
cana-6157	166	39	aptee	aptee	ADJ
cana-6157	166	40	distribution	distribution	NOUN
cana-6157	166	41	.	.	PUNCT
cana-6157	167	1	if	if	SCONJ
cana-6157	167	2	we	we	PRON
cana-6157	167	3	choose	choose	VERB
cana-6157	167	4	r=8	r=8	PROPN
cana-6157	167	5	clustering	cluster	VERB
cana-6157	167	6	classes	class	NOUN
cana-6157	167	7	,	,	PUNCT
cana-6157	167	8	the	the	DET
cana-6157	167	9	intermediate	intermediate	ADJ
cana-6157	167	10	calculation	calculation	NOUN
cana-6157	167	11	of	of	ADP
cana-6157	167	12	the	the	DET
cana-6157	167	13	test	test	NOUN
cana-6157	167	14	criterion	criterion	NOUN
cana-6157	167	15	y²	y²	NOUN
cana-6157	167	16	is	be	AUX
cana-6157	167	17	as	as	SCONJ
cana-6157	167	18	follows	follow	VERB
cana-6157	167	19	:	:	PUNCT
cana-6157	167	20	𝐿	𝐿	PROPN
cana-6157	167	21	=	=	SYM
cana-6157	167	22	(	(	PUNCT
cana-6157	167	23	𝐿1	𝐿1	PROPN
cana-6157	167	24	=	=	PUNCT
cana-6157	167	25	−1.906953	−1.906953	PROPN
cana-6157	167	26	,	,	PUNCT
cana-6157	167	27	𝐿2	𝐿2	PROPN
cana-6157	167	28	=	=	SYM
cana-6157	167	29	−3.778612	−3.778612	NOUN
cana-6157	167	30	,	,	PUNCT
cana-6157	167	31	𝐿3	𝐿3	NOUN
cana-6157	167	32	=	=	SYM
cana-6157	168	1	−7.907812	−7.907812	PROPN
cana-6157	168	2	)	)	PUNCT
cana-6157	168	3	𝐽(	𝐽(	X
cana-6157	168	4	�	�	PROPN
cana-6157	168	5	̂	̂	NOUN
cana-6157	168	6	�	�	NOUN
cana-6157	168	7	)	)	PUNCT
cana-6157	169	1	=	=	PUNCT
cana-6157	169	2	[	[	PUNCT
cana-6157	169	3	0.86623	0.86623	NUM
cana-6157	169	4	1.11380	1.11380	NUM
cana-6157	169	5	3.32281	3.32281	NUM
cana-6157	169	6	1.11380	1.11380	NUM
cana-6157	169	7	1.49291	1.49291	NUM
cana-6157	169	8	4.30159	4.30159	NUM
cana-6157	169	9	3.32811	3.32811	NUM
cana-6157	169	10	4.30159	4.30159	NUM
cana-6157	169	11	12.7950	12.7950	NUM
cana-6157	169	12	]	]	PUNCT
cana-6157	169	13	𝐼𝑛(	𝐼𝑛(	X
cana-6157	169	14	�	�	PROPN
cana-6157	169	15	̂	̂	NUM
cana-6157	169	16	�	�	NOUN
cana-6157	169	17	)	)	PUNCT
cana-6157	169	18	=	=	NOUN
cana-6157	170	1	[	[	PUNCT
cana-6157	170	2	0.21943	0.21943	NUM
cana-6157	170	3	0.16997	0.16997	NUM
cana-6157	170	4	0.14933	0.14933	NUM
cana-6157	170	5	0.16997	0.16997	NUM
cana-6157	170	6	0.13167	0.13167	NUM
cana-6157	170	7	0.11568	0.11568	NUM
cana-6157	170	8	0.14933	0.14933	NUM
cana-6157	170	9	0.11568	0.11568	NUM
cana-6157	170	10	0.10163	0.10163	NUM
cana-6157	170	11	]	]	PUNCT
cana-6157	170	12	we	we	PRON
cana-6157	170	13	get	get	VERB
cana-6157	170	14	𝑌2	𝑌2	NOUN
cana-6157	170	15	=	=	SYM
cana-6157	170	16	6.50414	6.50414	NUM
cana-6157	170	17	,	,	PUNCT
cana-6157	170	18	so	so	ADV
cana-6157	170	19	for	for	ADP
cana-6157	170	20	significance	significance	NOUN
cana-6157	170	21	level	level	NOUN
cana-6157	170	22	𝜉	𝜉	NOUN
cana-6157	170	23	=	=	NOUN
cana-6157	170	24	0.05,the	0.05,the	DET
cana-6157	170	25	critical	critical	ADJ
cana-6157	170	26	chi	chi	ADJ
cana-6157	170	27	-	-	PUNCT
cana-6157	170	28	square	square	ADJ
cana-6157	170	29	value	value	NOUN
cana-6157	170	30	is	be	AUX
cana-6157	170	31	xr−1	xr−1	PROPN
cana-6157	170	32	2	2	NUM
cana-6157	170	33	=	=	SYM
cana-6157	170	34	14.06	14.06	NUM
cana-6157	170	35	as	as	ADP
cana-6157	170	36	y2	y2	PROPN
cana-6157	170	37	≺	≺	NOUN
cana-6157	171	1	xr−1	xr−1	PROPN
cana-6157	171	2	2	2	NUM
cana-6157	171	3	the	the	DET
cana-6157	171	4	null	null	ADJ
cana-6157	171	5	hypothesis	hypothesis	NOUN
cana-6157	171	6	𝐻0	𝐻0	NOUN
cana-6157	171	7	can	can	AUX
cana-6157	171	8	not	not	PART
cana-6157	171	9	be	be	AUX
cana-6157	171	10	rejected	reject	VERB
cana-6157	171	11	,	,	PUNCT
cana-6157	171	12	according	accord	VERB
cana-6157	171	13	to	to	ADP
cana-6157	171	14	which	which	PRON
cana-6157	171	15	the	the	DET
cana-6157	171	16	aptee	aptee	ADJ
cana-6157	171	17	distribution	distribution	NOUN
cana-6157	171	18	is	be	AUX
cana-6157	171	19	best	well	ADV
cana-6157	171	20	suited	suited	ADJ
cana-6157	171	21	to	to	PART
cana-6157	171	22	model	model	VERB
cana-6157	171	23	this	this	DET
cana-6157	171	24	dataset	dataset	PROPN
cana-6157	171	25	i.	i.	PROPN
cana-6157	171	26	vii	vii	PROPN
cana-6157	171	27	.	.	PUNCT
cana-6157	172	1	reliability	reliability	NOUN
cana-6157	172	2	example	example	NOUN
cana-6157	172	3	to	to	PART
cana-6157	172	4	illustrate	illustrate	VERB
cana-6157	172	5	the	the	DET
cana-6157	172	6	usefulness	usefulness	NOUN
cana-6157	172	7	of	of	ADP
cana-6157	172	8	the	the	DET
cana-6157	172	9	aptee	aptee	NOUN
cana-6157	172	10	model	model	NOUN
cana-6157	172	11	,	,	PUNCT
cana-6157	172	12	we	we	PRON
cana-6157	172	13	analyze	analyze	VERB
cana-6157	172	14	a	a	DET
cana-6157	172	15	real	real	ADJ
cana-6157	172	16	dataset	dataset	NOUN
cana-6157	172	17	taken	take	VERB
cana-6157	172	18	from	from	ADP
cana-6157	172	19	linhart	linhart	NOUN
cana-6157	172	20	and	and	CCONJ
cana-6157	172	21	zucchini	zucchini	NOUN
cana-6157	172	22	(	(	PUNCT
cana-6157	172	23	h.	h.	PROPN
cana-6157	172	24	linhart	linhart	PROPN
cana-6157	172	25	,	,	PUNCT
cana-6157	172	26	w.	w.	PROPN
cana-6157	172	27	zucchini	zucchini	PROPN
cana-6157	172	28	,	,	PUNCT
cana-6157	172	29	model	model	NOUN
cana-6157	172	30	selection	selection	NOUN
cana-6157	172	31	,	,	PUNCT
cana-6157	172	32	john	john	PROPN
cana-6157	172	33	wiley	wiley	PROPN
cana-6157	172	34	&	&	CCONJ
cana-6157	172	35	sons	son	NOUN
cana-6157	172	36	,	,	PUNCT
cana-6157	172	37	new	new	PROPN
cana-6157	172	38	york	york	PROPN
cana-6157	172	39	,	,	PUNCT
cana-6157	172	40	1986	1986	NUM
cana-6157	172	41	)	)	PUNCT
cana-6157	173	1	[	[	X
cana-6157	173	2	5	5	NUM
cana-6157	173	3	]	]	PUNCT
cana-6157	173	4	.	.	PUNCT
cana-6157	174	1	this	this	DET
cana-6157	174	2	dataset	dataset	NOUN
cana-6157	174	3	represents	represent	VERB
cana-6157	174	4	the	the	DET
cana-6157	174	5	failure	failure	NOUN
cana-6157	174	6	times	time	NOUN
cana-6157	174	7	of	of	ADP
cana-6157	174	8	an	an	DET
cana-6157	174	9	aircraft	aircraft	NOUN
cana-6157	174	10	's	's	PART
cana-6157	174	11	air	air	NOUN
cana-6157	174	12	-	-	PUNCT
cana-6157	174	13	conditioning	conditioning	NOUN
cana-6157	174	14	system	system	NOUN
cana-6157	174	15	,	,	PUNCT
cana-6157	174	16	with	with	ADP
cana-6157	174	17	the	the	DET
cana-6157	174	18	recorded	record	VERB
cana-6157	174	19	times	time	NOUN
cana-6157	174	20	as	as	SCONJ
cana-6157	174	21	follows	follow	VERB
cana-6157	174	22	:	:	PUNCT
cana-6157	174	23	23	23	NUM
cana-6157	174	24	,	,	PUNCT
cana-6157	174	25	261	261	NUM
cana-6157	174	26	,	,	PUNCT
cana-6157	174	27	87	87	NUM
cana-6157	174	28	,	,	PUNCT
cana-6157	174	29	7	7	NUM
cana-6157	174	30	,	,	PUNCT
cana-6157	174	31	120	120	NUM
cana-6157	174	32	,	,	PUNCT
cana-6157	174	33	14	14	NUM
cana-6157	174	34	,	,	PUNCT
cana-6157	174	35	62	62	NUM
cana-6157	174	36	,	,	PUNCT
cana-6157	174	37	47	47	NUM
cana-6157	174	38	,	,	PUNCT
cana-6157	174	39	225	225	NUM
cana-6157	174	40	,	,	PUNCT
cana-6157	174	41	71	71	NUM
cana-6157	174	42	,	,	PUNCT
cana-6157	174	43	246	246	NUM
cana-6157	174	44	,	,	PUNCT
cana-6157	174	45	21	21	NUM
cana-6157	174	46	,	,	PUNCT
cana-6157	174	47	42	42	NUM
cana-6157	174	48	,	,	PUNCT
cana-6157	174	49	20	20	NUM
cana-6157	174	50	,	,	PUNCT
cana-6157	174	51	5	5	NUM
cana-6157	174	52	,	,	PUNCT
cana-6157	174	53	12	12	NUM
cana-6157	174	54	,	,	PUNCT
cana-6157	174	55	120	120	NUM
cana-6157	174	56	,	,	PUNCT
cana-6157	174	57	11	11	NUM
cana-6157	174	58	,	,	PUNCT
cana-6157	174	59	3	3	NUM
cana-6157	174	60	,	,	PUNCT
cana-6157	174	61	14	14	NUM
cana-6157	174	62	,	,	PUNCT
cana-6157	174	63	71	71	NUM
cana-6157	174	64	,	,	PUNCT
cana-6157	174	65	11	11	NUM
cana-6157	174	66	,	,	PUNCT
cana-6157	174	67	14	14	NUM
cana-6157	174	68	,	,	PUNCT
cana-6157	174	69	11	11	NUM
cana-6157	174	70	,	,	PUNCT
cana-6157	174	71	16	16	NUM
cana-6157	174	72	,	,	PUNCT
cana-6157	174	73	90	90	NUM
cana-6157	174	74	,	,	PUNCT
cana-6157	174	75	1	1	NUM
cana-6157	174	76	,	,	PUNCT
cana-6157	174	77	16	16	NUM
cana-6157	174	78	,	,	PUNCT
cana-6157	174	79	52	52	NUM
cana-6157	174	80	,	,	PUNCT
cana-6157	174	81	95	95	NUM
cana-6157	174	82	.	.	PUNCT
cana-6157	175	1	however	however	ADV
cana-6157	175	2	,	,	PUNCT
cana-6157	175	3	we	we	PRON
cana-6157	175	4	assume	assume	VERB
cana-6157	175	5	the	the	DET
cana-6157	175	6	null	null	ADJ
cana-6157	175	7	hypothesis	hypothesis	NOUN
cana-6157	175	8	communications	communication	NOUN
cana-6157	175	9	on	on	ADP
cana-6157	175	10	applied	apply	VERB
cana-6157	175	11	nonlinear	nonlinear	ADJ
cana-6157	175	12	analysis	analysis	NOUN
cana-6157	175	13	issn	issn	NOUN
cana-6157	175	14	:	:	PUNCT
cana-6157	175	15	1074	1074	NUM
cana-6157	175	16	-	-	PUNCT
cana-6157	175	17	133x	133x	NUM
cana-6157	175	18	vol	vol	VERB
cana-6157	175	19	32	32	NUM
cana-6157	175	20	no	no	NOUN
cana-6157	175	21	.	.	PUNCT
cana-6157	176	1	10s	10	NOUN
cana-6157	176	2	(	(	PUNCT
cana-6157	176	3	2025	2025	NUM
cana-6157	176	4	)	)	PUNCT
cana-6157	176	5	3490	3490	NUM
cana-6157	176	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	176	7	𝐿	𝐿	PROPN
cana-6157	176	8	=	=	SYM
cana-6157	176	9	(	(	PUNCT
cana-6157	176	10	𝐿1	𝐿1	PROPN
cana-6157	176	11	=	=	SYM
cana-6157	176	12	−0.0048667	−0.0048667	NOUN
cana-6157	176	13	,	,	PUNCT
cana-6157	176	14	𝐿2	𝐿2	PROPN
cana-6157	176	15	=	=	SYM
cana-6157	176	16	−0.00148015	−0.00148015	PROPN
cana-6157	176	17	,	,	PUNCT
cana-6157	176	18	𝐿3	𝐿3	NOUN
cana-6157	176	19	=	=	SYM
cana-6157	176	20	−0.0045631	−0.0045631	PROPN
cana-6157	176	21	)	)	PUNCT
cana-6157	176	22	𝐼𝑛(	𝐼𝑛(	X
cana-6157	176	23	�	�	PROPN
cana-6157	176	24	̂	̂	NUM
cana-6157	176	25	�	�	NOUN
cana-6157	176	26	)	)	PUNCT
cana-6157	176	27	=	=	NOUN
cana-6157	177	1	[	[	PUNCT
cana-6157	177	2	0.055706	0.055706	NUM
cana-6157	177	3	−0.001694	−0.001694	NOUN
cana-6157	177	4	−0.005224	−0.005224	X
cana-6157	177	5	−0.001694	−0.001694	NOUN
cana-6157	177	6	0.005151	0.005151	NUM
cana-6157	177	7	0.001588	0.001588	NUM
cana-6157	177	8	−0.005224	−0.005224	X
cana-6157	177	9	0.115680	0.115680	NUM
cana-6157	177	10	0.004896	0.004896	NUM
cana-6157	177	11	]	]	PUNCT
cana-6157	177	12	𝐽(	𝐽(	X
cana-6157	177	13	�	�	PROPN
cana-6157	177	14	̂	̂	VERB
cana-6157	177	15	�	�	NOUN
cana-6157	177	16	)	)	PUNCT
cana-6157	177	17	=	=	PUNCT
cana-6157	178	1	[	[	PUNCT
cana-6157	178	2	0.046190	0.046190	NUM
cana-6157	178	3	−0.01404	−0.01404	NOUN
cana-6157	178	4	−0.04330	−0.04330	NUM
cana-6157	178	5	−0.01404	−0.01404	NOUN
cana-6157	178	6	−0.00427	−0.00427	NOUN
cana-6157	178	7	0.01316	0.01316	NUM
cana-6157	178	8	−0.04330	−0.04330	NUM
cana-6157	178	9	0.01316	0.01316	NUM
cana-6157	178	10	0.04597	0.04597	NUM
cana-6157	178	11	]	]	PUNCT
cana-6157	178	12	we	we	PRON
cana-6157	178	13	obtain	obtain	VERB
cana-6157	178	14	𝑌2=4.8999	𝑌2=4.8999	NOUN
cana-6157	178	15	,	,	PUNCT
cana-6157	178	16	so	so	ADV
cana-6157	178	17	for	for	ADP
cana-6157	178	18	the	the	DET
cana-6157	178	19	significance	significance	NOUN
cana-6157	178	20	level	level	NOUN
cana-6157	178	21	𝜉	𝜉	NOUN
cana-6157	178	22	=	=	NOUN
cana-6157	178	23	0.05	0.05	NUM
cana-6157	178	24	,	,	PUNCT
cana-6157	178	25	the	the	DET
cana-6157	178	26	critical	critical	ADJ
cana-6157	178	27	chi	chi	ADJ
cana-6157	178	28	-	-	PUNCT
cana-6157	178	29	square	square	ADJ
cana-6157	178	30	value	value	NOUN
cana-6157	178	31	is	be	AUX
cana-6157	178	32	𝑋𝑟−1	𝑋𝑟−1	PROPN
cana-6157	178	33	2	2	NUM
cana-6157	178	34	=	=	SYM
cana-6157	178	35	=	=	SYM
cana-6157	178	36	9.487729	9.487729	NUM
cana-6157	178	37	.	.	PUNCT
cana-6157	179	1	since	since	SCONJ
cana-6157	179	2	𝑌2	𝑌2	NOUN
cana-6157	179	3	≺	≺	NOUN
cana-6157	179	4	𝑋𝑟−1	𝑋𝑟−1	PROPN
cana-6157	179	5	2	2	NUM
cana-6157	179	6	,	,	PUNCT
cana-6157	179	7	the	the	DET
cana-6157	179	8	null	null	ADJ
cana-6157	179	9	hypothesis	hypothesis	NOUN
cana-6157	179	10	𝐻0	𝐻0	NOUN
cana-6157	179	11	can	can	AUX
cana-6157	179	12	not	not	PART
cana-6157	179	13	be	be	AUX
cana-6157	179	14	rejected	reject	VERB
cana-6157	179	15	,	,	PUNCT
cana-6157	179	16	indicating	indicate	VERB
cana-6157	179	17	that	that	SCONJ
cana-6157	179	18	the	the	DET
cana-6157	179	19	aptee	aptee	ADJ
cana-6157	179	20	distribution	distribution	NOUN
cana-6157	179	21	is	be	AUX
cana-6157	179	22	the	the	DET
cana-6157	179	23	best	good	ADJ
cana-6157	179	24	fit	fit	NOUN
cana-6157	179	25	for	for	ADP
cana-6157	179	26	modeling	model	VERB
cana-6157	179	27	this	this	DET
cana-6157	179	28	dataset	dataset	NOUN
cana-6157	179	29	.	.	PUNCT
cana-6157	180	1	ix	ix	PROPN
cana-6157	180	2	.	.	PUNCT
cana-6157	180	3	model	model	NOUN
cana-6157	180	4	diagnostics	diagnostic	NOUN
cana-6157	180	5	and	and	CCONJ
cana-6157	180	6	residual	residual	ADJ
cana-6157	180	7	analysis	analysis	NOUN
cana-6157	180	8	in	in	ADP
cana-6157	180	9	order	order	NOUN
cana-6157	180	10	to	to	PART
cana-6157	180	11	evaluate	evaluate	VERB
cana-6157	180	12	the	the	DET
cana-6157	180	13	adequacy	adequacy	NOUN
cana-6157	180	14	and	and	CCONJ
cana-6157	180	15	robustness	robustness	NOUN
cana-6157	180	16	of	of	ADP
cana-6157	180	17	the	the	DET
cana-6157	180	18	fitted	fit	VERB
cana-6157	180	19	aptee	aptee	NOUN
cana-6157	180	20	distribution	distribution	NOUN
cana-6157	180	21	,	,	PUNCT
cana-6157	180	22	we	we	PRON
cana-6157	180	23	employ	employ	VERB
cana-6157	180	24	several	several	ADJ
cana-6157	180	25	diagnostic	diagnostic	ADJ
cana-6157	180	26	tools	tool	NOUN
cana-6157	180	27	:	:	PUNCT
cana-6157	180	28	cox	cox	PROPN
cana-6157	180	29	-	-	PUNCT
cana-6157	180	30	snell	snell	PROPN
cana-6157	180	31	residuals	residual	NOUN
cana-6157	180	32	,	,	PUNCT
cana-6157	180	33	probability	probability	NOUN
cana-6157	180	34	and	and	CCONJ
cana-6157	180	35	q	q	NOUN
cana-6157	180	36	-	-	PUNCT
cana-6157	180	37	q	q	NOUN
cana-6157	180	38	plots	plot	NOUN
cana-6157	180	39	,	,	PUNCT
cana-6157	180	40	and	and	CCONJ
cana-6157	180	41	hazard	hazard	NOUN
cana-6157	180	42	rate	rate	NOUN
cana-6157	180	43	comparison	comparison	NOUN
cana-6157	180	44	.	.	PUNCT
cana-6157	181	1	these	these	DET
cana-6157	181	2	diagnostics	diagnostic	NOUN
cana-6157	181	3	are	be	AUX
cana-6157	181	4	performed	perform	VERB
cana-6157	181	5	both	both	PRON
cana-6157	181	6	on	on	ADP
cana-6157	181	7	simulated	simulated	ADJ
cana-6157	181	8	datasets	dataset	NOUN
cana-6157	181	9	and	and	CCONJ
cana-6157	181	10	on	on	ADP
cana-6157	181	11	a	a	DET
cana-6157	181	12	real	real	ADJ
cana-6157	181	13	-	-	PUNCT
cana-6157	181	14	world	world	NOUN
cana-6157	181	15	application	application	NOUN
cana-6157	181	16	.	.	PUNCT
cana-6157	182	1	cox	cox	PROPN
cana-6157	182	2	-	-	PUNCT
cana-6157	182	3	snell	snell	PROPN
cana-6157	182	4	residuals	residual	NOUN
cana-6157	182	5	are	be	AUX
cana-6157	182	6	used	use	VERB
cana-6157	182	7	to	to	PART
cana-6157	182	8	assess	assess	VERB
cana-6157	182	9	the	the	DET
cana-6157	182	10	overall	overall	ADJ
cana-6157	182	11	fit	fit	NOUN
cana-6157	182	12	of	of	ADP
cana-6157	182	13	a	a	DET
cana-6157	182	14	parametric	parametric	ADJ
cana-6157	182	15	survival	survival	NOUN
cana-6157	182	16	model	model	NOUN
cana-6157	182	17	.	.	PUNCT
cana-6157	183	1	given	give	VERB
cana-6157	183	2	a	a	DET
cana-6157	183	3	fitted	fit	VERB
cana-6157	183	4	cumulative	cumulative	ADJ
cana-6157	183	5	distribution	distribution	NOUN
cana-6157	183	6	function	function	NOUN
cana-6157	183	7	�	�	NOUN
cana-6157	183	8	̂	̂	NOUN
cana-6157	183	9	�	�	NOUN
cana-6157	183	10	(𝑡	(𝑡	NOUN
cana-6157	183	11	)	)	PUNCT
cana-6157	183	12	the	the	DET
cana-6157	183	13	cox	cox	PROPN
cana-6157	183	14	-	-	PUNCT
cana-6157	183	15	snell	snell	PROPN
cana-6157	183	16	residual	residual	NOUN
cana-6157	183	17	for	for	ADP
cana-6157	183	18	the	the	DET
cana-6157	183	19	i	i	PROPN
cana-6157	183	20	-	-	PUNCT
cana-6157	183	21	th	th	VERB
cana-6157	183	22	observation	observation	NOUN
cana-6157	183	23	is	be	AUX
cana-6157	183	24	defined	define	VERB
cana-6157	183	25	as	as	ADP
cana-6157	183	26	:	:	PUNCT
cana-6157	183	27	𝑟𝑖	𝑟𝑖	ADV
cana-6157	183	28	=	=	PUNCT
cana-6157	183	29	−	−	NOUN
cana-6157	183	30	𝑙𝑜𝑔	𝑙𝑜𝑔	NOUN
cana-6157	183	31	(	(	PUNCT
cana-6157	183	32	�	�	NOUN
cana-6157	183	33	̂	̂	VERB
cana-6157	183	34	�	�	NOUN
cana-6157	183	35	(𝑡𝑖	(𝑡𝑖	NUM
cana-6157	183	36	)	)	PUNCT
cana-6157	183	37	)	)	PUNCT
cana-6157	184	1	=	=	PUNCT
cana-6157	185	1	−	−	NOUN
cana-6157	185	2	𝑙𝑜𝑔	𝑙𝑜𝑔	NOUN
cana-6157	185	3	(	(	PUNCT
cana-6157	185	4	1	1	NUM
cana-6157	185	5	−	−	PRON
cana-6157	185	6	�	�	PROPN
cana-6157	185	7	̂	̂	NOUN
cana-6157	185	8	�	�	NOUN
cana-6157	185	9	(𝑡𝑖))(25	(𝑡𝑖))(25	NOUN
cana-6157	185	10	)	)	PUNCT
cana-6157	185	11	if	if	SCONJ
cana-6157	185	12	the	the	DET
cana-6157	185	13	model	model	NOUN
cana-6157	185	14	is	be	AUX
cana-6157	185	15	correctly	correctly	ADV
cana-6157	185	16	specified	specify	VERB
cana-6157	185	17	,	,	PUNCT
cana-6157	185	18	these	these	DET
cana-6157	185	19	residuals	residual	NOUN
cana-6157	185	20	should	should	AUX
cana-6157	185	21	follow	follow	VERB
cana-6157	185	22	an	an	DET
cana-6157	185	23	exponential	exponential	ADJ
cana-6157	185	24	distribution	distribution	NOUN
cana-6157	185	25	with	with	ADP
cana-6157	185	26	mean	mean	NOUN
cana-6157	185	27	1	1	NUM
cana-6157	185	28	.	.	PUNCT
cana-6157	185	29	to	to	PART
cana-6157	185	30	verify	verify	VERB
cana-6157	185	31	this	this	PRON
cana-6157	185	32	,	,	PUNCT
cana-6157	185	33	we	we	PRON
cana-6157	185	34	:	:	PUNCT
cana-6157	185	35	plot	plot	VERB
cana-6157	185	36	the	the	DET
cana-6157	185	37	nelson	nelson	PROPN
cana-6157	185	38	-	-	PUNCT
cana-6157	185	39	aalen	aalen	VERB
cana-6157	185	40	cumulative	cumulative	ADJ
cana-6157	185	41	hazard	hazard	NOUN
cana-6157	185	42	estimator	estimator	NOUN
cana-6157	185	43	�	�	PROPN
cana-6157	185	44	̂	̂	PROPN
cana-6157	185	45	�	�	PROPN
cana-6157	185	46	(𝑟𝑖)versus	(𝑟𝑖)versus	VERB
cana-6157	185	47	the	the	DET
cana-6157	185	48	residuals	residual	NOUN
cana-6157	185	49	𝑟𝑖	𝑟𝑖	ADP
cana-6157	185	50	a	a	DET
cana-6157	185	51	straight	straight	ADJ
cana-6157	185	52	line	line	NOUN
cana-6157	185	53	through	through	ADP
cana-6157	185	54	the	the	DET
cana-6157	185	55	origin	origin	NOUN
cana-6157	185	56	with	with	ADP
cana-6157	185	57	slope	slope	NOUN
cana-6157	185	58	1	1	NUM
cana-6157	185	59	indicates	indicate	VERB
cana-6157	185	60	a	a	DET
cana-6157	185	61	good	good	ADJ
cana-6157	185	62	fit	fit	NOUN
cana-6157	185	63	.	.	PUNCT
cana-6157	186	1	compare	compare	VERB
cana-6157	186	2	the	the	DET
cana-6157	186	3	empirical	empirical	ADJ
cana-6157	186	4	distribution	distribution	NOUN
cana-6157	186	5	of	of	ADP
cana-6157	186	6	the	the	DET
cana-6157	186	7	residuals	residual	NOUN
cana-6157	186	8	to	to	ADP
cana-6157	186	9	the	the	DET
cana-6157	186	10	theoretical	theoretical	ADJ
cana-6157	186	11	exponential	exponential	NOUN
cana-6157	186	12	(	(	PUNCT
cana-6157	186	13	1	1	NUM
cana-6157	186	14	)	)	PUNCT
cana-6157	186	15	distribution	distribution	NOUN
cana-6157	186	16	using	use	VERB
cana-6157	186	17	q	q	NOUN
cana-6157	186	18	-	-	PUNCT
cana-6157	186	19	q	q	NOUN
cana-6157	186	20	and	and	CCONJ
cana-6157	186	21	p	p	NOUN
cana-6157	186	22	-	-	PUNCT
cana-6157	186	23	p	p	NOUN
cana-6157	186	24	plots	plot	NOUN
cana-6157	186	25	.	.	PUNCT
cana-6157	187	1	probability	probability	NOUN
cana-6157	187	2	and	and	CCONJ
cana-6157	187	3	q	q	NOUN
cana-6157	187	4	-	-	PUNCT
cana-6157	187	5	q	q	NOUN
cana-6157	187	6	plots	plot	NOUN
cana-6157	187	7	graphical	graphical	ADJ
cana-6157	187	8	diagnostic	diagnostic	ADJ
cana-6157	187	9	tools	tool	NOUN
cana-6157	187	10	are	be	AUX
cana-6157	187	11	essential	essential	ADJ
cana-6157	187	12	for	for	ADP
cana-6157	187	13	assessing	assess	VERB
cana-6157	187	14	how	how	SCONJ
cana-6157	187	15	closely	closely	ADV
cana-6157	187	16	the	the	DET
cana-6157	187	17	fitted	fit	VERB
cana-6157	187	18	distribution	distribution	NOUN
cana-6157	187	19	aligns	align	VERB
cana-6157	187	20	with	with	ADP
cana-6157	187	21	the	the	DET
cana-6157	187	22	observed	observed	ADJ
cana-6157	187	23	data	datum	NOUN
cana-6157	187	24	:	:	PUNCT
cana-6157	187	25	•	•	ADP
cana-6157	187	26	p	p	NOUN
cana-6157	187	27	-	-	PUNCT
cana-6157	187	28	p	p	NOUN
cana-6157	187	29	plot	plot	NOUN
cana-6157	187	30	:	:	PUNCT
cana-6157	187	31	plots	plot	NOUN
cana-6157	187	32	(	(	PUNCT
cana-6157	187	33	�	�	NOUN
cana-6157	187	34	̂	̂	NOUN
cana-6157	187	35	�	�	NOUN
cana-6157	187	36	(𝑡(𝑖	(𝑡(𝑖	NOUN
cana-6157	187	37	)	)	PUNCT
cana-6157	187	38	)	)	PUNCT
cana-6157	187	39	,	,	PUNCT
cana-6157	187	40	𝑖	𝑖	PROPN
cana-6157	187	41	𝑛+1	𝑛+1	PROPN
cana-6157	187	42	)	)	PUNCT
cana-6157	187	43	𝑓𝑜𝑟𝑖	𝑓𝑜𝑟𝑖	NOUN
cana-6157	187	44	=	=	SYM
cana-6157	187	45	1	1	NUM
cana-6157	187	46	,	,	PUNCT
cana-6157	187	47	…	…	PUNCT
cana-6157	187	48	,	,	PUNCT
cana-6157	187	49	𝑛.	𝑛.	NOUN
cana-6157	187	50	a	a	DET
cana-6157	187	51	45	45	NUM
cana-6157	187	52	-	-	PUNCT
cana-6157	187	53	degree	degree	NOUN
cana-6157	187	54	line	line	NOUN
cana-6157	187	55	indicates	indicate	VERB
cana-6157	187	56	a	a	DET
cana-6157	187	57	good	good	ADJ
cana-6157	187	58	fit	fit	NOUN
cana-6157	187	59	.	.	PUNCT
cana-6157	188	1	•	•	NUM
cana-6157	188	2	q	q	NOUN
cana-6157	188	3	-	-	PUNCT
cana-6157	188	4	q	q	NOUN
cana-6157	188	5	plot	plot	NOUN
cana-6157	188	6	:	:	PUNCT
cana-6157	188	7	plots	plot	NOUN
cana-6157	188	8	(	(	PUNCT
cana-6157	188	9	𝐹−1̂	𝐹−1̂	X
cana-6157	188	10	(	(	PUNCT
cana-6157	188	11	𝑖	𝑖	NOUN
cana-6157	188	12	𝑛+1	𝑛+1	PROPN
cana-6157	188	13	)	)	PUNCT
cana-6157	188	14	,	,	PUNCT
cana-6157	188	15	𝑡(𝑖))for	𝑡(𝑖))for	ADP
cana-6157	188	16	𝑖	𝑖	SYM
cana-6157	188	17	=	=	SYM
cana-6157	188	18	1	1	NUM
cana-6157	188	19	,	,	PUNCT
cana-6157	188	20	…	…	PUNCT
cana-6157	188	21	,	,	PUNCT
cana-6157	188	22	𝑛.	𝑛.	NOUN
cana-6157	188	23	deviations	deviation	NOUN
cana-6157	188	24	from	from	ADP
cana-6157	188	25	the	the	DET
cana-6157	188	26	diagonal	diagonal	ADJ
cana-6157	188	27	line	line	NOUN
cana-6157	188	28	suggestdiscrepancies	suggestdiscrepancie	NOUN
cana-6157	188	29	between	between	ADP
cana-6157	188	30	the	the	DET
cana-6157	188	31	empirical	empirical	ADJ
cana-6157	188	32	and	and	CCONJ
cana-6157	188	33	theoretical	theoretical	ADJ
cana-6157	188	34	distributions	distribution	NOUN
cana-6157	188	35	.	.	PUNCT
cana-6157	189	1	hazard	hazard	NOUN
cana-6157	189	2	rate	rate	NOUN
cana-6157	189	3	function	function	NOUN
cana-6157	189	4	comparison	comparison	NOUN
cana-6157	189	5	we	we	PRON
cana-6157	189	6	compare	compare	VERB
cana-6157	189	7	the	the	DET
cana-6157	189	8	empirical	empirical	ADJ
cana-6157	189	9	hazard	hazard	NOUN
cana-6157	189	10	rate	rate	NOUN
cana-6157	189	11	to	to	ADP
cana-6157	189	12	the	the	DET
cana-6157	189	13	theoretical	theoretical	ADJ
cana-6157	189	14	hazard	hazard	NOUN
cana-6157	189	15	function	function	NOUN
cana-6157	189	16	of	of	ADP
cana-6157	189	17	the	the	DET
cana-6157	189	18	aptee	aptee	NOUN
cana-6157	189	19	model	model	NOUN
cana-6157	189	20	,	,	PUNCT
cana-6157	189	21	which	which	PRON
cana-6157	189	22	is	be	AUX
cana-6157	189	23	given	give	VERB
cana-6157	189	24	by	by	ADP
cana-6157	189	25	:	:	PUNCT
cana-6157	189	26	ℎ(𝑡	ℎ(𝑡	PROPN
cana-6157	189	27	)	)	PUNCT
cana-6157	190	1	=	=	PUNCT
cana-6157	190	2	𝛽𝜆	𝛽𝜆	ADP
cana-6157	190	3	𝑙𝑜𝑔(𝛼	𝑙𝑜𝑔(𝛼	NUM
cana-6157	190	4	)	)	PUNCT
cana-6157	190	5	(	(	PUNCT
cana-6157	190	6	1	1	NUM
cana-6157	190	7	+	+	NUM
cana-6157	190	8	𝜆𝑡)𝛽−1	𝜆𝑡)𝛽−1	NOUN
cana-6157	190	9	𝑒𝑥𝑝(1	𝑒𝑥𝑝(1	NOUN
cana-6157	190	10	−	−	PROPN
cana-6157	190	11	(	(	PUNCT
cana-6157	190	12	1	1	NUM
cana-6157	190	13	+	+	CCONJ
cana-6157	190	14	𝜆𝑡)𝛽	𝜆𝑡)𝛽	NOUN
cana-6157	190	15	)	)	PUNCT
cana-6157	190	16	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	NOUN
cana-6157	190	17	)	)	PUNCT
cana-6157	190	18	𝛽	𝛽	NOUN
cana-6157	190	19	)	)	PUNCT
cana-6157	190	20	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	𝛼1−𝑒𝑥𝑝(1−(1+𝜆𝑡	NOUN
cana-6157	190	21	)	)	PUNCT
cana-6157	190	22	𝛽	𝛽	NOUN
cana-6157	190	23	)	)	PUNCT
cana-6157	190	24	−	−	PROPN
cana-6157	190	25	1	1	NUM
cana-6157	191	1	the	the	DET
cana-6157	191	2	empirical	empirical	ADJ
cana-6157	191	3	hazard	hazard	NOUN
cana-6157	191	4	function	function	NOUN
cana-6157	191	5	can	can	AUX
cana-6157	191	6	be	be	AUX
cana-6157	191	7	estimated	estimate	VERB
cana-6157	191	8	using	use	VERB
cana-6157	191	9	non	non	ADJ
cana-6157	191	10	-	-	ADJ
cana-6157	191	11	parametric	parametric	ADJ
cana-6157	191	12	kernel	kernel	NOUN
cana-6157	191	13	smoothing	smoothing	NOUN
cana-6157	191	14	or	or	CCONJ
cana-6157	191	15	the	the	DET
cana-6157	191	16	nelson	nelson	PROPN
cana-6157	191	17	-	-	PUNCT
cana-6157	191	18	aalen	aalen	VERB
cana-6157	191	19	estimator	estimator	NOUN
cana-6157	191	20	.	.	PUNCT
cana-6157	192	1	close	close	ADJ
cana-6157	192	2	agreement	agreement	NOUN
cana-6157	192	3	between	between	ADP
cana-6157	192	4	the	the	DET
cana-6157	192	5	two	two	NUM
cana-6157	192	6	curves	curve	NOUN
cana-6157	192	7	confirms	confirm	VERB
cana-6157	192	8	the	the	DET
cana-6157	192	9	modeladequacy	modeladequacy	NOUN
cana-6157	192	10	in	in	ADP
cana-6157	192	11	capturing	capture	VERB
cana-6157	192	12	the	the	DET
cana-6157	192	13	hazard	hazard	NOUN
cana-6157	192	14	structure	structure	NOUN
cana-6157	192	15	of	of	ADP
cana-6157	192	16	the	the	DET
cana-6157	192	17	data	datum	NOUN
cana-6157	192	18	.	.	PUNCT
cana-6157	193	1	communications	communication	NOUN
cana-6157	193	2	on	on	ADP
cana-6157	193	3	applied	apply	VERB
cana-6157	193	4	nonlinear	nonlinear	ADJ
cana-6157	193	5	analysis	analysis	NOUN
cana-6157	193	6	issn	issn	NOUN
cana-6157	193	7	:	:	PUNCT
cana-6157	193	8	1074	1074	NUM
cana-6157	193	9	-	-	PUNCT
cana-6157	193	10	133x	133x	NUM
cana-6157	193	11	vol	vol	VERB
cana-6157	193	12	32	32	NUM
cana-6157	193	13	no	no	NOUN
cana-6157	193	14	.	.	PUNCT
cana-6157	194	1	10s	10	NOUN
cana-6157	194	2	(	(	PUNCT
cana-6157	194	3	2025	2025	NUM
cana-6157	194	4	)	)	PUNCT
cana-6157	194	5	3491	3491	NUM
cana-6157	194	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	194	7	i.cox	i.cox	VERB
cana-6157	194	8	-	-	PUNCT
cana-6157	194	9	snell	snell	NOUN
cana-6157	194	10	residuals	residual	NOUN
cana-6157	194	11	simulation	simulation	NOUN
cana-6157	194	12	-	-	PUNCT
cana-6157	194	13	based	base	VERB
cana-6157	194	14	diagnostic	diagnostic	ADJ
cana-6157	194	15	evaluation	evaluation	NOUN
cana-6157	194	16	to	to	PART
cana-6157	194	17	validate	validate	VERB
cana-6157	194	18	the	the	DET
cana-6157	194	19	diagnostic	diagnostic	ADJ
cana-6157	194	20	tools	tool	NOUN
cana-6157	194	21	under	under	ADP
cana-6157	194	22	controlled	control	VERB
cana-6157	194	23	conditions	condition	NOUN
cana-6157	194	24	,	,	PUNCT
cana-6157	194	25	we	we	PRON
cana-6157	194	26	conduct	conduct	VERB
cana-6157	194	27	a	a	DET
cana-6157	194	28	simulation	simulation	NOUN
cana-6157	194	29	study	study	NOUN
cana-6157	194	30	:	:	PUNCT
cana-6157	194	31	•	•	PUNCT
cana-6157	194	32	generate	generate	VERB
cana-6157	194	33	n=1000	n=1000	PROPN
cana-6157	194	34	samples	sample	NOUN
cana-6157	194	35	of	of	ADP
cana-6157	194	36	size	size	NOUN
cana-6157	194	37	n=100	n=100	NUM
cana-6157	194	38	from	from	ADP
cana-6157	194	39	an	an	DET
cana-6157	194	40	aptee	aptee	ADJ
cana-6157	194	41	distribution	distribution	NOUN
cana-6157	194	42	with	with	ADP
cana-6157	194	43	known	known	ADJ
cana-6157	194	44	parameters	parameter	NOUN
cana-6157	194	45	(	(	PUNCT
cana-6157	194	46	α=1.5	α=1.5	NOUN
cana-6157	194	47	,	,	PUNCT
cana-6157	194	48	β=2.0	β=2.0	ADJ
cana-6157	194	49	,	,	PUNCT
cana-6157	194	50	λ=0.3	λ=0.3	ADJ
cana-6157	194	51	)	)	PUNCT
cana-6157	194	52	.	.	PUNCT
cana-6157	195	1	•	•	NUM
cana-6157	195	2	estimate	estimate	VERB
cana-6157	195	3	the	the	DET
cana-6157	195	4	parameters	parameter	NOUN
cana-6157	195	5	using	use	VERB
cana-6157	195	6	the	the	DET
cana-6157	195	7	maximum	maximum	ADJ
cana-6157	195	8	likelihood	likelihood	NOUN
cana-6157	195	9	method	method	NOUN
cana-6157	195	10	.	.	PUNCT
cana-6157	196	1	•	•	NUM
cana-6157	196	2	compute	compute	PROPN
cana-6157	196	3	cox	cox	PROPN
cana-6157	196	4	-	-	PUNCT
cana-6157	196	5	snell	snell	PROPN
cana-6157	196	6	residuals	residual	NOUN
cana-6157	196	7	,	,	PUNCT
cana-6157	196	8	p	p	NOUN
cana-6157	196	9	-	-	PUNCT
cana-6157	196	10	p	p	NOUN
cana-6157	196	11	and	and	CCONJ
cana-6157	196	12	q	q	ADJ
cana-6157	196	13	-	-	PUNCT
cana-6157	196	14	q	q	NOUN
cana-6157	196	15	plots	plot	NOUN
cana-6157	196	16	,	,	PUNCT
cana-6157	196	17	and	and	CCONJ
cana-6157	196	18	hazard	hazard	NOUN
cana-6157	196	19	rate	rate	NOUN
cana-6157	196	20	curves	curve	NOUN
cana-6157	196	21	for	for	ADP
cana-6157	196	22	each	each	DET
cana-6157	196	23	replicate	replicate	NOUN
cana-6157	196	24	.	.	PUNCT
cana-6157	197	1	•	•	NUM
cana-6157	197	2	calculate	calculate	VERB
cana-6157	197	3	the	the	DET
cana-6157	197	4	average	average	ADJ
cana-6157	197	5	deviation	deviation	NOUN
cana-6157	197	6	of	of	ADP
cana-6157	197	7	the	the	DET
cana-6157	197	8	empirical	empirical	ADJ
cana-6157	197	9	residual	residual	ADJ
cana-6157	197	10	distribution	distribution	NOUN
cana-6157	197	11	from	from	ADP
cana-6157	197	12	the	the	DET
cana-6157	197	13	exponential	exponential	NOUN
cana-6157	197	14	(	(	PUNCT
cana-6157	197	15	1	1	NUM
cana-6157	197	16	)	)	PUNCT
cana-6157	197	17	distribution	distribution	NOUN
cana-6157	197	18	using	use	VERB
cana-6157	197	19	the	the	DET
cana-6157	197	20	kolmogorov	kolmogorov	ADJ
cana-6157	197	21	-	-	PUNCT
cana-6157	197	22	smirnov	smirnov	PROPN
cana-6157	197	23	distance	distance	NOUN
cana-6157	197	24	.	.	PUNCT
cana-6157	198	1	ii	ii	PROPN
cana-6157	198	2	.	.	PUNCT
cana-6157	199	1	simulation	simulation	NOUN
cana-6157	199	2	results	result	VERB
cana-6157	199	3	:	:	PUNCT
cana-6157	199	4	in	in	ADP
cana-6157	199	5	over	over	ADP
cana-6157	199	6	95	95	NUM
cana-6157	199	7	%	%	NOUN
cana-6157	199	8	of	of	ADP
cana-6157	199	9	the	the	DET
cana-6157	199	10	simulated	simulate	VERB
cana-6157	199	11	samples	sample	NOUN
cana-6157	199	12	,	,	PUNCT
cana-6157	199	13	the	the	DET
cana-6157	199	14	residual	residual	ADJ
cana-6157	199	15	plots	plot	NOUN
cana-6157	199	16	adhered	adhere	VERB
cana-6157	199	17	closely	closely	ADV
cana-6157	199	18	to	to	ADP
cana-6157	199	19	the	the	DET
cana-6157	199	20	45	45	NUM
cana-6157	199	21	-	-	PUNCT
cana-6157	199	22	degree	degree	NOUN
cana-6157	199	23	line	line	NOUN
cana-6157	199	24	.	.	PUNCT
cana-6157	200	1	the	the	DET
cana-6157	200	2	hazard	hazard	NOUN
cana-6157	200	3	rate	rate	NOUN
cana-6157	200	4	estimates	estimate	NOUN
cana-6157	200	5	from	from	ADP
cana-6157	200	6	the	the	DET
cana-6157	200	7	aptee	aptee	PROPN
cana-6157	200	8	model	model	NOUN
cana-6157	200	9	overlapped	overlap	VERB
cana-6157	200	10	significantly	significantly	ADV
cana-6157	200	11	with	with	ADP
cana-6157	200	12	the	the	DET
cana-6157	200	13	empirical	empirical	ADJ
cana-6157	200	14	hazard	hazard	NOUN
cana-6157	200	15	,	,	PUNCT
cana-6157	200	16	indicating	indicate	VERB
cana-6157	200	17	a	a	DET
cana-6157	200	18	consistent	consistent	ADJ
cana-6157	200	19	model	model	NOUN
cana-6157	200	20	fit	fit	VERB
cana-6157	200	21	across	across	ADP
cana-6157	200	22	replications	replication	NOUN
cana-6157	200	23	.	.	PUNCT
cana-6157	201	1	iii	iii	X
cana-6157	201	2	.	.	PUNCT
cana-6157	201	3	application	application	NOUN
cana-6157	201	4	results	result	NOUN
cana-6157	201	5	:	:	PUNCT
cana-6157	201	6	the	the	DET
cana-6157	201	7	cox	cox	PROPN
cana-6157	201	8	-	-	PUNCT
cana-6157	201	9	snell	snell	PROPN
cana-6157	201	10	residuals	residual	NOUN
cana-6157	201	11	closely	closely	ADV
cana-6157	201	12	followed	follow	VERB
cana-6157	201	13	the	the	DET
cana-6157	201	14	exponential	exponential	ADJ
cana-6157	201	15	distribution	distribution	NOUN
cana-6157	201	16	,	,	PUNCT
cana-6157	201	17	and	and	CCONJ
cana-6157	201	18	diagnostic	diagnostic	ADJ
cana-6157	201	19	plots	plot	NOUN
cana-6157	201	20	indicated	indicate	VERB
cana-6157	201	21	a	a	DET
cana-6157	201	22	very	very	ADV
cana-6157	201	23	good	good	ADJ
cana-6157	201	24	fit	fit	NOUN
cana-6157	201	25	.	.	PUNCT
cana-6157	202	1	the	the	DET
cana-6157	202	2	aptee	aptee	PROPN
cana-6157	202	3	model	model	NOUN
cana-6157	202	4	showed	show	VERB
cana-6157	202	5	lower	low	ADJ
cana-6157	202	6	aic	aic	PROPN
cana-6157	202	7	and	and	CCONJ
cana-6157	202	8	bic	bic	PROPN
cana-6157	202	9	values	value	NOUN
cana-6157	202	10	than	than	ADP
cana-6157	202	11	alternatives	alternative	NOUN
cana-6157	202	12	such	such	ADJ
cana-6157	202	13	as	as	ADP
cana-6157	202	14	the	the	DET
cana-6157	202	15	weibull	weibull	NOUN
cana-6157	202	16	and	and	CCONJ
cana-6157	202	17	generalized	generalized	ADJ
cana-6157	202	18	exponential	exponential	ADJ
cana-6157	202	19	distributions	distribution	NOUN
cana-6157	202	20	.	.	PUNCT
cana-6157	203	1	hazard	hazard	NOUN
cana-6157	203	2	rate	rate	NOUN
cana-6157	203	3	analysis	analysis	NOUN
cana-6157	203	4	revealed	reveal	VERB
cana-6157	203	5	that	that	SCONJ
cana-6157	203	6	aptee	aptee	NOUN
cana-6157	203	7	better	well	ADV
cana-6157	203	8	captured	capture	VERB
cana-6157	203	9	the	the	DET
cana-6157	203	10	bathtubshaped	bathtubshape	VERB
cana-6157	203	11	hazard	hazard	NOUN
cana-6157	203	12	observed	observe	VERB
cana-6157	203	13	in	in	ADP
cana-6157	203	14	the	the	DET
cana-6157	203	15	dataset	dataset	NOUN
cana-6157	203	16	.	.	PUNCT
cana-6157	204	1	reference	reference	NOUN
cana-6157	204	2	of	of	ADP
cana-6157	204	3	the	the	DET
cana-6157	204	4	dataset	dataset	NOUN
cana-6157	204	5	the	the	DET
cana-6157	204	6	dataset	dataset	NOUN
cana-6157	204	7	used	use	VERB
cana-6157	204	8	for	for	ADP
cana-6157	204	9	the	the	DET
cana-6157	204	10	diagnostic	diagnostic	ADJ
cana-6157	204	11	analysis	analysis	NOUN
cana-6157	204	12	was	be	AUX
cana-6157	204	13	simulated	simulate	VERB
cana-6157	204	14	from	from	ADP
cana-6157	204	15	the	the	DET
cana-6157	204	16	alpha	alpha	NOUN
cana-6157	204	17	-	-	PUNCT
cana-6157	204	18	power	power	NOUN
cana-6157	204	19	transformed	transform	VERB
cana-6157	204	20	extended	extend	VERB
cana-6157	204	21	exponential	exponential	NOUN
cana-6157	204	22	(	(	PUNCT
cana-6157	204	23	aptee	aptee	NOUN
cana-6157	204	24	)	)	PUNCT
cana-6157	204	25	distribution	distribution	NOUN
cana-6157	204	26	using	use	VERB
cana-6157	204	27	the	the	DET
cana-6157	204	28	inverse	inverse	NOUN
cana-6157	204	29	transform	transform	NOUN
cana-6157	204	30	sampling	sample	VERB
cana-6157	204	31	method	method	NOUN
cana-6157	204	32	.	.	PUNCT
cana-6157	205	1	the	the	DET
cana-6157	205	2	parameter	parameter	NOUN
cana-6157	205	3	values	value	NOUN
cana-6157	205	4	used	use	VERB
cana-6157	205	5	for	for	ADP
cana-6157	205	6	the	the	DET
cana-6157	205	7	simulation	simulation	NOUN
cana-6157	205	8	are	be	AUX
cana-6157	205	9	:	:	PUNCT
cana-6157	205	10	•	•	ADJ
cana-6157	205	11	shape	shape	NOUN
cana-6157	205	12	parameter	parameter	NOUN
cana-6157	205	13	:	:	PUNCT
cana-6157	205	14	α=	α=	NUM
cana-6157	205	15	1.5	1.5	NUM
cana-6157	205	16	•	•	NOUN
cana-6157	205	17	shape	shape	NOUN
cana-6157	205	18	parameter	parameter	NOUN
cana-6157	205	19	:	:	PUNCT
cana-6157	205	20	β=	β=	NOUN
cana-6157	205	21	2.0	2.0	NUM
cana-6157	205	22	•	•	NOUN
cana-6157	205	23	scale	scale	NOUN
cana-6157	205	24	parameter	parameter	NOUN
cana-6157	205	25	:	:	PUNCT
cana-6157	205	26	λ=	λ=	VERB
cana-6157	205	27	0.3	0.3	NUM
cana-6157	205	28	•	•	NOUN
cana-6157	205	29	sample	sample	NOUN
cana-6157	205	30	size	size	NOUN
cana-6157	205	31	:	:	PUNCT
cana-6157	205	32	n	n	NOUN
cana-6157	205	33	=	=	SYM
cana-6157	205	34	100	100	NUM
cana-6157	205	35	this	this	DET
cana-6157	205	36	synthetic	synthetic	ADJ
cana-6157	205	37	dataset	dataset	NOUN
cana-6157	205	38	is	be	AUX
cana-6157	205	39	designed	design	VERB
cana-6157	205	40	to	to	PART
cana-6157	205	41	reflect	reflect	VERB
cana-6157	205	42	the	the	DET
cana-6157	205	43	structure	structure	NOUN
cana-6157	205	44	of	of	ADP
cana-6157	205	45	real	real	ADJ
cana-6157	205	46	-	-	PUNCT
cana-6157	205	47	world	world	NOUN
cana-6157	205	48	survival	survival	NOUN
cana-6157	205	49	or	or	CCONJ
cana-6157	205	50	reliability	reliability	NOUN
cana-6157	205	51	data	datum	NOUN
cana-6157	205	52	often	often	ADV
cana-6157	205	53	encountered	encounter	VERB
cana-6157	205	54	in	in	ADP
cana-6157	205	55	applications	application	NOUN
cana-6157	205	56	involving	involve	VERB
cana-6157	205	57	competing	compete	VERB
cana-6157	205	58	risks	risk	NOUN
cana-6157	205	59	.	.	PUNCT
cana-6157	206	1	vii	vii	PROPN
cana-6157	206	2	.	.	PROPN
cana-6157	206	3	interpretation	interpretation	NOUN
cana-6157	206	4	of	of	ADP
cana-6157	206	5	diagnostic	diagnostic	ADJ
cana-6157	206	6	plots	plot	NOUN
cana-6157	206	7	to	to	PART
cana-6157	206	8	assess	assess	VERB
cana-6157	206	9	the	the	DET
cana-6157	206	10	model	model	NOUN
cana-6157	206	11	's	's	PART
cana-6157	206	12	adequacy	adequacy	NOUN
cana-6157	206	13	,	,	PUNCT
cana-6157	206	14	we	we	PRON
cana-6157	206	15	employed	employ	VERB
cana-6157	206	16	graphical	graphical	ADJ
cana-6157	206	17	diagnostics	diagnostic	NOUN
cana-6157	206	18	including	include	VERB
cana-6157	206	19	cox	cox	PROPN
cana-6157	206	20	-	-	PUNCT
cana-6157	206	21	snell	snell	PROPN
cana-6157	206	22	residual	residual	ADJ
cana-6157	206	23	analysis	analysis	NOUN
cana-6157	206	24	and	and	CCONJ
cana-6157	206	25	a	a	DET
cana-6157	206	26	q	q	ADJ
cana-6157	206	27	-	-	PUNCT
cana-6157	206	28	q	q	NOUN
cana-6157	206	29	plot	plot	NOUN
cana-6157	206	30	of	of	ADP
cana-6157	206	31	the	the	DET
cana-6157	206	32	residuals	residual	NOUN
cana-6157	206	33	.	.	PUNCT
cana-6157	207	1	cox	cox	PROPN
cana-6157	207	2	-	-	PUNCT
cana-6157	207	3	snell	snell	PROPN
cana-6157	207	4	residual	residual	ADJ
cana-6157	207	5	plot	plot	NOUN
cana-6157	207	6	figure	figure	NOUN
cana-6157	207	7	3	3	NUM
cana-6157	207	8	:	:	PUNCT
cana-6157	207	9	cox	cox	PROPN
cana-6157	207	10	-	-	PUNCT
cana-6157	207	11	snell	snell	PROPN
cana-6157	207	12	residual	residual	ADJ
cana-6157	207	13	plot	plot	NOUN
cana-6157	207	14	:	:	PUNCT
cana-6157	207	15	cumulative	cumulative	ADJ
cana-6157	207	16	hazard	hazard	NOUN
cana-6157	207	17	estimate	estimate	VERB
cana-6157	207	18	vs.cox	vs.cox	ADJ
cana-6157	207	19	-	-	PUNCT
cana-6157	207	20	snell	snell	NOUN
cana-6157	207	21	residuals	residual	NOUN
cana-6157	207	22	figure	figure	NOUN
cana-6157	207	23	3	3	NUM
cana-6157	207	24	presents	present	VERB
cana-6157	207	25	the	the	DET
cana-6157	207	26	nelson	nelson	PROPN
cana-6157	207	27	-	-	PUNCT
cana-6157	207	28	aalen	aalen	VERB
cana-6157	207	29	cumulative	cumulative	ADJ
cana-6157	207	30	hazard	hazard	NOUN
cana-6157	207	31	estimate	estimate	NOUN
cana-6157	207	32	of	of	ADP
cana-6157	207	33	the	the	DET
cana-6157	207	34	cox	cox	PROPN
cana-6157	207	35	-	-	PUNCT
cana-6157	207	36	snell	snell	PROPN
cana-6157	207	37	residuals	residual	NOUN
cana-6157	207	38	plotted	plot	VERB
cana-6157	207	39	communications	communication	NOUN
cana-6157	207	40	on	on	ADP
cana-6157	207	41	applied	apply	VERB
cana-6157	207	42	nonlinear	nonlinear	ADJ
cana-6157	207	43	analysis	analysis	NOUN
cana-6157	207	44	issn	issn	NOUN
cana-6157	207	45	:	:	PUNCT
cana-6157	207	46	1074	1074	NUM
cana-6157	207	47	-	-	PUNCT
cana-6157	207	48	133x	133x	NUM
cana-6157	207	49	vol	vol	VERB
cana-6157	207	50	32	32	NUM
cana-6157	207	51	no	no	NOUN
cana-6157	207	52	.	.	PUNCT
cana-6157	208	1	10s	10	NOUN
cana-6157	208	2	(	(	PUNCT
cana-6157	208	3	2025	2025	NUM
cana-6157	208	4	)	)	PUNCT
cana-6157	208	5	3492	3492	NUM
cana-6157	208	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	208	7	against	against	ADP
cana-6157	208	8	the	the	DET
cana-6157	208	9	residuals	residual	NOUN
cana-6157	208	10	themselves	themselves	PRON
cana-6157	208	11	.	.	PUNCT
cana-6157	209	1	under	under	ADP
cana-6157	209	2	a	a	DET
cana-6157	209	3	correctly	correctly	ADV
cana-6157	209	4	specified	specify	VERB
cana-6157	209	5	model	model	NOUN
cana-6157	209	6	,	,	PUNCT
cana-6157	209	7	the	the	DET
cana-6157	209	8	points	point	NOUN
cana-6157	209	9	should	should	AUX
cana-6157	209	10	align	align	VERB
cana-6157	209	11	closely	closely	ADV
cana-6157	209	12	with	with	ADP
cana-6157	209	13	the	the	DET
cana-6157	209	14	45degree	45degree	NUM
cana-6157	209	15	line	line	NOUN
cana-6157	209	16	(	(	PUNCT
cana-6157	209	17	shown	show	VERB
cana-6157	209	18	as	as	ADP
cana-6157	209	19	a	a	DET
cana-6157	209	20	red	red	ADJ
cana-6157	209	21	dashed	dash	VERB
cana-6157	209	22	line	line	NOUN
cana-6157	209	23	)	)	PUNCT
cana-6157	209	24	,	,	PUNCT
cana-6157	209	25	indicating	indicate	VERB
cana-6157	209	26	that	that	SCONJ
cana-6157	209	27	the	the	DET
cana-6157	209	28	residuals	residual	NOUN
cana-6157	209	29	follow	follow	VERB
cana-6157	209	30	an	an	DET
cana-6157	209	31	exponential	exponential	NOUN
cana-6157	209	32	(	(	PUNCT
cana-6157	209	33	1	1	NUM
cana-6157	209	34	)	)	PUNCT
cana-6157	209	35	distribution	distribution	NOUN
cana-6157	209	36	.	.	PUNCT
cana-6157	210	1	interpretation	interpretation	NOUN
cana-6157	210	2	:	:	PUNCT
cana-6157	210	3	the	the	DET
cana-6157	210	4	plotted	plot	VERB
cana-6157	210	5	points	point	NOUN
cana-6157	210	6	in	in	ADP
cana-6157	210	7	figure	figure	NOUN
cana-6157	210	8	3	3	NUM
cana-6157	210	9	show	show	VERB
cana-6157	210	10	a	a	DET
cana-6157	210	11	strong	strong	ADJ
cana-6157	210	12	agreement	agreement	NOUN
cana-6157	210	13	with	with	ADP
cana-6157	210	14	the	the	DET
cana-6157	210	15	reference	reference	NOUN
cana-6157	210	16	line	line	NOUN
cana-6157	210	17	,	,	PUNCT
cana-6157	210	18	suggesting	suggest	VERB
cana-6157	210	19	that	that	SCONJ
cana-6157	210	20	the	the	DET
cana-6157	210	21	aptee	aptee	NOUN
cana-6157	210	22	model	model	NOUN
cana-6157	210	23	provides	provide	VERB
cana-6157	210	24	a	a	DET
cana-6157	210	25	good	good	ADJ
cana-6157	210	26	fit	fit	NOUN
cana-6157	210	27	to	to	ADP
cana-6157	210	28	the	the	DET
cana-6157	210	29	data	datum	NOUN
cana-6157	210	30	.	.	PUNCT
cana-6157	211	1	q	q	X
cana-6157	211	2	-	-	PUNCT
cana-6157	211	3	q	q	NOUN
cana-6157	211	4	plot	plot	NOUN
cana-6157	211	5	of	of	ADP
cana-6157	211	6	cox	cox	PROPN
cana-6157	211	7	-	-	PUNCT
cana-6157	211	8	snell	snell	PROPN
cana-6157	211	9	residuals	residual	NOUN
cana-6157	211	10	figure	figure	NOUN
cana-6157	211	11	4	4	NUM
cana-6157	211	12	shows	show	VERB
cana-6157	211	13	the	the	DET
cana-6157	211	14	quantile	quantile	NOUN
cana-6157	211	15	-	-	PUNCT
cana-6157	211	16	quantile	quantile	NOUN
cana-6157	211	17	(	(	PUNCT
cana-6157	211	18	q	q	NOUN
cana-6157	211	19	-	-	PUNCT
cana-6157	211	20	q	q	NOUN
cana-6157	211	21	)	)	PUNCT
cana-6157	211	22	plot	plot	NOUN
cana-6157	211	23	comparing	compare	VERB
cana-6157	211	24	the	the	DET
cana-6157	211	25	empirical	empirical	ADJ
cana-6157	211	26	quantiles	quantile	NOUN
cana-6157	211	27	of	of	ADP
cana-6157	211	28	the	the	DET
cana-6157	211	29	cox	cox	PROPN
cana-6157	211	30	-	-	PUNCT
cana-6157	211	31	snell	snell	PROPN
cana-6157	211	32	residuals	residual	NOUN
cana-6157	211	33	with	with	ADP
cana-6157	211	34	the	the	DET
cana-6157	211	35	theoretical	theoretical	ADJ
cana-6157	211	36	quantiles	quantile	NOUN
cana-6157	211	37	of	of	ADP
cana-6157	211	38	the	the	DET
cana-6157	211	39	standard	standard	ADJ
cana-6157	211	40	exponential	exponential	NOUN
cana-6157	211	41	(	(	PUNCT
cana-6157	211	42	1	1	NUM
cana-6157	211	43	)	)	PUNCT
cana-6157	211	44	distribution	distribution	NOUN
cana-6157	211	45	.	.	PUNCT
cana-6157	212	1	figure	figure	VERB
cana-6157	212	2	4	4	NUM
cana-6157	212	3	:	:	PUNCT
cana-6157	212	4	q	q	ADJ
cana-6157	212	5	-	-	PUNCT
cana-6157	212	6	q	q	NOUN
cana-6157	212	7	plot	plot	NOUN
cana-6157	212	8	of	of	ADP
cana-6157	212	9	cox	cox	PROPN
cana-6157	212	10	-	-	PUNCT
cana-6157	212	11	snell	snell	PROPN
cana-6157	212	12	residuals	residual	NOUN
cana-6157	212	13	vs.	vs.	ADP
cana-6157	212	14	theoretical	theoretical	ADJ
cana-6157	212	15	exponential	exponential	NOUN
cana-6157	212	16	(	(	PUNCT
cana-6157	212	17	1	1	X
cana-6157	212	18	)	)	PUNCT
cana-6157	212	19	quantiles	quantile	VERB
cana-6157	212	20	interpretation	interpretation	NOUN
cana-6157	212	21	:	:	PUNCT
cana-6157	212	22	the	the	DET
cana-6157	212	23	residuals	residual	NOUN
cana-6157	212	24	closely	closely	ADV
cana-6157	212	25	follow	follow	VERB
cana-6157	212	26	the	the	DET
cana-6157	212	27	45	45	NUM
cana-6157	212	28	-	-	PUNCT
cana-6157	212	29	degree	degree	NOUN
cana-6157	212	30	line	line	NOUN
cana-6157	212	31	,	,	PUNCT
cana-6157	212	32	especially	especially	ADV
cana-6157	212	33	in	in	ADP
cana-6157	212	34	the	the	DET
cana-6157	212	35	central	central	ADJ
cana-6157	212	36	region	region	NOUN
cana-6157	212	37	of	of	ADP
cana-6157	212	38	the	the	DET
cana-6157	212	39	distribution	distribution	NOUN
cana-6157	212	40	.	.	PUNCT
cana-6157	213	1	minor	minor	ADJ
cana-6157	213	2	deviations	deviation	NOUN
cana-6157	213	3	at	at	ADP
cana-6157	213	4	the	the	DET
cana-6157	213	5	extremes	extreme	NOUN
cana-6157	213	6	are	be	AUX
cana-6157	213	7	expected	expect	VERB
cana-6157	213	8	due	due	ADJ
cana-6157	213	9	to	to	ADP
cana-6157	213	10	sampling	sample	VERB
cana-6157	213	11	variability	variability	NOUN
cana-6157	213	12	.	.	PUNCT
cana-6157	214	1	overall	overall	ADV
cana-6157	214	2	,	,	PUNCT
cana-6157	214	3	the	the	DET
cana-6157	214	4	q	q	ADJ
cana-6157	214	5	-	-	PUNCT
cana-6157	214	6	q	q	NOUN
cana-6157	214	7	plot	plot	NOUN
cana-6157	214	8	supports	support	VERB
cana-6157	214	9	the	the	DET
cana-6157	214	10	suitability	suitability	NOUN
cana-6157	214	11	of	of	ADP
cana-6157	214	12	the	the	DET
cana-6157	214	13	aptee	aptee	NOUN
cana-6157	214	14	model	model	NOUN
cana-6157	214	15	.	.	PUNCT
cana-6157	215	1	the	the	DET
cana-6157	215	2	graphical	graphical	ADJ
cana-6157	215	3	diagnostics	diagnostic	NOUN
cana-6157	215	4	based	base	VERB
cana-6157	215	5	on	on	ADP
cana-6157	215	6	both	both	CCONJ
cana-6157	215	7	the	the	DET
cana-6157	215	8	cox	cox	PROPN
cana-6157	215	9	-	-	PUNCT
cana-6157	215	10	snell	snell	PROPN
cana-6157	215	11	residual	residual	ADJ
cana-6157	215	12	plot	plot	NOUN
cana-6157	215	13	and	and	CCONJ
cana-6157	215	14	the	the	DET
cana-6157	215	15	q	q	ADJ
cana-6157	215	16	-	-	PUNCT
cana-6157	215	17	q	q	ADJ
cana-6157	215	18	plot	plot	NOUN
cana-6157	215	19	demonstrate	demonstrate	NOUN
cana-6157	215	20	that	that	SCONJ
cana-6157	215	21	the	the	DET
cana-6157	215	22	aptee	aptee	NOUN
cana-6157	215	23	model	model	NOUN
cana-6157	215	24	captures	capture	VERB
cana-6157	215	25	the	the	DET
cana-6157	215	26	underlying	underlie	VERB
cana-6157	215	27	structure	structure	NOUN
cana-6157	215	28	of	of	ADP
cana-6157	215	29	the	the	DET
cana-6157	215	30	data	datum	NOUN
cana-6157	215	31	effectively	effectively	ADV
cana-6157	215	32	.	.	PUNCT
cana-6157	216	1	these	these	DET
cana-6157	216	2	results	result	NOUN
cana-6157	216	3	,	,	PUNCT
cana-6157	216	4	derived	derive	VERB
cana-6157	216	5	from	from	ADP
cana-6157	216	6	a	a	DET
cana-6157	216	7	controlled	control	VERB
cana-6157	216	8	simulation	simulation	NOUN
cana-6157	216	9	,	,	PUNCT
cana-6157	216	10	further	far	ADV
cana-6157	216	11	validate	validate	VERB
cana-6157	216	12	the	the	DET
cana-6157	216	13	use	use	NOUN
cana-6157	216	14	of	of	ADP
cana-6157	216	15	the	the	DET
cana-6157	216	16	aptee	aptee	ADJ
cana-6157	216	17	distribution	distribution	NOUN
cana-6157	216	18	in	in	ADP
cana-6157	216	19	modeling	model	VERB
cana-6157	216	20	lifetime	lifetime	NOUN
cana-6157	216	21	data	datum	NOUN
cana-6157	216	22	under	under	ADP
cana-6157	216	23	competing	compete	VERB
cana-6157	216	24	risks	risk	NOUN
cana-6157	216	25	.	.	PUNCT
cana-6157	217	1	x.conclusion	x.conclusion	PROPN
cana-6157	218	1	in	in	ADP
cana-6157	218	2	this	this	DET
cana-6157	218	3	study	study	NOUN
cana-6157	218	4	,	,	PUNCT
cana-6157	218	5	we	we	PRON
cana-6157	218	6	investigated	investigate	VERB
cana-6157	218	7	the	the	DET
cana-6157	218	8	alpha	alpha	NOUN
cana-6157	218	9	-	-	PUNCT
cana-6157	218	10	power	power	NOUN
cana-6157	218	11	transformed	transform	VERB
cana-6157	218	12	extended	extend	VERB
cana-6157	218	13	exponential	exponential	NOUN
cana-6157	218	14	(	(	PUNCT
cana-6157	218	15	aptee	aptee	NOUN
cana-6157	218	16	)	)	PUNCT
cana-6157	218	17	distribution	distribution	NOUN
cana-6157	218	18	as	as	ADP
cana-6157	218	19	a	a	DET
cana-6157	218	20	flexible	flexible	ADJ
cana-6157	218	21	and	and	CCONJ
cana-6157	218	22	robust	robust	ADJ
cana-6157	218	23	model	model	NOUN
cana-6157	218	24	for	for	ADP
cana-6157	218	25	analyzing	analyze	VERB
cana-6157	218	26	lifetime	lifetime	NOUN
cana-6157	218	27	data	datum	NOUN
cana-6157	218	28	in	in	ADP
cana-6157	218	29	the	the	DET
cana-6157	218	30	presence	presence	NOUN
cana-6157	218	31	of	of	ADP
cana-6157	218	32	competing	compete	VERB
cana-6157	218	33	risks	risk	NOUN
cana-6157	218	34	.	.	PUNCT
cana-6157	219	1	the	the	DET
cana-6157	219	2	aptee	aptee	ADJ
cana-6157	219	3	distribution	distribution	NOUN
cana-6157	219	4	generalizes	generalize	VERB
cana-6157	219	5	several	several	ADJ
cana-6157	219	6	classical	classical	ADJ
cana-6157	219	7	models	model	NOUN
cana-6157	219	8	and	and	CCONJ
cana-6157	219	9	accommodates	accommodate	VERB
cana-6157	219	10	a	a	DET
cana-6157	219	11	variety	variety	NOUN
cana-6157	219	12	of	of	ADP
cana-6157	219	13	hazard	hazard	NOUN
cana-6157	219	14	rate	rate	NOUN
cana-6157	219	15	shapes	shape	NOUN
cana-6157	219	16	,	,	PUNCT
cana-6157	219	17	making	make	VERB
cana-6157	219	18	it	it	PRON
cana-6157	219	19	suitable	suitable	ADJ
cana-6157	219	20	for	for	ADP
cana-6157	219	21	a	a	DET
cana-6157	219	22	broad	broad	ADJ
cana-6157	219	23	range	range	NOUN
cana-6157	219	24	of	of	ADP
cana-6157	219	25	applications	application	NOUN
cana-6157	219	26	in	in	ADP
cana-6157	219	27	reliability	reliability	NOUN
cana-6157	219	28	and	and	CCONJ
cana-6157	219	29	biomedical	biomedical	ADJ
cana-6157	219	30	sciences	science	NOUN
cana-6157	219	31	.	.	PUNCT
cana-6157	220	1	we	we	PRON
cana-6157	220	2	applied	apply	VERB
cana-6157	220	3	multiple	multiple	ADJ
cana-6157	220	4	estimation	estimation	NOUN
cana-6157	220	5	techniques	technique	NOUN
cana-6157	220	6	-	-	PUNCT
cana-6157	220	7	including	include	VERB
cana-6157	220	8	maximum	maximum	ADJ
cana-6157	220	9	likelihood	likelihood	NOUN
cana-6157	220	10	,	,	PUNCT
cana-6157	220	11	kolmogorov	kolmogorov	PROPN
cana-6157	220	12	-	-	PUNCT
cana-6157	220	13	smirnov	smirnov	NOUN
cana-6157	220	14	,	,	PUNCT
cana-6157	220	15	andersondarling	andersondarling	NOUN
cana-6157	220	16	,	,	PUNCT
cana-6157	220	17	and	and	CCONJ
cana-6157	220	18	cramer	cramer	PROPN
cana-6157	220	19	-	-	PUNCT
cana-6157	220	20	von	von	PROPN
cana-6157	220	21	mises	mises	PROPN
cana-6157	220	22	methods	method	NOUN
cana-6157	220	23	-	-	PUNCT
cana-6157	220	24	to	to	PART
cana-6157	220	25	obtain	obtain	VERB
cana-6157	220	26	parameter	parameter	NOUN
cana-6157	220	27	estimates	estimate	NOUN
cana-6157	220	28	for	for	ADP
cana-6157	220	29	the	the	DET
cana-6157	220	30	aptee	aptee	NOUN
cana-6157	220	31	model	model	NOUN
cana-6157	220	32	.	.	PUNCT
cana-6157	221	1	to	to	PART
cana-6157	221	2	assess	assess	VERB
cana-6157	221	3	the	the	DET
cana-6157	221	4	model	model	NOUN
cana-6157	221	5	's	's	PART
cana-6157	221	6	fit	fit	ADJ
cana-6157	221	7	and	and	CCONJ
cana-6157	221	8	discrimination	discrimination	NOUN
cana-6157	221	9	power	power	NOUN
cana-6157	221	10	,	,	PUNCT
cana-6157	221	11	we	we	PRON
cana-6157	221	12	developed	develop	VERB
cana-6157	221	13	a	a	DET
cana-6157	221	14	modified	modified	ADJ
cana-6157	221	15	chi	chi	ADJ
cana-6157	221	16	-	-	PUNCT
cana-6157	221	17	square	square	ADJ
cana-6157	221	18	statistic	statistic	NOUN
cana-6157	221	19	designed	design	VERB
cana-6157	221	20	to	to	PART
cana-6157	221	21	recover	recover	VERB
cana-6157	221	22	information	information	NOUN
cana-6157	221	23	lost	lose	VERB
cana-6157	221	24	in	in	ADP
cana-6157	221	25	grouped	group	VERB
cana-6157	221	26	data	datum	NOUN
cana-6157	221	27	and	and	CCONJ
cana-6157	221	28	improve	improve	VERB
cana-6157	221	29	goodness	goodness	NOUN
cana-6157	221	30	-	-	PUNCT
cana-6157	221	31	of	of	ADP
cana-6157	221	32	-	-	PUNCT
cana-6157	221	33	fit	fit	ADJ
cana-6157	221	34	testing	testing	NOUN
cana-6157	221	35	performance	performance	NOUN
cana-6157	221	36	.	.	PUNCT
cana-6157	222	1	to	to	PART
cana-6157	222	2	further	far	ADV
cana-6157	222	3	validate	validate	VERB
cana-6157	222	4	the	the	DET
cana-6157	222	5	model	model	NOUN
cana-6157	222	6	,	,	PUNCT
cana-6157	222	7	we	we	PRON
cana-6157	222	8	conducted	conduct	VERB
cana-6157	222	9	extensive	extensive	ADJ
cana-6157	222	10	model	model	NOUN
cana-6157	222	11	diagnostics	diagnostic	NOUN
cana-6157	222	12	using	use	VERB
cana-6157	222	13	cox	cox	PROPN
cana-6157	222	14	-	-	PUNCT
cana-6157	222	15	snell	snell	PROPN
cana-6157	222	16	residual	residual	ADJ
cana-6157	222	17	analysis	analysis	NOUN
cana-6157	222	18	,	,	PUNCT
cana-6157	222	19	qq	qq	ADJ
cana-6157	222	20	plots	plot	NOUN
cana-6157	222	21	,	,	PUNCT
cana-6157	222	22	and	and	CCONJ
cana-6157	222	23	hazard	hazard	NOUN
cana-6157	222	24	rate	rate	NOUN
cana-6157	222	25	comparisons	comparison	NOUN
cana-6157	222	26	.	.	PUNCT
cana-6157	223	1	these	these	DET
cana-6157	223	2	diagnostic	diagnostic	ADJ
cana-6157	223	3	tools	tool	NOUN
cana-6157	223	4	confirmed	confirm	VERB
cana-6157	223	5	the	the	DET
cana-6157	223	6	adequacy	adequacy	NOUN
cana-6157	223	7	of	of	ADP
cana-6157	223	8	the	the	DET
cana-6157	223	9	aptee	aptee	NOUN
cana-6157	223	10	model	model	NOUN
cana-6157	223	11	,	,	PUNCT
cana-6157	223	12	with	with	ADP
cana-6157	223	13	residuals	residual	NOUN
cana-6157	223	14	closely	closely	ADV
cana-6157	223	15	following	follow	VERB
cana-6157	223	16	the	the	DET
cana-6157	223	17	expected	expect	VERB
cana-6157	223	18	exponential	exponential	NOUN
cana-6157	223	19	(	(	PUNCT
cana-6157	223	20	1	1	NUM
cana-6157	223	21	)	)	PUNCT
cana-6157	223	22	behavior	behavior	NOUN
cana-6157	223	23	and	and	CCONJ
cana-6157	223	24	hazard	hazard	NOUN
cana-6157	223	25	functions	function	NOUN
cana-6157	223	26	matching	match	VERB
cana-6157	223	27	the	the	DET
cana-6157	223	28	empirical	empirical	ADJ
cana-6157	223	29	patterns	pattern	NOUN
cana-6157	223	30	observed	observe	VERB
cana-6157	223	31	in	in	ADP
cana-6157	223	32	the	the	DET
cana-6157	223	33	data	datum	NOUN
cana-6157	223	34	.	.	PUNCT
cana-6157	224	1	simulation	simulation	NOUN
cana-6157	224	2	studies	study	NOUN
cana-6157	224	3	confirmed	confirm	VERB
cana-6157	224	4	the	the	DET
cana-6157	224	5	accuracy	accuracy	NOUN
cana-6157	224	6	and	and	CCONJ
cana-6157	224	7	consistency	consistency	NOUN
cana-6157	224	8	of	of	ADP
cana-6157	224	9	the	the	DET
cana-6157	224	10	estimators	estimator	NOUN
cana-6157	224	11	and	and	CCONJ
cana-6157	224	12	the	the	DET
cana-6157	224	13	effectiveness	effectiveness	NOUN
cana-6157	224	14	of	of	ADP
cana-6157	224	15	the	the	DET
cana-6157	224	16	modified	modified	ADJ
cana-6157	224	17	chi	chi	ADJ
cana-6157	224	18	-	-	PUNCT
cana-6157	224	19	square	square	ADJ
cana-6157	224	20	test	test	NOUN
cana-6157	224	21	.	.	PUNCT
cana-6157	225	1	application	application	NOUN
cana-6157	225	2	to	to	ADP
cana-6157	225	3	a	a	DET
cana-6157	225	4	real	real	ADJ
cana-6157	225	5	-	-	PUNCT
cana-6157	225	6	world	world	NOUN
cana-6157	225	7	medical	medical	ADJ
cana-6157	225	8	dataset	dataset	NOUN
cana-6157	225	9	demonstrated	demonstrate	VERB
cana-6157	225	10	that	that	SCONJ
cana-6157	225	11	the	the	DET
cana-6157	225	12	aptee	aptee	ADJ
cana-6157	225	13	distribution	distribution	NOUN
cana-6157	225	14	provides	provide	VERB
cana-6157	225	15	a	a	DET
cana-6157	225	16	better	well	ADJ
cana-6157	225	17	fit	fit	ADJ
cana-6157	225	18	than	than	ADP
cana-6157	225	19	traditional	traditional	ADJ
cana-6157	225	20	alternatives	alternative	NOUN
cana-6157	225	21	such	such	ADJ
cana-6157	225	22	as	as	ADP
cana-6157	225	23	weibull	weibull	NOUN
cana-6157	225	24	,	,	PUNCT
cana-6157	225	25	generalized	generalized	ADJ
cana-6157	225	26	exponential	exponential	NOUN
cana-6157	225	27	(	(	PUNCT
cana-6157	225	28	ge	ge	PROPN
cana-6157	225	29	)	)	PUNCT
cana-6157	225	30	,	,	PUNCT
cana-6157	225	31	and	and	CCONJ
cana-6157	225	32	exponentiated	exponentiate	VERB
cana-6157	225	33	nadarajah	nadarajah	PROPN
cana-6157	225	34	-	-	PUNCT
cana-6157	225	35	haghighi	haghighi	PROPN
cana-6157	225	36	(	(	PUNCT
cana-6157	225	37	enh	enh	NOUN
cana-6157	225	38	)	)	PUNCT
cana-6157	225	39	models	model	NOUN
cana-6157	225	40	.	.	PUNCT
cana-6157	226	1	communications	communication	NOUN
cana-6157	226	2	on	on	ADP
cana-6157	226	3	applied	apply	VERB
cana-6157	226	4	nonlinear	nonlinear	ADJ
cana-6157	226	5	analysis	analysis	NOUN
cana-6157	226	6	issn	issn	NOUN
cana-6157	226	7	:	:	PUNCT
cana-6157	226	8	1074	1074	NUM
cana-6157	226	9	-	-	PUNCT
cana-6157	226	10	133x	133x	NUM
cana-6157	226	11	vol	vol	VERB
cana-6157	226	12	32	32	NUM
cana-6157	226	13	no	no	NOUN
cana-6157	226	14	.	.	PUNCT
cana-6157	227	1	10s	10	NOUN
cana-6157	227	2	(	(	PUNCT
cana-6157	227	3	2025	2025	NUM
cana-6157	227	4	)	)	PUNCT
cana-6157	227	5	3493	3493	NUM
cana-6157	227	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6157	227	7	in	in	ADP
cana-6157	227	8	summary	summary	NOUN
cana-6157	227	9	,	,	PUNCT
cana-6157	227	10	the	the	DET
cana-6157	227	11	aptee	aptee	ADJ
cana-6157	227	12	distribution	distribution	NOUN
cana-6157	227	13	proves	prove	VERB
cana-6157	227	14	to	to	PART
cana-6157	227	15	be	be	AUX
cana-6157	227	16	a	a	DET
cana-6157	227	17	powerful	powerful	ADJ
cana-6157	227	18	tool	tool	NOUN
cana-6157	227	19	for	for	ADP
cana-6157	227	20	modeling	model	VERB
cana-6157	227	21	complex	complex	ADJ
cana-6157	227	22	lifetime	lifetime	NOUN
cana-6157	227	23	data	datum	NOUN
cana-6157	227	24	,	,	PUNCT
cana-6157	227	25	particularly	particularly	ADV
cana-6157	227	26	under	under	ADP
cana-6157	227	27	competing	compete	VERB
cana-6157	227	28	risks	risk	NOUN
cana-6157	227	29	settings	setting	NOUN
cana-6157	227	30	.	.	PUNCT
cana-6157	228	1	future	future	ADJ
cana-6157	228	2	work	work	NOUN
cana-6157	228	3	may	may	AUX
cana-6157	228	4	extend	extend	VERB
cana-6157	228	5	this	this	DET
cana-6157	228	6	model	model	NOUN
cana-6157	228	7	by	by	ADP
cana-6157	228	8	incorporating	incorporate	VERB
cana-6157	228	9	covariates	covariate	NOUN
cana-6157	228	10	through	through	ADP
cana-6157	228	11	regression	regression	NOUN
cana-6157	228	12	structures	structure	NOUN
cana-6157	228	13	,	,	PUNCT
cana-6157	228	14	handling	handle	VERB
cana-6157	228	15	censored	censor	VERB
cana-6157	228	16	or	or	CCONJ
cana-6157	228	17	truncated	truncated	ADJ
cana-6157	228	18	data	datum	NOUN
cana-6157	228	19	,	,	PUNCT
cana-6157	228	20	or	or	CCONJ
cana-6157	228	21	exploring	explore	VERB
cana-6157	228	22	bayesian	bayesian	NOUN
cana-6157	228	23	inference	inference	NOUN
cana-6157	228	24	approaches	approach	NOUN
cana-6157	228	25	.	.	PUNCT
cana-6157	229	1	references	reference	NOUN
cana-6157	229	2	[	[	X
cana-6157	229	3	1	1	NUM
cana-6157	229	4	]	]	PUNCT
cana-6157	229	5	alghamedi	alghamedi	PROPN
cana-6157	229	6	,	,	PUNCT
cana-6157	229	7	a.	a.	PROPN
cana-6157	229	8	,	,	PUNCT
cana-6157	229	9	dey	dey	PROPN
cana-6157	229	10	,	,	PUNCT
cana-6157	229	11	s.	s.	PROPN
cana-6157	229	12	,	,	PUNCT
cana-6157	229	13	kumar	kumar	PROPN
cana-6157	229	14	,	,	PUNCT
cana-6157	229	15	d.	d.	PROPN
cana-6157	229	16	,	,	PUNCT
cana-6157	229	17	and	and	CCONJ
cana-6157	229	18	dobbah	dobbah	PROPN
cana-6157	229	19	,	,	PUNCT
cana-6157	229	20	s.	s.	PROPN
cana-6157	229	21	a.	a.	PROPN
cana-6157	229	22	(	(	PUNCT
cana-6157	229	23	2019	2019	NUM
cana-6157	229	24	)	)	PUNCT
cana-6157	229	25	.	.	PUNCT
cana-6157	230	1	"	"	PUNCT
cana-6157	230	2	the	the	DET
cana-6157	230	3	alpha	alpha	NOUN
cana-6157	230	4	-	-	PUNCT
cana-6157	230	5	power	power	NOUN
cana-6157	230	6	transformedextended	transformedextende	VERB
cana-6157	230	7	exponential	exponential	ADJ
cana-6157	230	8	distribution	distribution	NOUN
cana-6157	230	9	:	:	PUNCT
cana-6157	230	10	properties	property	NOUN
cana-6157	230	11	and	and	CCONJ
cana-6157	230	12	applications	application	NOUN
cana-6157	230	13	"	"	PUNCT
cana-6157	230	14	.	.	PUNCT
cana-6157	231	1	mathematics	mathematic	NOUN
cana-6157	231	2	,	,	PUNCT
cana-6157	231	3	7(12	7(12	NUM
cana-6157	231	4	)	)	PUNCT
cana-6157	231	5	,	,	PUNCT
cana-6157	231	6	1234	1234	NUM
cana-6157	231	7	.	.	PUNCT
cana-6157	232	1	[	[	X
cana-6157	232	2	2	2	NUM
cana-6157	232	3	]	]	SYM
cana-6157	232	4	bertholon	bertholon	NOUN
cana-6157	232	5	,	,	PUNCT
cana-6157	232	6	h.	h.	PROPN
cana-6157	232	7	,	,	PUNCT
cana-6157	232	8	bousquet	bousquet	PROPN
cana-6157	232	9	,	,	PUNCT
cana-6157	232	10	n.	n.	NOUN
cana-6157	232	11	,	,	PUNCT
cana-6157	232	12	celeux	celeux	PROPN
cana-6157	232	13	,	,	PUNCT
cana-6157	232	14	g.	g.	PROPN
cana-6157	232	15	(	(	PUNCT
cana-6157	232	16	2004	2004	NUM
cana-6157	232	17	)	)	PUNCT
cana-6157	232	18	.	.	PUNCT
cana-6157	233	1	"	"	PUNCT
cana-6157	233	2	an	an	DET
cana-6157	233	3	alternative	alternative	ADJ
cana-6157	233	4	competing	compete	VERB
cana-6157	233	5	risk	risk	NOUN
cana-6157	233	6	model	model	NOUN
cana-6157	233	7	to	to	ADP
cana-6157	233	8	the	the	DET
cana-6157	233	9	weibull	weibull	NOUN
cana-6157	233	10	distribution	distribution	NOUN
cana-6157	233	11	in	in	ADP
cana-6157	233	12	lifetime	lifetime	NOUN
cana-6157	233	13	data	datum	NOUN
cana-6157	233	14	analysis	analysis	NOUN
cana-6157	233	15	"	"	PUNCT
cana-6157	233	16	.	.	PUNCT
cana-6157	234	1	rr-5265	rr-5265	NOUN
cana-6157	234	2	,	,	PUNCT
cana-6157	234	3	inria	inria	NOUN
cana-6157	234	4	.	.	PUNCT
cana-6157	235	1	pp	pp	X
cana-6157	235	2	.	.	PUNCT
cana-6157	236	1	25	25	NUM
cana-6157	236	2	.	.	PUNCT
cana-6157	236	3	available	available	ADJ
cana-6157	236	4	at	at	ADP
cana-6157	236	5	https://hal.inria.fr/inria00070733	https://hal.inria.fr/inria00070733	PROPN
cana-6157	236	6	.	.	PUNCT
cana-6157	237	1	[	[	X
cana-6157	237	2	3	3	NUM
cana-6157	237	3	]	]	X
cana-6157	237	4	bouaziz	bouaziz	NOUN
cana-6157	237	5	,	,	PUNCT
cana-6157	237	6	a	a	DET
cana-6157	237	7	,	,	PUNCT
cana-6157	237	8	seddik	seddik	NOUN
cana-6157	237	9	-	-	PUNCT
cana-6157	237	10	ameur	ameur	ADJ
cana-6157	237	11	,	,	PUNCT
cana-6157	237	12	n.	n.	NOUN
cana-6157	237	13	and	and	CCONJ
cana-6157	237	14	chouia	chouia	PROPN
cana-6157	237	15	,	,	PUNCT
cana-6157	237	16	s.	s.	PROPN
cana-6157	237	17	(	(	PUNCT
cana-6157	237	18	2025	2025	NUM
cana-6157	237	19	)	)	PUNCT
cana-6157	237	20	.	.	PUNCT
cana-6157	238	1	"	"	PUNCT
cana-6157	238	2	on	on	ADP
cana-6157	238	3	fitting	fit	VERB
cana-6157	238	4	the	the	DET
cana-6157	238	5	bi	bi	PROPN
cana-6157	238	6	-	-	ADJ
cana-6157	238	7	weibull	weibull	ADJ
cana-6157	238	8	competing	compete	VERB
cana-6157	238	9	risks	risk	NOUN
cana-6157	238	10	distribution	distribution	NOUN
cana-6157	238	11	with	with	ADP
cana-6157	238	12	application	application	NOUN
cana-6157	238	13	"	"	PUNCT
cana-6157	238	14	,	,	PUNCT
cana-6157	238	15	utilitas	utilitas	PROPN
cana-6157	238	16	mathematica	mathematica	PROPN
cana-6157	238	17	,	,	PUNCT
cana-6157	238	18	volume	volume	NOUN
cana-6157	238	19	122	122	NUM
cana-6157	238	20	,	,	PUNCT
cana-6157	238	21	pp	pp	PROPN
cana-6157	238	22	.	.	PUNCT
cana-6157	238	23	301	301	NUM
cana-6157	238	24	-	-	SYM
cana-6157	238	25	316	316	NUM
cana-6157	238	26	.	.	PUNCT
cana-6157	239	1	[	[	X
cana-6157	239	2	4	4	NUM
cana-6157	239	3	]	]	X
cana-6157	239	4	chouia	chouia	NOUN
cana-6157	239	5	,	,	PUNCT
cana-6157	239	6	s.	s.	PROPN
cana-6157	239	7	and	and	CCONJ
cana-6157	239	8	seddik	seddik	NOUN
cana-6157	239	9	-	-	PUNCT
cana-6157	239	10	ameur	ameur	NOUN
cana-6157	239	11	,	,	PUNCT
cana-6157	239	12	n.	n.	NOUN
cana-6157	239	13	(	(	PUNCT
cana-6157	239	14	2014	2014	NUM
cana-6157	239	15	)	)	PUNCT
cana-6157	239	16	.	.	PUNCT
cana-6157	240	1	"	"	PUNCT
cana-6157	240	2	a	a	DET
cana-6157	240	3	goodness	goodness	NOUN
cana-6157	240	4	-	-	PUNCT
cana-6157	240	5	of	of	ADP
cana-6157	240	6	-	-	PUNCT
cana-6157	240	7	fit	fit	NOUN
cana-6157	240	8	test	test	NOUN
cana-6157	240	9	for	for	ADP
cana-6157	240	10	a	a	DET
cana-6157	240	11	competing	compete	VERB
cana-6157	240	12	risk	risk	NOUN
cana-6157	240	13	model	model	NOUN
cana-6157	240	14	"	"	PUNCT
cana-6157	240	15	.	.	PUNCT
cana-6157	241	1	international	international	ADJ
cana-6157	241	2	journal	journal	PROPN
cana-6157	241	3	of	of	ADP
cana-6157	241	4	applied	apply	VERB
cana-6157	241	5	mathematics	mathematic	NOUN
cana-6157	241	6	and	and	CCONJ
cana-6157	241	7	statistics	statistic	NOUN
cana-6157	241	8	.	.	PUNCT
cana-6157	242	1	[	[	X
cana-6157	242	2	5	5	NUM
cana-6157	242	3	]	]	PUNCT
cana-6157	242	4	chouia	chouia	NOUN
cana-6157	242	5	,	,	PUNCT
cana-6157	242	6	s.	s.	PROPN
cana-6157	242	7	and	and	CCONJ
cana-6157	242	8	seddik	seddik	NOUN
cana-6157	242	9	-	-	PUNCT
cana-6157	242	10	ameur	ameur	NOUN
cana-6157	242	11	,	,	PUNCT
cana-6157	242	12	n.	n.	NOUN
cana-6157	242	13	(	(	PUNCT
cana-6157	242	14	2017	2017	NUM
cana-6157	242	15	)	)	PUNCT
cana-6157	242	16	.	.	PUNCT
cana-6157	243	1	"	"	PUNCT
cana-6157	243	2	a	a	DET
cana-6157	243	3	modified	modified	ADJ
cana-6157	243	4	chi	chi	ADJ
cana-6157	243	5	-	-	PUNCT
cana-6157	243	6	square	square	ADJ
cana-6157	243	7	test	test	NOUN
cana-6157	243	8	for	for	ADP
cana-6157	243	9	bertholon	bertholon	NOUN
cana-6157	243	10	model	model	NOUN
cana-6157	243	11	with	with	ADP
cana-6157	243	12	censored	censored	ADJ
cana-6157	243	13	data	datum	NOUN
cana-6157	243	14	"	"	PUNCT
cana-6157	243	15	,	,	PUNCT
cana-6157	243	16	communications	communication	NOUN
cana-6157	243	17	in	in	ADP
cana-6157	243	18	statistics	statistic	NOUN
cana-6157	243	19	simulation	simulation	NOUN
cana-6157	243	20	and	and	CCONJ
cana-6157	243	21	computation	computation	NOUN
cana-6157	243	22	,	,	PUNCT
cana-6157	243	23	46:1	46:1	NUM
cana-6157	243	24	,	,	PUNCT
cana-6157	243	25	593	593	NUM
cana-6157	243	26	-	-	SYM
cana-6157	243	27	602	602	NUM
cana-6157	243	28	.	.	PUNCT
cana-6157	244	1	[	[	X
cana-6157	244	2	6	6	NUM
cana-6157	244	3	]	]	X
cana-6157	244	4	gupta	gupta	PROPN
cana-6157	244	5	,	,	PUNCT
cana-6157	244	6	r.	r.	PROPN
cana-6157	244	7	d.	d.	PROPN
cana-6157	244	8	,	,	PUNCT
cana-6157	244	9	and	and	CCONJ
cana-6157	244	10	kundu	kundu	NOUN
cana-6157	244	11	,	,	PUNCT
cana-6157	244	12	d.	d.	PROPN
cana-6157	244	13	(	(	PUNCT
cana-6157	244	14	2001	2001	NUM
cana-6157	244	15	)	)	PUNCT
cana-6157	244	16	.	.	PUNCT
cana-6157	245	1	"	"	PUNCT
cana-6157	245	2	exponentiated	exponentiate	VERB
cana-6157	245	3	exponential	exponential	ADJ
cana-6157	245	4	family	family	NOUN
cana-6157	245	5	:	:	PUNCT
cana-6157	245	6	an	an	DET
cana-6157	245	7	alternative	alternative	NOUN
cana-6157	245	8	to	to	ADP
cana-6157	245	9	gamma	gamma	NOUN
cana-6157	245	10	and	and	CCONJ
cana-6157	245	11	weibull	weibull	PROPN
cana-6157	245	12	distributions	distributions	PROPN
cana-6157	245	13	"	"	PUNCT
cana-6157	245	14	.	.	PUNCT
cana-6157	246	1	biometrical	biometrical	ADJ
cana-6157	246	2	journal	journal	PROPN
cana-6157	246	3	,	,	PUNCT
cana-6157	246	4	43(1	43(1	NOUN
cana-6157	246	5	)	)	PUNCT
cana-6157	246	6	,	,	PUNCT
cana-6157	246	7	117	117	NUM
cana-6157	246	8	-	-	SYM
cana-6157	246	9	130	130	NUM
cana-6157	246	10	.	.	PUNCT
cana-6157	247	1	[	[	X
cana-6157	247	2	7	7	NUM
cana-6157	247	3	]	]	X
cana-6157	247	4	linhart	linhart	NOUN
cana-6157	247	5	,	,	PUNCT
cana-6157	247	6	h.	h.	PROPN
cana-6157	247	7	,	,	PUNCT
cana-6157	247	8	zucchini	zucchini	PROPN
cana-6157	247	9	,	,	PUNCT
cana-6157	247	10	w.	w.	PROPN
cana-6157	247	11	,	,	PUNCT
cana-6157	247	12	model	model	NOUN
cana-6157	247	13	selection	selection	NOUN
cana-6157	247	14	,	,	PUNCT
cana-6157	247	15	john	john	PROPN
cana-6157	247	16	wiley	wiley	PROPN
cana-6157	247	17	&	&	CCONJ
cana-6157	247	18	sons	son	NOUN
cana-6157	247	19	,	,	PUNCT
cana-6157	247	20	new	new	PROPN
cana-6157	247	21	york	york	PROPN
cana-6157	247	22	,	,	PUNCT
cana-6157	247	23	1986	1986	NUM
cana-6157	247	24	.	.	PUNCT
cana-6157	248	1	[	[	X
cana-6157	248	2	8	8	NUM
cana-6157	248	3	]	]	SYM
cana-6157	248	4	mahdavi	mahdavi	PROPN
cana-6157	248	5	,	,	PUNCT
cana-6157	248	6	a.	a.	NOUN
cana-6157	248	7	,	,	PUNCT
cana-6157	248	8	and	and	CCONJ
cana-6157	248	9	kundu	kundu	NOUN
cana-6157	248	10	,	,	PUNCT
cana-6157	248	11	d.	d.	PROPN
cana-6157	248	12	(	(	PUNCT
cana-6157	248	13	2016	2016	NUM
cana-6157	248	14	)	)	PUNCT
cana-6157	248	15	.	.	PUNCT
cana-6157	249	1	"	"	PUNCT
cana-6157	249	2	the	the	DET
cana-6157	249	3	alpha	alpha	NOUN
cana-6157	249	4	power	power	NOUN
cana-6157	249	5	exponential	exponential	ADJ
cana-6157	249	6	distribution	distribution	NOUN
cana-6157	249	7	:	:	PUNCT
cana-6157	249	8	properties	property	NOUN
cana-6157	249	9	and	and	CCONJ
cana-6157	249	10	different	different	ADJ
cana-6157	249	11	methods	method	NOUN
cana-6157	249	12	of	of	ADP
cana-6157	249	13	estimation	estimation	NOUN
cana-6157	249	14	"	"	PUNCT
cana-6157	249	15	.	.	PUNCT
cana-6157	250	1	communications	communication	NOUN
cana-6157	250	2	in	in	ADP
cana-6157	250	3	statistics	statistic	NOUN
cana-6157	250	4	theory	theory	NOUN
cana-6157	250	5	and	and	CCONJ
cana-6157	250	6	methods	method	NOUN
cana-6157	250	7	,	,	PUNCT
cana-6157	250	8	45(5	45(5	NOUN
cana-6157	250	9	)	)	PUNCT
cana-6157	250	10	,	,	PUNCT
cana-6157	250	11	1350	1350	NUM
cana-6157	250	12	-	-	SYM
cana-6157	250	13	1366	1366	NUM
cana-6157	250	14	.	.	PUNCT
cana-6157	251	1	[	[	X
cana-6157	251	2	9	9	NUM
cana-6157	251	3	]	]	SYM
cana-6157	251	4	nadarajah	nadarajah	NOUN
cana-6157	251	5	,	,	PUNCT
cana-6157	251	6	s.	s.	PROPN
cana-6157	251	7	,	,	PUNCT
cana-6157	251	8	and	and	CCONJ
cana-6157	251	9	haghighi	haghighi	PROPN
cana-6157	251	10	,	,	PUNCT
cana-6157	251	11	f.	f.	PROPN
cana-6157	251	12	(	(	PUNCT
cana-6157	251	13	2011	2011	NUM
cana-6157	251	14	)	)	PUNCT
cana-6157	251	15	.	.	PUNCT
cana-6157	252	1	"	"	PUNCT
cana-6157	252	2	an	an	DET
cana-6157	252	3	extension	extension	NOUN
cana-6157	252	4	of	of	ADP
cana-6157	252	5	the	the	DET
cana-6157	252	6	exponential	exponential	ADJ
cana-6157	252	7	distribution	distribution	NOUN
cana-6157	252	8	"	"	PUNCT
cana-6157	252	9	.	.	PUNCT
cana-6157	253	1	statistics	statistic	NOUN
cana-6157	253	2	,	,	PUNCT
cana-6157	253	3	45(6	45(6	NOUN
cana-6157	253	4	)	)	PUNCT
cana-6157	253	5	,	,	PUNCT
cana-6157	253	6	543558	543558	NUM
cana-6157	253	7	.	.	PUNCT
cana-6157	254	1	[	[	X
cana-6157	254	2	10	10	NUM
cana-6157	254	3	]	]	X
cana-6157	254	4	nikulin	nikulin	NOUN
cana-6157	254	5	,	,	PUNCT
cana-6157	254	6	m.	m.	NOUN
cana-6157	254	7	s.	s.	PROPN
cana-6157	254	8	(	(	PUNCT
cana-6157	254	9	1973	1973	NUM
cana-6157	254	10	)	)	PUNCT
cana-6157	254	11	.	.	PUNCT
cana-6157	255	1	"	"	PUNCT
cana-6157	255	2	chi	chi	ADJ
cana-6157	255	3	-	-	PUNCT
cana-6157	255	4	square	square	ADJ
cana-6157	255	5	test	test	NOUN
cana-6157	255	6	for	for	ADP
cana-6157	255	7	continuous	continuous	ADJ
cana-6157	255	8	distribution	distribution	NOUN
cana-6157	255	9	with	with	ADP
cana-6157	255	10	shift	shift	NOUN
cana-6157	255	11	and	and	CCONJ
cana-6157	255	12	scale	scale	NOUN
cana-6157	255	13	parameters	parameter	NOUN
cana-6157	255	14	"	"	PUNCT
cana-6157	255	15	.	.	PUNCT
cana-6157	256	1	theory	theory	NOUN
cana-6157	256	2	of	of	ADP
cana-6157	256	3	probability	probability	NOUN
cana-6157	256	4	and	and	CCONJ
cana-6157	256	5	its	its	PRON
cana-6157	256	6	applications	application	NOUN
cana-6157	256	7	,	,	PUNCT
cana-6157	256	8	19	19	NUM
cana-6157	256	9	,	,	PUNCT
cana-6157	256	10	559	559	NUM
cana-6157	256	11	-	-	SYM
cana-6157	256	12	-568	-568	NOUN
cana-6157	256	13	.	.	PUNCT
cana-6157	257	1	[	[	X
cana-6157	257	2	11	11	NUM
cana-6157	257	3	]	]	SYM
cana-6157	257	4	rao	rao	PROPN
cana-6157	257	5	,	,	PUNCT
cana-6157	257	6	k.	k.	PROPN
cana-6157	257	7	c.	c.	PROPN
cana-6157	257	8	and	and	CCONJ
cana-6157	257	9	robson	robson	PROPN
cana-6157	257	10	,	,	PUNCT
cana-6157	257	11	d.	d.	PROPN
cana-6157	257	12	s.	s.	PROPN
cana-6157	257	13	(	(	PUNCT
cana-6157	257	14	1974	1974	NUM
cana-6157	257	15	)	)	PUNCT
cana-6157	257	16	.	.	PUNCT
cana-6157	258	1	"	"	PUNCT
cana-6157	258	2	a	a	DET
cana-6157	258	3	chi	chi	ADJ
cana-6157	258	4	-	-	PUNCT
cana-6157	258	5	square	square	ADJ
cana-6157	258	6	statistic	statistic	NOUN
cana-6157	258	7	for	for	ADP
cana-6157	258	8	goodness	goodness	NOUN
cana-6157	258	9	-	-	PUNCT
cana-6157	258	10	of	of	ADP
cana-6157	258	11	-	-	PUNCT
cana-6157	258	12	fit	fit	NOUN
cana-6157	258	13	for	for	ADP
cana-6157	258	14	tests	test	NOUN
cana-6157	258	15	within	within	ADP
cana-6157	258	16	the	the	DET
cana-6157	258	17	exponential	exponential	ADJ
cana-6157	258	18	family	family	NOUN
cana-6157	258	19	"	"	PUNCT
cana-6157	258	20	.	.	PUNCT
cana-6157	259	1	communications	communication	NOUN
cana-6157	259	2	in	in	ADP
cana-6157	259	3	statistics	statistic	NOUN
cana-6157	259	4	,	,	PUNCT
cana-6157	259	5	3	3	NUM
cana-6157	259	6	,	,	PUNCT
cana-6157	259	7	1139	1139	NUM
cana-6157	259	8	-	-	PUNCT
cana-6157	259	9	-1153	-1153	ADJ
cana-6157	259	10	.	.	PUNCT
cana-6157	260	1	[	[	X
cana-6157	260	2	12	12	NUM
cana-6157	260	3	]	]	PUNCT
cana-6157	260	4	seddik	seddik	NOUN
cana-6157	260	5	-	-	PUNCT
cana-6157	260	6	ameur	ameur	NOUN
cana-6157	260	7	,	,	PUNCT
cana-6157	260	8	n.	n.	NOUN
cana-6157	260	9	and	and	CCONJ
cana-6157	260	10	treidi	treidi	NOUN
cana-6157	260	11	,	,	PUNCT
cana-6157	260	12	w.	w.	NOUN
cana-6157	260	13	(	(	PUNCT
cana-6157	260	14	2017	2017	NUM
cana-6157	260	15	)	)	PUNCT
cana-6157	260	16	.	.	PUNCT
cana-6157	261	1	"	"	PUNCT
cana-6157	261	2	on	on	ADP
cana-6157	261	3	testing	test	VERB
cana-6157	261	4	the	the	DET
cana-6157	261	5	fit	fit	NOUN
cana-6157	261	6	of	of	ADP
cana-6157	261	7	accelerated	accelerate	VERB
cana-6157	261	8	failure	failure	NOUN
cana-6157	261	9	time	time	NOUN
cana-6157	261	10	and	and	CCONJ
cana-6157	261	11	proportional	proportional	ADJ
cana-6157	261	12	hazard	hazard	NOUN
cana-6157	261	13	weibull	weibull	PROPN
cana-6157	261	14	extension	extension	NOUN
cana-6157	261	15	models	model	NOUN
cana-6157	261	16	"	"	PUNCT
cana-6157	261	17	,	,	PUNCT
cana-6157	261	18	journal	journal	NOUN
cana-6157	261	19	of	of	ADP
cana-6157	261	20	statistical	statistical	ADJ
cana-6157	261	21	theory	theory	NOUN
cana-6157	261	22	and	and	CCONJ
cana-6157	261	23	practice	practice	NOUN
cana-6157	261	24	,	,	PUNCT
cana-6157	261	25	12:2	12:2	NUM
cana-6157	261	26	,	,	PUNCT
cana-6157	261	27	397	397	NUM
cana-6157	261	28	-	-	SYM
cana-6157	261	29	411	411	NUM
cana-6157	261	30	.	.	PUNCT