id	sid	tid	token	lemma	pos
iajs-3842	1	1	388	388	NUM
iajs-3842	1	2	©	©	PROPN
iajs-3842	1	3	2025	2025	NUM
iajs-3842	1	4	the	the	DET
iajs-3842	1	5	author(s	author(s	NOUN
iajs-3842	1	6	)	)	PUNCT
iajs-3842	1	7	.	.	PUNCT
iajs-3842	2	1	published	publish	VERB
iajs-3842	2	2	by	by	ADP
iajs-3842	2	3	college	college	NOUN
iajs-3842	2	4	of	of	ADP
iajs-3842	2	5	education	education	NOUN
iajs-3842	2	6	for	for	ADP
iajs-3842	2	7	pure	pure	ADJ
iajs-3842	2	8	science	science	NOUN
iajs-3842	2	9	(	(	PUNCT
iajs-3842	2	10	ibn	ibn	PROPN
iajs-3842	2	11	al	al	PROPN
iajs-3842	2	12	-	-	PUNCT
iajs-3842	2	13	haitham	haitham	PROPN
iajs-3842	2	14	)	)	PUNCT
iajs-3842	2	15	,	,	PUNCT
iajs-3842	2	16	university	university	NOUN
iajs-3842	2	17	of	of	ADP
iajs-3842	2	18	baghdad	baghdad	PROPN
iajs-3842	2	19	.	.	PUNCT
iajs-3842	3	1	this	this	PRON
iajs-3842	3	2	is	be	AUX
iajs-3842	3	3	an	an	DET
iajs-3842	3	4	open	open	ADJ
iajs-3842	3	5	-	-	PUNCT
iajs-3842	3	6	access	access	NOUN
iajs-3842	3	7	article	article	NOUN
iajs-3842	3	8	distributed	distribute	VERB
iajs-3842	3	9	under	under	ADP
iajs-3842	3	10	the	the	DET
iajs-3842	3	11	terms	term	NOUN
iajs-3842	3	12	of	of	ADP
iajs-3842	3	13	the	the	DET
iajs-3842	3	14	creative	creative	ADJ
iajs-3842	3	15	commons	common	NOUN
iajs-3842	3	16	attribution	attribution	NOUN
iajs-3842	3	17	4.0	4.0	NUM
iajs-3842	3	18	international	international	ADJ
iajs-3842	3	19	license	license	NOUN
iajs-3842	3	20	new	new	ADJ
iajs-3842	3	21	lifetime	lifetime	NOUN
iajs-3842	3	22	shanker	shanker	NOUN
iajs-3842	3	23	weibull	weibull	PROPN
iajs-3842	3	24	distribution	distribution	NOUN
iajs-3842	3	25	:	:	PUNCT
iajs-3842	3	26	structure	structure	NOUN
iajs-3842	3	27	and	and	CCONJ
iajs-3842	3	28	properties	property	NOUN
iajs-3842	3	29	noor	noor	PROPN
iajs-3842	3	30	ebadi	ebadi	VERB
iajs-3842	3	31	ashoor1	ashoor1	PROPN
iajs-3842	3	32	*	*	PUNCT
iajs-3842	3	33	,	,	PUNCT
iajs-3842	3	34	maysaa	maysaa	PROPN
iajs-3842	3	35	jalil	jalil	PROPN
iajs-3842	3	36	mohammed2	mohammed2	PROPN
iajs-3842	3	37	and	and	CCONJ
iajs-3842	3	38	umar	umar	PROPN
iajs-3842	3	39	yusuf	yusuf	PROPN
iajs-3842	3	40	madaki3	madaki3	PROPN
iajs-3842	4	1	1,2department	1,2department	NUM
iajs-3842	4	2	of	of	ADP
iajs-3842	4	3	mathematics	mathematic	NOUN
iajs-3842	4	4	,	,	PUNCT
iajs-3842	4	5	college	college	NOUN
iajs-3842	4	6	of	of	ADP
iajs-3842	4	7	education	education	NOUN
iajs-3842	4	8	for	for	ADP
iajs-3842	4	9	pure	pure	ADJ
iajs-3842	4	10	science	science	NOUN
iajs-3842	4	11	(	(	PUNCT
iajs-3842	4	12	ibn	ibn	PROPN
iajs-3842	4	13	al	al	PROPN
iajs-3842	4	14	-	-	PUNCT
iajs-3842	4	15	haitham	haitham	PROPN
iajs-3842	4	16	)	)	PUNCT
iajs-3842	4	17	,	,	PUNCT
iajs-3842	4	18	university	university	NOUN
iajs-3842	4	19	of	of	ADP
iajs-3842	4	20	baghdad	baghdad	PROPN
iajs-3842	4	21	,	,	PUNCT
iajs-3842	4	22	baghdad	baghdad	PROPN
iajs-3842	4	23	,	,	PUNCT
iajs-3842	4	24	iraq	iraq	PROPN
iajs-3842	4	25	.	.	PUNCT
iajs-3842	5	1	3department	3department	NUM
iajs-3842	5	2	of	of	ADP
iajs-3842	5	3	mathematics	mathematic	NOUN
iajs-3842	5	4	and	and	CCONJ
iajs-3842	5	5	statistics	statistic	NOUN
iajs-3842	5	6	,	,	PUNCT
iajs-3842	5	7	faculty	faculty	NOUN
iajs-3842	5	8	of	of	ADP
iajs-3842	5	9	science	science	NOUN
iajs-3842	5	10	,	,	PUNCT
iajs-3842	5	11	yobe	yobe	PROPN
iajs-3842	5	12	state	state	PROPN
iajs-3842	5	13	university	university	NOUN
iajs-3842	5	14	damaturu	damaturu	NOUN
iajs-3842	5	15	,	,	PUNCT
iajs-3842	5	16	nigeria	nigeria	PROPN
iajs-3842	5	17	.	.	PUNCT
iajs-3842	6	1	*	*	PUNCT
iajs-3842	6	2	corresponding	correspond	VERB
iajs-3842	6	3	author	author	NOUN
iajs-3842	6	4	.	.	PUNCT
iajs-3842	7	1	received	receive	VERB
iajs-3842	7	2	:	:	PUNCT
iajs-3842	7	3	20	20	NUM
iajs-3842	7	4	november	november	PROPN
iajs-3842	7	5	2023	2023	NUM
iajs-3842	7	6	accepted	accept	VERB
iajs-3842	7	7	:	:	PUNCT
iajs-3842	7	8	22	22	NUM
iajs-3842	7	9	january	january	NOUN
iajs-3842	7	10	2024	2024	NUM
iajs-3842	7	11	published	publish	VERB
iajs-3842	7	12	:	:	PUNCT
iajs-3842	7	13	20	20	NUM
iajs-3842	7	14	april	april	PROPN
iajs-3842	7	15	2025	2025	NUM
iajs-3842	7	16	doi.org/10.30526/38.2.3842	doi.org/10.30526/38.2.3842	NOUN
iajs-3842	7	17	abstract	abstract	NOUN
iajs-3842	7	18	this	this	DET
iajs-3842	7	19	paper	paper	NOUN
iajs-3842	7	20	introduces	introduce	VERB
iajs-3842	7	21	a	a	DET
iajs-3842	7	22	new	new	ADJ
iajs-3842	7	23	model	model	NOUN
iajs-3842	7	24	with	with	ADP
iajs-3842	7	25	two	two	NUM
iajs-3842	7	26	parameters	parameter	NOUN
iajs-3842	7	27	titled	title	VERB
iajs-3842	7	28	“	"	PUNCT
iajs-3842	7	29	shanker	shanker	PROPN
iajs-3842	7	30	weibull	weibull	PROPN
iajs-3842	7	31	distribution	distribution	NOUN
iajs-3842	7	32	"	"	PUNCT
iajs-3842	7	33	.	.	PUNCT
iajs-3842	8	1	this	this	DET
iajs-3842	8	2	distribution	distribution	NOUN
iajs-3842	8	3	is	be	AUX
iajs-3842	8	4	obtained	obtain	VERB
iajs-3842	8	5	by	by	ADP
iajs-3842	8	6	merging	merge	VERB
iajs-3842	8	7	the	the	DET
iajs-3842	8	8	shanker	shanker	NOUN
iajs-3842	8	9	distribution	distribution	NOUN
iajs-3842	8	10	with	with	ADP
iajs-3842	8	11	a	a	DET
iajs-3842	8	12	scale	scale	NOUN
iajs-3842	8	13	of	of	ADP
iajs-3842	8	14	one	one	NUM
iajs-3842	8	15	parameter	parameter	NOUN
iajs-3842	8	16	and	and	CCONJ
iajs-3842	8	17	the	the	DET
iajs-3842	8	18	weibull	weibull	NOUN
iajs-3842	8	19	distribution	distribution	NOUN
iajs-3842	8	20	with	with	ADP
iajs-3842	8	21	a	a	DET
iajs-3842	8	22	shape	shape	NOUN
iajs-3842	8	23	parameter	parameter	NOUN
iajs-3842	8	24	.	.	PUNCT
iajs-3842	9	1	first	first	ADV
iajs-3842	9	2	,	,	PUNCT
iajs-3842	9	3	we	we	PRON
iajs-3842	9	4	present	present	VERB
iajs-3842	9	5	the	the	DET
iajs-3842	9	6	mathematical	mathematical	ADJ
iajs-3842	9	7	structure	structure	NOUN
iajs-3842	9	8	of	of	ADP
iajs-3842	9	9	the	the	DET
iajs-3842	9	10	new	new	ADJ
iajs-3842	9	11	distribution	distribution	NOUN
iajs-3842	9	12	,	,	PUNCT
iajs-3842	9	13	which	which	PRON
iajs-3842	9	14	depends	depend	VERB
iajs-3842	9	15	on	on	ADP
iajs-3842	9	16	the	the	DET
iajs-3842	9	17	survival	survival	NOUN
iajs-3842	9	18	function	function	NOUN
iajs-3842	9	19	for	for	ADP
iajs-3842	9	20	each	each	PRON
iajs-3842	9	21	of	of	ADP
iajs-3842	9	22	the	the	DET
iajs-3842	9	23	shanker	shanker	NOUN
iajs-3842	9	24	and	and	CCONJ
iajs-3842	9	25	weibull	weibull	PROPN
iajs-3842	9	26	distributions	distribution	NOUN
iajs-3842	9	27	.	.	PUNCT
iajs-3842	10	1	the	the	DET
iajs-3842	10	2	statistical	statistical	ADJ
iajs-3842	10	3	functions	function	NOUN
iajs-3842	10	4	of	of	ADP
iajs-3842	10	5	this	this	DET
iajs-3842	10	6	new	new	ADJ
iajs-3842	10	7	distribution	distribution	NOUN
iajs-3842	10	8	are	be	AUX
iajs-3842	10	9	presented	present	VERB
iajs-3842	10	10	,	,	PUNCT
iajs-3842	10	11	such	such	ADJ
iajs-3842	10	12	as	as	ADP
iajs-3842	10	13	the	the	DET
iajs-3842	10	14	cumulative	cumulative	ADJ
iajs-3842	10	15	,	,	PUNCT
iajs-3842	10	16	probability	probability	NOUN
iajs-3842	10	17	density	density	NOUN
iajs-3842	10	18	,	,	PUNCT
iajs-3842	10	19	hazard	hazard	NOUN
iajs-3842	10	20	and	and	CCONJ
iajs-3842	10	21	survival	survival	NOUN
iajs-3842	10	22	functions	function	NOUN
iajs-3842	10	23	.	.	PUNCT
iajs-3842	11	1	in	in	ADP
iajs-3842	11	2	addition	addition	NOUN
iajs-3842	11	3	,	,	PUNCT
iajs-3842	11	4	we	we	PRON
iajs-3842	11	5	discuss	discuss	VERB
iajs-3842	11	6	the	the	DET
iajs-3842	11	7	behavior	behavior	NOUN
iajs-3842	11	8	of	of	ADP
iajs-3842	11	9	the	the	DET
iajs-3842	11	10	probability	probability	NOUN
iajs-3842	11	11	density	density	NOUN
iajs-3842	11	12	function	function	NOUN
iajs-3842	11	13	and	and	CCONJ
iajs-3842	11	14	the	the	DET
iajs-3842	11	15	hazard	hazard	NOUN
iajs-3842	11	16	function	function	NOUN
iajs-3842	11	17	by	by	ADP
iajs-3842	11	18	mxamining	mxamine	VERB
iajs-3842	11	19	their	their	PRON
iajs-3842	11	20	shape	shape	NOUN
iajs-3842	11	21	.	.	PUNCT
iajs-3842	12	1	we	we	PRON
iajs-3842	12	2	also	also	ADV
iajs-3842	12	3	present	present	VERB
iajs-3842	12	4	the	the	DET
iajs-3842	12	5	statistical	statistical	ADJ
iajs-3842	12	6	properties	property	NOUN
iajs-3842	12	7	of	of	ADP
iajs-3842	12	8	this	this	DET
iajs-3842	12	9	distribution	distribution	NOUN
iajs-3842	12	10	,	,	PUNCT
iajs-3842	12	11	which	which	PRON
iajs-3842	12	12	include	include	VERB
iajs-3842	12	13	mode	mode	NOUN
iajs-3842	12	14	,	,	PUNCT
iajs-3842	12	15	median	median	NOUN
iajs-3842	12	16	and	and	CCONJ
iajs-3842	12	17	moments	moment	NOUN
iajs-3842	12	18	around	around	ADP
iajs-3842	12	19	the	the	DET
iajs-3842	12	20	origin	origin	NOUN
iajs-3842	12	21	.	.	PUNCT
iajs-3842	13	1	as	as	ADP
iajs-3842	13	2	a	a	DET
iajs-3842	13	3	result	result	NOUN
iajs-3842	13	4	of	of	ADP
iajs-3842	13	5	studying	study	VERB
iajs-3842	13	6	the	the	DET
iajs-3842	13	7	moments	moment	NOUN
iajs-3842	13	8	around	around	ADP
iajs-3842	13	9	the	the	DET
iajs-3842	13	10	origin	origin	NOUN
iajs-3842	13	11	,	,	PUNCT
iajs-3842	13	12	we	we	PRON
iajs-3842	13	13	obtain	obtain	VERB
iajs-3842	13	14	the	the	DET
iajs-3842	13	15	variance	variance	NOUN
iajs-3842	13	16	and	and	CCONJ
iajs-3842	13	17	the	the	DET
iajs-3842	13	18	first	first	ADJ
iajs-3842	13	19	expected	expect	VERB
iajs-3842	13	20	value	value	NOUN
iajs-3842	13	21	(	(	PUNCT
iajs-3842	13	22	mean	mean	NOUN
iajs-3842	13	23	)	)	PUNCT
iajs-3842	13	24	,	,	PUNCT
iajs-3842	13	25	the	the	DET
iajs-3842	13	26	moment	moment	NOUN
iajs-3842	13	27	generating	generate	VERB
iajs-3842	13	28	function	function	NOUN
iajs-3842	13	29	,	,	PUNCT
iajs-3842	13	30	the	the	DET
iajs-3842	13	31	skewness	skewness	NOUN
iajs-3842	13	32	,	,	PUNCT
iajs-3842	13	33	the	the	DET
iajs-3842	13	34	kurtosis	kurtosis	NOUN
iajs-3842	13	35	,	,	PUNCT
iajs-3842	13	36	the	the	DET
iajs-3842	13	37	characteristic	characteristic	ADJ
iajs-3842	13	38	function	function	NOUN
iajs-3842	13	39	,	,	PUNCT
iajs-3842	13	40	the	the	DET
iajs-3842	13	41	factorial	factorial	ADJ
iajs-3842	13	42	generating	generating	NOUN
iajs-3842	13	43	function	function	NOUN
iajs-3842	13	44	,	,	PUNCT
iajs-3842	13	45	the	the	DET
iajs-3842	13	46	quantile	quantile	ADJ
iajs-3842	13	47	function	function	NOUN
iajs-3842	13	48	and	and	CCONJ
iajs-3842	13	49	the	the	DET
iajs-3842	13	50	mean	mean	ADJ
iajs-3842	13	51	time	time	NOUN
iajs-3842	13	52	to	to	ADP
iajs-3842	13	53	failure	failure	NOUN
iajs-3842	13	54	.	.	PUNCT
iajs-3842	14	1	keywords	keyword	NOUN
iajs-3842	14	2	:	:	PUNCT
iajs-3842	14	3	shanker	shank	ADJ
iajs-3842	14	4	distribution	distribution	NOUN
iajs-3842	14	5	,	,	PUNCT
iajs-3842	14	6	exponential	exponential	ADJ
iajs-3842	14	7	distribution	distribution	NOUN
iajs-3842	14	8	,	,	PUNCT
iajs-3842	14	9	survival	survival	NOUN
iajs-3842	14	10	function	function	NOUN
iajs-3842	14	11	,	,	PUNCT
iajs-3842	14	12	moments	moment	NOUN
iajs-3842	14	13	arond	arond	VERB
iajs-3842	14	14	the	the	DET
iajs-3842	14	15	origin	origin	NOUN
iajs-3842	14	16	,	,	PUNCT
iajs-3842	14	17	moment	moment	NOUN
iajs-3842	14	18	generating	generate	VERB
iajs-3842	14	19	function	function	NOUN
iajs-3842	14	20	.	.	PUNCT
iajs-3842	15	1	1	1	X
iajs-3842	15	2	.	.	X
iajs-3842	15	3	introduction	introduction	NOUN
iajs-3842	15	4	although	although	SCONJ
iajs-3842	15	5	the	the	DET
iajs-3842	15	6	process	process	NOUN
iajs-3842	15	7	of	of	ADP
iajs-3842	15	8	mixing	mix	VERB
iajs-3842	15	9	the	the	DET
iajs-3842	15	10	distributions	distribution	NOUN
iajs-3842	15	11	to	to	PART
iajs-3842	15	12	create	create	VERB
iajs-3842	15	13	a	a	DET
iajs-3842	15	14	new	new	ADJ
iajs-3842	15	15	distribution	distribution	NOUN
iajs-3842	15	16	is	be	AUX
iajs-3842	15	17	not	not	PART
iajs-3842	15	18	new	new	ADJ
iajs-3842	15	19	,	,	PUNCT
iajs-3842	15	20	it	it	PRON
iajs-3842	15	21	has	have	AUX
iajs-3842	15	22	gone	go	VERB
iajs-3842	15	23	through	through	ADP
iajs-3842	15	24	several	several	ADJ
iajs-3842	15	25	stages	stage	NOUN
iajs-3842	15	26	of	of	ADP
iajs-3842	15	27	development	development	NOUN
iajs-3842	15	28	depending	depend	VERB
iajs-3842	15	29	on	on	ADP
iajs-3842	15	30	how	how	SCONJ
iajs-3842	15	31	to	to	PART
iajs-3842	15	32	choose	choose	VERB
iajs-3842	15	33	which	which	DET
iajs-3842	15	34	distributions	distribution	NOUN
iajs-3842	15	35	to	to	PART
iajs-3842	15	36	mix	mix	VERB
iajs-3842	15	37	(	(	PUNCT
iajs-3842	15	38	1	1	NUM
iajs-3842	15	39	)	)	PUNCT
iajs-3842	15	40	.	.	PUNCT
iajs-3842	16	1	all	all	PRON
iajs-3842	16	2	of	of	ADP
iajs-3842	16	3	this	this	PRON
iajs-3842	16	4	is	be	AUX
iajs-3842	16	5	done	do	VERB
iajs-3842	16	6	using	use	VERB
iajs-3842	16	7	the	the	DET
iajs-3842	16	8	data	datum	NOUN
iajs-3842	16	9	available	available	ADJ
iajs-3842	16	10	to	to	ADP
iajs-3842	16	11	the	the	DET
iajs-3842	16	12	researcher	researcher	NOUN
iajs-3842	16	13	about	about	ADP
iajs-3842	16	14	the	the	DET
iajs-3842	16	15	properties	property	NOUN
iajs-3842	16	16	and	and	CCONJ
iajs-3842	16	17	nature	nature	NOUN
iajs-3842	16	18	of	of	ADP
iajs-3842	16	19	the	the	DET
iajs-3842	16	20	work	work	NOUN
iajs-3842	16	21	of	of	ADP
iajs-3842	16	22	each	each	DET
iajs-3842	16	23	distribution	distribution	NOUN
iajs-3842	16	24	(	(	PUNCT
iajs-3842	16	25	2	2	NUM
iajs-3842	16	26	)	)	PUNCT
iajs-3842	16	27	.	.	PUNCT
iajs-3842	17	1	many	many	ADJ
iajs-3842	17	2	researchers	researcher	NOUN
iajs-3842	17	3	have	have	AUX
iajs-3842	17	4	combined	combine	VERB
iajs-3842	17	5	two	two	NUM
iajs-3842	17	6	distributions	distribution	NOUN
iajs-3842	17	7	.	.	PUNCT
iajs-3842	18	1	for	for	ADP
iajs-3842	18	2	example	example	NOUN
iajs-3842	18	3	,	,	PUNCT
iajs-3842	18	4	in	in	ADP
iajs-3842	18	5	2015	2015	NUM
iajs-3842	18	6	,	,	PUNCT
iajs-3842	18	7	rama	rama	PROPN
iajs-3842	18	8	(	(	PUNCT
iajs-3842	18	9	3	3	NUM
iajs-3842	18	10	-	-	SYM
iajs-3842	18	11	4	4	NUM
iajs-3842	18	12	)	)	PUNCT
iajs-3842	18	13	proposed	propose	VERB
iajs-3842	18	14	modelling	model	VERB
iajs-3842	18	15	lifetime	lifetime	NOUN
iajs-3842	18	16	data	datum	NOUN
iajs-3842	18	17	with	with	ADP
iajs-3842	18	18	a	a	DET
iajs-3842	18	19	new	new	ADJ
iajs-3842	18	20	one	one	NUM
iajs-3842	18	21	-	-	PUNCT
iajs-3842	18	22	parameter	parameter	NOUN
iajs-3842	18	23	lifetime	lifetime	NOUN
iajs-3842	18	24	distribution	distribution	NOUN
iajs-3842	18	25	,	,	PUNCT
iajs-3842	18	26	the	the	DET
iajs-3842	18	27	"	"	PUNCT
iajs-3842	18	28	shanker	shanker	NOUN
iajs-3842	18	29	distribution	distribution	NOUN
iajs-3842	18	30	"	"	PUNCT
iajs-3842	18	31	,	,	PUNCT
iajs-3842	18	32	by	by	ADP
iajs-3842	18	33	combining	combine	VERB
iajs-3842	18	34	the	the	DET
iajs-3842	18	35	'	'	PUNCT
iajs-3842	18	36	gamma(2,𝛽	gamma(2,𝛽	NOUN
iajs-3842	18	37	)	)	PUNCT
iajs-3842	18	38	distribution	distribution	NOUN
iajs-3842	18	39	''	''	PUNCT
iajs-3842	18	40	with	with	ADP
iajs-3842	18	41	the	the	DET
iajs-3842	18	42	''	''	PUNCT
iajs-3842	18	43	exponential	exponential	ADJ
iajs-3842	18	44	distribution	distribution	NOUN
iajs-3842	18	45	''	''	PUNCT
iajs-3842	18	46	where	where	SCONJ
iajs-3842	18	47	are	be	AUX
iajs-3842	18	48	the	the	DET
iajs-3842	18	49	(	(	PUNCT
iajs-3842	18	50	p.d.f	p.d.f	NOUN
iajs-3842	18	51	.	.	PUNCT
iajs-3842	18	52	)	)	PUNCT
iajs-3842	19	1	and	and	CCONJ
iajs-3842	19	2	the	the	DET
iajs-3842	19	3	(	(	PUNCT
iajs-3842	19	4	c.d.f	c.d.f	NOUN
iajs-3842	19	5	.	.	PUNCT
iajs-3842	19	6	)	)	PUNCT
iajs-3842	20	1	of	of	ADP
iajs-3842	20	2	this	this	DET
iajs-3842	20	3	distribution	distribution	NOUN
iajs-3842	20	4	:	:	PUNCT
iajs-3842	20	5	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3842	20	6	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3842	20	7	mailto	mailto	PROPN
iajs-3842	20	8	:	:	PUNCT
iajs-3842	20	9	https://orcid.org/0009	https://orcid.org/0009	NOUN
iajs-3842	20	10	-	-	PUNCT
iajs-3842	20	11	0009	0009	NUM
iajs-3842	20	12	-	-	PUNCT
iajs-3842	20	13	0187	0187	NUM
iajs-3842	20	14	-	-	PUNCT
iajs-3842	20	15	5419	5419	NUM
iajs-3842	20	16	mailto:noor.abadi2103m@ihcoedu.uobaghdad.edu.iq	mailto:noor.abadi2103m@ihcoedu.uobaghdad.edu.iq	X
iajs-3842	20	17	mailto	mailto	PROPN
iajs-3842	20	18	:	:	PUNCT
iajs-3842	20	19	https://orcid.org/0000	https://orcid.org/0000	X
iajs-3842	20	20	-	-	PUNCT
iajs-3842	20	21	0002	0002	NUM
iajs-3842	20	22	-	-	PUNCT
iajs-3842	20	23	9155	9155	NUM
iajs-3842	20	24	-	-	SYM
iajs-3842	20	25	7159	7159	NUM
iajs-3842	20	26	mailto:maysaa.j.m@ihcoedu.uobaghdad.edu.iq	mailto:maysaa.j.m@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3842	20	27	https://orcid.org/	https://orcid.org/	NOUN
iajs-3842	20	28	mailto:uymadaki84@gmail.com	mailto:uymadaki84@gmail.com	PROPN
iajs-3842	20	29	ihjpas	ihjpas	PROPN
iajs-3842	20	30	.	.	PUNCT
iajs-3842	21	1	2025,38(2	2025,38(2	NOUN
iajs-3842	21	2	)	)	PUNCT
iajs-3842	21	3	389	389	NUM
iajs-3842	21	4	𝑓𝑆𝐻(𝑧	𝑓𝑆𝐻(𝑧	NOUN
iajs-3842	21	5	,	,	PUNCT
iajs-3842	21	6	𝛽	𝛽	NOUN
iajs-3842	21	7	)	)	PUNCT
iajs-3842	21	8	=	=	SYM
iajs-3842	21	9	𝛽2	𝛽2	PROPN
iajs-3842	21	10	𝛽2	𝛽2	PROPN
iajs-3842	21	11	+	+	PROPN
iajs-3842	21	12	1	1	NUM
iajs-3842	21	13	(	(	PUNCT
iajs-3842	21	14	𝛽	𝛽	NOUN
iajs-3842	21	15	+	+	X
iajs-3842	21	16	𝑧)𝑒−𝛽𝑧	𝑧)𝑒−𝛽𝑧	ADJ
iajs-3842	21	17	;	;	PUNCT
iajs-3842	21	18	𝑧	𝑧	X
iajs-3842	21	19	>	>	X
iajs-3842	21	20	0	0	NUM
iajs-3842	21	21	,	,	PUNCT
iajs-3842	21	22	𝛽	𝛽	NOUN
iajs-3842	21	23	>	>	X
iajs-3842	21	24	0	0	PUNCT
iajs-3842	21	25	(	(	PUNCT
iajs-3842	21	26	1	1	NUM
iajs-3842	21	27	)	)	PUNCT
iajs-3842	21	28	𝐹𝑆𝐻(𝑧	𝐹𝑆𝐻(𝑧	NUM
iajs-3842	21	29	)	)	PUNCT
iajs-3842	21	30	=	=	SYM
iajs-3842	22	1	1	1	NUM
iajs-3842	22	2	−	−	PROPN
iajs-3842	22	3	(	(	PUNCT
iajs-3842	22	4	𝛽2	𝛽2	PROPN
iajs-3842	22	5	+	+	ADJ
iajs-3842	22	6	1)+𝛽𝑧	1)+𝛽𝑧	ADJ
iajs-3842	22	7	𝛽2	𝛽2	NOUN
iajs-3842	22	8	+	+	PROPN
iajs-3842	22	9	1	1	NUM
iajs-3842	22	10	𝑒−𝛽𝑧	𝑒−𝛽𝑧	NOUN
iajs-3842	22	11	(	(	PUNCT
iajs-3842	22	12	2	2	NUM
iajs-3842	22	13	)	)	PUNCT
iajs-3842	22	14	and	and	CCONJ
iajs-3842	22	15	survival	survival	NOUN
iajs-3842	22	16	(	(	PUNCT
iajs-3842	22	17	reliability	reliability	NOUN
iajs-3842	22	18	)	)	PUNCT
iajs-3842	22	19	function	function	NOUN
iajs-3842	22	20	defined	define	VERB
iajs-3842	22	21	as	as	ADP
iajs-3842	22	22	:	:	PUNCT
iajs-3842	22	23	𝑆𝑆𝐻(𝑧	𝑆𝑆𝐻(𝑧	NUM
iajs-3842	22	24	)	)	PUNCT
iajs-3842	22	25	=	=	SYM
iajs-3842	22	26	(	(	PUNCT
iajs-3842	22	27	𝛽2	𝛽2	PROPN
iajs-3842	22	28	+	+	PROPN
iajs-3842	22	29	1)+𝛽𝑧	1)+𝛽𝑧	ADJ
iajs-3842	22	30	𝛽2	𝛽2	NOUN
iajs-3842	22	31	+	+	PROPN
iajs-3842	22	32	1	1	NUM
iajs-3842	22	33	𝑒−𝛽𝑧	𝑒−𝛽𝑧	NOUN
iajs-3842	22	34	(	(	PUNCT
iajs-3842	22	35	3	3	X
iajs-3842	22	36	)	)	PUNCT
iajs-3842	22	37	gauss	gauss	NOUN
iajs-3842	22	38	(	(	PUNCT
iajs-3842	22	39	5	5	NUM
iajs-3842	22	40	)	)	PUNCT
iajs-3842	22	41	,	,	PUNCT
iajs-3842	22	42	introduced	introduce	VERB
iajs-3842	22	43	a	a	DET
iajs-3842	22	44	three	three	NUM
iajs-3842	22	45	-	-	PUNCT
iajs-3842	22	46	parameter	parameter	NOUN
iajs-3842	22	47	model	model	NOUN
iajs-3842	22	48	in	in	ADP
iajs-3842	22	49	2014	2014	NUM
iajs-3842	22	50	,	,	PUNCT
iajs-3842	22	51	which	which	PRON
iajs-3842	22	52	is	be	AUX
iajs-3842	22	53	a	a	DET
iajs-3842	22	54	mixture	mixture	NOUN
iajs-3842	22	55	of	of	ADP
iajs-3842	22	56	exponential	exponential	NOUN
iajs-3842	22	57	and	and	CCONJ
iajs-3842	22	58	weibull	weibull	NOUN
iajs-3842	22	59	distribution	distribution	NOUN
iajs-3842	22	60	.	.	PUNCT
iajs-3842	23	1	in	in	ADP
iajs-3842	23	2	addition	addition	NOUN
iajs-3842	23	3	,	,	PUNCT
iajs-3842	23	4	the	the	DET
iajs-3842	23	5	three	three	NUM
iajs-3842	23	6	-	-	PUNCT
iajs-3842	23	7	parameter	parameter	NOUN
iajs-3842	23	8	lifetime	lifetime	NOUN
iajs-3842	23	9	model	model	NOUN
iajs-3842	23	10	was	be	AUX
iajs-3842	23	11	first	first	ADV
iajs-3842	23	12	introduced	introduce	VERB
iajs-3842	23	13	in	in	ADP
iajs-3842	23	14	2015	2015	NUM
iajs-3842	23	15	by	by	ADP
iajs-3842	23	16	faton	faton	PROPN
iajs-3842	23	17	and	and	CCONJ
iajs-3842	23	18	ibrahim	ibrahim	PROPN
iajs-3842	23	19	(	(	PUNCT
iajs-3842	23	20	6	6	NUM
iajs-3842	23	21	)	)	PUNCT
iajs-3842	23	22	.	.	PUNCT
iajs-3842	24	1	this	this	PRON
iajs-3842	24	2	is	be	AUX
iajs-3842	24	3	a	a	DET
iajs-3842	24	4	mixture	mixture	NOUN
iajs-3842	24	5	of	of	ADP
iajs-3842	24	6	weibull	weibull	PROPN
iajs-3842	24	7	and	and	CCONJ
iajs-3842	24	8	rayleigh	rayleigh	ADJ
iajs-3842	24	9	distribution	distribution	NOUN
iajs-3842	24	10	to	to	PART
iajs-3842	24	11	obtain	obtain	VERB
iajs-3842	24	12	a	a	DET
iajs-3842	24	13	new	new	ADJ
iajs-3842	24	14	distribution	distribution	NOUN
iajs-3842	24	15	.	.	PUNCT
iajs-3842	25	1	the	the	DET
iajs-3842	25	2	structure	structure	NOUN
iajs-3842	25	3	was	be	AUX
iajs-3842	25	4	based	base	VERB
iajs-3842	25	5	on	on	ADP
iajs-3842	25	6	pdf	pdf	NOUN
iajs-3842	25	7	integration	integration	NOUN
iajs-3842	25	8	and	and	CCONJ
iajs-3842	25	9	the	the	DET
iajs-3842	25	10	bounds	bound	NOUN
iajs-3842	25	11	of	of	ADP
iajs-3842	25	12	the	the	DET
iajs-3842	25	13	integration	integration	NOUN
iajs-3842	25	14	ranged	range	VERB
iajs-3842	25	15	from	from	ADP
iajs-3842	25	16	zero	zero	NUM
iajs-3842	25	17	to	to	ADP
iajs-3842	25	18	the	the	DET
iajs-3842	25	19	survival	survival	NOUN
iajs-3842	25	20	function	function	NOUN
iajs-3842	25	21	.	.	PUNCT
iajs-3842	26	1	suleman	suleman	NOUN
iajs-3842	26	2	(	(	PUNCT
iajs-3842	26	3	7	7	NUM
iajs-3842	26	4	)	)	PUNCT
iajs-3842	26	5	presented	present	VERB
iajs-3842	26	6	a	a	DET
iajs-3842	26	7	new	new	ADJ
iajs-3842	26	8	distribution	distribution	NOUN
iajs-3842	26	9	in	in	ADP
iajs-3842	26	10	2016	2016	NUM
iajs-3842	26	11	,	,	PUNCT
iajs-3842	26	12	which	which	PRON
iajs-3842	26	13	is	be	AUX
iajs-3842	26	14	a	a	DET
iajs-3842	26	15	mixture	mixture	NOUN
iajs-3842	26	16	of	of	ADP
iajs-3842	26	17	weibull	weibull	PROPN
iajs-3842	26	18	and	and	CCONJ
iajs-3842	26	19	rayleigh	rayleigh	PROPN
iajs-3842	26	20	distribution	distribution	NOUN
iajs-3842	26	21	.	.	PUNCT
iajs-3842	27	1	mohammed	mohammed	PROPN
iajs-3842	27	2	,	,	PUNCT
iajs-3842	27	3	maysaa	maysaa	PROPN
iajs-3842	27	4	and	and	CCONJ
iajs-3842	27	5	hussein	hussein	PROPN
iajs-3842	27	6	(	(	PUNCT
iajs-3842	27	7	8)	8)	NUM
iajs-3842	27	8	presented	present	VERB
iajs-3842	27	9	a	a	DET
iajs-3842	27	10	new	new	ADJ
iajs-3842	27	11	mixture	mixture	NOUN
iajs-3842	27	12	distribution	distribution	NOUN
iajs-3842	27	13	of	of	ADP
iajs-3842	27	14	weibull	weibull	PROPN
iajs-3842	27	15	,	,	PUNCT
iajs-3842	27	16	rayleigh	rayleigh	NOUN
iajs-3842	27	17	and	and	CCONJ
iajs-3842	27	18	exponential	exponential	ADJ
iajs-3842	27	19	distribution	distribution	NOUN
iajs-3842	27	20	in	in	ADP
iajs-3842	27	21	2018	2018	NUM
iajs-3842	27	22	.	.	PUNCT
iajs-3842	28	1	in	in	ADP
iajs-3842	28	2	addition	addition	NOUN
iajs-3842	28	3	,	,	PUNCT
iajs-3842	28	4	mundher	mundher	NOUN
iajs-3842	28	5	et	et	PROPN
iajs-3842	28	6	al	al	PROPN
iajs-3842	28	7	.	.	PROPN
iajs-3842	29	1	(	(	PUNCT
iajs-3842	29	2	9	9	X
iajs-3842	29	3	)	)	PUNCT
iajs-3842	29	4	presented	present	VERB
iajs-3842	29	5	an	an	DET
iajs-3842	29	6	extension	extension	NOUN
iajs-3842	29	7	of	of	ADP
iajs-3842	29	8	the	the	DET
iajs-3842	29	9	burr	burr	NOUN
iajs-3842	29	10	type	type	NOUN
iajs-3842	29	11	x	x	NOUN
iajs-3842	29	12	distribution	distribution	NOUN
iajs-3842	29	13	.	.	PUNCT
iajs-3842	30	1	also	also	ADV
iajs-3842	30	2	,	,	PUNCT
iajs-3842	30	3	maysaa	maysaa	PROPN
iajs-3842	30	4	and	and	CCONJ
iajs-3842	30	5	iden	iden	PROPN
iajs-3842	30	6	(	(	PUNCT
iajs-3842	30	7	10	10	NUM
iajs-3842	30	8	)	)	PUNCT
iajs-3842	30	9	estimated	estimate	VERB
iajs-3842	30	10	the	the	DET
iajs-3842	30	11	parameters	parameter	NOUN
iajs-3842	30	12	of	of	ADP
iajs-3842	30	13	the	the	DET
iajs-3842	30	14	new	new	ADJ
iajs-3842	30	15	mixture	mixture	NOUN
iajs-3842	30	16	distribution	distribution	NOUN
iajs-3842	30	17	using	use	VERB
iajs-3842	30	18	classical	classical	ADJ
iajs-3842	30	19	methods	method	NOUN
iajs-3842	30	20	.	.	PUNCT
iajs-3842	31	1	in	in	ADP
iajs-3842	31	2	addition	addition	NOUN
iajs-3842	31	3	,	,	PUNCT
iajs-3842	31	4	ali	ali	PROPN
iajs-3842	31	5	and	and	CCONJ
iajs-3842	31	6	iden	iden	PROPN
iajs-3842	31	7	(	(	PUNCT
iajs-3842	31	8	11	11	NUM
iajs-3842	31	9	)	)	PUNCT
iajs-3842	31	10	estimated	estimate	VERB
iajs-3842	31	11	the	the	DET
iajs-3842	31	12	density	density	NOUN
iajs-3842	31	13	function	function	NOUN
iajs-3842	31	14	using	use	VERB
iajs-3842	31	15	a	a	DET
iajs-3842	31	16	hybrid	hybrid	ADJ
iajs-3842	31	17	breslow	breslow	NOUN
iajs-3842	31	18	and	and	CCONJ
iajs-3842	31	19	a	a	DET
iajs-3842	31	20	semi	semi	ADJ
iajs-3842	31	21	-	-	ADJ
iajs-3842	31	22	symmetric	symmetric	ADJ
iajs-3842	31	23	wavelet	wavelet	NOUN
iajs-3842	31	24	.	.	PUNCT
iajs-3842	32	1	also	also	ADV
iajs-3842	32	2	,	,	PUNCT
iajs-3842	32	3	hameed	hameed	PROPN
iajs-3842	32	4	et	et	PROPN
iajs-3842	32	5	al	al	PROPN
iajs-3842	32	6	.	.	PUNCT
iajs-3842	33	1	(	(	PUNCT
iajs-3842	33	2	12	12	NUM
iajs-3842	33	3	)	)	PUNCT
iajs-3842	33	4	presented	present	VERB
iajs-3842	33	5	the	the	DET
iajs-3842	33	6	estimation	estimation	NOUN
iajs-3842	33	7	of	of	ADP
iajs-3842	33	8	(	(	PUNCT
iajs-3842	33	9	𝑌<𝑋	𝑌<𝑋	PROPN
iajs-3842	33	10	)	)	PUNCT
iajs-3842	33	11	in	in	ADP
iajs-3842	33	12	the	the	DET
iajs-3842	33	13	case	case	NOUN
iajs-3842	33	14	of	of	ADP
iajs-3842	33	15	the	the	DET
iajs-3842	33	16	inverse	inverse	ADJ
iajs-3842	33	17	kumaraswamy	kumaraswamy	NOUN
iajs-3842	33	18	distribution	distribution	NOUN
iajs-3842	33	19	.	.	PUNCT
iajs-3842	34	1	in	in	ADP
iajs-3842	34	2	addition	addition	NOUN
iajs-3842	34	3	,	,	PUNCT
iajs-3842	34	4	maysaa	maysaa	PROPN
iajs-3842	34	5	and	and	CCONJ
iajs-3842	34	6	ali	ali	PROPN
iajs-3842	34	7	(	(	PUNCT
iajs-3842	34	8	13	13	NUM
iajs-3842	34	9	)	)	PUNCT
iajs-3842	34	10	presented	present	VERB
iajs-3842	34	11	the	the	DET
iajs-3842	34	12	inverse	inverse	NOUN
iajs-3842	34	13	exponential	exponential	NOUN
iajs-3842	34	14	rayleigh	rayleigh	NOUN
iajs-3842	34	15	distribution	distribution	NOUN
iajs-3842	34	16	(	(	PUNCT
iajs-3842	34	17	ierd	ierd	NOUN
iajs-3842	34	18	)	)	PUNCT
iajs-3842	34	19	.	.	PUNCT
iajs-3842	35	1	there	there	PRON
iajs-3842	35	2	are	be	VERB
iajs-3842	35	3	many	many	ADJ
iajs-3842	35	4	applications	application	NOUN
iajs-3842	35	5	of	of	ADP
iajs-3842	35	6	continuous	continuous	ADJ
iajs-3842	35	7	distributions	distribution	NOUN
iajs-3842	35	8	,	,	PUNCT
iajs-3842	35	9	such	such	ADJ
iajs-3842	35	10	as	as	ADP
iajs-3842	35	11	wang	wang	PROPN
iajs-3842	35	12	(	(	PUNCT
iajs-3842	35	13	14	14	NUM
iajs-3842	35	14	)	)	PUNCT
iajs-3842	35	15	,	,	PUNCT
iajs-3842	35	16	who	who	PRON
iajs-3842	35	17	presents	present	VERB
iajs-3842	35	18	a	a	DET
iajs-3842	35	19	new	new	ADJ
iajs-3842	35	20	model	model	NOUN
iajs-3842	35	21	with	with	ADP
iajs-3842	35	22	a	a	DET
iajs-3842	35	23	bathtub	bathtub	NOUN
iajs-3842	35	24	-	-	PUNCT
iajs-3842	35	25	shaped	shape	VERB
iajs-3842	35	26	failure	failure	NOUN
iajs-3842	35	27	rate	rate	NOUN
iajs-3842	35	28	using	use	VERB
iajs-3842	35	29	the	the	DET
iajs-3842	35	30	burr	burr	NOUN
iajs-3842	35	31	xii	xii	NOUN
iajs-3842	35	32	distribution	distribution	NOUN
iajs-3842	35	33	.	.	PUNCT
iajs-3842	36	1	moreover	moreover	ADV
iajs-3842	36	2	,	,	PUNCT
iajs-3842	36	3	rama	rama	PROPN
iajs-3842	36	4	(	(	PUNCT
iajs-3842	36	5	15	15	NUM
iajs-3842	36	6	)	)	PUNCT
iajs-3842	36	7	introduced	introduce	VERB
iajs-3842	36	8	a	a	DET
iajs-3842	36	9	new	new	ADJ
iajs-3842	36	10	distribution	distribution	NOUN
iajs-3842	36	11	that	that	PRON
iajs-3842	36	12	depends	depend	VERB
iajs-3842	36	13	on	on	ADP
iajs-3842	36	14	gama	gama	NOUN
iajs-3842	36	15	(	(	PUNCT
iajs-3842	36	16	3,θ	3,θ	NUM
iajs-3842	36	17	)	)	PUNCT
iajs-3842	36	18	.	.	PUNCT
iajs-3842	37	1	moreover	moreover	ADV
iajs-3842	37	2	,	,	PUNCT
iajs-3842	37	3	kilany	kilany	NOUN
iajs-3842	37	4	(	(	PUNCT
iajs-3842	37	5	16	16	NUM
iajs-3842	37	6	)	)	PUNCT
iajs-3842	37	7	introduced	introduce	VERB
iajs-3842	37	8	a	a	DET
iajs-3842	37	9	weighted	weight	VERB
iajs-3842	37	10	lomax	lomax	NOUN
iajs-3842	37	11	distribution	distribution	NOUN
iajs-3842	37	12	in	in	ADP
iajs-3842	37	13	2016	2016	NUM
iajs-3842	37	14	.	.	PUNCT
iajs-3842	38	1	in	in	ADP
iajs-3842	38	2	addition	addition	NOUN
iajs-3842	38	3	,	,	PUNCT
iajs-3842	38	4	oguntunde	oguntunde	NOUN
iajs-3842	38	5	et	et	PROPN
iajs-3842	38	6	al	al	PROPN
iajs-3842	38	7	.	.	PUNCT
iajs-3842	39	1	(	(	PUNCT
iajs-3842	39	2	17	17	NUM
iajs-3842	39	3	)	)	PUNCT
iajs-3842	39	4	introduced	introduce	VERB
iajs-3842	39	5	the	the	DET
iajs-3842	39	6	inverted	inverted	ADJ
iajs-3842	39	7	weighted	weight	VERB
iajs-3842	39	8	exponential	exponential	ADJ
iajs-3842	39	9	distribution	distribution	NOUN
iajs-3842	39	10	.	.	PUNCT
iajs-3842	40	1	okagbue	okagbue	PROPN
iajs-3842	40	2	,	,	PUNCT
iajs-3842	40	3	et	et	PROPN
iajs-3842	40	4	al	al	PROPN
iajs-3842	40	5	.	.	PUNCT
iajs-3842	41	1	(	(	PUNCT
iajs-3842	41	2	18	18	NUM
iajs-3842	41	3	)	)	PUNCT
iajs-3842	41	4	also	also	ADV
iajs-3842	41	5	compared	compare	VERB
iajs-3842	41	6	some	some	PRON
iajs-3842	41	7	of	of	ADP
iajs-3842	41	8	the	the	DET
iajs-3842	41	9	estimation	estimation	NOUN
iajs-3842	41	10	methods	method	NOUN
iajs-3842	41	11	.	.	PUNCT
iajs-3842	42	1	jebur	jebur	ADV
iajs-3842	42	2	,	,	PUNCT
iajs-3842	42	3	et	et	PROPN
iajs-3842	42	4	al	al	PROPN
iajs-3842	42	5	.	.	PROPN
iajs-3842	42	6	2021	2021	NUM
iajs-3842	42	7	(	(	PUNCT
iajs-3842	42	8	19	19	NUM
iajs-3842	42	9	)	)	PUNCT
iajs-3842	42	10	also	also	ADV
iajs-3842	42	11	presented	present	VERB
iajs-3842	42	12	the	the	DET
iajs-3842	42	13	efficient	efficient	ADJ
iajs-3842	42	14	shrinkage	shrinkage	NOUN
iajs-3842	42	15	estimation	estimation	NOUN
iajs-3842	42	16	method	method	NOUN
iajs-3842	42	17	for	for	ADP
iajs-3842	42	18	the	the	DET
iajs-3842	42	19	generalized	generalized	ADJ
iajs-3842	42	20	inverse	inverse	NOUN
iajs-3842	42	21	rayleigh	rayleigh	NOUN
iajs-3842	42	22	distribution	distribution	NOUN
iajs-3842	42	23	.	.	PUNCT
iajs-3842	43	1	maysaa	maysaa	PROPN
iajs-3842	43	2	and	and	CCONJ
iajs-3842	43	3	ali	ali	PROPN
iajs-3842	43	4	(	(	PUNCT
iajs-3842	43	5	20	20	NUM
iajs-3842	43	6	)	)	PUNCT
iajs-3842	43	7	estimated	estimate	VERB
iajs-3842	43	8	the	the	DET
iajs-3842	43	9	parameters	parameter	NOUN
iajs-3842	43	10	of	of	ADP
iajs-3842	43	11	the	the	DET
iajs-3842	43	12	new	new	ADJ
iajs-3842	43	13	inverse	inverse	NOUN
iajs-3842	43	14	exponential	exponential	ADJ
iajs-3842	43	15	rayleigh	rayleigh	NOUN
iajs-3842	43	16	distribution	distribution	NOUN
iajs-3842	43	17	.	.	PUNCT
iajs-3842	44	1	also	also	ADV
iajs-3842	44	2	,	,	PUNCT
iajs-3842	44	3	jabar	jabar	PROPN
iajs-3842	44	4	et	et	PROPN
iajs-3842	44	5	al	al	PROPN
iajs-3842	44	6	.	.	PROPN
iajs-3842	45	1	(	(	PUNCT
iajs-3842	45	2	21	21	NUM
iajs-3842	45	3	)	)	PUNCT
iajs-3842	45	4	,	,	PUNCT
iajs-3842	45	5	introduced	introduce	VERB
iajs-3842	45	6	the	the	DET
iajs-3842	45	7	truncated	truncated	ADJ
iajs-3842	45	8	inverse	inverse	NOUN
iajs-3842	45	9	generalized	generalize	VERB
iajs-3842	45	10	rayleigh	rayleigh	NOUN
iajs-3842	45	11	distribution	distribution	NOUN
iajs-3842	45	12	.	.	PUNCT
iajs-3842	46	1	moreover	moreover	ADV
iajs-3842	46	2	,	,	PUNCT
iajs-3842	46	3	mahmood	mahmood	PROPN
iajs-3842	46	4	and	and	CCONJ
iajs-3842	46	5	iden	iden	PROPN
iajs-3842	46	6	(	(	PUNCT
iajs-3842	46	7	22	22	NUM
iajs-3842	46	8	)	)	PUNCT
iajs-3842	46	9	introduced	introduce	VERB
iajs-3842	46	10	the	the	DET
iajs-3842	46	11	comparison	comparison	NOUN
iajs-3842	46	12	between	between	ADP
iajs-3842	46	13	the	the	DET
iajs-3842	46	14	modified	modify	VERB
iajs-3842	46	15	weighted	weight	VERB
iajs-3842	46	16	pareto	pareto	ADJ
iajs-3842	46	17	distribution	distribution	NOUN
iajs-3842	46	18	and	and	CCONJ
iajs-3842	46	19	other	other	ADJ
iajs-3842	46	20	distributions	distribution	NOUN
iajs-3842	46	21	.	.	PUNCT
iajs-3842	47	1	in	in	ADP
iajs-3842	47	2	addition	addition	NOUN
iajs-3842	47	3	,	,	PUNCT
iajs-3842	47	4	pedro	pedro	PROPN
iajs-3842	47	5	(	(	PUNCT
iajs-3842	47	6	23	23	NUM
iajs-3842	47	7	)	)	PUNCT
iajs-3842	47	8	presented	present	VERB
iajs-3842	47	9	a	a	DET
iajs-3842	47	10	new	new	ADJ
iajs-3842	47	11	distribution	distribution	NOUN
iajs-3842	47	12	,	,	PUNCT
iajs-3842	47	13	the	the	DET
iajs-3842	47	14	fréchet	fréchet	NOUN
iajs-3842	47	15	distribution	distribution	NOUN
iajs-3842	47	16	.	.	PUNCT
iajs-3842	48	1	finally	finally	ADV
iajs-3842	48	2	,	,	PUNCT
iajs-3842	48	3	lamyaa	lamyaa	PROPN
iajs-3842	48	4	and	and	CCONJ
iajs-3842	48	5	iden	iden	PROPN
iajs-3842	48	6	(	(	PUNCT
iajs-3842	48	7	24	24	NUM
iajs-3842	48	8	)	)	PUNCT
iajs-3842	48	9	introduced	introduce	VERB
iajs-3842	48	10	a	a	DET
iajs-3842	48	11	new	new	ADJ
iajs-3842	48	12	distribution	distribution	NOUN
iajs-3842	48	13	in	in	ADP
iajs-3842	48	14	2023	2023	NUM
iajs-3842	48	15	,	,	PUNCT
iajs-3842	48	16	which	which	PRON
iajs-3842	48	17	is	be	AUX
iajs-3842	48	18	a	a	DET
iajs-3842	48	19	mixture	mixture	NOUN
iajs-3842	48	20	of	of	ADP
iajs-3842	48	21	exponential	exponential	ADJ
iajs-3842	48	22	and	and	CCONJ
iajs-3842	48	23	rayleigh	rayleigh	ADJ
iajs-3842	48	24	distribution	distribution	NOUN
iajs-3842	48	25	.	.	PUNCT
iajs-3842	49	1	in	in	ADP
iajs-3842	49	2	this	this	DET
iajs-3842	49	3	paper	paper	NOUN
iajs-3842	49	4	,	,	PUNCT
iajs-3842	49	5	we	we	PRON
iajs-3842	49	6	introduce	introduce	VERB
iajs-3842	49	7	a	a	DET
iajs-3842	49	8	new	new	ADJ
iajs-3842	49	9	mixture	mixture	NOUN
iajs-3842	49	10	of	of	ADP
iajs-3842	49	11	continuous	continuous	ADJ
iajs-3842	49	12	distributions	distribution	NOUN
iajs-3842	49	13	,	,	PUNCT
iajs-3842	49	14	which	which	PRON
iajs-3842	49	15	we	we	PRON
iajs-3842	49	16	call	call	VERB
iajs-3842	49	17	the	the	DET
iajs-3842	49	18	'	'	PUNCT
iajs-3842	49	19	shanker	shanker	NOUN
iajs-3842	49	20	-	-	PUNCT
iajs-3842	49	21	weibull	weibull	NOUN
iajs-3842	49	22	distribution	distribution	NOUN
iajs-3842	49	23	'	'	PUNCT
iajs-3842	49	24	,	,	PUNCT
iajs-3842	49	25	by	by	ADP
iajs-3842	49	26	mixing	mix	VERB
iajs-3842	49	27	both	both	CCONJ
iajs-3842	49	28	the	the	DET
iajs-3842	49	29	'	'	PUNCT
iajs-3842	49	30	shanker	shank	ADJ
iajs-3842	49	31	distribution	distribution	NOUN
iajs-3842	49	32	'	'	PUNCT
iajs-3842	49	33	and	and	CCONJ
iajs-3842	49	34	the	the	DET
iajs-3842	49	35	'	'	PUNCT
iajs-3842	49	36	weibull	weibull	NOUN
iajs-3842	49	37	distribution	distribution	NOUN
iajs-3842	49	38	'	'	PUNCT
iajs-3842	49	39	based	base	VERB
iajs-3842	49	40	on	on	ADP
iajs-3842	49	41	the	the	DET
iajs-3842	49	42	survival	survival	NOUN
iajs-3842	49	43	function	function	NOUN
iajs-3842	49	44	for	for	ADP
iajs-3842	49	45	both	both	DET
iajs-3842	49	46	distributions	distribution	NOUN
iajs-3842	49	47	.	.	PUNCT
iajs-3842	50	1	section	section	NOUN
iajs-3842	50	2	2	2	NUM
iajs-3842	50	3	describes	describe	VERB
iajs-3842	50	4	how	how	SCONJ
iajs-3842	50	5	we	we	PRON
iajs-3842	50	6	mixed	mix	VERB
iajs-3842	50	7	the	the	DET
iajs-3842	50	8	'	'	PUNCT
iajs-3842	50	9	shanker	shank	ADJ
iajs-3842	50	10	distribution	distribution	NOUN
iajs-3842	50	11	'	'	PUNCT
iajs-3842	50	12	with	with	ADP
iajs-3842	50	13	the	the	DET
iajs-3842	50	14	'	'	PUNCT
iajs-3842	50	15	weibull	weibull	NOUN
iajs-3842	50	16	distribution	distribution	NOUN
iajs-3842	50	17	'	'	PUNCT
iajs-3842	50	18	to	to	PART
iajs-3842	50	19	obtain	obtain	VERB
iajs-3842	50	20	the	the	DET
iajs-3842	50	21	'	'	PUNCT
iajs-3842	50	22	shanker	shanker	NOUN
iajs-3842	50	23	-	-	PUNCT
iajs-3842	50	24	weibull	weibull	NOUN
iajs-3842	50	25	distribution	distribution	NOUN
iajs-3842	50	26	'	'	PUNCT
iajs-3842	50	27	(	(	PUNCT
iajs-3842	50	28	shwd	shwd	PROPN
iajs-3842	50	29	)	)	PUNCT
iajs-3842	50	30	and	and	CCONJ
iajs-3842	50	31	introduces	introduce	VERB
iajs-3842	50	32	the	the	DET
iajs-3842	50	33	basic	basic	ADJ
iajs-3842	50	34	statistical	statistical	ADJ
iajs-3842	50	35	functions	function	NOUN
iajs-3842	50	36	such	such	ADJ
iajs-3842	50	37	as	as	ADP
iajs-3842	50	38	the	the	DET
iajs-3842	50	39	probability	probability	NOUN
iajs-3842	50	40	density	density	NOUN
iajs-3842	50	41	function	function	NOUN
iajs-3842	50	42	,	,	PUNCT
iajs-3842	50	43	the	the	DET
iajs-3842	50	44	commutative	commutative	ADJ
iajs-3842	50	45	density	density	NOUN
iajs-3842	50	46	function	function	NOUN
iajs-3842	50	47	,	,	PUNCT
iajs-3842	50	48	the	the	DET
iajs-3842	50	49	survival	survival	NOUN
iajs-3842	50	50	function	function	NOUN
iajs-3842	50	51	and	and	CCONJ
iajs-3842	50	52	the	the	DET
iajs-3842	50	53	hazard	hazard	NOUN
iajs-3842	50	54	rate	rate	NOUN
iajs-3842	50	55	function	function	NOUN
iajs-3842	50	56	.	.	PUNCT
iajs-3842	51	1	finally	finally	ADV
iajs-3842	51	2	,	,	PUNCT
iajs-3842	51	3	section	section	NOUN
iajs-3842	51	4	3	3	NUM
iajs-3842	51	5	presents	present	VERB
iajs-3842	51	6	the	the	DET
iajs-3842	51	7	statistical	statistical	ADJ
iajs-3842	51	8	and	and	CCONJ
iajs-3842	51	9	mathematical	mathematical	ADJ
iajs-3842	51	10	properties	property	NOUN
iajs-3842	51	11	of	of	ADP
iajs-3842	51	12	the	the	DET
iajs-3842	51	13	new	new	ADJ
iajs-3842	51	14	distribution	distribution	NOUN
iajs-3842	51	15	,	,	PUNCT
iajs-3842	51	16	such	such	ADJ
iajs-3842	51	17	as	as	ADP
iajs-3842	51	18	mode	mode	NOUN
iajs-3842	51	19	,	,	PUNCT
iajs-3842	51	20	median	median	NOUN
iajs-3842	51	21	,	,	PUNCT
iajs-3842	51	22	moments	moment	NOUN
iajs-3842	51	23	around	around	ADP
iajs-3842	51	24	the	the	DET
iajs-3842	51	25	origin	origin	NOUN
iajs-3842	51	26	,	,	PUNCT
iajs-3842	51	27	mean	mean	VERB
iajs-3842	51	28	,	,	PUNCT
iajs-3842	51	29	variance	variance	NOUN
iajs-3842	51	30	,	,	PUNCT
iajs-3842	51	31	skewness	skewness	NOUN
iajs-3842	51	32	coefficient	coefficient	NOUN
iajs-3842	51	33	,	,	PUNCT
iajs-3842	51	34	kurtosis	kurtosis	VERB
iajs-3842	51	35	coefficient	coefficient	NOUN
iajs-3842	51	36	,	,	PUNCT
iajs-3842	51	37	characteristic	characteristic	ADJ
iajs-3842	51	38	function	function	NOUN
iajs-3842	51	39	,	,	PUNCT
iajs-3842	51	40	moment	moment	NOUN
iajs-3842	51	41	generation	generation	NOUN
iajs-3842	51	42	function	function	NOUN
iajs-3842	51	43	,	,	PUNCT
iajs-3842	51	44	factorial	factorial	ADJ
iajs-3842	51	45	moment	moment	NOUN
iajs-3842	51	46	generation	generation	NOUN
iajs-3842	51	47	function	function	NOUN
iajs-3842	51	48	and	and	CCONJ
iajs-3842	51	49	mean	mean	VERB
iajs-3842	51	50	time	time	NOUN
iajs-3842	51	51	to	to	ADP
iajs-3842	51	52	failure	failure	NOUN
iajs-3842	51	53	.	.	PUNCT
iajs-3842	52	1	ihjpas	ihjpas	PROPN
iajs-3842	52	2	.	.	PUNCT
iajs-3842	53	1	2025,38(2	2025,38(2	PROPN
iajs-3842	53	2	)	)	PUNCT
iajs-3842	53	3	390	390	NUM
iajs-3842	53	4	2	2	NUM
iajs-3842	53	5	.	.	PUNCT
iajs-3842	53	6	materials	material	NOUN
iajs-3842	53	7	and	and	CCONJ
iajs-3842	53	8	methods	method	NOUN
iajs-3842	53	9	2.1	2.1	NUM
iajs-3842	53	10	.	.	PUNCT
iajs-3842	53	11	structure	structure	NOUN
iajs-3842	53	12	of	of	ADP
iajs-3842	53	13	new	new	ADJ
iajs-3842	53	14	shanker	shanker	PROPN
iajs-3842	53	15	weibull	weibull	PROPN
iajs-3842	53	16	distribution	distribution	NOUN
iajs-3842	53	17	equations	equation	NOUN
iajs-3842	53	18	(	(	PUNCT
iajs-3842	53	19	1and	1and	NOUN
iajs-3842	53	20	2	2	NUM
iajs-3842	53	21	)	)	PUNCT
iajs-3842	53	22	represent	represent	VERB
iajs-3842	53	23	the	the	DET
iajs-3842	53	24	pdf	pdf	NOUN
iajs-3842	53	25	and	and	CCONJ
iajs-3842	53	26	cdf	cdf	PROPN
iajs-3842	53	27	of	of	ADP
iajs-3842	53	28	the	the	DET
iajs-3842	53	29	shanker	shanker	NOUN
iajs-3842	53	30	distribution	distribution	NOUN
iajs-3842	53	31	.	.	PUNCT
iajs-3842	54	1	in	in	ADP
iajs-3842	54	2	addition	addition	NOUN
iajs-3842	54	3	,	,	PUNCT
iajs-3842	54	4	the	the	DET
iajs-3842	54	5	pdf	pdf	NOUN
iajs-3842	54	6	,	,	PUNCT
iajs-3842	54	7	cdf	cdf	PROPN
iajs-3842	54	8	,	,	PUNCT
iajs-3842	54	9	and	and	CCONJ
iajs-3842	54	10	the	the	DET
iajs-3842	54	11	survival	survival	NOUN
iajs-3842	54	12	function	function	NOUN
iajs-3842	54	13	of	of	ADP
iajs-3842	54	14	standard	standard	ADJ
iajs-3842	54	15	weibull	weibull	PROPN
iajs-3842	54	16	distribution	distribution	PROPN
iajs-3842	54	17	are(25	are(25	PROPN
iajs-3842	54	18	)	)	PUNCT
iajs-3842	54	19	fw(v	fw(v	NOUN
iajs-3842	54	20	)	)	PUNCT
iajs-3842	55	1	=	=	SYM
iajs-3842	55	2	λvλ−1e−vλ	λvλ−1e−vλ	NOUN
iajs-3842	55	3	,	,	PUNCT
iajs-3842	55	4	λ	λ	X
iajs-3842	55	5	>	>	X
iajs-3842	55	6	0	0	NUM
iajs-3842	55	7	,	,	PUNCT
iajs-3842	55	8	v	v	ADP
iajs-3842	55	9	>	>	X
iajs-3842	55	10	0	0	PUNCT
iajs-3842	56	1	(	(	PUNCT
iajs-3842	56	2	4	4	NUM
iajs-3842	56	3	)	)	PUNCT
iajs-3842	56	4	fw(v	fw(v	NOUN
iajs-3842	56	5	)	)	PUNCT
iajs-3842	56	6	=	=	SYM
iajs-3842	57	1	1	1	NUM
iajs-3842	57	2	−	−	NOUN
iajs-3842	57	3	e−vλ	e−vλ	NOUN
iajs-3842	57	4	sw(v	sw(v	NOUN
iajs-3842	57	5	)	)	PUNCT
iajs-3842	58	1	=	=	SYM
iajs-3842	58	2	e−vλ	e−vλ	NOUN
iajs-3842	58	3	(	(	PUNCT
iajs-3842	58	4	5	5	NUM
iajs-3842	58	5	)	)	PUNCT
iajs-3842	58	6	let	let	VERB
iajs-3842	58	7	z	z	NOUN
iajs-3842	58	8	,	,	PUNCT
iajs-3842	58	9	and	and	CCONJ
iajs-3842	58	10	v	v	NOUN
iajs-3842	58	11	are	be	AUX
iajs-3842	58	12	independent	independent	ADJ
iajs-3842	58	13	random	random	ADJ
iajs-3842	58	14	variables	variable	NOUN
iajs-3842	58	15	and	and	CCONJ
iajs-3842	58	16	𝑋	𝑋	PROPN
iajs-3842	58	17	=	=	PUNCT
iajs-3842	58	18	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
iajs-3842	58	19	(	(	PUNCT
iajs-3842	58	20	𝑍	𝑍	PROPN
iajs-3842	58	21	,	,	PUNCT
iajs-3842	58	22	𝑉	𝑉	NOUN
iajs-3842	58	23	)	)	PUNCT
iajs-3842	58	24	𝑆(𝑥	𝑆(𝑥	PROPN
iajs-3842	58	25	)	)	PUNCT
iajs-3842	58	26	=	=	SYM
iajs-3842	58	27	𝑝𝑟(𝑋	𝑝𝑟(𝑋	X
iajs-3842	58	28	>	>	PUNCT
iajs-3842	58	29	𝑥	𝑥	NOUN
iajs-3842	58	30	)	)	PUNCT
iajs-3842	58	31	=	=	SYM
iajs-3842	58	32	𝑝𝑟(𝑚𝑖𝑛(𝑍	𝑝𝑟(𝑚𝑖𝑛(𝑍	PROPN
iajs-3842	58	33	,	,	PUNCT
iajs-3842	58	34	𝑉	𝑉	PROPN
iajs-3842	58	35	)	)	PUNCT
iajs-3842	58	36	>	>	X
iajs-3842	59	1	𝑥	𝑥	NOUN
iajs-3842	59	2	)	)	PUNCT
iajs-3842	59	3	,	,	PUNCT
iajs-3842	59	4	because	because	SCONJ
iajs-3842	59	5	z	z	NOUN
iajs-3842	59	6	and	and	CCONJ
iajs-3842	59	7	v	v	NOUN
iajs-3842	59	8	are	be	AUX
iajs-3842	59	9	independent	independent	ADJ
iajs-3842	59	10	random	random	ADJ
iajs-3842	59	11	variables	variable	NOUN
iajs-3842	59	12	then	then	ADV
iajs-3842	59	13	:	:	PUNCT
iajs-3842	59	14	𝑆(𝑆𝐻𝑊𝐷	𝑆(𝑆𝐻𝑊𝐷	PROPN
iajs-3842	59	15	)	)	PUNCT
iajs-3842	59	16	(	(	PUNCT
iajs-3842	60	1	𝑥	𝑥	X
iajs-3842	60	2	)	)	PUNCT
iajs-3842	60	3	=	=	SYM
iajs-3842	60	4	𝑝𝑟(𝑍	𝑝𝑟(𝑍	PROPN
iajs-3842	60	5	>	>	X
iajs-3842	60	6	𝑥	𝑥	NOUN
iajs-3842	60	7	)	)	PUNCT
iajs-3842	60	8	.	.	PUNCT
iajs-3842	61	1	𝑝𝑟(𝑉	𝑝𝑟(𝑉	PROPN
iajs-3842	61	2	>	>	PUNCT
iajs-3842	62	1	𝑥	𝑥	X
iajs-3842	62	2	)	)	PUNCT
iajs-3842	62	3	=	=	SYM
iajs-3842	62	4	(	(	PUNCT
iajs-3842	62	5	1	1	NUM
iajs-3842	62	6	−	−	PROPN
iajs-3842	62	7	𝑝𝑟(𝑍	𝑝𝑟(𝑍	PROPN
iajs-3842	62	8	≤	≤	NUM
iajs-3842	62	9	𝑥	𝑥	NOUN
iajs-3842	62	10	)	)	PUNCT
iajs-3842	62	11	)	)	PUNCT
iajs-3842	63	1	∙	∙	PROPN
iajs-3842	63	2	(	(	PUNCT
iajs-3842	63	3	1	1	NUM
iajs-3842	63	4	−	−	PROPN
iajs-3842	63	5	𝑝𝑟(𝑉	𝑝𝑟(𝑉	PROPN
iajs-3842	63	6	≤	≤	NUM
iajs-3842	63	7	𝑥	𝑥	NOUN
iajs-3842	63	8	)	)	PUNCT
iajs-3842	63	9	)	)	PUNCT
iajs-3842	64	1	=	=	PUNCT
iajs-3842	64	2	(	(	PUNCT
iajs-3842	64	3	1	1	NUM
iajs-3842	64	4	−	−	PROPN
iajs-3842	64	5	𝐹𝑠ℎ	𝐹𝑠ℎ	PROPN
iajs-3842	64	6	(	(	PUNCT
iajs-3842	64	7	𝑧	𝑧	NOUN
iajs-3842	64	8	)	)	PUNCT
iajs-3842	64	9	)	)	PUNCT
iajs-3842	65	1	∙	∙	PROPN
iajs-3842	65	2	(	(	PUNCT
iajs-3842	65	3	1	1	NUM
iajs-3842	65	4	−	−	PROPN
iajs-3842	65	5	𝐹𝑤	𝐹𝑤	PROPN
iajs-3842	65	6	(	(	PUNCT
iajs-3842	65	7	𝑣	𝑣	NOUN
iajs-3842	65	8	)	)	PUNCT
iajs-3842	65	9	)	)	PUNCT
iajs-3842	66	1	=	=	PUNCT
iajs-3842	66	2	𝑆𝑠ℎ	𝑆𝑠ℎ	PROPN
iajs-3842	66	3	(	(	PUNCT
iajs-3842	66	4	𝑥	𝑥	NOUN
iajs-3842	66	5	)	)	PUNCT
iajs-3842	66	6	∙	∙	PROPN
iajs-3842	66	7	𝑆𝑤	𝑆𝑤	PROPN
iajs-3842	66	8	(	(	PUNCT
iajs-3842	66	9	𝑥	𝑥	NOUN
iajs-3842	66	10	)	)	PUNCT
iajs-3842	66	11	from	from	ADP
iajs-3842	66	12	equations	equation	NOUN
iajs-3842	66	13	(	(	PUNCT
iajs-3842	66	14	3	3	NUM
iajs-3842	66	15	)	)	PUNCT
iajs-3842	66	16	and	and	CCONJ
iajs-3842	66	17	(	(	PUNCT
iajs-3842	66	18	5	5	X
iajs-3842	66	19	)	)	PUNCT
iajs-3842	66	20	we	we	PRON
iajs-3842	66	21	get	get	VERB
iajs-3842	66	22	:	:	PUNCT
iajs-3842	66	23	𝑆(𝑆𝐻𝑊𝐷	𝑆(𝑆𝐻𝑊𝐷	PROPN
iajs-3842	66	24	)	)	PUNCT
iajs-3842	66	25	(	(	PUNCT
iajs-3842	66	26	𝑥	𝑥	NOUN
iajs-3842	66	27	)	)	PUNCT
iajs-3842	66	28	=	=	SYM
iajs-3842	66	29	(	(	PUNCT
iajs-3842	66	30	𝛽2	𝛽2	PROPN
iajs-3842	66	31	+	+	PROPN
iajs-3842	66	32	1)+𝛽𝑥	1)+𝛽𝑥	PROPN
iajs-3842	66	33	𝛽2	𝛽2	PROPN
iajs-3842	66	34	+	+	ADJ
iajs-3842	66	35	1	1	NUM
iajs-3842	66	36	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	66	37	)	)	PUNCT
iajs-3842	66	38	(	(	PUNCT
iajs-3842	66	39	6	6	NUM
iajs-3842	66	40	)	)	PUNCT
iajs-3842	66	41	where	where	SCONJ
iajs-3842	66	42	x	x	PUNCT
iajs-3842	66	43	>	>	X
iajs-3842	66	44	0	0	NUM
iajs-3842	66	45	,	,	PUNCT
iajs-3842	66	46	and	and	CCONJ
iajs-3842	66	47	𝛽	𝛽	NOUN
iajs-3842	66	48	>	>	X
iajs-3842	66	49	0	0	NUM
iajs-3842	66	50	is	be	AUX
iajs-3842	66	51	the	the	DET
iajs-3842	66	52	scale	scale	NOUN
iajs-3842	66	53	parameter	parameter	NOUN
iajs-3842	66	54	,	,	PUNCT
iajs-3842	66	55	𝜆	𝜆	PROPN
iajs-3842	66	56	>	>	X
iajs-3842	66	57	0	0	NUM
iajs-3842	66	58	is	be	AUX
iajs-3842	66	59	the	the	DET
iajs-3842	66	60	shape	shape	NOUN
iajs-3842	66	61	parameter	parameter	NOUN
iajs-3842	66	62	.	.	PUNCT
iajs-3842	67	1	the	the	DET
iajs-3842	67	2	(	(	PUNCT
iajs-3842	67	3	cdf	cdf	PROPN
iajs-3842	67	4	)	)	PUNCT
iajs-3842	67	5	of	of	ADP
iajs-3842	67	6	the	the	DET
iajs-3842	67	7	new	new	ADJ
iajs-3842	67	8	(	(	PUNCT
iajs-3842	67	9	𝑆𝐻𝑊𝐷	𝑆𝐻𝑊𝐷	PROPN
iajs-3842	67	10	)	)	PUNCT
iajs-3842	67	11	distribution	distribution	NOUN
iajs-3842	67	12	is	be	AUX
iajs-3842	67	13	:	:	PUNCT
iajs-3842	67	14	𝐹(𝑥	𝐹(𝑥	X
iajs-3842	67	15	)	)	PUNCT
iajs-3842	67	16	=	=	SYM
iajs-3842	67	17	1	1	NUM
iajs-3842	67	18	−	−	PROPN
iajs-3842	67	19	(	(	PUNCT
iajs-3842	67	20	(	(	PUNCT
iajs-3842	67	21	𝛽2	𝛽2	PROPN
iajs-3842	67	22	+	+	PROPN
iajs-3842	67	23	1)+𝛽𝑥	1)+𝛽𝑥	PROPN
iajs-3842	67	24	𝛽2	𝛽2	PROPN
iajs-3842	67	25	+	+	PROPN
iajs-3842	67	26	1	1	NUM
iajs-3842	67	27	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	67	28	)	)	PUNCT
iajs-3842	67	29	)	)	PUNCT
iajs-3842	67	30	(	(	PUNCT
iajs-3842	67	31	7	7	X
iajs-3842	67	32	)	)	PUNCT
iajs-3842	67	33	therefore	therefore	ADV
iajs-3842	67	34	,	,	PUNCT
iajs-3842	67	35	the	the	DET
iajs-3842	67	36	pdf	pdf	NOUN
iajs-3842	67	37	of	of	ADP
iajs-3842	67	38	the	the	DET
iajs-3842	67	39	new	new	ADJ
iajs-3842	67	40	(	(	PUNCT
iajs-3842	67	41	𝑆𝐻𝑊𝐷	𝑆𝐻𝑊𝐷	PROPN
iajs-3842	67	42	)	)	PUNCT
iajs-3842	67	43	is	be	AUX
iajs-3842	67	44	:	:	PUNCT
iajs-3842	67	45	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	67	46	)	)	PUNCT
iajs-3842	67	47	=	=	SYM
iajs-3842	67	48	(	(	PUNCT
iajs-3842	67	49	(	(	PUNCT
iajs-3842	67	50	𝛽2	𝛽2	PROPN
iajs-3842	67	51	+	+	PROPN
iajs-3842	67	52	1)+𝛽𝑥	1)+𝛽𝑥	PROPN
iajs-3842	67	53	𝛽2	𝛽2	NOUN
iajs-3842	67	54	+	+	NOUN
iajs-3842	67	55	1	1	NUM
iajs-3842	67	56	(	(	PUNCT
iajs-3842	67	57	𝛽	𝛽	NOUN
iajs-3842	67	58	+	+	NOUN
iajs-3842	67	59	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	67	60	)	)	PUNCT
iajs-3842	67	61	−	−	PROPN
iajs-3842	67	62	𝛽	𝛽	PROPN
iajs-3842	67	63	(	(	PUNCT
iajs-3842	67	64	𝛽2	𝛽2	PROPN
iajs-3842	67	65	+	+	NOUN
iajs-3842	67	66	1	1	NUM
iajs-3842	67	67	)	)	PUNCT
iajs-3842	67	68	)	)	PUNCT
iajs-3842	68	1	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	68	2	)	)	PUNCT
iajs-3842	68	3	(	(	PUNCT
iajs-3842	68	4	8)	8)	NUM
iajs-3842	68	5	f(x	f(x	PROPN
iajs-3842	68	6	)	)	PUNCT
iajs-3842	68	7	is	be	AUX
iajs-3842	68	8	a	a	DET
iajs-3842	68	9	probability	probability	NOUN
iajs-3842	68	10	density	density	NOUN
iajs-3842	68	11	function	function	NOUN
iajs-3842	68	12	,	,	PUNCT
iajs-3842	68	13	since,𝛽	since,𝛽	X
iajs-3842	68	14	>	>	X
iajs-3842	68	15	0	0	NUM
iajs-3842	68	16	,	,	PUNCT
iajs-3842	68	17	𝜆	𝜆	ADJ
iajs-3842	68	18	>	>	X
iajs-3842	68	19	0	0	NUM
iajs-3842	68	20	,	,	PUNCT
iajs-3842	68	21	and	and	CCONJ
iajs-3842	68	22	𝑥	𝑥	X
iajs-3842	68	23	>	>	X
iajs-3842	68	24	0	0	NUM
iajs-3842	68	25	,	,	PUNCT
iajs-3842	68	26	which	which	PRON
iajs-3842	68	27	implies	imply	VERB
iajs-3842	68	28	that	that	SCONJ
iajs-3842	68	29	f(x	f(x	PROPN
iajs-3842	68	30	)	)	PUNCT
iajs-3842	68	31	>	>	X
iajs-3842	69	1	0	0	X
iajs-3842	69	2	.	.	PUNCT
iajs-3842	70	1	now	now	ADV
iajs-3842	70	2	,	,	PUNCT
iajs-3842	70	3	to	to	PART
iajs-3842	70	4	prove	prove	VERB
iajs-3842	70	5	that∫	that∫	NOUN
iajs-3842	70	6	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	70	7	)	)	PUNCT
iajs-3842	70	8	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	70	9	=	=	SYM
iajs-3842	70	10	1	1	NUM
iajs-3842	70	11	∞	∞	NUM
iajs-3842	70	12	0	0	NUM
iajs-3842	70	13	,	,	PUNCT
iajs-3842	70	14	∫	∫	PROPN
iajs-3842	70	15	f(x)dx	f(x)dx	NUM
iajs-3842	70	16	=	=	SYM
iajs-3842	70	17	∫	∫	PROPN
iajs-3842	70	18	(	(	PUNCT
iajs-3842	70	19	𝛽x	𝛽x	PROPN
iajs-3842	70	20	+	+	PROPN
iajs-3842	70	21	𝛽2	𝛽2	NOUN
iajs-3842	70	22	+	+	CCONJ
iajs-3842	70	23	1	1	NUM
iajs-3842	70	24	𝛽2	𝛽2	NOUN
iajs-3842	70	25	+	+	CCONJ
iajs-3842	70	26	1	1	NUM
iajs-3842	70	27	(	(	PUNCT
iajs-3842	70	28	𝛽	𝛽	NOUN
iajs-3842	70	29	+	+	NOUN
iajs-3842	70	30	λxλ−1	λxλ−1	PROPN
iajs-3842	70	31	)	)	PUNCT
iajs-3842	71	1	−	−	PROPN
iajs-3842	71	2	𝛽	𝛽	PROPN
iajs-3842	71	3	𝛽2	𝛽2	NOUN
iajs-3842	71	4	+	+	CCONJ
iajs-3842	71	5	1	1	NUM
iajs-3842	71	6	)	)	PUNCT
iajs-3842	71	7	e−(𝛽x+xλ	e−(𝛽x+xλ	PRON
iajs-3842	71	8	)	)	PUNCT
iajs-3842	71	9	dx	dx	PROPN
iajs-3842	71	10	∞	∞	NUM
iajs-3842	71	11	0	0	NUM
iajs-3842	72	1	∞	∞	NUM
iajs-3842	72	2	0	0	NUM
iajs-3842	73	1	∫	∫	PROPN
iajs-3842	73	2	f(x)dx	f(x)dx	NUM
iajs-3842	73	3	=	=	SYM
iajs-3842	73	4	lim	lim	PROPN
iajs-3842	73	5	y→∞	y→∞	PROPN
iajs-3842	73	6	(	(	PUNCT
iajs-3842	73	7	∫	∫	PROPN
iajs-3842	73	8	(	(	PUNCT
iajs-3842	73	9	𝛽x	𝛽x	PROPN
iajs-3842	73	10	+	+	PROPN
iajs-3842	73	11	𝛽2	𝛽2	NOUN
iajs-3842	73	12	+	+	CCONJ
iajs-3842	73	13	1	1	NUM
iajs-3842	73	14	𝛽2	𝛽2	NOUN
iajs-3842	73	15	+	+	CCONJ
iajs-3842	73	16	1	1	NUM
iajs-3842	73	17	(	(	PUNCT
iajs-3842	73	18	𝛽	𝛽	NOUN
iajs-3842	73	19	+	+	NOUN
iajs-3842	73	20	λxλ−1	λxλ−1	PROPN
iajs-3842	73	21	)	)	PUNCT
iajs-3842	74	1	−	−	PROPN
iajs-3842	74	2	𝛽	𝛽	PROPN
iajs-3842	74	3	𝛽2	𝛽2	NOUN
iajs-3842	74	4	+	+	CCONJ
iajs-3842	74	5	1	1	NUM
iajs-3842	74	6	)	)	PUNCT
iajs-3842	74	7	e−(𝛽x+xλ	e−(𝛽x+xλ	PRON
iajs-3842	74	8	)	)	PUNCT
iajs-3842	74	9	dx	dx	PROPN
iajs-3842	74	10	y	y	PROPN
iajs-3842	74	11	0	0	NUM
iajs-3842	74	12	)	)	PUNCT
iajs-3842	75	1	∞	∞	NOUN
iajs-3842	75	2	0	0	X
iajs-3842	76	1	=	=	SYM
iajs-3842	76	2	lim	lim	PROPN
iajs-3842	76	3	y→∞	y→∞	NOUN
iajs-3842	76	4	1	1	NUM
iajs-3842	76	5	𝛽2	𝛽2	NOUN
iajs-3842	76	6	+	+	CCONJ
iajs-3842	76	7	1	1	NUM
iajs-3842	76	8	(	(	PUNCT
iajs-3842	76	9	∫(𝛽x	∫(𝛽x	PROPN
iajs-3842	76	10	+	+	NUM
iajs-3842	76	11	𝛽2	𝛽2	PROPN
iajs-3842	76	12	+	+	CCONJ
iajs-3842	76	13	1)(𝛽	1)(𝛽	NUM
iajs-3842	76	14	+	+	CCONJ
iajs-3842	76	15	λxλ−1)e−(𝛽x+xλ	λxλ−1)e−(𝛽x+xλ	PROPN
iajs-3842	76	16	)	)	PUNCT
iajs-3842	76	17	dx	dx	PROPN
iajs-3842	77	1	y	y	PROPN
iajs-3842	77	2	0	0	NUM
iajs-3842	78	1	−	−	NUM
iajs-3842	78	2	∫	∫	PROPN
iajs-3842	78	3	𝛽	𝛽	PROPN
iajs-3842	78	4	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	78	5	)	)	PUNCT
iajs-3842	78	6	dx	dx	PROPN
iajs-3842	78	7	y	y	PROPN
iajs-3842	78	8	0	0	NUM
iajs-3842	78	9	)	)	PUNCT
iajs-3842	78	10	𝑢	𝑢	PROPN
iajs-3842	78	11	=	=	SYM
iajs-3842	78	12	(	(	PUNCT
iajs-3842	78	13	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	78	14	+	+	PROPN
iajs-3842	78	15	𝛽2	𝛽2	NOUN
iajs-3842	78	16	+	+	CCONJ
iajs-3842	78	17	1	1	NUM
iajs-3842	78	18	)	)	PUNCT
iajs-3842	78	19	⇨	⇨	PROPN
iajs-3842	78	20	𝑑𝑢	𝑑𝑢	PROPN
iajs-3842	78	21	=	=	NOUN
iajs-3842	78	22	𝛽𝑑𝑥	𝛽𝑑𝑥	PROPN
iajs-3842	78	23	𝑑𝑣	𝑑𝑣	NOUN
iajs-3842	78	24	=	=	X
iajs-3842	78	25	(	(	PUNCT
iajs-3842	78	26	𝛽	𝛽	NOUN
iajs-3842	78	27	+	+	NUM
iajs-3842	78	28	𝜆𝑥𝜆−1)𝑒−(𝛽𝑥+𝑥𝜆)𝑑𝑥	𝜆𝑥𝜆−1)𝑒−(𝛽𝑥+𝑥𝜆)𝑑𝑥	PROPN
iajs-3842	78	29	⇨	⇨	PROPN
iajs-3842	79	1	𝑣	𝑣	X
iajs-3842	79	2	=	=	SYM
iajs-3842	79	3	−	−	PROPN
iajs-3842	79	4	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	79	5	)	)	PUNCT
iajs-3842	79	6	∫	∫	PROPN
iajs-3842	79	7	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	79	8	)	)	PUNCT
iajs-3842	79	9	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	79	10	=	=	SYM
iajs-3842	79	11	𝐿𝑖𝑚	𝐿𝑖𝑚	PROPN
iajs-3842	79	12	𝑦→∞	𝑦→∞	NUM
iajs-3842	79	13	1	1	NUM
iajs-3842	79	14	𝛽2	𝛽2	NOUN
iajs-3842	79	15	+	+	CCONJ
iajs-3842	79	16	1	1	NUM
iajs-3842	79	17	(	(	PUNCT
iajs-3842	79	18	(	(	PUNCT
iajs-3842	79	19	−(𝛽𝑥	−(𝛽𝑥	PROPN
iajs-3842	79	20	+	+	NUM
iajs-3842	79	21	𝛽2	𝛽2	PROPN
iajs-3842	79	22	+	+	CCONJ
iajs-3842	79	23	1)𝑒−(𝛽𝑥+𝑥𝜆	1)𝑒−(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	79	24	)	)	PUNCT
iajs-3842	79	25	)	)	PUNCT
iajs-3842	80	1	𝑦	𝑦	NOUN
iajs-3842	80	2	|	|	ADV
iajs-3842	80	3	0	0	NUM
iajs-3842	81	1	+	+	NUM
iajs-3842	81	2	∫	∫	PROPN
iajs-3842	81	3	𝛽	𝛽	X
iajs-3842	81	4	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	81	5	)	)	PUNCT
iajs-3842	81	6	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	81	7	𝑦	𝑦	NOUN
iajs-3842	81	8	0	0	NUM
iajs-3842	81	9	∞	∞	NUM
iajs-3842	81	10	0	0	NUM
iajs-3842	82	1	−	−	NUM
iajs-3842	82	2	∫	∫	PROPN
iajs-3842	82	3	𝛽	𝛽	PROPN
iajs-3842	82	4	𝑒−(𝛽𝑥+𝑥𝜆)𝑑𝑥	𝑒−(𝛽𝑥+𝑥𝜆)𝑑𝑥	X
iajs-3842	82	5	𝑦	𝑦	NOUN
iajs-3842	82	6	0	0	NUM
iajs-3842	82	7	)	)	PUNCT
iajs-3842	82	8	=	=	PUNCT
iajs-3842	83	1	−	−	PROPN
iajs-3842	83	2	𝐿𝑖𝑚	𝐿𝑖𝑚	NOUN
iajs-3842	83	3	𝑦→∞	𝑦→∞	NUM
iajs-3842	83	4	(	(	PUNCT
iajs-3842	83	5	(	(	PUNCT
iajs-3842	83	6	𝛽𝑦	𝛽𝑦	ADP
iajs-3842	83	7	+	+	NUM
iajs-3842	83	8	𝛽2	𝛽2	NOUN
iajs-3842	83	9	+	+	CCONJ
iajs-3842	83	10	1	1	NUM
iajs-3842	83	11	)	)	PUNCT
iajs-3842	83	12	𝛽2	𝛽2	PROPN
iajs-3842	83	13	+	+	CCONJ
iajs-3842	83	14	1)𝑒(𝛽𝑦+𝑦𝜆	1)𝑒(𝛽𝑦+𝑦𝜆	NUM
iajs-3842	83	15	)	)	PUNCT
iajs-3842	83	16	−	−	PROPN
iajs-3842	83	17	𝛽2	𝛽2	NOUN
iajs-3842	83	18	+	+	CCONJ
iajs-3842	83	19	1	1	NUM
iajs-3842	83	20	𝛽2	𝛽2	NOUN
iajs-3842	83	21	+	+	CCONJ
iajs-3842	83	22	1	1	NUM
iajs-3842	83	23	)	)	PUNCT
iajs-3842	83	24	ihjpas	ihjpa	NOUN
iajs-3842	83	25	.	.	PUNCT
iajs-3842	84	1	2025,38(2	2025,38(2	PROPN
iajs-3842	84	2	)	)	PUNCT
iajs-3842	84	3	391	391	NUM
iajs-3842	84	4	by	by	ADP
iajs-3842	84	5	using	use	VERB
iajs-3842	84	6	l’hopital	l’hopital	PROPN
iajs-3842	84	7	’s	’s	PART
iajs-3842	84	8	role	role	NOUN
iajs-3842	84	9	for	for	ADP
iajs-3842	84	10	the	the	DET
iajs-3842	84	11	above	above	ADJ
iajs-3842	84	12	limit	limit	NOUN
iajs-3842	84	13	,	,	PUNCT
iajs-3842	84	14	∫	∫	PROPN
iajs-3842	84	15	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	84	16	)	)	PUNCT
iajs-3842	84	17	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	84	18	∞	∞	NUM
iajs-3842	84	19	0	0	NUM
iajs-3842	84	20	=	=	PUNCT
iajs-3842	85	1	−	−	PROPN
iajs-3842	85	2	𝐿𝑖𝑚	𝐿𝑖𝑚	NOUN
iajs-3842	85	3	𝑦→∞	𝑦→∞	NUM
iajs-3842	85	4	(	(	PUNCT
iajs-3842	85	5	𝛽	𝛽	NOUN
iajs-3842	85	6	(	(	PUNCT
iajs-3842	85	7	𝛽2	𝛽2	PROPN
iajs-3842	85	8	+	+	CCONJ
iajs-3842	85	9	1)(𝛽	1)(𝛽	NUM
iajs-3842	85	10	+	+	NUM
iajs-3842	85	11	𝜆𝑦𝜆−1)𝑒(𝛽𝑦+𝑦𝜆	𝜆𝑦𝜆−1)𝑒(𝛽𝑦+𝑦𝜆	NUM
iajs-3842	85	12	)	)	PUNCT
iajs-3842	86	1	−	−	ADP
iajs-3842	86	2	1	1	NUM
iajs-3842	86	3	)	)	PUNCT
iajs-3842	86	4	=	=	SYM
iajs-3842	86	5	−	−	PROPN
iajs-3842	86	6	𝛽	𝛽	NOUN
iajs-3842	86	7	∞	∞	NUM
iajs-3842	86	8	+	+	CCONJ
iajs-3842	86	9	1	1	NUM
iajs-3842	86	10	=	=	SYM
iajs-3842	86	11	1	1	NUM
iajs-3842	86	12	based	base	VERB
iajs-3842	86	13	on	on	ADP
iajs-3842	86	14	what	what	PRON
iajs-3842	86	15	was	be	AUX
iajs-3842	86	16	stated	state	VERB
iajs-3842	86	17	above	above	ADV
iajs-3842	86	18	,	,	PUNCT
iajs-3842	86	19	the	the	DET
iajs-3842	86	20	hazard	hazard	NOUN
iajs-3842	86	21	function	function	NOUN
iajs-3842	86	22	can	can	AUX
iajs-3842	86	23	be	be	AUX
iajs-3842	86	24	defined	define	VERB
iajs-3842	86	25	as	as	SCONJ
iajs-3842	86	26	follows	follow	VERB
iajs-3842	86	27	:	:	PUNCT
iajs-3842	86	28	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3842	86	29	)	)	PUNCT
iajs-3842	86	30	=	=	SYM
iajs-3842	86	31	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	86	32	)	)	PUNCT
iajs-3842	86	33	𝑆(𝑥	𝑆(𝑥	NUM
iajs-3842	86	34	)	)	PUNCT
iajs-3842	87	1	=	=	SYM
iajs-3842	87	2	(	(	PUNCT
iajs-3842	87	3	(	(	PUNCT
iajs-3842	87	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	87	5	+	+	PROPN
iajs-3842	87	6	𝛽2	𝛽2	NOUN
iajs-3842	87	7	+	+	CCONJ
iajs-3842	87	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	87	9	+	+	SYM
iajs-3842	87	10	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	87	11	)	)	PUNCT
iajs-3842	87	12	−	−	PROPN
iajs-3842	87	13	𝛽	𝛽	NOUN
iajs-3842	87	14	)	)	PUNCT
iajs-3842	87	15	1	1	NUM
iajs-3842	87	16	(	(	PUNCT
iajs-3842	87	17	𝛽2	𝛽2	NOUN
iajs-3842	87	18	+	+	CCONJ
iajs-3842	87	19	1	1	NUM
iajs-3842	87	20	)	)	PUNCT
iajs-3842	87	21	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	87	22	)	)	PUNCT
iajs-3842	87	23	(	(	PUNCT
iajs-3842	87	24	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	87	25	+	+	CCONJ
iajs-3842	87	26	𝛽2	𝛽2	NOUN
iajs-3842	87	27	+	+	CCONJ
iajs-3842	87	28	1	1	NUM
iajs-3842	87	29	)	)	PUNCT
iajs-3842	87	30	1	1	NUM
iajs-3842	87	31	(	(	PUNCT
iajs-3842	87	32	𝛽2	𝛽2	NOUN
iajs-3842	87	33	+	+	CCONJ
iajs-3842	87	34	1	1	NUM
iajs-3842	87	35	)	)	PUNCT
iajs-3842	87	36	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	VERB
iajs-3842	87	37	)	)	PUNCT
iajs-3842	87	38	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3842	87	39	)	)	PUNCT
iajs-3842	87	40	=	=	PRON
iajs-3842	87	41	(	(	PUNCT
iajs-3842	87	42	𝛽	𝛽	NOUN
iajs-3842	87	43	+	+	CCONJ
iajs-3842	87	44	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	87	45	)	)	PUNCT
iajs-3842	87	46	−	−	PROPN
iajs-3842	87	47	𝛽	𝛽	NOUN
iajs-3842	87	48	(	(	PUNCT
iajs-3842	87	49	𝛽𝑥+𝛽2	𝛽𝑥+𝛽2	PROPN
iajs-3842	87	50	+	+	NOUN
iajs-3842	87	51	1	1	NUM
iajs-3842	87	52	)	)	PUNCT
iajs-3842	87	53	(	(	PUNCT
iajs-3842	87	54	9	9	NUM
iajs-3842	87	55	)	)	PUNCT
iajs-3842	87	56	2.1.1	2.1.1	NUM
iajs-3842	87	57	.	.	PUNCT
iajs-3842	88	1	the	the	DET
iajs-3842	88	2	shapes	shape	NOUN
iajs-3842	88	3	of	of	ADP
iajs-3842	88	4	the	the	DET
iajs-3842	88	5	new	new	ADJ
iajs-3842	88	6	shanker	shanker	PROPN
iajs-3842	88	7	weibull	weibull	PROPN
iajs-3842	88	8	distribution	distribution	NOUN
iajs-3842	88	9	knowing	know	VERB
iajs-3842	88	10	the	the	DET
iajs-3842	88	11	shape	shape	NOUN
iajs-3842	88	12	of	of	ADP
iajs-3842	88	13	the	the	DET
iajs-3842	88	14	(	(	PUNCT
iajs-3842	88	15	shwd	shwd	PROPN
iajs-3842	88	16	)	)	PUNCT
iajs-3842	88	17	helps	help	VERB
iajs-3842	88	18	us	we	PRON
iajs-3842	88	19	understand	understand	VERB
iajs-3842	88	20	the	the	DET
iajs-3842	88	21	behavior	behavior	NOUN
iajs-3842	88	22	and	and	CCONJ
iajs-3842	88	23	approach	approach	NOUN
iajs-3842	88	24	of	of	ADP
iajs-3842	88	25	distribution	distribution	NOUN
iajs-3842	88	26	functions	function	NOUN
iajs-3842	88	27	in	in	ADP
iajs-3842	88	28	dealing	deal	VERB
iajs-3842	88	29	with	with	ADP
iajs-3842	88	30	data	datum	NOUN
iajs-3842	88	31	,	,	PUNCT
iajs-3842	88	32	to	to	PART
iajs-3842	88	33	understand	understand	VERB
iajs-3842	88	34	this	this	PRON
iajs-3842	88	35	mathematically	mathematically	ADV
iajs-3842	88	36	,	,	PUNCT
iajs-3842	88	37	especially	especially	ADV
iajs-3842	88	38	through	through	ADP
iajs-3842	88	39	the	the	DET
iajs-3842	88	40	limit	limit	NOUN
iajs-3842	88	41	values	value	NOUN
iajs-3842	88	42	of	of	ADP
iajs-3842	88	43	the	the	DET
iajs-3842	88	44	probability	probability	NOUN
iajs-3842	88	45	density	density	NOUN
iajs-3842	88	46	and	and	CCONJ
iajs-3842	88	47	hazard	hazard	NOUN
iajs-3842	88	48	functions	function	NOUN
iajs-3842	88	49	when(𝑥	when(𝑥	NOUN
iajs-3842	88	50	→	→	SYM
iajs-3842	88	51	0	0	PROPN
iajs-3842	88	52	&	&	CCONJ
iajs-3842	88	53	𝑥	𝑥	X
iajs-3842	88	54	→	→	SYM
iajs-3842	88	55	∞	∞	NUM
iajs-3842	88	56	)	)	PUNCT
iajs-3842	88	57	.	.	PUNCT
iajs-3842	89	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	89	2	𝑥→0	𝑥→0	X
iajs-3842	89	3	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	89	4	)	)	PUNCT
iajs-3842	90	1	=	=	PRON
iajs-3842	90	2	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	90	3	𝑥→0	𝑥→0	X
iajs-3842	90	4	(	(	PUNCT
iajs-3842	90	5	(	(	PUNCT
iajs-3842	90	6	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	90	7	+	+	PROPN
iajs-3842	90	8	𝛽2	𝛽2	NOUN
iajs-3842	90	9	+	+	CCONJ
iajs-3842	90	10	1)(𝛽	1)(𝛽	NUM
iajs-3842	90	11	+	+	SYM
iajs-3842	90	12	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	90	13	)	)	PUNCT
iajs-3842	90	14	−	−	PROPN
iajs-3842	91	1	𝛽	𝛽	NOUN
iajs-3842	91	2	)	)	PUNCT
iajs-3842	91	3	1	1	NUM
iajs-3842	91	4	(	(	PUNCT
iajs-3842	91	5	𝛽2	𝛽2	NOUN
iajs-3842	91	6	+	+	CCONJ
iajs-3842	91	7	1	1	NUM
iajs-3842	91	8	)	)	PUNCT
iajs-3842	91	9	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	91	10	)	)	PUNCT
iajs-3842	91	11	=	=	PROPN
iajs-3842	91	12	𝛽3	𝛽3	PROPN
iajs-3842	91	13	(	(	PUNCT
iajs-3842	91	14	𝛽2	𝛽2	PROPN
iajs-3842	91	15	+	+	CCONJ
iajs-3842	91	16	1	1	NUM
iajs-3842	91	17	)	)	PUNCT
iajs-3842	91	18	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	91	19	𝑥→∞	𝑥→∞	NUM
iajs-3842	91	20	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	91	21	)	)	PUNCT
iajs-3842	91	22	=	=	PRON
iajs-3842	92	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	92	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	92	3	(	(	PUNCT
iajs-3842	92	4	(	(	PUNCT
iajs-3842	92	5	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	92	6	+	+	PROPN
iajs-3842	92	7	𝛽2	𝛽2	NOUN
iajs-3842	92	8	+	+	CCONJ
iajs-3842	92	9	1)(𝛽	1)(𝛽	NUM
iajs-3842	92	10	+	+	SYM
iajs-3842	92	11	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	92	12	)	)	PUNCT
iajs-3842	92	13	−	−	PROPN
iajs-3842	93	1	𝛽	𝛽	NOUN
iajs-3842	93	2	)	)	PUNCT
iajs-3842	93	3	1	1	NUM
iajs-3842	93	4	(	(	PUNCT
iajs-3842	93	5	𝛽2	𝛽2	NOUN
iajs-3842	93	6	+	+	CCONJ
iajs-3842	93	7	1	1	NUM
iajs-3842	93	8	)	)	PUNCT
iajs-3842	93	9	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	93	10	)	)	PUNCT
iajs-3842	94	1	=	=	PRON
iajs-3842	95	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	95	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	95	3	(	(	PUNCT
iajs-3842	95	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	95	5	+	+	PROPN
iajs-3842	95	6	𝛽2	𝛽2	NOUN
iajs-3842	95	7	+	+	CCONJ
iajs-3842	95	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	95	9	+	+	SYM
iajs-3842	95	10	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	95	11	)	)	PUNCT
iajs-3842	95	12	(	(	PUNCT
iajs-3842	95	13	𝛽2	𝛽2	PROPN
iajs-3842	95	14	+	+	NOUN
iajs-3842	95	15	1)𝑒(𝛽𝑥+𝑥𝜆	1)𝑒(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	95	16	)	)	PUNCT
iajs-3842	95	17	−	−	NOUN
iajs-3842	96	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	96	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	96	3	𝛽	𝛽	NOUN
iajs-3842	96	4	(	(	PUNCT
iajs-3842	96	5	𝛽2	𝛽2	PROPN
iajs-3842	96	6	+	+	NOUN
iajs-3842	96	7	1)𝑒(𝛽𝑥+𝑥𝜆	1)𝑒(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	96	8	)	)	PUNCT
iajs-3842	96	9	=	=	PRON
iajs-3842	97	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	97	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	97	3	(	(	PUNCT
iajs-3842	97	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	97	5	+	+	PROPN
iajs-3842	97	6	𝛽2	𝛽2	NOUN
iajs-3842	97	7	+	+	CCONJ
iajs-3842	97	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	97	9	+	+	SYM
iajs-3842	97	10	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	97	11	)	)	PUNCT
iajs-3842	97	12	(	(	PUNCT
iajs-3842	97	13	𝛽2	𝛽2	PROPN
iajs-3842	97	14	+	+	NOUN
iajs-3842	97	15	1)𝑒(𝛽𝑥+𝑥𝜆	1)𝑒(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	97	16	)	)	PUNCT
iajs-3842	97	17	−	−	PROPN
iajs-3842	97	18	𝛽	𝛽	NOUN
iajs-3842	97	19	∞	∞	PROPN
iajs-3842	97	20	=	=	PRON
iajs-3842	98	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	98	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	98	3	(	(	PUNCT
iajs-3842	98	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	98	5	+	+	PROPN
iajs-3842	98	6	𝛽2	𝛽2	NOUN
iajs-3842	98	7	+	+	CCONJ
iajs-3842	98	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	98	9	+	+	SYM
iajs-3842	98	10	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	98	11	)	)	PUNCT
iajs-3842	98	12	(	(	PUNCT
iajs-3842	98	13	𝛽2	𝛽2	PROPN
iajs-3842	98	14	+	+	NOUN
iajs-3842	98	15	1)𝑒(𝛽𝑥+𝑥𝜆	1)𝑒(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	98	16	)	)	PUNCT
iajs-3842	98	17	applied	apply	VERB
iajs-3842	98	18	l'hospital	l'hospital	PROPN
iajs-3842	98	19	's	's	PART
iajs-3842	98	20	rule	rule	NOUN
iajs-3842	98	21	:	:	PUNCT
iajs-3842	98	22	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	98	23	𝑥→∞	𝑥→∞	NUM
iajs-3842	98	24	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	98	25	)	)	PUNCT
iajs-3842	99	1	=	=	PRON
iajs-3842	100	1	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-3842	100	2	𝑥→∞	𝑥→∞	NUM
iajs-3842	100	3	(	(	PUNCT
iajs-3842	100	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	100	5	+	+	PROPN
iajs-3842	100	6	𝛽2	𝛽2	NOUN
iajs-3842	100	7	+	+	CCONJ
iajs-3842	100	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	100	9	+	+	NUM
iajs-3842	100	10	𝜆𝑥𝜆−1)(𝜆(𝜆	𝜆𝑥𝜆−1)(𝜆(𝜆	NOUN
iajs-3842	101	1	−	−	PROPN
iajs-3842	101	2	1)𝑥𝜆−2	1)𝑥𝜆−2	NUM
iajs-3842	101	3	)	)	PUNCT
iajs-3842	102	1	−	−	PROPN
iajs-3842	103	1	𝛽(𝛽	𝛽(𝛽	NOUN
iajs-3842	103	2	+	+	CCONJ
iajs-3842	103	3	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	103	4	)	)	PUNCT
iajs-3842	103	5	(	(	PUNCT
iajs-3842	103	6	𝛽2	𝛽2	PROPN
iajs-3842	103	7	+	+	CCONJ
iajs-3842	103	8	1)(𝛽	1)(𝛽	NUM
iajs-3842	103	9	+	+	NUM
iajs-3842	103	10	𝜆𝑥𝜆−1)𝑒(𝛽𝑥+𝑥𝜆	𝜆𝑥𝜆−1)𝑒(𝛽𝑥+𝑥𝜆	PUNCT
iajs-3842	103	11	)	)	PUNCT
iajs-3842	103	12	as	as	SCONJ
iajs-3842	103	13	we	we	PRON
iajs-3842	103	14	continue	continue	VERB
iajs-3842	103	15	to	to	PART
iajs-3842	103	16	derive	derive	VERB
iajs-3842	103	17	for	for	ADP
iajs-3842	103	18	𝑥	𝑥	PROPN
iajs-3842	103	19	the	the	DET
iajs-3842	103	20	result	result	NOUN
iajs-3842	103	21	of	of	ADP
iajs-3842	103	22	the	the	DET
iajs-3842	103	23	numerator	numerator	NOUN
iajs-3842	103	24	will	will	AUX
iajs-3842	103	25	be	be	AUX
iajs-3842	103	26	equal	equal	ADJ
iajs-3842	103	27	constant	constant	ADJ
iajs-3842	103	28	as	as	SCONJ
iajs-3842	103	29	considered	consider	VERB
iajs-3842	103	30	an	an	DET
iajs-3842	103	31	integer	integer	NOUN
iajs-3842	103	32	value	value	NOUN
iajs-3842	103	33	for	for	ADP
iajs-3842	103	34	𝑥	𝑥	PROPN
iajs-3842	103	35	and	and	CCONJ
iajs-3842	103	36	as	as	SCONJ
iajs-3842	103	37	contained	contain	VERB
iajs-3842	103	38	to	to	PART
iajs-3842	103	39	derive	derive	VERB
iajs-3842	103	40	the	the	DET
iajs-3842	103	41	denominator	denominator	NOUN
iajs-3842	103	42	it	it	PRON
iajs-3842	103	43	always	always	ADV
iajs-3842	103	44	contains	contain	VERB
iajs-3842	103	45	the	the	DET
iajs-3842	103	46	exponential	exponential	ADJ
iajs-3842	103	47	part	part	NOUN
iajs-3842	103	48	which	which	PRON
iajs-3842	103	49	is	be	AUX
iajs-3842	103	50	equal	equal	ADJ
iajs-3842	103	51	to	to	ADP
iajs-3842	103	52	∞	∞	PROPN
iajs-3842	103	53	as(𝑥	as(𝑥	X
iajs-3842	103	54	→∞	→∞	NOUN
iajs-3842	103	55	)	)	PUNCT
iajs-3842	103	56	.	.	PUNCT
iajs-3842	104	1	the	the	DET
iajs-3842	104	2	final	final	ADJ
iajs-3842	104	3	result	result	NOUN
iajs-3842	104	4	of	of	ADP
iajs-3842	104	5	the	the	DET
iajs-3842	104	6	limit	limit	NOUN
iajs-3842	104	7	is	be	AUX
iajs-3842	104	8	a	a	DET
iajs-3842	104	9	constant	constant	ADJ
iajs-3842	104	10	divide	divide	NOUN
iajs-3842	104	11	by	by	ADP
iajs-3842	104	12	∞	∞	PROPN
iajs-3842	104	13	which	which	PRON
iajs-3842	104	14	equal	equal	ADJ
iajs-3842	104	15	to	to	ADP
iajs-3842	104	16	zero	zero	NUM
iajs-3842	104	17	lim	lim	PROPN
iajs-3842	104	18	x→∞	x→∞	SYM
iajs-3842	104	19	f(x	f(x	PROPN
iajs-3842	104	20	)	)	PUNCT
iajs-3842	104	21	=	=	PUNCT
iajs-3842	105	1	0	0	X
iajs-3842	105	2	.	.	PUNCT
iajs-3842	106	1	lim	lim	PROPN
iajs-3842	106	2	𝑥→0	𝑥→0	X
iajs-3842	106	3	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3842	106	4	)	)	PUNCT
iajs-3842	106	5	=	=	SYM
iajs-3842	106	6	lim	lim	PROPN
iajs-3842	106	7	𝑥→0	𝑥→0	PROPN
iajs-3842	106	8	(	(	PUNCT
iajs-3842	106	9	(	(	PUNCT
iajs-3842	106	10	𝛽	𝛽	NOUN
iajs-3842	106	11	+	+	NOUN
iajs-3842	106	12	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	106	13	)	)	PUNCT
iajs-3842	107	1	−	−	PROPN
iajs-3842	107	2	𝛽	𝛽	PROPN
iajs-3842	107	3	𝛽𝑥	𝛽𝑥	ADJ
iajs-3842	107	4	+	+	CCONJ
iajs-3842	107	5	𝛽2	𝛽2	NOUN
iajs-3842	107	6	+	+	CCONJ
iajs-3842	107	7	1	1	NUM
iajs-3842	107	8	)	)	PUNCT
iajs-3842	107	9	=	=	PROPN
iajs-3842	107	10	𝛽3	𝛽3	NOUN
iajs-3842	107	11	𝛽2	𝛽2	NOUN
iajs-3842	107	12	+	+	CCONJ
iajs-3842	107	13	1	1	NUM
iajs-3842	107	14	lim	lim	NOUN
iajs-3842	107	15	𝑥→∞	𝑥→∞	NUM
iajs-3842	107	16	ℎ(𝑥	ℎ(𝑥	NUM
iajs-3842	107	17	)	)	PUNCT
iajs-3842	107	18	=	=	SYM
iajs-3842	107	19	lim	lim	PROPN
iajs-3842	107	20	𝑥→∞	𝑥→∞	NUM
iajs-3842	107	21	(	(	PUNCT
iajs-3842	107	22	(	(	PUNCT
iajs-3842	107	23	𝛽	𝛽	NOUN
iajs-3842	107	24	+	+	NOUN
iajs-3842	107	25	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	107	26	)	)	PUNCT
iajs-3842	107	27	−	−	PROPN
iajs-3842	107	28	𝛽	𝛽	PROPN
iajs-3842	107	29	𝛽𝑥	𝛽𝑥	ADJ
iajs-3842	107	30	+	+	CCONJ
iajs-3842	107	31	𝛽2	𝛽2	NOUN
iajs-3842	107	32	+	+	CCONJ
iajs-3842	107	33	1	1	NUM
iajs-3842	107	34	)	)	PUNCT
iajs-3842	107	35	=	=	SYM
iajs-3842	108	1	∞	∞	NUM
iajs-3842	108	2	ihjpas	ihjpa	NOUN
iajs-3842	108	3	.	.	PUNCT
iajs-3842	109	1	2025,38(2	2025,38(2	PROPN
iajs-3842	109	2	)	)	PUNCT
iajs-3842	109	3	392	392	NUM
iajs-3842	109	4	figure	figure	NOUN
iajs-3842	109	5	1	1	NUM
iajs-3842	109	6	.	.	PUNCT
iajs-3842	110	1	the	the	DET
iajs-3842	110	2	shape	shape	NOUN
iajs-3842	110	3	of	of	ADP
iajs-3842	110	4	pdf	pdf	NOUN
iajs-3842	110	5	for	for	ADP
iajs-3842	110	6	new	new	ADJ
iajs-3842	110	7	shanker	shanker	NOUN
iajs-3842	110	8	weibull	weibull	PROPN
iajs-3842	110	9	distribution	distribution	NOUN
iajs-3842	110	10	with	with	ADP
iajs-3842	110	11	different	different	ADJ
iajs-3842	110	12	values	value	NOUN
iajs-3842	110	13	of	of	ADP
iajs-3842	110	14	β	β	X
iajs-3842	110	15	and	and	CCONJ
iajs-3842	110	16	𝜆.	𝜆.	PROPN
iajs-3842	110	17	figure	figure	NOUN
iajs-3842	110	18	2	2	NUM
iajs-3842	110	19	.	.	PUNCT
iajs-3842	111	1	the	the	DET
iajs-3842	111	2	shape	shape	NOUN
iajs-3842	111	3	of	of	ADP
iajs-3842	111	4	cdf	cdf	PROPN
iajs-3842	111	5	for	for	ADP
iajs-3842	111	6	new	new	ADJ
iajs-3842	111	7	shanker	shanker	NOUN
iajs-3842	111	8	weibull	weibull	PROPN
iajs-3842	111	9	distribution	distribution	NOUN
iajs-3842	111	10	with	with	ADP
iajs-3842	111	11	different	different	ADJ
iajs-3842	111	12	values	value	NOUN
iajs-3842	111	13	of	of	ADP
iajs-3842	111	14	β	β	PROPN
iajs-3842	111	15	and𝜆.	and𝜆.	PROPN
iajs-3842	111	16	figure	figure	NOUN
iajs-3842	111	17	3	3	NUM
iajs-3842	111	18	.	.	PUNCT
iajs-3842	112	1	the	the	DET
iajs-3842	112	2	shape	shape	NOUN
iajs-3842	112	3	of	of	ADP
iajs-3842	112	4	s(x	s(x	PROPN
iajs-3842	112	5	)	)	PUNCT
iajs-3842	112	6	for	for	ADP
iajs-3842	112	7	new	new	ADJ
iajs-3842	112	8	shanker	shanker	PROPN
iajs-3842	112	9	weibull	weibull	PROPN
iajs-3842	112	10	distribution	distribution	NOUN
iajs-3842	112	11	with	with	ADP
iajs-3842	112	12	different	different	ADJ
iajs-3842	112	13	values	value	NOUN
iajs-3842	112	14	of	of	ADP
iajs-3842	112	15	λ	λ	PROPN
iajs-3842	112	16	and𝛽.	and𝛽.	NOUN
iajs-3842	112	17	ihjpas	ihjpas	PROPN
iajs-3842	112	18	.	.	PUNCT
iajs-3842	113	1	2025,38(2	2025,38(2	PROPN
iajs-3842	113	2	)	)	PUNCT
iajs-3842	113	3	393	393	NUM
iajs-3842	113	4	figure	figure	NOUN
iajs-3842	113	5	4	4	NUM
iajs-3842	113	6	.	.	PUNCT
iajs-3842	114	1	the	the	DET
iajs-3842	114	2	shape	shape	NOUN
iajs-3842	114	3	of	of	ADP
iajs-3842	114	4	h(x	h(x	PROPN
iajs-3842	114	5	)	)	PUNCT
iajs-3842	114	6	for	for	ADP
iajs-3842	114	7	new	new	ADJ
iajs-3842	114	8	shanker	shanker	PROPN
iajs-3842	114	9	weibull	weibull	PROPN
iajs-3842	114	10	distribution	distribution	NOUN
iajs-3842	114	11	with	with	ADP
iajs-3842	114	12	different	different	ADJ
iajs-3842	114	13	values	value	NOUN
iajs-3842	114	14	of	of	ADP
iajs-3842	114	15	λ	λ	PROPN
iajs-3842	114	16	and𝛽.	and𝛽.	NOUN
iajs-3842	114	17	in	in	ADP
iajs-3842	114	18	the	the	DET
iajs-3842	114	19	special	special	ADJ
iajs-3842	114	20	case	case	NOUN
iajs-3842	114	21	,	,	PUNCT
iajs-3842	114	22	if	if	SCONJ
iajs-3842	114	23	𝜆	𝜆	PRON
iajs-3842	114	24	=	=	SYM
iajs-3842	114	25	1	1	NUM
iajs-3842	114	26	,	,	PUNCT
iajs-3842	114	27	then	then	ADV
iajs-3842	114	28	the	the	DET
iajs-3842	114	29	distribution	distribution	NOUN
iajs-3842	114	30	becomes	become	VERB
iajs-3842	114	31	the	the	DET
iajs-3842	114	32	shanker	shanker	NOUN
iajs-3842	114	33	exponential	exponential	ADJ
iajs-3842	114	34	distribution	distribution	NOUN
iajs-3842	114	35	,	,	PUNCT
iajs-3842	114	36	also	also	ADV
iajs-3842	114	37	if	if	SCONJ
iajs-3842	114	38	𝛽=0	𝛽=0	NUM
iajs-3842	114	39	,	,	PUNCT
iajs-3842	114	40	then	then	ADV
iajs-3842	114	41	the	the	DET
iajs-3842	114	42	distribution	distribution	NOUN
iajs-3842	114	43	becomes	become	VERB
iajs-3842	114	44	weibull	weibull	NOUN
iajs-3842	114	45	distribution	distribution	NOUN
iajs-3842	114	46	.	.	PUNCT
iajs-3842	115	1	2.2	2.2	NUM
iajs-3842	115	2	.	.	NOUN
iajs-3842	115	3	mathematical	mathematical	ADJ
iajs-3842	115	4	and	and	CCONJ
iajs-3842	115	5	statistical	statistical	ADJ
iajs-3842	115	6	properties	property	NOUN
iajs-3842	115	7	of	of	ADP
iajs-3842	115	8	shwd	shwd	NOUN
iajs-3842	115	9	2.2.1	2.2.1	NUM
iajs-3842	115	10	.	.	PUNCT
iajs-3842	116	1	the	the	DET
iajs-3842	116	2	mode	mode	NOUN
iajs-3842	116	3	the	the	DET
iajs-3842	116	4	mod	mod	NOUN
iajs-3842	116	5	is	be	AUX
iajs-3842	116	6	defined	define	VERB
iajs-3842	116	7	as	as	ADP
iajs-3842	116	8	the	the	DET
iajs-3842	116	9	point	point	NOUN
iajs-3842	116	10	at	at	ADP
iajs-3842	116	11	which	which	PRON
iajs-3842	116	12	the	the	DET
iajs-3842	116	13	probability	probability	NOUN
iajs-3842	116	14	density	density	NOUN
iajs-3842	116	15	function	function	NOUN
iajs-3842	116	16	achieves	achieve	VERB
iajs-3842	116	17	its	its	PRON
iajs-3842	116	18	maximum	maximum	ADJ
iajs-3842	116	19	value	value	NOUN
iajs-3842	116	20	,	,	PUNCT
iajs-3842	116	21	the	the	DET
iajs-3842	116	22	mode	mode	NOUN
iajs-3842	116	23	of	of	ADP
iajs-3842	116	24	(	(	PUNCT
iajs-3842	116	25	shwd	shwd	PROPN
iajs-3842	116	26	)	)	PUNCT
iajs-3842	116	27	is	be	AUX
iajs-3842	116	28	obtained	obtain	VERB
iajs-3842	116	29	as	as	ADP
iajs-3842	116	30	follows	follow	VERB
iajs-3842	116	31	:	:	PUNCT
iajs-3842	117	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	117	2	)	)	PUNCT
iajs-3842	117	3	=	=	SYM
iajs-3842	117	4	(	(	PUNCT
iajs-3842	117	5	𝛽2𝑥	𝛽2𝑥	VERB
iajs-3842	117	6	+	+	NUM
iajs-3842	117	7	𝛽𝜆𝑥𝜆	𝛽𝜆𝑥𝜆	NOUN
iajs-3842	117	8	+	+	CCONJ
iajs-3842	117	9	𝛽3	𝛽3	NOUN
iajs-3842	117	10	+	+	CCONJ
iajs-3842	117	11	𝛽2𝜆𝑥𝜆−1	𝛽2𝜆𝑥𝜆−1	PROPN
iajs-3842	117	12	+	+	CCONJ
iajs-3842	117	13	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	117	14	)	)	PUNCT
iajs-3842	117	15	1	1	NUM
iajs-3842	117	16	(	(	PUNCT
iajs-3842	117	17	𝛽2	𝛽2	NOUN
iajs-3842	117	18	+	+	CCONJ
iajs-3842	117	19	1	1	NUM
iajs-3842	117	20	)	)	PUNCT
iajs-3842	117	21	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	117	22	)	)	PUNCT
iajs-3842	117	23	𝜕𝑓(𝑥	𝜕𝑓(𝑥	NOUN
iajs-3842	117	24	)	)	PUNCT
iajs-3842	117	25	𝜕𝑥	𝜕𝑥	NOUN
iajs-3842	117	26	=	=	SYM
iajs-3842	117	27	(	(	PUNCT
iajs-3842	117	28	(	(	PUNCT
iajs-3842	117	29	𝛽2	𝛽2	PROPN
iajs-3842	117	30	+	+	CCONJ
iajs-3842	117	31	𝛽𝜆2𝑥𝜆−1	𝛽𝜆2𝑥𝜆−1	PROPN
iajs-3842	117	32	+	+	CCONJ
iajs-3842	117	33	𝛽2𝜆(𝜆	𝛽2𝜆(𝜆	PROPN
iajs-3842	117	34	−	−	PROPN
iajs-3842	117	35	1)𝑥𝜆−2	1)𝑥𝜆−2	PROPN
iajs-3842	117	36	+	+	CCONJ
iajs-3842	117	37	𝜆(𝜆	𝜆(𝜆	PROPN
iajs-3842	117	38	−	−	PROPN
iajs-3842	117	39	1)𝑥𝜆−2	1)𝑥𝜆−2	NUM
iajs-3842	117	40	)	)	PUNCT
iajs-3842	117	41	−	−	PROPN
iajs-3842	117	42	(	(	PUNCT
iajs-3842	117	43	𝛽2𝑥	𝛽2𝑥	VERB
iajs-3842	117	44	+	+	NUM
iajs-3842	117	45	𝛽𝜆𝑥𝜆	𝛽𝜆𝑥𝜆	NOUN
iajs-3842	117	46	+	+	CCONJ
iajs-3842	117	47	𝛽3	𝛽3	NOUN
iajs-3842	117	48	+	+	CCONJ
iajs-3842	117	49	𝛽2𝜆𝑥𝜆−1	𝛽2𝜆𝑥𝜆−1	PROPN
iajs-3842	117	50	+	+	CCONJ
iajs-3842	117	51	𝜆𝑥𝜆−1)(𝛽	𝜆𝑥𝜆−1)(𝛽	ADJ
iajs-3842	117	52	+	+	X
iajs-3842	117	53	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	117	54	)	)	PUNCT
iajs-3842	117	55	)	)	PUNCT
iajs-3842	117	56	1	1	NUM
iajs-3842	117	57	(	(	PUNCT
iajs-3842	117	58	𝛽2	𝛽2	NOUN
iajs-3842	117	59	+	+	CCONJ
iajs-3842	117	60	1	1	NUM
iajs-3842	117	61	)	)	PUNCT
iajs-3842	117	62	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	117	63	)	)	PUNCT
iajs-3842	117	64	=	=	SYM
iajs-3842	117	65	0	0	PUNCT
iajs-3842	117	66	since	since	SCONJ
iajs-3842	117	67	that	that	PRON
iajs-3842	117	68	𝑒	𝑒	PROPN
iajs-3842	117	69	−(𝛽𝑥+𝑥𝜆	−(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	117	70	)	)	PUNCT
iajs-3842	117	71	(	(	PUNCT
iajs-3842	117	72	𝛽2	𝛽2	PROPN
iajs-3842	117	73	+	+	NOUN
iajs-3842	117	74	1	1	NUM
iajs-3842	117	75	)	)	PUNCT
iajs-3842	117	76	≠	≠	PROPN
iajs-3842	117	77	0	0	NUM
iajs-3842	117	78	for	for	ADP
iajs-3842	117	79	each	each	DET
iajs-3842	117	80	selected	select	VERB
iajs-3842	117	81	value	value	NOUN
iajs-3842	117	82	of	of	ADP
iajs-3842	117	83	β	β	X
iajs-3842	117	84	,	,	PUNCT
iajs-3842	117	85	λ	λ	PROPN
iajs-3842	117	86	,	,	PUNCT
iajs-3842	117	87	and	and	CCONJ
iajs-3842	117	88	x	x	X
iajs-3842	117	89	,	,	PUNCT
iajs-3842	117	90	this	this	PRON
iajs-3842	117	91	leads	lead	VERB
iajs-3842	117	92	to	to	ADP
iajs-3842	117	93	the	the	DET
iajs-3842	117	94	following	following	NOUN
iajs-3842	117	95	:	:	PUNCT
iajs-3842	117	96	(	(	PUNCT
iajs-3842	117	97	𝛽2	𝛽2	PROPN
iajs-3842	117	98	+	+	CCONJ
iajs-3842	117	99	𝛽𝜆2𝑥𝜆−1	𝛽𝜆2𝑥𝜆−1	PROPN
iajs-3842	117	100	+	+	CCONJ
iajs-3842	117	101	𝛽2𝜆(𝜆	𝛽2𝜆(𝜆	PROPN
iajs-3842	117	102	−	−	PROPN
iajs-3842	117	103	1)𝑥𝜆−2	1)𝑥𝜆−2	PROPN
iajs-3842	117	104	+	+	CCONJ
iajs-3842	117	105	𝜆(𝜆	𝜆(𝜆	PROPN
iajs-3842	117	106	−	−	PROPN
iajs-3842	117	107	1)𝑥𝜆−2	1)𝑥𝜆−2	NUM
iajs-3842	117	108	)	)	PUNCT
iajs-3842	117	109	−	−	PROPN
iajs-3842	117	110	(	(	PUNCT
iajs-3842	117	111	𝛽2𝑥	𝛽2𝑥	VERB
iajs-3842	117	112	+	+	NUM
iajs-3842	117	113	𝛽𝜆𝑥𝜆	𝛽𝜆𝑥𝜆	NOUN
iajs-3842	117	114	+	+	CCONJ
iajs-3842	117	115	𝛽3	𝛽3	NOUN
iajs-3842	117	116	+	+	CCONJ
iajs-3842	117	117	𝛽2𝜆𝑥𝜆−1	𝛽2𝜆𝑥𝜆−1	PROPN
iajs-3842	117	118	+	+	CCONJ
iajs-3842	117	119	𝜆𝑥𝜆−1)(𝛽	𝜆𝑥𝜆−1)(𝛽	ADJ
iajs-3842	117	120	+	+	X
iajs-3842	117	121	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	NOUN
iajs-3842	117	122	)	)	PUNCT
iajs-3842	117	123	=	=	SYM
iajs-3842	117	124	0	0	NUM
iajs-3842	118	1	this	this	PRON
iajs-3842	118	2	is	be	AUX
iajs-3842	118	3	a	a	DET
iajs-3842	118	4	polynomial	polynomial	NOUN
iajs-3842	118	5	of	of	ADP
iajs-3842	118	6	degree	degree	NOUN
iajs-3842	118	7	(	(	PUNCT
iajs-3842	118	8	𝜆	𝜆	NOUN
iajs-3842	118	9	−	−	PROPN
iajs-3842	118	10	2	2	NUM
iajs-3842	118	11	)	)	PUNCT
iajs-3842	118	12	and	and	CCONJ
iajs-3842	118	13	if	if	SCONJ
iajs-3842	118	14	𝜆	𝜆	PRON
iajs-3842	118	15	=	=	SYM
iajs-3842	118	16	1that	1that	PROPN
iajs-3842	118	17	will	will	AUX
iajs-3842	118	18	imply	imply	VERB
iajs-3842	118	19	the	the	DET
iajs-3842	118	20	following	following	NOUN
iajs-3842	118	21	:	:	PUNCT
iajs-3842	118	22	(	(	PUNCT
iajs-3842	118	23	(	(	PUNCT
iajs-3842	118	24	𝛽2	𝛽2	PROPN
iajs-3842	118	25	+	+	NOUN
iajs-3842	118	26	𝛽	𝛽	NOUN
iajs-3842	118	27	)	)	PUNCT
iajs-3842	118	28	−	−	PROPN
iajs-3842	118	29	(	(	PUNCT
iajs-3842	118	30	𝛽2𝑥	𝛽2𝑥	VERB
iajs-3842	118	31	+	+	CCONJ
iajs-3842	118	32	𝛽𝑥	𝛽𝑥	ADJ
iajs-3842	118	33	+	+	NUM
iajs-3842	118	34	𝛽3	𝛽3	NOUN
iajs-3842	118	35	+	+	CCONJ
iajs-3842	118	36	𝛽2	𝛽2	NOUN
iajs-3842	118	37	+	+	CCONJ
iajs-3842	118	38	1)(𝛽	1)(𝛽	NUM
iajs-3842	118	39	+	+	SYM
iajs-3842	118	40	1	1	NUM
iajs-3842	118	41	)	)	PUNCT
iajs-3842	118	42	)	)	PUNCT
iajs-3842	119	1	=	=	SYM
iajs-3842	119	2	0	0	PUNCT
iajs-3842	119	3	(	(	PUNCT
iajs-3842	119	4	𝛽2	𝛽2	PROPN
iajs-3842	119	5	+	+	CCONJ
iajs-3842	119	6	𝛽)−.	𝛽)−.	NOUN
iajs-3842	119	7	(	(	PUNCT
iajs-3842	119	8	𝛽3𝑥	𝛽3𝑥	PROPN
iajs-3842	119	9	+	+	CCONJ
iajs-3842	119	10	𝛽2𝑥	𝛽2𝑥	PROPN
iajs-3842	119	11	+	+	CCONJ
iajs-3842	119	12	𝛽4	𝛽4	PROPN
iajs-3842	119	13	+	+	CCONJ
iajs-3842	119	14	𝛽3	𝛽3	NOUN
iajs-3842	119	15	+	+	CCONJ
iajs-3842	119	16	𝛽	𝛽	PROPN
iajs-3842	119	17	+	+	CCONJ
iajs-3842	119	18	𝛽2𝑥	𝛽2𝑥	VERB
iajs-3842	119	19	+	+	CCONJ
iajs-3842	119	20	𝛽𝑥	𝛽𝑥	ADJ
iajs-3842	119	21	+	+	NUM
iajs-3842	119	22	𝛽3	𝛽3	NOUN
iajs-3842	119	23	+	+	CCONJ
iajs-3842	119	24	𝛽2	𝛽2	NOUN
iajs-3842	119	25	+	+	CCONJ
iajs-3842	119	26	1	1	NUM
iajs-3842	119	27	)	)	PUNCT
iajs-3842	119	28	=	=	SYM
iajs-3842	119	29	0	0	NUM
iajs-3842	119	30	−(𝛽3	−(𝛽3	NUM
iajs-3842	119	31	+	+	SYM
iajs-3842	119	32	2𝛽2	2𝛽2	NUM
iajs-3842	119	33	+	+	CCONJ
iajs-3842	119	34	𝛽)𝑥	𝛽)𝑥	ADJ
iajs-3842	119	35	=	=	SYM
iajs-3842	119	36	𝛽4	𝛽4	PROPN
iajs-3842	119	37	+	+	CCONJ
iajs-3842	119	38	2𝛽3	2𝛽3	NUM
iajs-3842	119	39	+	+	CCONJ
iajs-3842	119	40	1	1	NUM
iajs-3842	119	41	𝑥	𝑥	NOUN
iajs-3842	119	42	=	=	PUNCT
iajs-3842	119	43	−(𝛽4	−(𝛽4	NUM
iajs-3842	119	44	+	+	CCONJ
iajs-3842	119	45	2𝛽3	2𝛽3	NUM
iajs-3842	119	46	+	+	CCONJ
iajs-3842	119	47	1	1	NUM
iajs-3842	119	48	)	)	PUNCT
iajs-3842	119	49	(	(	PUNCT
iajs-3842	119	50	𝛽3	𝛽3	NOUN
iajs-3842	119	51	+	+	CCONJ
iajs-3842	119	52	2𝛽2	2𝛽2	NUM
iajs-3842	119	53	+	+	CCONJ
iajs-3842	119	54	𝛽	𝛽	NOUN
iajs-3842	119	55	)	)	PUNCT
iajs-3842	119	56	2.2.2	2.2.2	NUM
iajs-3842	119	57	.	.	PUNCT
iajs-3842	119	58	quantile	quantile	ADJ
iajs-3842	119	59	function	function	NOUN
iajs-3842	119	60	let	let	VERB
iajs-3842	119	61	𝑋	𝑋	NOUN
iajs-3842	119	62	be	be	AUX
iajs-3842	119	63	a	a	DET
iajs-3842	119	64	continuous	continuous	ADJ
iajs-3842	119	65	random	random	ADJ
iajs-3842	119	66	variable	variable	NOUN
iajs-3842	119	67	distributed	distribute	VERB
iajs-3842	119	68	with	with	ADP
iajs-3842	119	69	"	"	PUNCT
iajs-3842	119	70	shwd	shwd	NOUN
iajs-3842	119	71	"	"	PUNCT
iajs-3842	119	72	then	then	ADV
iajs-3842	119	73	the	the	DET
iajs-3842	119	74	quantile	quantile	ADJ
iajs-3842	119	75	function	function	NOUN
iajs-3842	119	76	is	be	AUX
iajs-3842	119	77	defined	define	VERB
iajs-3842	119	78	as	as	SCONJ
iajs-3842	119	79	given	give	VERB
iajs-3842	119	80	:	:	PUNCT
iajs-3842	119	81	let	let	VERB
iajs-3842	119	82	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3842	119	83	)	)	PUNCT
iajs-3842	119	84	=	=	SYM
iajs-3842	119	85	𝑢	𝑢	NOUN
iajs-3842	119	86	,	,	PUNCT
iajs-3842	119	87	𝑢~𝑈(0,1	𝑢~𝑈(0,1	NOUN
iajs-3842	119	88	)	)	PUNCT
iajs-3842	119	89	,	,	PUNCT
iajs-3842	119	90	then	then	ADV
iajs-3842	119	91	𝐹(𝑥	𝐹(𝑥	NUM
iajs-3842	119	92	)	)	PUNCT
iajs-3842	119	93	=	=	SYM
iajs-3842	119	94	𝑈	𝑈	PROPN
iajs-3842	119	95	,	,	PUNCT
iajs-3842	119	96	𝑥	𝑥	X
iajs-3842	119	97	=	=	SYM
iajs-3842	119	98	𝐹−1(𝑢	𝐹−1(𝑢	NUM
iajs-3842	119	99	)	)	PUNCT
iajs-3842	119	100	(	(	PUNCT
iajs-3842	119	101	1	1	NUM
iajs-3842	119	102	−	−	PROPN
iajs-3842	119	103	𝛽𝑥+𝛽2	𝛽𝑥+𝛽2	PROPN
iajs-3842	119	104	+	+	ADJ
iajs-3842	119	105	1	1	NUM
iajs-3842	119	106	𝛽2	𝛽2	NOUN
iajs-3842	119	107	+	+	ADJ
iajs-3842	119	108	1	1	NUM
iajs-3842	119	109	∙	∙	PROPN
iajs-3842	119	110	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	119	111	)	)	PUNCT
iajs-3842	119	112	)	)	PUNCT
iajs-3842	120	1	=	=	PUNCT
iajs-3842	120	2	𝑢	𝑢	X
iajs-3842	120	3	−	−	X
iajs-3842	120	4	(	(	PUNCT
iajs-3842	120	5	1	1	NUM
iajs-3842	120	6	−	−	PROPN
iajs-3842	120	7	𝛽𝑥+𝛽2	𝛽𝑥+𝛽2	PROPN
iajs-3842	120	8	+	+	ADJ
iajs-3842	120	9	1	1	NUM
iajs-3842	120	10	𝛽2	𝛽2	NOUN
iajs-3842	120	11	+	+	ADJ
iajs-3842	120	12	1	1	NUM
iajs-3842	120	13	∙	∙	PROPN
iajs-3842	120	14	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NUM
iajs-3842	120	15	)	)	PUNCT
iajs-3842	120	16	)	)	PUNCT
iajs-3842	121	1	=	=	PUNCT
iajs-3842	121	2	𝑢	𝑢	X
iajs-3842	121	3	−	−	NUM
iajs-3842	121	4	1	1	NUM
iajs-3842	121	5	1	1	NUM
iajs-3842	121	6	−	−	NUM
iajs-3842	121	7	𝑢	𝑢	NOUN
iajs-3842	121	8	=	=	PUNCT
iajs-3842	121	9	𝛽𝑥+𝛽2	𝛽𝑥+𝛽2	PROPN
iajs-3842	121	10	+	+	ADJ
iajs-3842	121	11	1	1	NUM
iajs-3842	121	12	𝛽2	𝛽2	NOUN
iajs-3842	121	13	+	+	ADJ
iajs-3842	121	14	1	1	NUM
iajs-3842	121	15	∙	∙	PROPN
iajs-3842	121	16	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	121	17	)	)	PUNCT
iajs-3842	121	18	,	,	PUNCT
iajs-3842	121	19	𝜆=1	𝜆=1	PROPN
iajs-3842	121	20	ihjpas	ihjpas	PROPN
iajs-3842	121	21	.	.	PUNCT
iajs-3842	122	1	2025,38(2	2025,38(2	PROPN
iajs-3842	122	2	)	)	PUNCT
iajs-3842	122	3	394	394	NUM
iajs-3842	122	4	for	for	ADP
iajs-3842	122	5	lambert	lambert	NOUN
iajs-3842	122	6	form	form	NOUN
iajs-3842	122	7	(	(	PUNCT
iajs-3842	122	8	26	26	NUM
iajs-3842	122	9	-	-	SYM
iajs-3842	122	10	27	27	NUM
iajs-3842	122	11	)	)	PUNCT
iajs-3842	122	12	(	(	PUNCT
iajs-3842	122	13	1	1	NUM
iajs-3842	122	14	−	−	NOUN
iajs-3842	122	15	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	123	1	+	+	CCONJ
iajs-3842	123	2	1	1	X
iajs-3842	123	3	)	)	PUNCT
iajs-3842	123	4	=	=	SYM
iajs-3842	123	5	(	(	PUNCT
iajs-3842	123	6	𝛽𝑥	𝛽𝑥	NOUN
iajs-3842	123	7	+	+	PROPN
iajs-3842	123	8	𝛽2	𝛽2	NOUN
iajs-3842	123	9	+	+	CCONJ
iajs-3842	123	10	1	1	NUM
iajs-3842	123	11	)	)	PUNCT
iajs-3842	123	12	∙	∙	PROPN
iajs-3842	123	13	𝑒−(𝛽𝑥+𝑥	𝑒−(𝛽𝑥+𝑥	PROPN
iajs-3842	123	14	)	)	PUNCT
iajs-3842	123	15	where	where	SCONJ
iajs-3842	123	16	,	,	PUNCT
iajs-3842	123	17	𝑥	𝑥	X
iajs-3842	123	18	=	=	PUNCT
iajs-3842	123	19	𝛽𝑏−(−𝛽−1)(𝛽2	𝛽𝑏−(−𝛽−1)(𝛽2	PROPN
iajs-3842	123	20	+	+	PROPN
iajs-3842	123	21	1	1	NUM
iajs-3842	123	22	)	)	PUNCT
iajs-3842	123	23	𝛽(−𝛽−1	𝛽(−𝛽−1	PROPN
iajs-3842	123	24	)	)	PUNCT
iajs-3842	123	25	hence	hence	ADV
iajs-3842	123	26	the	the	DET
iajs-3842	123	27	value	value	NOUN
iajs-3842	123	28	of	of	ADP
iajs-3842	123	29	𝑏	𝑏	NOUN
iajs-3842	123	30	=	=	PUNCT
iajs-3842	123	31	(	(	PUNCT
iajs-3842	123	32	−𝛽	−𝛽	PROPN
iajs-3842	123	33	−	−	PROPN
iajs-3842	123	34	1)𝑥	1)𝑥	NUM
iajs-3842	124	1	+	+	CCONJ
iajs-3842	124	2	(	(	PUNCT
iajs-3842	124	3	𝛽2	𝛽2	PROPN
iajs-3842	124	4	+	+	NOUN
iajs-3842	124	5	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	124	6	)	)	PUNCT
iajs-3842	124	7	𝛽	𝛽	NOUN
iajs-3842	124	8	(	(	PUNCT
iajs-3842	124	9	1	1	NUM
iajs-3842	124	10	−	−	NOUN
iajs-3842	124	11	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	125	1	+	+	CCONJ
iajs-3842	125	2	1	1	X
iajs-3842	125	3	)	)	PUNCT
iajs-3842	125	4	=	=	SYM
iajs-3842	125	5	(	(	PUNCT
iajs-3842	125	6	𝛽	𝛽	NOUN
iajs-3842	125	7	(	(	PUNCT
iajs-3842	125	8	(	(	PUNCT
iajs-3842	125	9	𝛽𝑏−(−𝛽−1)(𝛽2	𝛽𝑏−(−𝛽−1)(𝛽2	PROPN
iajs-3842	125	10	+	+	ADJ
iajs-3842	125	11	1	1	NUM
iajs-3842	125	12	)	)	PUNCT
iajs-3842	125	13	𝛽(−𝛽−1	𝛽(−𝛽−1	PROPN
iajs-3842	125	14	)	)	PUNCT
iajs-3842	125	15	)	)	PUNCT
iajs-3842	126	1	+	+	CCONJ
iajs-3842	126	2	𝛽2	𝛽2	NOUN
iajs-3842	126	3	+	+	CCONJ
iajs-3842	126	4	1	1	NUM
iajs-3842	126	5	)	)	PUNCT
iajs-3842	126	6	𝑒	𝑒	PROPN
iajs-3842	126	7	(	(	PUNCT
iajs-3842	126	8	−𝛽−1)((𝛽𝑏−(−𝛽−1)(𝛽2	−𝛽−1)((𝛽𝑏−(−𝛽−1)(𝛽2	PUNCT
iajs-3842	126	9	+	+	NOUN
iajs-3842	126	10	1	1	NUM
iajs-3842	126	11	)	)	PUNCT
iajs-3842	126	12	)	)	PUNCT
iajs-3842	127	1	𝛽(−𝛽−1	𝛽(−𝛽−1	PROPN
iajs-3842	127	2	)	)	PUNCT
iajs-3842	127	3	(	(	PUNCT
iajs-3842	127	4	1	1	NUM
iajs-3842	127	5	−	−	NOUN
iajs-3842	127	6	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	128	1	+	+	CCONJ
iajs-3842	128	2	1	1	X
iajs-3842	128	3	)	)	PUNCT
iajs-3842	128	4	=	=	NOUN
iajs-3842	128	5	(	(	PUNCT
iajs-3842	128	6	𝛽𝑏	𝛽𝑏	NOUN
iajs-3842	128	7	−𝛽−1	−𝛽−1	NUM
iajs-3842	128	8	−	−	PROPN
iajs-3842	128	9	(	(	PUNCT
iajs-3842	128	10	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	128	11	+	+	NOUN
iajs-3842	128	12	1	1	NUM
iajs-3842	128	13	)	)	PUNCT
iajs-3842	128	14	(	(	PUNCT
iajs-3842	128	15	−𝛽−1	−𝛽−1	NUM
iajs-3842	128	16	)	)	PUNCT
iajs-3842	129	1	+	+	NUM
iajs-3842	129	2	𝛽2	𝛽2	NOUN
iajs-3842	129	3	+	+	CCONJ
iajs-3842	129	4	1)𝑒	1)𝑒	NUM
iajs-3842	129	5	𝛽𝑏−(−𝛽−1)(𝛽2	𝛽𝑏−(−𝛽−1)(𝛽2	PROPN
iajs-3842	129	6	+	+	NOUN
iajs-3842	129	7	1	1	NUM
iajs-3842	129	8	)	)	PUNCT
iajs-3842	129	9	𝛽	𝛽	NOUN
iajs-3842	129	10	(	(	PUNCT
iajs-3842	129	11	1	1	NUM
iajs-3842	129	12	−	−	NOUN
iajs-3842	129	13	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	130	1	+	+	CCONJ
iajs-3842	130	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	130	3	−	−	NOUN
iajs-3842	130	4	1	1	NUM
iajs-3842	130	5	)	)	PUNCT
iajs-3842	130	6	=	=	NOUN
iajs-3842	130	7	𝛽𝑏	𝛽𝑏	ADP
iajs-3842	130	8	∙	∙	PROPN
iajs-3842	130	9	𝑒	𝑒	PROPN
iajs-3842	130	10	𝛽𝑏	𝛽𝑏	ADP
iajs-3842	130	11	𝛽	𝛽	PROPN
iajs-3842	130	12	∙	∙	PROPN
iajs-3842	130	13	𝑒	𝑒	ADP
iajs-3842	130	14	−(−𝛽−1)(𝛽2	−(−𝛽−1)(𝛽2	PROPN
iajs-3842	130	15	+	+	NOUN
iajs-3842	130	16	1	1	NUM
iajs-3842	130	17	)	)	PUNCT
iajs-3842	130	18	𝛽	𝛽	NOUN
iajs-3842	130	19	(	(	PUNCT
iajs-3842	130	20	1	1	NUM
iajs-3842	130	21	−	−	NOUN
iajs-3842	130	22	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	131	1	+	+	CCONJ
iajs-3842	131	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	131	3	−	−	NOUN
iajs-3842	131	4	1	1	NUM
iajs-3842	131	5	)	)	PUNCT
iajs-3842	131	6	=	=	NOUN
iajs-3842	131	7	𝛽𝑏	𝛽𝑏	ADP
iajs-3842	131	8	∙	∙	PROPN
iajs-3842	131	9	𝑒𝑏	𝑒𝑏	ADP
iajs-3842	131	10	∙	∙	PROPN
iajs-3842	131	11	𝑒	𝑒	PROPN
iajs-3842	131	12	−(−𝛽−1)(𝛽2	−(−𝛽−1)(𝛽2	PROPN
iajs-3842	131	13	+	+	NOUN
iajs-3842	131	14	1	1	NUM
iajs-3842	131	15	)	)	PUNCT
iajs-3842	131	16	𝛽	𝛽	NOUN
iajs-3842	131	17	(	(	PUNCT
iajs-3842	131	18	1	1	NUM
iajs-3842	131	19	−	−	NOUN
iajs-3842	131	20	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	132	1	+	+	CCONJ
iajs-3842	132	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	132	3	−	−	PROPN
iajs-3842	132	4	1)𝑒	1)𝑒	NUM
iajs-3842	132	5	(	(	PUNCT
iajs-3842	132	6	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	NUM
iajs-3842	132	7	+	+	NOUN
iajs-3842	132	8	1	1	NUM
iajs-3842	132	9	)	)	PUNCT
iajs-3842	132	10	𝛽	𝛽	NOUN
iajs-3842	132	11	=	=	SYM
iajs-3842	132	12	𝛽𝑏	𝛽𝑏	ADP
iajs-3842	132	13	∙	∙	PROPN
iajs-3842	132	14	𝑒𝑏	𝑒𝑏	PROPN
iajs-3842	132	15	(	(	PUNCT
iajs-3842	132	16	1	1	NUM
iajs-3842	132	17	−	−	NOUN
iajs-3842	132	18	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	133	1	+	+	CCONJ
iajs-3842	133	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	133	3	−	−	NUM
iajs-3842	133	4	1	1	NUM
iajs-3842	133	5	)	)	PUNCT
iajs-3842	133	6	𝛽	𝛽	NOUN
iajs-3842	133	7	𝑒	𝑒	X
iajs-3842	133	8	(	(	PUNCT
iajs-3842	133	9	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PROPN
iajs-3842	133	10	+	+	NOUN
iajs-3842	133	11	1	1	NUM
iajs-3842	133	12	)	)	PUNCT
iajs-3842	133	13	𝛽	𝛽	NOUN
iajs-3842	133	14	=	=	SYM
iajs-3842	133	15	𝑏	𝑏	PROPN
iajs-3842	133	16	∙	∙	PROPN
iajs-3842	133	17	𝑒𝑏	𝑒𝑏	ADJ
iajs-3842	133	18	𝑊	𝑊	PROPN
iajs-3842	133	19	(	(	PUNCT
iajs-3842	133	20	𝑏𝑒𝑏	𝑏𝑒𝑏	NOUN
iajs-3842	133	21	=	=	SYM
iajs-3842	133	22	(	(	PUNCT
iajs-3842	133	23	1	1	NUM
iajs-3842	133	24	−	−	NOUN
iajs-3842	133	25	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	134	1	+	+	CCONJ
iajs-3842	134	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	134	3	−	−	NUM
iajs-3842	134	4	1	1	NUM
iajs-3842	134	5	)	)	PUNCT
iajs-3842	134	6	𝛽	𝛽	NOUN
iajs-3842	134	7	.	.	PUNCT
iajs-3842	135	1	𝑒	𝑒	PROPN
iajs-3842	135	2	(	(	PUNCT
iajs-3842	135	3	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	135	4	+	+	ADJ
iajs-3842	135	5	1	1	NUM
iajs-3842	135	6	)	)	PUNCT
iajs-3842	135	7	𝛽	𝛽	NOUN
iajs-3842	135	8	)	)	PUNCT
iajs-3842	135	9	𝑏	𝑏	PROPN
iajs-3842	135	10	=	=	SYM
iajs-3842	135	11	𝑊	𝑊	PROPN
iajs-3842	135	12	(	(	PUNCT
iajs-3842	135	13	(	(	PUNCT
iajs-3842	135	14	1	1	NUM
iajs-3842	135	15	−	−	NOUN
iajs-3842	135	16	𝑢)(𝛽2	𝑢)(𝛽2	ADV
iajs-3842	136	1	+	+	CCONJ
iajs-3842	136	2	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	136	3	−	−	NUM
iajs-3842	136	4	1	1	NUM
iajs-3842	136	5	)	)	PUNCT
iajs-3842	136	6	𝛽	𝛽	NOUN
iajs-3842	136	7	.	.	PUNCT
iajs-3842	137	1	𝑒	𝑒	PROPN
iajs-3842	137	2	(	(	PUNCT
iajs-3842	137	3	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	137	4	+	+	ADJ
iajs-3842	137	5	1	1	NUM
iajs-3842	137	6	)	)	PUNCT
iajs-3842	137	7	𝛽	𝛽	NOUN
iajs-3842	137	8	)	)	PUNCT
iajs-3842	137	9	since	since	SCONJ
iajs-3842	137	10	𝑏	𝑏	NOUN
iajs-3842	137	11	=	=	PUNCT
iajs-3842	137	12	(	(	PUNCT
iajs-3842	137	13	−𝛽	−𝛽	PROPN
iajs-3842	137	14	−	−	PROPN
iajs-3842	137	15	1)𝑥	1)𝑥	NUM
iajs-3842	137	16	+	+	CCONJ
iajs-3842	137	17	(	(	PUNCT
iajs-3842	137	18	𝛽2	𝛽2	PROPN
iajs-3842	137	19	+	+	CCONJ
iajs-3842	137	20	1)(−𝛽	1)(−𝛽	NUM
iajs-3842	137	21	−	−	PROPN
iajs-3842	137	22	1	1	NUM
iajs-3842	137	23	)	)	PUNCT
iajs-3842	137	24	𝛽	𝛽	NOUN
iajs-3842	137	25	(	(	PUNCT
iajs-3842	137	26	−𝛽	−𝛽	PROPN
iajs-3842	137	27	−	−	PROPN
iajs-3842	137	28	1)𝑥	1)𝑥	NUM
iajs-3842	137	29	+	+	CCONJ
iajs-3842	137	30	(	(	PUNCT
iajs-3842	137	31	𝛽2	𝛽2	PROPN
iajs-3842	137	32	+	+	NOUN
iajs-3842	137	33	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	137	34	)	)	PUNCT
iajs-3842	137	35	𝛽	𝛽	NOUN
iajs-3842	137	36	=	=	SYM
iajs-3842	137	37	𝑊	𝑊	PROPN
iajs-3842	137	38	(	(	PUNCT
iajs-3842	137	39	(	(	PUNCT
iajs-3842	137	40	1−𝑢)(𝛽2	1−𝑢)(𝛽2	NUM
iajs-3842	137	41	+	+	NOUN
iajs-3842	137	42	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	137	43	)	)	PUNCT
iajs-3842	137	44	𝛽	𝛽	NOUN
iajs-3842	137	45	.	.	PUNCT
iajs-3842	138	1	𝑒	𝑒	PROPN
iajs-3842	138	2	(	(	PUNCT
iajs-3842	138	3	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	138	4	+	+	ADJ
iajs-3842	138	5	1	1	NUM
iajs-3842	138	6	)	)	PUNCT
iajs-3842	138	7	𝛽	𝛽	NOUN
iajs-3842	138	8	)	)	PUNCT
iajs-3842	138	9	(	(	PUNCT
iajs-3842	138	10	−𝛽	−𝛽	PROPN
iajs-3842	138	11	−	−	PROPN
iajs-3842	138	12	1)𝑥	1)𝑥	NUM
iajs-3842	138	13	=	=	SYM
iajs-3842	138	14	𝑊	𝑊	PROPN
iajs-3842	138	15	(	(	PUNCT
iajs-3842	138	16	(	(	PUNCT
iajs-3842	138	17	1−𝑢)(𝛽2	1−𝑢)(𝛽2	NUM
iajs-3842	138	18	+	+	NOUN
iajs-3842	138	19	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	138	20	)	)	PUNCT
iajs-3842	138	21	𝛽	𝛽	NOUN
iajs-3842	138	22	.	.	PUNCT
iajs-3842	139	1	𝑒	𝑒	PROPN
iajs-3842	139	2	(	(	PUNCT
iajs-3842	139	3	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	139	4	+	+	ADJ
iajs-3842	139	5	1	1	NUM
iajs-3842	139	6	)	)	PUNCT
iajs-3842	139	7	𝛽	𝛽	NOUN
iajs-3842	139	8	)	)	PUNCT
iajs-3842	139	9	−	−	PROPN
iajs-3842	140	1	(	(	PUNCT
iajs-3842	140	2	𝛽2	𝛽2	PROPN
iajs-3842	140	3	+	+	NOUN
iajs-3842	140	4	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	140	5	)	)	PUNCT
iajs-3842	140	6	𝛽	𝛽	NOUN
iajs-3842	140	7	𝑥	𝑥	NOUN
iajs-3842	140	8	=	=	SYM
iajs-3842	140	9	𝑊	𝑊	PROPN
iajs-3842	140	10	(	(	PUNCT
iajs-3842	140	11	(	(	PUNCT
iajs-3842	140	12	1−𝑢)(𝛽2	1−𝑢)(𝛽2	NUM
iajs-3842	140	13	+	+	NOUN
iajs-3842	140	14	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	140	15	)	)	PUNCT
iajs-3842	140	16	𝛽	𝛽	NOUN
iajs-3842	140	17	∙𝑒	∙𝑒	PROPN
iajs-3842	140	18	(	(	PUNCT
iajs-3842	140	19	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PROPN
iajs-3842	140	20	+	+	NOUN
iajs-3842	140	21	1	1	NUM
iajs-3842	140	22	)	)	PUNCT
iajs-3842	140	23	𝛽	𝛽	NOUN
iajs-3842	140	24	)	)	PUNCT
iajs-3842	140	25	−	−	PROPN
iajs-3842	140	26	(	(	PUNCT
iajs-3842	140	27	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	140	28	+	+	NOUN
iajs-3842	140	29	1	1	NUM
iajs-3842	140	30	)	)	PUNCT
iajs-3842	140	31	𝛽	𝛽	NOUN
iajs-3842	140	32	(	(	PUNCT
iajs-3842	140	33	−𝛽−1	−𝛽−1	NUM
iajs-3842	140	34	)	)	PUNCT
iajs-3842	140	35	.	.	PUNCT
iajs-3842	141	1	(	(	PUNCT
iajs-3842	141	2	10	10	NUM
iajs-3842	141	3	)	)	PUNCT
iajs-3842	141	4	a	a	DET
iajs-3842	141	5	special	special	ADJ
iajs-3842	141	6	case	case	NOUN
iajs-3842	141	7	from	from	ADP
iajs-3842	141	8	quantity	quantity	NOUN
iajs-3842	141	9	function	function	NOUN
iajs-3842	141	10	(	(	PUNCT
iajs-3842	141	11	10	10	NUM
iajs-3842	141	12	)	)	PUNCT
iajs-3842	141	13	is	be	AUX
iajs-3842	141	14	the	the	DET
iajs-3842	141	15	median	median	PROPN
iajs-3842	141	16	whene	whene	PROPN
iajs-3842	141	17	𝑢	𝑢	PROPN
iajs-3842	141	18	=	=	NOUN
iajs-3842	141	19	1	1	NUM
iajs-3842	141	20	2	2	NUM
iajs-3842	141	21	.	.	PUNCT
iajs-3842	142	1	𝑥	𝑥	X
iajs-3842	142	2	=	=	SYM
iajs-3842	142	3	𝑊	𝑊	PROPN
iajs-3842	142	4	(	(	PUNCT
iajs-3842	142	5	(	(	PUNCT
iajs-3842	142	6	1−	1−	NUM
iajs-3842	142	7	1	1	NUM
iajs-3842	142	8	2	2	NUM
iajs-3842	142	9	)	)	PUNCT
iajs-3842	142	10	(	(	PUNCT
iajs-3842	142	11	𝛽2	𝛽2	PROPN
iajs-3842	142	12	+	+	NOUN
iajs-3842	142	13	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	142	14	)	)	PUNCT
iajs-3842	142	15	𝛽	𝛽	NOUN
iajs-3842	142	16	∙𝑒	∙𝑒	PROPN
iajs-3842	142	17	(	(	PUNCT
iajs-3842	142	18	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PROPN
iajs-3842	142	19	+	+	NOUN
iajs-3842	142	20	1	1	NUM
iajs-3842	142	21	)	)	PUNCT
iajs-3842	142	22	𝛽	𝛽	NOUN
iajs-3842	142	23	)	)	PUNCT
iajs-3842	142	24	−	−	PROPN
iajs-3842	142	25	(	(	PUNCT
iajs-3842	142	26	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	142	27	+	+	NOUN
iajs-3842	142	28	1	1	NUM
iajs-3842	142	29	)	)	PUNCT
iajs-3842	142	30	𝛽	𝛽	NOUN
iajs-3842	142	31	(	(	PUNCT
iajs-3842	142	32	−𝛽−1	−𝛽−1	NUM
iajs-3842	142	33	)	)	PUNCT
iajs-3842	142	34	𝑥	𝑥	NOUN
iajs-3842	143	1	=	=	SYM
iajs-3842	143	2	𝑊	𝑊	PROPN
iajs-3842	143	3	(	(	PUNCT
iajs-3842	143	4	(	(	PUNCT
iajs-3842	143	5	1	1	NUM
iajs-3842	143	6	2	2	NUM
iajs-3842	143	7	)	)	PUNCT
iajs-3842	143	8	(	(	PUNCT
iajs-3842	143	9	𝛽2	𝛽2	PROPN
iajs-3842	143	10	+	+	NOUN
iajs-3842	143	11	1)(−𝛽−1	1)(−𝛽−1	NUM
iajs-3842	143	12	)	)	PUNCT
iajs-3842	143	13	𝛽	𝛽	NOUN
iajs-3842	143	14	∙𝑒	∙𝑒	PROPN
iajs-3842	143	15	(	(	PUNCT
iajs-3842	143	16	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PROPN
iajs-3842	143	17	+	+	NOUN
iajs-3842	143	18	1	1	NUM
iajs-3842	143	19	)	)	PUNCT
iajs-3842	143	20	𝛽	𝛽	NOUN
iajs-3842	143	21	)	)	PUNCT
iajs-3842	143	22	−	−	PROPN
iajs-3842	143	23	(	(	PUNCT
iajs-3842	143	24	−𝛽−1)(𝛽2	−𝛽−1)(𝛽2	PUNCT
iajs-3842	143	25	+	+	NOUN
iajs-3842	143	26	1	1	NUM
iajs-3842	143	27	)	)	PUNCT
iajs-3842	143	28	𝛽	𝛽	NOUN
iajs-3842	143	29	(	(	PUNCT
iajs-3842	143	30	−𝛽−1	−𝛽−1	NUM
iajs-3842	143	31	)	)	PUNCT
iajs-3842	143	32	2.2.3	2.2.3	NUM
iajs-3842	143	33	.	.	PUNCT
iajs-3842	144	1	moments	moment	NOUN
iajs-3842	144	2	about	about	ADP
iajs-3842	144	3	the	the	DET
iajs-3842	144	4	origin	origin	NOUN
iajs-3842	144	5	one	one	NUM
iajs-3842	144	6	of	of	ADP
iajs-3842	144	7	the	the	DET
iajs-3842	144	8	most	most	ADV
iajs-3842	144	9	important	important	ADJ
iajs-3842	144	10	distribution	distribution	NOUN
iajs-3842	144	11	properties	property	NOUN
iajs-3842	144	12	is	be	AUX
iajs-3842	144	13	moments	moment	NOUN
iajs-3842	144	14	,	,	PUNCT
iajs-3842	144	15	as	as	SCONJ
iajs-3842	144	16	they	they	PRON
iajs-3842	144	17	play	play	VERB
iajs-3842	144	18	a	a	DET
iajs-3842	144	19	role	role	NOUN
iajs-3842	144	20	in	in	ADP
iajs-3842	144	21	the	the	DET
iajs-3842	144	22	determination	determination	NOUN
iajs-3842	144	23	of	of	ADP
iajs-3842	144	24	many	many	ADJ
iajs-3842	144	25	other	other	ADJ
iajs-3842	144	26	distribution	distribution	NOUN
iajs-3842	144	27	properties	property	NOUN
iajs-3842	144	28	,	,	PUNCT
iajs-3842	144	29	such	such	ADJ
iajs-3842	144	30	as	as	ADP
iajs-3842	144	31	(	(	PUNCT
iajs-3842	144	32	mean	mean	ADJ
iajs-3842	144	33	,	,	PUNCT
iajs-3842	144	34	variance	variance	NOUN
iajs-3842	144	35	,	,	PUNCT
iajs-3842	144	36	skewness	skewness	NOUN
iajs-3842	144	37	,	,	PUNCT
iajs-3842	144	38	and	and	CCONJ
iajs-3842	144	39	kurtosis	kurtosis	NOUN
iajs-3842	144	40	)	)	PUNCT
iajs-3842	144	41	.	.	PUNCT
iajs-3842	145	1	the	the	DET
iajs-3842	145	2	moments	moment	NOUN
iajs-3842	145	3	of	of	ADP
iajs-3842	145	4	(	(	PUNCT
iajs-3842	145	5	shwd	shwd	PROPN
iajs-3842	145	6	)	)	PUNCT
iajs-3842	145	7	can	can	AUX
iajs-3842	145	8	be	be	AUX
iajs-3842	145	9	determined	determine	VERB
iajs-3842	145	10	as	as	SCONJ
iajs-3842	145	11	follows	follow	VERB
iajs-3842	145	12	:	:	PUNCT
iajs-3842	145	13	ihjpas	ihjpas	PROPN
iajs-3842	145	14	.	.	PUNCT
iajs-3842	146	1	2025,38(2	2025,38(2	PROPN
iajs-3842	146	2	)	)	PUNCT
iajs-3842	146	3	395	395	NUM
iajs-3842	146	4	𝑀𝑟	𝑀𝑟	PROPN
iajs-3842	146	5	′	′	NUM
iajs-3842	146	6	(	(	PUNCT
iajs-3842	146	7	𝑥	𝑥	NOUN
iajs-3842	146	8	)	)	PUNCT
iajs-3842	146	9	=	=	SYM
iajs-3842	147	1	∫	∫	PROPN
iajs-3842	147	2	𝑥𝑟	𝑥𝑟	X
iajs-3842	148	1	∞	∞	PROPN
iajs-3842	148	2	0	0	NUM
iajs-3842	148	3	𝑓(𝑥)𝑑𝑥	𝑓(𝑥)𝑑𝑥	PROPN
iajs-3842	148	4	=	=	SYM
iajs-3842	148	5	∫	∫	PROPN
iajs-3842	148	6	𝑥𝑟	𝑥𝑟	X
iajs-3842	149	1	∞	∞	PROPN
iajs-3842	149	2	0	0	PUNCT
iajs-3842	149	3	(	(	PUNCT
iajs-3842	149	4	𝛽𝑒−(𝛽𝑥+𝑥𝜆	𝛽𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	149	5	)	)	PUNCT
iajs-3842	149	6	+	+	PUNCT
iajs-3842	149	7	𝜆𝑥𝜆−1𝑒−(𝛽𝑥+𝑥𝜆	𝜆𝑥𝜆−1𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	149	8	)	)	PUNCT
iajs-3842	150	1	+	+	NUM
iajs-3842	150	2	𝛽2𝑥	𝛽2𝑥	ADJ
iajs-3842	150	3	𝛽2	𝛽2	NOUN
iajs-3842	150	4	+	+	CCONJ
iajs-3842	150	5	1	1	NUM
iajs-3842	150	6	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	150	7	)	)	PUNCT
iajs-3842	151	1	+	+	CCONJ
iajs-3842	151	2	𝛽𝜆	𝛽𝜆	X
iajs-3842	151	3	𝑥𝜆	𝑥𝜆	ADP
iajs-3842	151	4	𝛽2	𝛽2	PROPN
iajs-3842	151	5	+	+	CCONJ
iajs-3842	151	6	1	1	NUM
iajs-3842	151	7	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	151	8	)	)	PUNCT
iajs-3842	151	9	−	−	PROPN
iajs-3842	151	10	𝛽	𝛽	PROPN
iajs-3842	151	11	𝛽2	𝛽2	NOUN
iajs-3842	151	12	+	+	CCONJ
iajs-3842	151	13	1	1	NUM
iajs-3842	151	14	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	151	15	)	)	PUNCT
iajs-3842	151	16	)	)	PUNCT
iajs-3842	151	17	𝑑𝑥	𝑑𝑥	AUX
iajs-3842	151	18	let	let	VERB
iajs-3842	151	19	𝑒−𝑥𝜆	𝑒−𝑥𝜆	NOUN
iajs-3842	151	20	=	=	SYM
iajs-3842	151	21	∑	∑	PUNCT
iajs-3842	151	22	(	(	PUNCT
iajs-3842	151	23	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	151	24	𝑗	𝑗	PROPN
iajs-3842	151	25	!	!	PUNCT
iajs-3842	151	26	∞	∞	PROPN
iajs-3842	152	1	𝑗=0	𝑗=0	PROPN
iajs-3842	153	1	𝑥𝜆𝑗	𝑥𝜆𝑗	NOUN
iajs-3842	153	2	(	(	PUNCT
iajs-3842	153	3	28	28	NUM
iajs-3842	153	4	)	)	PUNCT
iajs-3842	153	5	∫	∫	NOUN
iajs-3842	154	1	𝑥𝑟	𝑥𝑟	X
iajs-3842	154	2	∞	∞	NOUN
iajs-3842	154	3	0	0	NUM
iajs-3842	154	4	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	154	5	)	)	PUNCT
iajs-3842	155	1	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	155	2	=	=	SYM
iajs-3842	155	3	∑	∑	PUNCT
iajs-3842	155	4	(	(	PUNCT
iajs-3842	155	5	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	155	6	𝑗	𝑗	PROPN
iajs-3842	155	7	!	!	PUNCT
iajs-3842	155	8	∞	∞	NUM
iajs-3842	155	9	𝑗=0	𝑗=0	PROPN
iajs-3842	156	1	(	(	PUNCT
iajs-3842	156	2	∫	∫	PROPN
iajs-3842	156	3	𝛽𝑥𝑟+𝜆𝑗	𝛽𝑥𝑟+𝜆𝑗	X
iajs-3842	156	4	∞	∞	NUM
iajs-3842	156	5	0	0	NUM
iajs-3842	156	6	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	X
iajs-3842	157	1	+	+	CCONJ
iajs-3842	157	2	∫	∫	PROPN
iajs-3842	157	3	𝜆𝑥𝑟+𝜆(𝑗+1)−1	𝜆𝑥𝑟+𝜆(𝑗+1)−1	PRON
iajs-3842	157	4	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	X
iajs-3842	157	5	∞	∞	X
iajs-3842	157	6	0	0	NUM
iajs-3842	158	1	+	+	NUM
iajs-3842	158	2	∫	∫	PROPN
iajs-3842	158	3	𝛽2	𝛽2	PROPN
iajs-3842	158	4	𝛽2	𝛽2	PROPN
iajs-3842	158	5	+	+	CCONJ
iajs-3842	158	6	1	1	NUM
iajs-3842	158	7	𝑥𝑟+𝜆𝑗+1	𝑥𝑟+𝜆𝑗+1	NUM
iajs-3842	158	8	∞	∞	NUM
iajs-3842	158	9	0	0	NUM
iajs-3842	158	10	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	X
iajs-3842	158	11	+	+	CCONJ
iajs-3842	158	12	∫	∫	X
iajs-3842	158	13	𝛽𝜆	𝛽𝜆	NOUN
iajs-3842	158	14	𝛽2	𝛽2	NOUN
iajs-3842	158	15	+	+	CCONJ
iajs-3842	158	16	1	1	NUM
iajs-3842	158	17	𝑥𝑟+𝜆(𝑗+1	𝑥𝑟+𝜆(𝑗+1	NUM
iajs-3842	158	18	)	)	PUNCT
iajs-3842	158	19	∞	∞	NUM
iajs-3842	158	20	0	0	NUM
iajs-3842	158	21	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	NOUN
iajs-3842	158	22	−	−	PROPN
iajs-3842	158	23	∫	∫	PROPN
iajs-3842	158	24	𝛽	𝛽	PROPN
iajs-3842	158	25	𝛽2	𝛽2	PROPN
iajs-3842	158	26	+	+	CCONJ
iajs-3842	158	27	1	1	NUM
iajs-3842	158	28	𝑥𝑟+𝜆𝑗	𝑥𝑟+𝜆𝑗	SYM
iajs-3842	158	29	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	X
iajs-3842	158	30	∞	∞	PROPN
iajs-3842	158	31	0	0	NUM
iajs-3842	158	32	)	)	PUNCT
iajs-3842	158	33	let	let	VERB
iajs-3842	158	34	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	158	35	=	=	NOUN
iajs-3842	158	36	𝑦	𝑦	PROPN
iajs-3842	158	37	,	,	PUNCT
iajs-3842	158	38	then	then	ADV
iajs-3842	158	39	𝑥	𝑥	PROPN
iajs-3842	158	40	=	=	PUNCT
iajs-3842	158	41	𝑦	𝑦	SYM
iajs-3842	158	42	𝛽	𝛽	NOUN
iajs-3842	158	43	and	and	CCONJ
iajs-3842	158	44	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	158	45	=	=	SYM
iajs-3842	158	46	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	158	47	𝛽	𝛽	PROPN
iajs-3842	158	48	,	,	PUNCT
iajs-3842	158	49	and	and	CCONJ
iajs-3842	158	50	since	since	SCONJ
iajs-3842	158	51	γ(𝛽	γ(𝛽	PROPN
iajs-3842	158	52	)	)	PUNCT
iajs-3842	158	53	=	=	PUNCT
iajs-3842	159	1	∫	∫	PROPN
iajs-3842	159	2	𝑥𝛽−1∞	𝑥𝛽−1∞	PROPN
iajs-3842	159	3	0	0	PUNCT
iajs-3842	160	1	𝑒−𝑥𝑑𝑥.	𝑒−𝑥𝑑𝑥.	VERB
iajs-3842	160	2	𝑀𝑟	𝑀𝑟	PROPN
iajs-3842	160	3	′	′	NUM
iajs-3842	161	1	(	(	PUNCT
iajs-3842	161	2	𝑥	𝑥	NOUN
iajs-3842	161	3	)	)	PUNCT
iajs-3842	161	4	=	=	SYM
iajs-3842	161	5	∑	∑	PUNCT
iajs-3842	161	6	(	(	PUNCT
iajs-3842	161	7	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	161	8	𝑗	𝑗	PROPN
iajs-3842	161	9	!	!	PUNCT
iajs-3842	161	10	∞	∞	NUM
iajs-3842	162	1	𝑗=0	𝑗=0	PUNCT
iajs-3842	162	2	(	(	PUNCT
iajs-3842	162	3	1	1	NUM
iajs-3842	162	4	𝛽𝑟+𝜆𝑗	𝛽𝑟+𝜆𝑗	NUM
iajs-3842	162	5	∫	∫	PROPN
iajs-3842	162	6	𝑦𝑟+𝜆𝑗	𝑦𝑟+𝜆𝑗	NUM
iajs-3842	162	7	∞	∞	PROPN
iajs-3842	162	8	0	0	NUM
iajs-3842	162	9	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	163	1	+	+	CCONJ
iajs-3842	163	2	𝜆	𝜆	X
iajs-3842	163	3	𝛽𝑟+𝜆(𝑗+1	𝛽𝑟+𝜆(𝑗+1	NUM
iajs-3842	163	4	)	)	PUNCT
iajs-3842	163	5	∫	∫	PROPN
iajs-3842	163	6	𝑦𝑟+𝜆(𝑗+1)−1	𝑦𝑟+𝜆(𝑗+1)−1	PROPN
iajs-3842	163	7	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	PROPN
iajs-3842	163	8	∞	∞	PROPN
iajs-3842	163	9	0	0	PUNCT
iajs-3842	164	1	+	+	CCONJ
iajs-3842	164	2	𝛽	𝛽	PROPN
iajs-3842	164	3	(	(	PUNCT
iajs-3842	164	4	𝛽2	𝛽2	PROPN
iajs-3842	164	5	+	+	SYM
iajs-3842	164	6	1)𝛽𝑟+𝜆𝑗+1	1)𝛽𝑟+𝜆𝑗+1	NUM
iajs-3842	164	7	∫	∫	NOUN
iajs-3842	165	1	𝑦𝑟+𝜆𝑗+1	𝑦𝑟+𝜆𝑗+1	ADP
iajs-3842	165	2	∞	∞	PROPN
iajs-3842	165	3	0	0	NUM
iajs-3842	165	4	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	165	5	+	+	CCONJ
iajs-3842	165	6	𝜆	𝜆	X
iajs-3842	165	7	(	(	PUNCT
iajs-3842	165	8	𝛽2	𝛽2	PROPN
iajs-3842	165	9	+	+	CCONJ
iajs-3842	165	10	1)𝛽𝑟+𝜆(𝑗+1	1)𝛽𝑟+𝜆(𝑗+1	NUM
iajs-3842	165	11	)	)	PUNCT
iajs-3842	165	12	∫	∫	NOUN
iajs-3842	165	13	𝑦𝑟+𝜆(𝑗+1	𝑦𝑟+𝜆(𝑗+1	PROPN
iajs-3842	165	14	)	)	PUNCT
iajs-3842	165	15	∞	∞	PROPN
iajs-3842	165	16	0	0	NUM
iajs-3842	165	17	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	165	18	−	−	NOUN
iajs-3842	165	19	1	1	NUM
iajs-3842	165	20	(	(	PUNCT
iajs-3842	165	21	𝛽2	𝛽2	NOUN
iajs-3842	165	22	+	+	CCONJ
iajs-3842	165	23	1)𝛽𝑟+𝜆𝑗	1)𝛽𝑟+𝜆𝑗	NUM
iajs-3842	165	24	∫	∫	NOUN
iajs-3842	165	25	𝑦𝑟+𝜆𝑗	𝑦𝑟+𝜆𝑗	NUM
iajs-3842	165	26	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	165	27	∞	∞	PROPN
iajs-3842	165	28	0	0	NUM
iajs-3842	165	29	)	)	PUNCT
iajs-3842	166	1	𝑀𝑟	𝑀𝑟	NOUN
iajs-3842	166	2	′	′	NUM
iajs-3842	166	3	(	(	PUNCT
iajs-3842	166	4	𝑥	𝑥	NOUN
iajs-3842	166	5	)	)	PUNCT
iajs-3842	166	6	=	=	SYM
iajs-3842	166	7	∑	∑	PUNCT
iajs-3842	166	8	(	(	PUNCT
iajs-3842	166	9	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	166	10	𝑗	𝑗	PROPN
iajs-3842	166	11	!	!	PUNCT
iajs-3842	166	12	∞	∞	NUM
iajs-3842	167	1	𝑗=0	𝑗=0	PROPN
iajs-3842	167	2	(	(	PUNCT
iajs-3842	167	3	𝛤(𝑟+𝜆𝑗+1	𝛤(𝑟+𝜆𝑗+1	ADV
iajs-3842	167	4	)	)	PUNCT
iajs-3842	168	1	𝛽𝑟+𝜆𝑗	𝛽𝑟+𝜆𝑗	ADP
iajs-3842	168	2	+	+	NUM
iajs-3842	168	3	𝜆∙γ(𝑟+𝜆(𝑗+1	𝜆∙γ(𝑟+𝜆(𝑗+1	NOUN
iajs-3842	168	4	)	)	PUNCT
iajs-3842	168	5	)	)	PUNCT
iajs-3842	169	1	𝛽𝑟+𝜆(𝑗+1	𝛽𝑟+𝜆(𝑗+1	NUM
iajs-3842	169	2	)	)	PUNCT
iajs-3842	169	3	+	+	NUM
iajs-3842	169	4	γ(𝑟+𝜆𝑗+1)−γ(𝑟+𝜆𝑗+2	γ(𝑟+𝜆𝑗+1)−γ(𝑟+𝜆𝑗+2	NOUN
iajs-3842	169	5	)	)	PUNCT
iajs-3842	169	6	(	(	PUNCT
iajs-3842	169	7	𝛽2	𝛽2	PROPN
iajs-3842	169	8	+	+	PROPN
iajs-3842	169	9	1)𝛽𝑟+𝜆𝑗	1)𝛽𝑟+𝜆𝑗	NUM
iajs-3842	169	10	+	+	NOUN
iajs-3842	169	11	𝜆	𝜆	ADP
iajs-3842	169	12	∙γ(𝑟+𝜆(𝑗+1)+1	∙γ(𝑟+𝜆(𝑗+1)+1	NOUN
iajs-3842	169	13	)	)	PUNCT
iajs-3842	169	14	(	(	PUNCT
iajs-3842	169	15	𝛽2	𝛽2	PROPN
iajs-3842	169	16	+	+	PROPN
iajs-3842	169	17	1)𝛽𝑟+𝜆(𝑗+1	1)𝛽𝑟+𝜆(𝑗+1	NUM
iajs-3842	169	18	)	)	PUNCT
iajs-3842	169	19	)	)	PUNCT
iajs-3842	169	20	(	(	PUNCT
iajs-3842	169	21	11	11	NUM
iajs-3842	169	22	)	)	PUNCT
iajs-3842	169	23	as	as	ADP
iajs-3842	169	24	a	a	DET
iajs-3842	169	25	direct	direct	ADJ
iajs-3842	169	26	result	result	NOUN
iajs-3842	169	27	,	,	PUNCT
iajs-3842	169	28	it	it	PRON
iajs-3842	169	29	can	can	AUX
iajs-3842	169	30	be	be	AUX
iajs-3842	169	31	found𝐸(𝑥	found𝐸(𝑥	PROPN
iajs-3842	169	32	)	)	PUNCT
iajs-3842	170	1	=	=	PUNCT
iajs-3842	171	1	𝑀1	𝑀1	PROPN
iajs-3842	171	2	′	′	NUM
iajs-3842	171	3	(	(	PUNCT
iajs-3842	171	4	𝑥	𝑥	NOUN
iajs-3842	171	5	)	)	PUNCT
iajs-3842	171	6	,	,	PUNCT
iajs-3842	171	7	𝐸(𝑥2	𝐸(𝑥2	NOUN
iajs-3842	171	8	)	)	PUNCT
iajs-3842	172	1	=	=	SYM
iajs-3842	172	2	𝑀2	𝑀2	PROPN
iajs-3842	172	3	′	′	NUM
iajs-3842	172	4	(	(	PUNCT
iajs-3842	172	5	𝑥	𝑥	NOUN
iajs-3842	172	6	)	)	PUNCT
iajs-3842	172	7	,	,	PUNCT
iajs-3842	172	8	and	and	CCONJ
iajs-3842	172	9	𝑣𝑎𝑟(𝑥	𝑣𝑎𝑟(𝑥	NUM
iajs-3842	172	10	)	)	PUNCT
iajs-3842	172	11	as	as	SCONJ
iajs-3842	172	12	follows	follow	VERB
iajs-3842	172	13	:	:	PUNCT
iajs-3842	172	14	𝐸(𝑥	𝐸(𝑥	NOUN
iajs-3842	172	15	)	)	PUNCT
iajs-3842	172	16	=	=	PUNCT
iajs-3842	172	17	∑	∑	PUNCT
iajs-3842	172	18	(	(	PUNCT
iajs-3842	172	19	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	172	20	𝑗	𝑗	PROPN
iajs-3842	172	21	!	!	PUNCT
iajs-3842	172	22	∞	∞	NUM
iajs-3842	173	1	𝑗=0	𝑗=0	PROPN
iajs-3842	173	2	(	(	PUNCT
iajs-3842	173	3	γ(𝜆𝑗+2	γ(𝜆𝑗+2	NOUN
iajs-3842	173	4	)	)	PUNCT
iajs-3842	173	5	𝛽𝜆𝑗+1	𝛽𝜆𝑗+1	ADP
iajs-3842	173	6	+	+	CCONJ
iajs-3842	173	7	𝜆	𝜆	ADP
iajs-3842	173	8	∙	∙	PROPN
iajs-3842	173	9	γ(𝜆(𝑗+1)+1	γ(𝜆(𝑗+1)+1	NOUN
iajs-3842	173	10	)	)	PUNCT
iajs-3842	173	11	𝛽𝜆(𝑗+1)+1	𝛽𝜆(𝑗+1)+1	NOUN
iajs-3842	173	12	+	+	NUM
iajs-3842	173	13	γ(𝜆𝑗+2	γ(𝜆𝑗+2	NOUN
iajs-3842	173	14	)	)	PUNCT
iajs-3842	173	15	−	−	ADP
iajs-3842	173	16	γ(𝜆𝑗+3	γ(𝜆𝑗+3	NOUN
iajs-3842	173	17	)	)	PUNCT
iajs-3842	173	18	(	(	PUNCT
iajs-3842	173	19	𝛽2	𝛽2	PROPN
iajs-3842	173	20	+	+	CCONJ
iajs-3842	173	21	1)𝛽𝜆𝑗+1	1)𝛽𝜆𝑗+1	NUM
iajs-3842	173	22	+	+	CCONJ
iajs-3842	173	23	𝜆	𝜆	ADP
iajs-3842	173	24	∙	∙	PROPN
iajs-3842	173	25	γ(𝜆(𝑗+1)+2	γ(𝜆(𝑗+1)+2	NUM
iajs-3842	173	26	)	)	PUNCT
iajs-3842	173	27	(	(	PUNCT
iajs-3842	173	28	𝛽2	𝛽2	PROPN
iajs-3842	173	29	+	+	CCONJ
iajs-3842	173	30	1)𝛽𝜆(𝑗+1)+1	1)𝛽𝜆(𝑗+1)+1	NOUN
iajs-3842	173	31	)	)	PUNCT
iajs-3842	173	32	𝐸(𝑥2	𝐸(𝑥2	NOUN
iajs-3842	173	33	)	)	PUNCT
iajs-3842	174	1	=	=	PUNCT
iajs-3842	174	2	∑	∑	PUNCT
iajs-3842	174	3	(	(	PUNCT
iajs-3842	174	4	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	174	5	𝑗	𝑗	PROPN
iajs-3842	174	6	!	!	PUNCT
iajs-3842	175	1	∞	∞	NUM
iajs-3842	175	2	𝑗=0	𝑗=0	PROPN
iajs-3842	175	3	(	(	PUNCT
iajs-3842	175	4	𝛤(𝜆𝑗+3	𝛤(𝜆𝑗+3	NOUN
iajs-3842	175	5	)	)	PUNCT
iajs-3842	175	6	𝛽𝜆𝑗+2	𝛽𝜆𝑗+2	NOUN
iajs-3842	175	7	+	+	CCONJ
iajs-3842	175	8	𝜆	𝜆	DET
iajs-3842	175	9	∙	∙	PROPN
iajs-3842	175	10	𝛤(𝜆(𝑗+1)+2	𝛤(𝜆(𝑗+1)+2	PROPN
iajs-3842	175	11	)	)	PUNCT
iajs-3842	175	12	𝛽𝜆(𝑗+1)+2	𝛽𝜆(𝑗+1)+2	NOUN
iajs-3842	175	13	+	+	CCONJ
iajs-3842	175	14	𝛤(𝜆𝑗+3	𝛤(𝜆𝑗+3	NOUN
iajs-3842	175	15	)	)	PUNCT
iajs-3842	175	16	−	−	PROPN
iajs-3842	175	17	𝛤(𝜆𝑗+4	𝛤(𝜆𝑗+4	NOUN
iajs-3842	175	18	)	)	PUNCT
iajs-3842	175	19	(	(	PUNCT
iajs-3842	175	20	𝛽2	𝛽2	PROPN
iajs-3842	175	21	+	+	CCONJ
iajs-3842	175	22	1)𝛽𝜆𝑗+2	1)𝛽𝜆𝑗+2	NUM
iajs-3842	175	23	+	+	CCONJ
iajs-3842	175	24	𝜆	𝜆	PROPN
iajs-3842	175	25	∙	∙	PROPN
iajs-3842	175	26	𝛤(𝜆(𝑗+1)+3	𝛤(𝜆(𝑗+1)+3	PROPN
iajs-3842	175	27	)	)	PUNCT
iajs-3842	175	28	(	(	PUNCT
iajs-3842	175	29	𝛽2	𝛽2	PROPN
iajs-3842	175	30	+	+	CCONJ
iajs-3842	175	31	1)𝛽𝑟+𝜆(𝑗+1)+2	1)𝛽𝑟+𝜆(𝑗+1)+2	NUM
iajs-3842	175	32	)	)	PUNCT
iajs-3842	175	33	𝑣𝑎𝑟(𝑥	𝑣𝑎𝑟(𝑥	PROPN
iajs-3842	175	34	)	)	PUNCT
iajs-3842	175	35	=	=	SYM
iajs-3842	176	1	𝑀2	𝑀2	PROPN
iajs-3842	176	2	′	′	NUM
iajs-3842	176	3	(	(	PUNCT
iajs-3842	176	4	𝑥	𝑥	NOUN
iajs-3842	176	5	)	)	PUNCT
iajs-3842	176	6	−	−	PROPN
iajs-3842	176	7	(	(	PUNCT
iajs-3842	176	8	𝑀1	𝑀1	NOUN
iajs-3842	176	9	′	′	NUM
iajs-3842	177	1	(	(	PUNCT
iajs-3842	177	2	𝑥	𝑥	NOUN
iajs-3842	177	3	)	)	PUNCT
iajs-3842	177	4	)	)	PUNCT
iajs-3842	177	5	2	2	NUM
iajs-3842	177	6	ihjpas	ihjpa	NOUN
iajs-3842	177	7	.	.	PUNCT
iajs-3842	178	1	2025,38(2	2025,38(2	NOUN
iajs-3842	178	2	)	)	PUNCT
iajs-3842	178	3	396	396	NUM
iajs-3842	178	4	2.2.4	2.2.4	NUM
iajs-3842	178	5	.	.	PUNCT
iajs-3842	179	1	coefficients	coefficient	NOUN
iajs-3842	179	2	of	of	ADP
iajs-3842	179	3	skewness	skewness	NOUN
iajs-3842	179	4	and	and	CCONJ
iajs-3842	179	5	kurtosis	kurtosis	VERB
iajs-3842	179	6	depending	depend	VERB
iajs-3842	179	7	on	on	ADP
iajs-3842	179	8	the	the	DET
iajs-3842	179	9	moment	moment	NOUN
iajs-3842	179	10	,	,	PUNCT
iajs-3842	179	11	the	the	DET
iajs-3842	179	12	coefficient	coefficient	NOUN
iajs-3842	179	13	skewness	skewness	NOUN
iajs-3842	179	14	(	(	PUNCT
iajs-3842	179	15	𝐶.	𝐶.	PROPN
iajs-3842	179	16	𝑆	𝑆	PROPN
iajs-3842	179	17	)	)	PUNCT
iajs-3842	179	18	and	and	CCONJ
iajs-3842	179	19	kurtosis(𝐶.	kurtosis(𝐶.	PROPN
iajs-3842	179	20	𝐾	𝐾	PROPN
iajs-3842	179	21	)	)	PUNCT
iajs-3842	179	22	can	can	AUX
iajs-3842	179	23	be	be	AUX
iajs-3842	179	24	found	find	VERB
iajs-3842	179	25	through	through	ADP
iajs-3842	179	26	the	the	DET
iajs-3842	179	27	following	follow	VERB
iajs-3842	179	28	formulas(29	formulas(29	NOUN
iajs-3842	179	29	):	):	PUNCT
iajs-3842	179	30	𝑀3	𝑀3	PROPN
iajs-3842	179	31	′	′	NUM
iajs-3842	179	32	(	(	PUNCT
iajs-3842	179	33	𝑥	𝑥	NOUN
iajs-3842	179	34	)	)	PUNCT
iajs-3842	179	35	=	=	SYM
iajs-3842	179	36	∑	∑	PUNCT
iajs-3842	179	37	(	(	PUNCT
iajs-3842	179	38	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	179	39	𝑗	𝑗	PROPN
iajs-3842	179	40	!	!	PUNCT
iajs-3842	180	1	∞	∞	NUM
iajs-3842	180	2	𝑗=0	𝑗=0	PROPN
iajs-3842	180	3	(	(	PUNCT
iajs-3842	180	4	𝛤(𝜆𝑗+4	𝛤(𝜆𝑗+4	NOUN
iajs-3842	180	5	)	)	PUNCT
iajs-3842	180	6	𝛽𝜆𝑗+3	𝛽𝜆𝑗+3	NOUN
iajs-3842	180	7	+	+	CCONJ
iajs-3842	180	8	𝜆	𝜆	PROPN
iajs-3842	180	9	∙	∙	PROPN
iajs-3842	180	10	𝛤(𝜆(𝑗+1)+3	𝛤(𝜆(𝑗+1)+3	PROPN
iajs-3842	180	11	)	)	PUNCT
iajs-3842	180	12	𝛽𝜆(𝑗+1)+3	𝛽𝜆(𝑗+1)+3	PROPN
iajs-3842	181	1	+	+	CCONJ
iajs-3842	182	1	𝛤(𝜆𝑗+4	𝛤(𝜆𝑗+4	NOUN
iajs-3842	182	2	)	)	PUNCT
iajs-3842	182	3	−	−	PROPN
iajs-3842	182	4	𝛤(𝜆𝑗+5	𝛤(𝜆𝑗+5	PROPN
iajs-3842	182	5	)	)	PUNCT
iajs-3842	182	6	(	(	PUNCT
iajs-3842	182	7	𝛽2	𝛽2	NOUN
iajs-3842	182	8	+	+	CCONJ
iajs-3842	182	9	1)𝛽𝜆𝑗+3	1)𝛽𝜆𝑗+3	NUM
iajs-3842	182	10	+	+	CCONJ
iajs-3842	182	11	𝜆	𝜆	DET
iajs-3842	182	12	∙	∙	PROPN
iajs-3842	182	13	𝛤(𝜆(𝑗+1)+4	𝛤(𝜆(𝑗+1)+4	ADJ
iajs-3842	182	14	)	)	PUNCT
iajs-3842	182	15	(	(	PUNCT
iajs-3842	182	16	𝛽2	𝛽2	PROPN
iajs-3842	182	17	+	+	CCONJ
iajs-3842	182	18	1)𝛽𝑟+𝜆(𝑗+1)+3	1)𝛽𝑟+𝜆(𝑗+1)+3	NUM
iajs-3842	182	19	)	)	PUNCT
iajs-3842	182	20	𝐶.	𝐶.	PROPN
iajs-3842	182	21	𝑆	𝑆	PROPN
iajs-3842	182	22	=	=	PUNCT
iajs-3842	182	23	𝑀3	𝑀3	PROPN
iajs-3842	182	24	′	′	NUM
iajs-3842	182	25	(	(	PUNCT
iajs-3842	182	26	𝑀2	𝑀2	PROPN
iajs-3842	182	27	′	′	NUM
iajs-3842	182	28	)	)	PUNCT
iajs-3842	182	29	3	3	NUM
iajs-3842	182	30	2	2	NUM
iajs-3842	182	31	𝑀4	𝑀4	NOUN
iajs-3842	182	32	′	′	NOUN
iajs-3842	182	33	(	(	PUNCT
iajs-3842	182	34	𝑥	𝑥	NOUN
iajs-3842	182	35	)	)	PUNCT
iajs-3842	183	1	=	=	SYM
iajs-3842	183	2	∑	∑	PUNCT
iajs-3842	183	3	(	(	PUNCT
iajs-3842	183	4	−1)𝑖	−1)𝑖	PROPN
iajs-3842	183	5	𝑖	𝑖	PROPN
iajs-3842	183	6	!	!	PUNCT
iajs-3842	184	1	∞	∞	PROPN
iajs-3842	184	2	𝑖=0	𝑖=0	PROPN
iajs-3842	184	3	(	(	PUNCT
iajs-3842	184	4	𝛤(𝜆𝑗+5	𝛤(𝜆𝑗+5	PROPN
iajs-3842	184	5	)	)	PUNCT
iajs-3842	184	6	𝛽𝜆𝑗+4	𝛽𝜆𝑗+4	X
iajs-3842	184	7	+	+	CCONJ
iajs-3842	184	8	𝜆	𝜆	DET
iajs-3842	184	9	∙	∙	PROPN
iajs-3842	184	10	𝛤(𝜆(𝑗+1)+4	𝛤(𝜆(𝑗+1)+4	ADJ
iajs-3842	184	11	)	)	PUNCT
iajs-3842	184	12	𝛽𝜆(𝑗+1)+4	𝛽𝜆(𝑗+1)+4	NOUN
iajs-3842	184	13	+	+	CCONJ
iajs-3842	184	14	𝛤(𝜆𝑗+5	𝛤(𝜆𝑗+5	PROPN
iajs-3842	184	15	)	)	PUNCT
iajs-3842	184	16	−	−	PROPN
iajs-3842	184	17	𝛤(𝜆𝑗+6	𝛤(𝜆𝑗+6	PROPN
iajs-3842	184	18	)	)	PUNCT
iajs-3842	184	19	(	(	PUNCT
iajs-3842	184	20	𝛽2	𝛽2	PROPN
iajs-3842	184	21	+	+	CCONJ
iajs-3842	184	22	1)𝛽𝜆𝑗+4	1)𝛽𝜆𝑗+4	NUM
iajs-3842	185	1	+	+	CCONJ
iajs-3842	185	2	𝜆	𝜆	ADP
iajs-3842	185	3	∙	∙	PROPN
iajs-3842	185	4	𝛤(𝜆(𝑗+1)+5	𝛤(𝜆(𝑗+1)+5	X
iajs-3842	185	5	)	)	PUNCT
iajs-3842	185	6	(	(	PUNCT
iajs-3842	185	7	𝛽2	𝛽2	PROPN
iajs-3842	185	8	+	+	CCONJ
iajs-3842	185	9	1)𝛽𝜆(𝑗+1)+4	1)𝛽𝜆(𝑗+1)+4	NUM
iajs-3842	185	10	)	)	PUNCT
iajs-3842	185	11	𝐶.	𝐶.	PROPN
iajs-3842	185	12	𝐾	𝐾	PROPN
iajs-3842	185	13	=	=	SYM
iajs-3842	185	14	𝑀4	𝑀4	PROPN
iajs-3842	185	15	′	′	NUM
iajs-3842	185	16	(	(	PUNCT
iajs-3842	185	17	𝑀2	𝑀2	PROPN
iajs-3842	185	18	′	′	NUM
iajs-3842	185	19	)	)	PUNCT
iajs-3842	185	20	2	2	NUM
iajs-3842	185	21	−	−	NUM
iajs-3842	185	22	3	3	NUM
iajs-3842	185	23	table	table	NOUN
iajs-3842	185	24	1	1	NUM
iajs-3842	185	25	.	.	PUNCT
iajs-3842	186	1	the	the	DET
iajs-3842	186	2	first	first	ADJ
iajs-3842	186	3	fourth	fourth	ADJ
iajs-3842	186	4	moments	moment	NOUN
iajs-3842	186	5	,	,	PUNCT
iajs-3842	186	6	variance	variance	NOUN
iajs-3842	186	7	,	,	PUNCT
iajs-3842	186	8	skewness	skewness	NOUN
iajs-3842	186	9	,	,	PUNCT
iajs-3842	186	10	and	and	CCONJ
iajs-3842	186	11	kurtosis	kurtosis	VERB
iajs-3842	186	12	for	for	ADP
iajs-3842	186	13	the	the	DET
iajs-3842	186	14	distribution	distribution	NOUN
iajs-3842	186	15	𝛃	𝛃	X
iajs-3842	186	16	𝛌	𝛌	NOUN
iajs-3842	186	17	𝛍𝟏	𝛍𝟏	NOUN
iajs-3842	186	18	′	′	NUM
iajs-3842	186	19	𝛍𝟐	𝛍𝟐	ADJ
iajs-3842	186	20	′	′	NUM
iajs-3842	186	21	𝛍𝟑	𝛍𝟑	NOUN
iajs-3842	186	22	′	′	NUM
iajs-3842	186	23	𝛍𝟒	𝛍𝟒	ADJ
iajs-3842	186	24	′	′	NUM
iajs-3842	186	25	𝐊	𝐊	PROPN
iajs-3842	186	26	𝐒	𝐒	PROPN
iajs-3842	186	27	𝐯𝐚𝐫	𝐯𝐚𝐫	VERB
iajs-3842	186	28	2	2	NUM
iajs-3842	186	29	0.5	0.5	NUM
iajs-3842	186	30	0.3222	0.3222	NUM
iajs-3842	186	31	0.2719	0.2719	NUM
iajs-3842	186	32	0.3665	0.3665	NUM
iajs-3842	186	33	0.6762	0.6762	NUM
iajs-3842	186	34	6.1462	6.1462	NUM
iajs-3842	186	35	2.5849	2.5849	NUM
iajs-3842	186	36	0.1681	0.1681	NUM
iajs-3842	186	37	0.3	0.3	NUM
iajs-3842	186	38	0.2879	0.2879	NUM
iajs-3842	186	39	0.2668	0.2668	NUM
iajs-3842	186	40	0.3952	0.3952	NUM
iajs-3842	186	41	0.7962	0.7962	NUM
iajs-3842	186	42	8.1838	8.1838	NUM
iajs-3842	186	43	2.8673	2.8673	NUM
iajs-3842	186	44	0.1839	0.1839	NUM
iajs-3842	186	45	0.5	0.5	NUM
iajs-3842	186	46	0.9	0.9	NUM
iajs-3842	186	47	0.8598	0.8598	NUM
iajs-3842	186	48	1.5289	1.5289	NUM
iajs-3842	186	49	4.0855	4.0855	NUM
iajs-3842	186	50	14.5190	14.5190	NUM
iajs-3842	186	51	3.2110	3.2110	NUM
iajs-3842	186	52	2.1610	2.1610	NUM
iajs-3842	186	53	0.7897	0.7897	NUM
iajs-3842	186	54	1.2	1.2	NUM
iajs-3842	186	55	0.8255	0.8255	NUM
iajs-3842	186	56	1.1479	1.1479	NUM
iajs-3842	186	57	2.1874	2.1874	NUM
iajs-3842	186	58	5.2296	5.2296	NUM
iajs-3842	186	59	0.9687	0.9687	NUM
iajs-3842	186	60	1.7785	1.7785	NUM
iajs-3842	186	61	0.4664	0.4664	NUM
iajs-3842	186	62	2.5	2.5	NUM
iajs-3842	186	63	2	2	NUM
iajs-3842	186	64	0.3579	0.3579	NUM
iajs-3842	186	65	0.2177	0.2177	NUM
iajs-3842	186	66	0.1765	0.1765	NUM
iajs-3842	186	67	0.1739	0.1739	NUM
iajs-3842	186	68	0.6687	0.6687	NUM
iajs-3842	186	69	1.7376	1.7376	NUM
iajs-3842	186	70	0.0896	0.0896	NUM
iajs-3842	186	71	3	3	NUM
iajs-3842	186	72	0.3754	0.3754	NUM
iajs-3842	186	73	0.2303	0.2303	NUM
iajs-3842	186	74	0.1792	0.1792	NUM
iajs-3842	186	75	0.1620	0.1620	NUM
iajs-3842	186	76	0.0543	0.0543	NUM
iajs-3842	186	77	1.6218	1.6218	NUM
iajs-3842	186	78	0.0893	0.0893	NUM
iajs-3842	186	79	since	since	SCONJ
iajs-3842	186	80	the	the	DET
iajs-3842	186	81	values	value	NOUN
iajs-3842	186	82	of	of	ADP
iajs-3842	186	83	skewness	skewness	NOUN
iajs-3842	186	84	are	be	AUX
iajs-3842	186	85	positive	positive	ADJ
iajs-3842	186	86	,	,	PUNCT
iajs-3842	186	87	the	the	DET
iajs-3842	186	88	distribution	distribution	NOUN
iajs-3842	186	89	is	be	AUX
iajs-3842	186	90	skewed	skew	VERB
iajs-3842	186	91	to	to	ADP
iajs-3842	186	92	the	the	DET
iajs-3842	186	93	right	right	NOUN
iajs-3842	186	94	according	accord	VERB
iajs-3842	186	95	to	to	ADP
iajs-3842	186	96	the	the	DET
iajs-3842	186	97	given	give	VERB
iajs-3842	186	98	data	data	NOUN
iajs-3842	186	99	values	value	NOUN
iajs-3842	186	100	.	.	PUNCT
iajs-3842	187	1	the	the	DET
iajs-3842	187	2	flatness	flatness	NOUN
iajs-3842	187	3	depends	depend	VERB
iajs-3842	187	4	on	on	ADP
iajs-3842	187	5	the	the	DET
iajs-3842	187	6	values	value	NOUN
iajs-3842	187	7	of	of	ADP
iajs-3842	187	8	the	the	DET
iajs-3842	187	9	given	give	VERB
iajs-3842	187	10	characteristics	characteristic	NOUN
iajs-3842	187	11	.	.	PUNCT
iajs-3842	188	1	sometimes	sometimes	ADV
iajs-3842	188	2	it	it	PRON
iajs-3842	188	3	is	be	AUX
iajs-3842	188	4	flattened	flatten	VERB
iajs-3842	188	5	for	for	ADP
iajs-3842	188	6	values	value	NOUN
iajs-3842	188	7	above	above	ADP
iajs-3842	188	8	3	3	NUM
iajs-3842	188	9	,	,	PUNCT
iajs-3842	188	10	and	and	CCONJ
iajs-3842	188	11	sometimes	sometimes	ADV
iajs-3842	188	12	it	it	PRON
iajs-3842	188	13	is	be	AUX
iajs-3842	188	14	peaked	peak	VERB
iajs-3842	188	15	for	for	ADP
iajs-3842	188	16	values	value	NOUN
iajs-3842	188	17	below	below	ADP
iajs-3842	188	18	3	3	NUM
iajs-3842	188	19	.	.	PUNCT
iajs-3842	189	1	2.2.5	2.2.5	NUM
iajs-3842	189	2	.	.	PUNCT
iajs-3842	189	3	characteristic	characteristic	ADJ
iajs-3842	189	4	function	function	NOUN
iajs-3842	189	5	𝜙𝑥(𝑖𝑡	𝜙𝑥(𝑖𝑡	NOUN
iajs-3842	189	6	)	)	PUNCT
iajs-3842	189	7	=	=	PUNCT
iajs-3842	190	1	𝐸(𝑒𝑖𝑡𝑥	𝐸(𝑒𝑖𝑡𝑥	PROPN
iajs-3842	190	2	)	)	PUNCT
iajs-3842	190	3	=	=	SYM
iajs-3842	191	1	∫	∫	PROPN
iajs-3842	191	2	𝑒𝑖𝑡𝑥	𝑒𝑖𝑡𝑥	PROPN
iajs-3842	191	3	∞	∞	PROPN
iajs-3842	191	4	0	0	NUM
iajs-3842	192	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	192	2	)	)	PUNCT
iajs-3842	193	1	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	193	2	=	=	SYM
iajs-3842	193	3	∫	∫	PROPN
iajs-3842	193	4	𝑒𝑖𝑡𝑥	𝑒𝑖𝑡𝑥	PROPN
iajs-3842	193	5	∞	∞	PROPN
iajs-3842	193	6	0	0	NUM
iajs-3842	194	1	(	(	PUNCT
iajs-3842	194	2	1	1	NUM
iajs-3842	194	3	+	+	CCONJ
iajs-3842	194	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	194	5	𝛽2	𝛽2	PROPN
iajs-3842	194	6	+	+	CCONJ
iajs-3842	194	7	1	1	NUM
iajs-3842	194	8	)	)	PUNCT
iajs-3842	194	9	(	(	PUNCT
iajs-3842	194	10	𝛽	𝛽	NOUN
iajs-3842	194	11	+	+	CCONJ
iajs-3842	194	12	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	194	13	)	)	PUNCT
iajs-3842	194	14	−	−	PROPN
iajs-3842	194	15	𝛽	𝛽	NOUN
iajs-3842	194	16	𝛽2	𝛽2	NOUN
iajs-3842	194	17	+	+	CCONJ
iajs-3842	194	18	1	1	NUM
iajs-3842	194	19	)	)	PUNCT
iajs-3842	194	20	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	VERB
iajs-3842	194	21	)	)	PUNCT
iajs-3842	194	22	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	194	23	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-3842	194	24	𝑒−𝑥𝛽	𝑒−𝑥𝛽	NOUN
iajs-3842	194	25	=	=	PUNCT
iajs-3842	194	26	∑	∑	PUNCT
iajs-3842	194	27	(	(	PUNCT
iajs-3842	194	28	−1)𝑛	−1)𝑛	X
iajs-3842	194	29	𝑛	𝑛	PROPN
iajs-3842	194	30	!	!	PUNCT
iajs-3842	194	31	∞	∞	NUM
iajs-3842	195	1	𝑛=0	𝑛=0	PROPN
iajs-3842	195	2	𝑥𝜆𝑛	𝑥𝜆𝑛	ADP
iajs-3842	195	3	𝜙𝑥(𝑖𝑡	𝜙𝑥(𝑖𝑡	NOUN
iajs-3842	195	4	)	)	PUNCT
iajs-3842	195	5	=	=	PUNCT
iajs-3842	195	6	∑	∑	PUNCT
iajs-3842	195	7	(	(	PUNCT
iajs-3842	195	8	−1)𝑛	−1)𝑛	X
iajs-3842	195	9	𝑛	𝑛	PROPN
iajs-3842	195	10	!	!	NOUN
iajs-3842	195	11	∞	∞	NUM
iajs-3842	196	1	𝑛=0	𝑛=0	NOUN
iajs-3842	196	2	(	(	PUNCT
iajs-3842	196	3	∫	∫	PROPN
iajs-3842	196	4	𝛽𝑥𝛽𝑛	𝛽𝑥𝛽𝑛	NOUN
iajs-3842	196	5	∞	∞	PROPN
iajs-3842	196	6	0	0	NUM
iajs-3842	196	7	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	196	8	+	+	CCONJ
iajs-3842	196	9	∫	∫	PROPN
iajs-3842	196	10	𝜆𝑥𝜆𝑛+𝜆−1	𝜆𝑥𝜆𝑛+𝜆−1	PROPN
iajs-3842	196	11	∞	∞	PROPN
iajs-3842	196	12	0	0	NUM
iajs-3842	196	13	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	196	14	+	+	CCONJ
iajs-3842	196	15	∫	∫	PROPN
iajs-3842	196	16	(	(	PUNCT
iajs-3842	196	17	𝛽2	𝛽2	PROPN
iajs-3842	196	18	𝛽2	𝛽2	PROPN
iajs-3842	196	19	+	+	CCONJ
iajs-3842	196	20	1	1	NUM
iajs-3842	196	21	)	)	PUNCT
iajs-3842	196	22	𝑥𝜆𝑛+1	𝑥𝜆𝑛+1	ADP
iajs-3842	196	23	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	196	24	∞	∞	NOUN
iajs-3842	196	25	0	0	PUNCT
iajs-3842	197	1	+	+	NUM
iajs-3842	197	2	∫	∫	PROPN
iajs-3842	197	3	(	(	PUNCT
iajs-3842	197	4	𝛽𝜆	𝛽𝜆	NOUN
iajs-3842	197	5	𝛽2	𝛽2	NOUN
iajs-3842	197	6	+	+	CCONJ
iajs-3842	197	7	1	1	NUM
iajs-3842	197	8	)	)	PUNCT
iajs-3842	197	9	𝑥𝜆𝑛+𝜆	𝑥𝜆𝑛+𝜆	PROPN
iajs-3842	197	10	∞	∞	NUM
iajs-3842	197	11	0	0	NUM
iajs-3842	197	12	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	197	13	−	−	PROPN
iajs-3842	197	14	∫	∫	PROPN
iajs-3842	197	15	(	(	PUNCT
iajs-3842	197	16	𝛽	𝛽	PROPN
iajs-3842	197	17	𝛽2	𝛽2	NOUN
iajs-3842	197	18	+	+	ADP
iajs-3842	197	19	1	1	NUM
iajs-3842	197	20	)	)	PUNCT
iajs-3842	197	21	𝑥𝜆𝑛	𝑥𝜆𝑛	VERB
iajs-3842	197	22	∞	∞	PROPN
iajs-3842	197	23	0	0	NUM
iajs-3842	197	24	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑖𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	197	25	)	)	PUNCT
iajs-3842	197	26	ihjpas	ihjpas	PROPN
iajs-3842	197	27	.	.	PUNCT
iajs-3842	198	1	2025,38(2	2025,38(2	PROPN
iajs-3842	198	2	)	)	PUNCT
iajs-3842	198	3	397	397	NUM
iajs-3842	198	4	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-3842	198	5	(	(	PUNCT
iajs-3842	198	6	𝛽	𝛽	NOUN
iajs-3842	198	7	−	−	PROPN
iajs-3842	198	8	𝑖𝑡)𝑥	𝑖𝑡)𝑥	PROPN
iajs-3842	198	9	=	=	SYM
iajs-3842	198	10	𝑦	𝑦	NOUN
iajs-3842	198	11	,	,	PUNCT
iajs-3842	198	12	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3842	198	13	𝑥	𝑥	X
iajs-3842	198	14	=	=	PUNCT
iajs-3842	198	15	𝑦	𝑦	SYM
iajs-3842	198	16	𝛽	𝛽	NOUN
iajs-3842	198	17	−	−	PUNCT
iajs-3842	198	18	𝑖𝑡	𝑖𝑡	NOUN
iajs-3842	198	19	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
iajs-3842	198	20	𝑑𝑥	𝑑𝑥	NOUN
iajs-3842	198	21	=	=	SYM
iajs-3842	198	22	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	198	23	𝛽	𝛽	NOUN
iajs-3842	198	24	−	−	PROPN
iajs-3842	198	25	𝑖𝑡	𝑖𝑡	SYM
iajs-3842	198	26	𝜙𝑥(𝑖𝑡	𝜙𝑥(𝑖𝑡	PROPN
iajs-3842	198	27	)	)	PUNCT
iajs-3842	199	1	=	=	PUNCT
iajs-3842	199	2	∑	∑	PUNCT
iajs-3842	199	3	(	(	PUNCT
iajs-3842	199	4	−1)𝑛	−1)𝑛	X
iajs-3842	199	5	𝑛	𝑛	PROPN
iajs-3842	199	6	!	!	NOUN
iajs-3842	199	7	∞	∞	NUM
iajs-3842	200	1	𝑛=0	𝑛=0	NOUN
iajs-3842	200	2	(	(	PUNCT
iajs-3842	200	3	𝛽	𝛽	NOUN
iajs-3842	200	4	(	(	PUNCT
iajs-3842	200	5	𝛽	𝛽	NOUN
iajs-3842	200	6	−	−	PROPN
iajs-3842	200	7	𝑖𝑡)𝜆𝑛+1	𝑖𝑡)𝜆𝑛+1	PROPN
iajs-3842	200	8	∫	∫	PROPN
iajs-3842	200	9	𝑦𝜆𝑛	𝑦𝜆𝑛	VERB
iajs-3842	200	10	∞	∞	PROPN
iajs-3842	200	11	0	0	NUM
iajs-3842	200	12	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	200	13	+	+	CCONJ
iajs-3842	200	14	𝜆	𝜆	X
iajs-3842	200	15	(	(	PUNCT
iajs-3842	200	16	𝛽	𝛽	NOUN
iajs-3842	200	17	−	−	PROPN
iajs-3842	200	18	𝑖𝑡)𝜆𝑛+𝜆	𝑖𝑡)𝜆𝑛+𝜆	NOUN
iajs-3842	200	19	∫	∫	PROPN
iajs-3842	200	20	𝑦𝜆𝑛+𝜆−1	𝑦𝜆𝑛+𝜆−1	NOUN
iajs-3842	200	21	∞	∞	PROPN
iajs-3842	200	22	0	0	NUM
iajs-3842	200	23	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	200	24	+	+	CCONJ
iajs-3842	200	25	𝛽2	𝛽2	PROPN
iajs-3842	200	26	(	(	PUNCT
iajs-3842	200	27	𝛽2	𝛽2	PROPN
iajs-3842	200	28	+	+	CCONJ
iajs-3842	200	29	1)(𝛽	1)(𝛽	NUM
iajs-3842	200	30	−	−	NOUN
iajs-3842	200	31	𝑖𝑡)𝜆𝑛+2	𝑖𝑡)𝜆𝑛+2	NUM
iajs-3842	200	32	∫	∫	NOUN
iajs-3842	200	33	𝑦𝜆𝑛+1	𝑦𝜆𝑛+1	PROPN
iajs-3842	200	34	∞	∞	PROPN
iajs-3842	200	35	0	0	NUM
iajs-3842	200	36	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	200	37	+	+	CCONJ
iajs-3842	200	38	𝛽𝜆	𝛽𝜆	X
iajs-3842	200	39	(	(	PUNCT
iajs-3842	200	40	𝛽2	𝛽2	PROPN
iajs-3842	200	41	+	+	CCONJ
iajs-3842	200	42	1)(𝛽	1)(𝛽	NUM
iajs-3842	200	43	−	−	NOUN
iajs-3842	200	44	𝑖𝑡)𝜆𝑛+𝜆+1	𝑖𝑡)𝜆𝑛+𝜆+1	X
iajs-3842	201	1	∫	∫	PROPN
iajs-3842	202	1	𝑦𝜆𝑛+𝜆	𝑦𝜆𝑛+𝜆	NUM
iajs-3842	202	2	∞	∞	PROPN
iajs-3842	202	3	0	0	NUM
iajs-3842	202	4	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	202	5	−	−	PROPN
iajs-3842	202	6	𝛽2	𝛽2	PROPN
iajs-3842	202	7	(	(	PUNCT
iajs-3842	202	8	𝛽2	𝛽2	PROPN
iajs-3842	202	9	+	+	CCONJ
iajs-3842	202	10	1)(𝛽	1)(𝛽	NUM
iajs-3842	202	11	−	−	NOUN
iajs-3842	202	12	𝑖𝑡)𝜆𝑛+1	𝑖𝑡)𝜆𝑛+1	NOUN
iajs-3842	202	13	∫	∫	NOUN
iajs-3842	202	14	𝑦𝜆𝑛	𝑦𝜆𝑛	VERB
iajs-3842	202	15	∞	∞	PROPN
iajs-3842	202	16	0	0	NUM
iajs-3842	202	17	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	202	18	)	)	PUNCT
iajs-3842	202	19	𝜙𝑥(𝑖𝑡	𝜙𝑥(𝑖𝑡	PROPN
iajs-3842	202	20	)	)	PUNCT
iajs-3842	203	1	=	=	PUNCT
iajs-3842	203	2	∑	∑	PUNCT
iajs-3842	203	3	(	(	PUNCT
iajs-3842	203	4	−1)𝑛	−1)𝑛	X
iajs-3842	203	5	𝑛	𝑛	PROPN
iajs-3842	203	6	!	!	NOUN
iajs-3842	203	7	∞	∞	NUM
iajs-3842	204	1	𝑛=0	𝑛=0	NOUN
iajs-3842	204	2	(	(	PUNCT
iajs-3842	204	3	𝛽	𝛽	PROPN
iajs-3842	204	4	∙	∙	PROPN
iajs-3842	204	5	𝛤(𝜆𝑛+1	𝛤(𝜆𝑛+1	PROPN
iajs-3842	204	6	)	)	PUNCT
iajs-3842	204	7	(	(	PUNCT
iajs-3842	204	8	𝛽	𝛽	NOUN
iajs-3842	204	9	−	−	PROPN
iajs-3842	204	10	𝑖𝑡)𝜆𝑛+1	𝑖𝑡)𝜆𝑛+1	NOUN
iajs-3842	205	1	+	+	CCONJ
iajs-3842	205	2	𝜆	𝜆	X
iajs-3842	205	3	∙	∙	PROPN
iajs-3842	205	4	𝛤(𝜆𝑛+𝜆	𝛤(𝜆𝑛+𝜆	NOUN
iajs-3842	205	5	)	)	PUNCT
iajs-3842	205	6	(	(	PUNCT
iajs-3842	205	7	𝛽	𝛽	NOUN
iajs-3842	205	8	−	−	NOUN
iajs-3842	205	9	𝑖𝑡)𝜆𝑛+𝜆	𝑖𝑡)𝜆𝑛+𝜆	PUNCT
iajs-3842	206	1	+	+	CCONJ
iajs-3842	206	2	𝛽2	𝛽2	PROPN
iajs-3842	206	3	∙	∙	PROPN
iajs-3842	206	4	𝛤(𝜆𝑛+2	𝛤(𝜆𝑛+2	NOUN
iajs-3842	206	5	)	)	PUNCT
iajs-3842	206	6	(	(	PUNCT
iajs-3842	206	7	𝛽2	𝛽2	PROPN
iajs-3842	206	8	+	+	NOUN
iajs-3842	206	9	1)(𝛽	1)(𝛽	NUM
iajs-3842	206	10	−	−	NOUN
iajs-3842	207	1	𝑖𝑡)𝜆𝑛+2	𝑖𝑡)𝜆𝑛+2	NOUN
iajs-3842	208	1	+	+	X
iajs-3842	208	2	𝛽𝜆	𝛽𝜆	ADP
iajs-3842	208	3	∙	∙	PROPN
iajs-3842	208	4	𝛤(𝜆𝑛+𝜆+1	𝛤(𝜆𝑛+𝜆+1	NUM
iajs-3842	208	5	)	)	PUNCT
iajs-3842	208	6	(	(	PUNCT
iajs-3842	208	7	𝛽2	𝛽2	PROPN
iajs-3842	208	8	+	+	CCONJ
iajs-3842	208	9	1)(𝛽	1)(𝛽	NUM
iajs-3842	208	10	−	−	NOUN
iajs-3842	208	11	𝑖𝑡)𝜆𝑛+𝜆+1	𝑖𝑡)𝜆𝑛+𝜆+1	NOUN
iajs-3842	208	12	−	−	PROPN
iajs-3842	208	13	𝛽2	𝛽2	PROPN
iajs-3842	208	14	∙	∙	PROPN
iajs-3842	208	15	𝛤(𝜆𝑛+1	𝛤(𝜆𝑛+1	PROPN
iajs-3842	208	16	)	)	PUNCT
iajs-3842	208	17	(	(	PUNCT
iajs-3842	208	18	𝛽2	𝛽2	PROPN
iajs-3842	208	19	+	+	CCONJ
iajs-3842	208	20	1)(𝛽	1)(𝛽	NUM
iajs-3842	208	21	−	−	NOUN
iajs-3842	208	22	𝑖𝑡)𝜆𝑛+1	𝑖𝑡)𝜆𝑛+1	NOUN
iajs-3842	208	23	)	)	PUNCT
iajs-3842	208	24	2.2.6	2.2.6	NUM
iajs-3842	208	25	.	.	PUNCT
iajs-3842	208	26	moment	moment	NOUN
iajs-3842	208	27	generating	generate	VERB
iajs-3842	208	28	function	function	NOUN
iajs-3842	208	29	𝑀𝑥(𝑡	𝑀𝑥(𝑡	NOUN
iajs-3842	208	30	)	)	PUNCT
iajs-3842	209	1	=	=	SYM
iajs-3842	209	2	𝐸(𝑒𝑡𝑥	𝐸(𝑒𝑡𝑥	VERB
iajs-3842	209	3	)	)	PUNCT
iajs-3842	210	1	=	=	SYM
iajs-3842	210	2	∫	∫	PROPN
iajs-3842	210	3	𝑒𝑡𝑥	𝑒𝑡𝑥	VERB
iajs-3842	210	4	∞	∞	NOUN
iajs-3842	210	5	0	0	NUM
iajs-3842	211	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	211	2	)	)	PUNCT
iajs-3842	212	1	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	212	2	=	=	SYM
iajs-3842	212	3	∫	∫	NOUN
iajs-3842	212	4	𝑒𝑡𝑥	𝑒𝑡𝑥	NOUN
iajs-3842	212	5	∞	∞	PROPN
iajs-3842	212	6	0	0	PUNCT
iajs-3842	213	1	(	(	PUNCT
iajs-3842	213	2	1	1	NUM
iajs-3842	213	3	+	+	CCONJ
iajs-3842	213	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	213	5	𝛽2	𝛽2	PROPN
iajs-3842	213	6	+	+	CCONJ
iajs-3842	213	7	1	1	NUM
iajs-3842	213	8	)	)	PUNCT
iajs-3842	213	9	(	(	PUNCT
iajs-3842	213	10	𝛽	𝛽	NOUN
iajs-3842	213	11	+	+	CCONJ
iajs-3842	213	12	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	213	13	)	)	PUNCT
iajs-3842	213	14	−	−	PROPN
iajs-3842	213	15	𝜆	𝜆	DET
iajs-3842	213	16	𝜆2	𝜆2	PROPN
iajs-3842	213	17	+	+	CCONJ
iajs-3842	213	18	1	1	NUM
iajs-3842	213	19	)	)	PUNCT
iajs-3842	213	20	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	VERB
iajs-3842	213	21	)	)	PUNCT
iajs-3842	213	22	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	213	23	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-3842	213	24	𝑒−𝑥𝛽	𝑒−𝑥𝛽	NOUN
iajs-3842	213	25	=	=	PUNCT
iajs-3842	213	26	∑	∑	PUNCT
iajs-3842	213	27	(	(	PUNCT
iajs-3842	213	28	−1)𝑘	−1)𝑘	X
iajs-3842	213	29	𝑘	𝑘	NOUN
iajs-3842	213	30	!	!	PUNCT
iajs-3842	214	1	∞	∞	PROPN
iajs-3842	214	2	𝑘=0	𝑘=0	PROPN
iajs-3842	214	3	𝑥𝜆𝑘	𝑥𝜆𝑘	NUM
iajs-3842	214	4	𝑀𝑥(𝑡	𝑀𝑥(𝑡	NOUN
iajs-3842	214	5	)	)	PUNCT
iajs-3842	215	1	=	=	PUNCT
iajs-3842	215	2	∑	∑	PUNCT
iajs-3842	215	3	(	(	PUNCT
iajs-3842	215	4	−1)𝑘	−1)𝑘	X
iajs-3842	215	5	𝑘	𝑘	NOUN
iajs-3842	215	6	!	!	PUNCT
iajs-3842	216	1	∞	∞	NUM
iajs-3842	216	2	𝑘=0	𝑘=0	PROPN
iajs-3842	216	3	(	(	PUNCT
iajs-3842	216	4	∫	∫	PROPN
iajs-3842	216	5	𝛽𝑥𝜆𝑘	𝛽𝑥𝜆𝑘	PROPN
iajs-3842	216	6	∞	∞	PROPN
iajs-3842	216	7	0	0	SYM
iajs-3842	216	8	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	X
iajs-3842	217	1	+	+	SYM
iajs-3842	217	2	∫	∫	PROPN
iajs-3842	217	3	𝜆𝑥𝜆𝑘+𝜆−1	𝜆𝑥𝜆𝑘+𝜆−1	NOUN
iajs-3842	217	4	∞	∞	PROPN
iajs-3842	217	5	0	0	NUM
iajs-3842	217	6	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	X
iajs-3842	218	1	+	+	NUM
iajs-3842	218	2	∫	∫	PROPN
iajs-3842	218	3	(	(	PUNCT
iajs-3842	218	4	𝛽2	𝛽2	PROPN
iajs-3842	218	5	𝛽2	𝛽2	PROPN
iajs-3842	218	6	+	+	CCONJ
iajs-3842	218	7	1	1	NUM
iajs-3842	218	8	)	)	PUNCT
iajs-3842	218	9	𝑥𝜆𝑘+1	𝑥𝜆𝑘+1	NOUN
iajs-3842	218	10	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	NUM
iajs-3842	218	11	∞	∞	NUM
iajs-3842	218	12	0	0	NUM
iajs-3842	219	1	+	+	NUM
iajs-3842	219	2	∫	∫	PROPN
iajs-3842	219	3	(	(	PUNCT
iajs-3842	219	4	𝛽𝜆	𝛽𝜆	NOUN
iajs-3842	219	5	𝛽2	𝛽2	NOUN
iajs-3842	219	6	+	+	CCONJ
iajs-3842	219	7	1	1	NUM
iajs-3842	219	8	)	)	PUNCT
iajs-3842	219	9	𝑥𝜆𝑘+𝜆	𝑥𝜆𝑘+𝜆	NUM
iajs-3842	219	10	∞	∞	NUM
iajs-3842	219	11	0	0	SYM
iajs-3842	219	12	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	PROPN
iajs-3842	220	1	−	−	PROPN
iajs-3842	220	2	∫	∫	PROPN
iajs-3842	220	3	(	(	PUNCT
iajs-3842	220	4	𝛽	𝛽	PROPN
iajs-3842	220	5	𝛽2	𝛽2	NOUN
iajs-3842	220	6	+	+	CCONJ
iajs-3842	220	7	1	1	X
iajs-3842	220	8	)	)	PUNCT
iajs-3842	220	9	𝑥𝜆𝑘	𝑥𝜆𝑘	NOUN
iajs-3842	220	10	∞	∞	PROPN
iajs-3842	220	11	0	0	SYM
iajs-3842	220	12	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑡)𝑥𝑑𝑥	PROPN
iajs-3842	220	13	)	)	PUNCT
iajs-3842	221	1	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-3842	221	2	(	(	PUNCT
iajs-3842	221	3	𝛽	𝛽	NOUN
iajs-3842	221	4	−	−	PROPN
iajs-3842	221	5	𝑡)𝑥	𝑡)𝑥	SYM
iajs-3842	221	6	=	=	SYM
iajs-3842	221	7	𝑦	𝑦	NOUN
iajs-3842	221	8	,	,	PUNCT
iajs-3842	221	9	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3842	221	10	𝑥	𝑥	X
iajs-3842	221	11	=	=	PUNCT
iajs-3842	221	12	𝑦	𝑦	SYM
iajs-3842	221	13	𝛽	𝛽	NOUN
iajs-3842	221	14	−	−	PROPN
iajs-3842	221	15	𝑡	𝑡	PROPN
iajs-3842	221	16	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
iajs-3842	221	17	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	221	18	=	=	SYM
iajs-3842	221	19	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	221	20	𝛽	𝛽	NOUN
iajs-3842	221	21	−	−	PROPN
iajs-3842	221	22	𝑡	𝑡	PROPN
iajs-3842	221	23	ihjpas	ihjpas	PROPN
iajs-3842	221	24	.	.	PUNCT
iajs-3842	222	1	2025,38(2	2025,38(2	PROPN
iajs-3842	222	2	)	)	PUNCT
iajs-3842	222	3	398	398	NUM
iajs-3842	222	4	𝑀𝑥(𝑡	𝑀𝑥(𝑡	NOUN
iajs-3842	222	5	)	)	PUNCT
iajs-3842	222	6	=	=	PUNCT
iajs-3842	222	7	∑	∑	PUNCT
iajs-3842	222	8	(	(	PUNCT
iajs-3842	222	9	−1)𝑘	−1)𝑘	X
iajs-3842	222	10	𝑘	𝑘	NOUN
iajs-3842	222	11	!	!	PUNCT
iajs-3842	223	1	∞	∞	NOUN
iajs-3842	223	2	𝑘=0	𝑘=0	PROPN
iajs-3842	223	3	(	(	PUNCT
iajs-3842	223	4	𝛽	𝛽	NOUN
iajs-3842	223	5	(	(	PUNCT
iajs-3842	223	6	𝛽	𝛽	PROPN
iajs-3842	223	7	−	−	PROPN
iajs-3842	223	8	𝑡)𝜆𝑘+1	𝑡)𝜆𝑘+1	NUM
iajs-3842	223	9	∫	∫	PROPN
iajs-3842	224	1	𝑦𝜆𝑘	𝑦𝜆𝑘	NOUN
iajs-3842	224	2	∞	∞	PROPN
iajs-3842	224	3	0	0	NUM
iajs-3842	224	4	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	224	5	+	+	CCONJ
iajs-3842	224	6	𝛽	𝛽	NOUN
iajs-3842	224	7	(	(	PUNCT
iajs-3842	224	8	𝛽	𝛽	NOUN
iajs-3842	224	9	−	−	PROPN
iajs-3842	224	10	𝑡)𝜆𝑘+𝜆	𝑡)𝜆𝑘+𝜆	PROPN
iajs-3842	224	11	∫	∫	PROPN
iajs-3842	224	12	𝑦𝜆𝑘+𝜆−1	𝑦𝜆𝑘+𝜆−1	PROPN
iajs-3842	224	13	∞	∞	PROPN
iajs-3842	224	14	0	0	NUM
iajs-3842	224	15	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	224	16	+	+	CCONJ
iajs-3842	224	17	𝛽2	𝛽2	PROPN
iajs-3842	224	18	(	(	PUNCT
iajs-3842	224	19	𝛽2	𝛽2	NOUN
iajs-3842	224	20	+	+	CCONJ
iajs-3842	224	21	1)(𝛽	1)(𝛽	NUM
iajs-3842	224	22	−	−	NOUN
iajs-3842	224	23	𝑡)𝜆𝑘+2	𝑡)𝜆𝑘+2	NOUN
iajs-3842	224	24	∫	∫	PROPN
iajs-3842	224	25	𝑦𝜆𝑘+1	𝑦𝜆𝑘+1	X
iajs-3842	224	26	∞	∞	PROPN
iajs-3842	224	27	0	0	NUM
iajs-3842	224	28	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	224	29	+	+	CCONJ
iajs-3842	224	30	𝛽𝜆	𝛽𝜆	X
iajs-3842	224	31	(	(	PUNCT
iajs-3842	224	32	𝛽2	𝛽2	PROPN
iajs-3842	224	33	+	+	CCONJ
iajs-3842	224	34	1)(𝛽	1)(𝛽	NUM
iajs-3842	224	35	−	−	NOUN
iajs-3842	224	36	𝑡)𝜆𝑘+𝜆+1	𝑡)𝜆𝑘+𝜆+1	PUNCT
iajs-3842	225	1	∫	∫	PROPN
iajs-3842	225	2	𝑦𝜆𝑘+𝜆	𝑦𝜆𝑘+𝜆	PROPN
iajs-3842	225	3	∞	∞	PROPN
iajs-3842	225	4	0	0	PROPN
iajs-3842	225	5	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	226	1	−	−	PROPN
iajs-3842	226	2	𝛽2	𝛽2	PROPN
iajs-3842	226	3	(	(	PUNCT
iajs-3842	226	4	𝛽2	𝛽2	PROPN
iajs-3842	226	5	+	+	CCONJ
iajs-3842	226	6	1)(𝛽	1)(𝛽	NUM
iajs-3842	226	7	−	−	NOUN
iajs-3842	226	8	𝑡)𝜆𝑘+1	𝑡)𝜆𝑘+1	NOUN
iajs-3842	226	9	∫	∫	X
iajs-3842	226	10	𝑦𝜆𝑘	𝑦𝜆𝑘	NOUN
iajs-3842	226	11	∞	∞	PROPN
iajs-3842	226	12	0	0	NUM
iajs-3842	226	13	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	226	14	)	)	PUNCT
iajs-3842	226	15	𝑀𝑥(𝑡	𝑀𝑥(𝑡	NOUN
iajs-3842	226	16	)	)	PUNCT
iajs-3842	226	17	=	=	PUNCT
iajs-3842	226	18	∑	∑	PUNCT
iajs-3842	226	19	(	(	PUNCT
iajs-3842	226	20	−1)𝑘	−1)𝑘	X
iajs-3842	226	21	𝑘	𝑘	NOUN
iajs-3842	226	22	!	!	PUNCT
iajs-3842	227	1	∞	∞	NOUN
iajs-3842	227	2	𝑘=0	𝑘=0	PROPN
iajs-3842	227	3	(	(	PUNCT
iajs-3842	227	4	𝛽	𝛽	NOUN
iajs-3842	227	5	∙	∙	PROPN
iajs-3842	227	6	𝛤(𝜆𝑘+1	𝛤(𝜆𝑘+1	NOUN
iajs-3842	227	7	)	)	PUNCT
iajs-3842	227	8	(	(	PUNCT
iajs-3842	227	9	𝛽	𝛽	NOUN
iajs-3842	227	10	−	−	NOUN
iajs-3842	227	11	𝑡)𝜆𝑘+1	𝑡)𝜆𝑘+1	NOUN
iajs-3842	227	12	+	+	CCONJ
iajs-3842	227	13	𝜆	𝜆	ADP
iajs-3842	227	14	∙	∙	PROPN
iajs-3842	227	15	𝛤(𝜆𝑘+𝛽	𝛤(𝜆𝑘+𝛽	NUM
iajs-3842	227	16	)	)	PUNCT
iajs-3842	227	17	(	(	PUNCT
iajs-3842	227	18	𝛽	𝛽	NOUN
iajs-3842	227	19	−	−	PROPN
iajs-3842	227	20	𝑡)𝜆𝑘+𝛽	𝑡)𝜆𝑘+𝛽	PROPN
iajs-3842	227	21	+	+	CCONJ
iajs-3842	227	22	𝛽2	𝛽2	PROPN
iajs-3842	227	23	∙	∙	PROPN
iajs-3842	227	24	𝛤(𝜆𝑘+2	𝛤(𝜆𝑘+2	NUM
iajs-3842	227	25	)	)	PUNCT
iajs-3842	227	26	(	(	PUNCT
iajs-3842	227	27	𝛽2	𝛽2	PROPN
iajs-3842	227	28	+	+	CCONJ
iajs-3842	227	29	1)(𝛽	1)(𝛽	NUM
iajs-3842	227	30	−	−	NOUN
iajs-3842	227	31	𝑡)𝜆𝑘+2	𝑡)𝜆𝑘+2	NOUN
iajs-3842	227	32	+	+	CCONJ
iajs-3842	227	33	𝛽𝜆	𝛽𝜆	ADP
iajs-3842	227	34	∙	∙	PROPN
iajs-3842	227	35	𝛤(𝜆𝑘+𝜆+1	𝛤(𝜆𝑘+𝜆+1	PROPN
iajs-3842	227	36	)	)	PUNCT
iajs-3842	227	37	(	(	PUNCT
iajs-3842	227	38	𝛽2	𝛽2	PROPN
iajs-3842	227	39	+	+	CCONJ
iajs-3842	227	40	1)(𝛽	1)(𝛽	NUM
iajs-3842	227	41	−	−	NOUN
iajs-3842	227	42	𝑡)𝜆𝑘+𝜆+1	𝑡)𝜆𝑘+𝜆+1	PUNCT
iajs-3842	228	1	−	−	PROPN
iajs-3842	228	2	𝛽2	𝛽2	PROPN
iajs-3842	228	3	∙	∙	PROPN
iajs-3842	228	4	𝛤(𝜆𝑘+1	𝛤(𝜆𝑘+1	PROPN
iajs-3842	228	5	)	)	PUNCT
iajs-3842	228	6	(	(	PUNCT
iajs-3842	228	7	𝛽2	𝛽2	PROPN
iajs-3842	228	8	+	+	CCONJ
iajs-3842	228	9	1)(𝛽	1)(𝛽	NUM
iajs-3842	228	10	−	−	NOUN
iajs-3842	228	11	𝑡)𝜆𝑘+1	𝑡)𝜆𝑘+1	NOUN
iajs-3842	228	12	)	)	PUNCT
iajs-3842	228	13	2.2.7	2.2.7	X
iajs-3842	228	14	.	.	PUNCT
iajs-3842	229	1	factorial	factorial	ADJ
iajs-3842	229	2	moments	moment	NOUN
iajs-3842	229	3	generating	generate	VERB
iajs-3842	229	4	function	function	NOUN
iajs-3842	229	5	ℳ𝑥(𝑡	ℳ𝑥(𝑡	NOUN
iajs-3842	229	6	)	)	PUNCT
iajs-3842	229	7	=	=	SYM
iajs-3842	229	8	𝐸(𝑡𝑥	𝐸(𝑡𝑥	NOUN
iajs-3842	229	9	)	)	PUNCT
iajs-3842	230	1	=	=	SYM
iajs-3842	230	2	∫	∫	PROPN
iajs-3842	231	1	𝑡𝑥	𝑡𝑥	NOUN
iajs-3842	231	2	∞	∞	NOUN
iajs-3842	231	3	0	0	NUM
iajs-3842	232	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3842	232	2	)	)	PUNCT
iajs-3842	233	1	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	233	2	=	=	SYM
iajs-3842	233	3	∫	∫	NOUN
iajs-3842	233	4	𝑒𝑥𝑙𝑛𝑡	𝑒𝑥𝑙𝑛𝑡	NOUN
iajs-3842	233	5	∞	∞	PROPN
iajs-3842	233	6	0	0	NUM
iajs-3842	234	1	(	(	PUNCT
iajs-3842	234	2	1	1	NUM
iajs-3842	234	3	+	+	CCONJ
iajs-3842	234	4	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	234	5	𝛽2	𝛽2	PROPN
iajs-3842	234	6	+	+	CCONJ
iajs-3842	234	7	1	1	NUM
iajs-3842	234	8	)	)	PUNCT
iajs-3842	234	9	(	(	PUNCT
iajs-3842	234	10	𝛽	𝛽	NOUN
iajs-3842	234	11	+	+	CCONJ
iajs-3842	234	12	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	234	13	)	)	PUNCT
iajs-3842	234	14	−	−	PROPN
iajs-3842	234	15	𝛽	𝛽	NOUN
iajs-3842	234	16	𝛽2	𝛽2	NOUN
iajs-3842	234	17	+	+	CCONJ
iajs-3842	234	18	1	1	NUM
iajs-3842	234	19	)	)	PUNCT
iajs-3842	234	20	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	PROPN
iajs-3842	234	21	)	)	PUNCT
iajs-3842	234	22	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	234	23	=	=	SYM
iajs-3842	234	24	∫	∫	PROPN
iajs-3842	234	25	(	(	PUNCT
iajs-3842	234	26	1	1	NUM
iajs-3842	234	27	+	+	CCONJ
iajs-3842	234	28	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	234	29	𝛽2	𝛽2	PROPN
iajs-3842	234	30	+	+	CCONJ
iajs-3842	234	31	1	1	NUM
iajs-3842	234	32	)	)	PUNCT
iajs-3842	234	33	(	(	PUNCT
iajs-3842	234	34	𝛽	𝛽	NOUN
iajs-3842	234	35	+	+	CCONJ
iajs-3842	234	36	𝜆𝑥𝜆−1	𝜆𝑥𝜆−1	PROPN
iajs-3842	234	37	)	)	PUNCT
iajs-3842	234	38	−	−	PROPN
iajs-3842	234	39	𝛽	𝛽	NOUN
iajs-3842	234	40	𝛽2	𝛽2	NOUN
iajs-3842	234	41	+	+	CCONJ
iajs-3842	234	42	1	1	NUM
iajs-3842	234	43	)	)	PUNCT
iajs-3842	234	44	𝑒−((𝛽−𝑙𝑛	𝑒−((𝛽−𝑙𝑛	PRON
iajs-3842	234	45	𝑡)𝑥+𝑥𝜆	𝑡)𝑥+𝑥𝜆	NOUN
iajs-3842	234	46	)	)	PUNCT
iajs-3842	234	47	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	234	48	∞	∞	PROPN
iajs-3842	234	49	0	0	PUNCT
iajs-3842	235	1	𝐿𝑒𝑡	𝐿𝑒𝑡	NOUN
iajs-3842	235	2	𝑒−𝑥𝛽	𝑒−𝑥𝛽	NOUN
iajs-3842	235	3	=	=	PUNCT
iajs-3842	235	4	∑	∑	PUNCT
iajs-3842	235	5	(	(	PUNCT
iajs-3842	235	6	−1)𝑠	−1)𝑠	X
iajs-3842	235	7	𝑠	𝑠	PROPN
iajs-3842	235	8	!	!	PUNCT
iajs-3842	235	9	∞	∞	PROPN
iajs-3842	235	10	𝑠=0	𝑠=0	PROPN
iajs-3842	235	11	𝑥𝜆𝑠	𝑥𝜆𝑠	PROPN
iajs-3842	235	12	ℳ𝑥(𝑡	ℳ𝑥(𝑡	NOUN
iajs-3842	235	13	)	)	PUNCT
iajs-3842	235	14	=	=	SYM
iajs-3842	235	15	∑	∑	PUNCT
iajs-3842	235	16	(	(	PUNCT
iajs-3842	235	17	−1)𝑠	−1)𝑠	X
iajs-3842	235	18	𝑠	𝑠	PROPN
iajs-3842	235	19	!	!	PUNCT
iajs-3842	235	20	∞	∞	PROPN
iajs-3842	235	21	𝑠=0	𝑠=0	PROPN
iajs-3842	235	22	(	(	PUNCT
iajs-3842	235	23	∫	∫	PROPN
iajs-3842	235	24	𝛽𝑥𝜆𝑠	𝛽𝑥𝜆𝑠	VERB
iajs-3842	235	25	∞	∞	PROPN
iajs-3842	235	26	0	0	PUNCT
iajs-3842	236	1	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	PUNCT
iajs-3842	237	1	+	+	CCONJ
iajs-3842	237	2	∫	∫	PROPN
iajs-3842	237	3	𝜆𝑥𝜆𝑠+𝜆−1	𝜆𝑥𝜆𝑠+𝜆−1	PROPN
iajs-3842	237	4	∞	∞	PROPN
iajs-3842	237	5	0	0	PUNCT
iajs-3842	237	6	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	PROPN
iajs-3842	238	1	+	+	CCONJ
iajs-3842	238	2	∫	∫	PROPN
iajs-3842	238	3	(	(	PUNCT
iajs-3842	238	4	𝛽2	𝛽2	PROPN
iajs-3842	238	5	𝛽2	𝛽2	PROPN
iajs-3842	238	6	+	+	CCONJ
iajs-3842	238	7	1	1	NUM
iajs-3842	238	8	)	)	PUNCT
iajs-3842	238	9	𝑥𝜆𝑠+1	𝑥𝜆𝑠+1	NOUN
iajs-3842	238	10	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	NOUN
iajs-3842	238	11	∞	∞	NUM
iajs-3842	238	12	0	0	NUM
iajs-3842	239	1	+	+	NUM
iajs-3842	239	2	∫	∫	PROPN
iajs-3842	239	3	(	(	PUNCT
iajs-3842	239	4	𝛽𝜆	𝛽𝜆	NOUN
iajs-3842	239	5	𝛽2	𝛽2	NOUN
iajs-3842	239	6	+	+	CCONJ
iajs-3842	239	7	1	1	NUM
iajs-3842	239	8	)	)	PUNCT
iajs-3842	239	9	𝑥𝜆𝑠+𝜆	𝑥𝜆𝑠+𝜆	PROPN
iajs-3842	240	1	∞	∞	PROPN
iajs-3842	240	2	0	0	NUM
iajs-3842	240	3	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	PROPN
iajs-3842	241	1	−	−	PROPN
iajs-3842	241	2	∫	∫	PROPN
iajs-3842	241	3	(	(	PUNCT
iajs-3842	241	4	𝛽	𝛽	PROPN
iajs-3842	241	5	𝛽2	𝛽2	NOUN
iajs-3842	241	6	+	+	CCONJ
iajs-3842	241	7	1	1	NUM
iajs-3842	241	8	)	)	PUNCT
iajs-3842	241	9	𝑥𝜆𝑠	𝑥𝜆𝑠	VERB
iajs-3842	241	10	∞	∞	PROPN
iajs-3842	241	11	0	0	NUM
iajs-3842	241	12	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	𝑒−(𝛽−𝑙𝑛𝑡)𝑥𝑑𝑥	ADJ
iajs-3842	241	13	)	)	PUNCT
iajs-3842	242	1	𝐿𝑒𝑡	𝐿𝑒𝑡	PROPN
iajs-3842	242	2	(	(	PUNCT
iajs-3842	242	3	𝛽	𝛽	NOUN
iajs-3842	242	4	−	−	PROPN
iajs-3842	242	5	𝑙𝑛𝑡)𝑥	𝑙𝑛𝑡)𝑥	PROPN
iajs-3842	242	6	=	=	SYM
iajs-3842	242	7	𝑦	𝑦	NOUN
iajs-3842	242	8	,	,	PUNCT
iajs-3842	242	9	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3842	242	10	𝑥	𝑥	X
iajs-3842	242	11	=	=	PUNCT
iajs-3842	242	12	𝑦	𝑦	SYM
iajs-3842	242	13	𝛽	𝛽	NOUN
iajs-3842	242	14	−	−	PROPN
iajs-3842	242	15	𝑙𝑛𝑡	𝑙𝑛𝑡	NOUN
iajs-3842	242	16	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
iajs-3842	242	17	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	242	18	=	=	SYM
iajs-3842	242	19	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	242	20	𝛽	𝛽	PROPN
iajs-3842	242	21	−	−	PROPN
iajs-3842	242	22	𝑙𝑛𝑡	𝑙𝑛𝑡	NOUN
iajs-3842	242	23	ihjpas	ihjpa	VERB
iajs-3842	242	24	.	.	PUNCT
iajs-3842	243	1	2025,38(2	2025,38(2	NOUN
iajs-3842	243	2	)	)	PUNCT
iajs-3842	243	3	399	399	NUM
iajs-3842	243	4	ℳ𝑥(𝑡	ℳ𝑥(𝑡	NOUN
iajs-3842	243	5	)	)	PUNCT
iajs-3842	243	6	=	=	SYM
iajs-3842	244	1	∑	∑	PUNCT
iajs-3842	244	2	(	(	PUNCT
iajs-3842	244	3	−1)𝑠	−1)𝑠	X
iajs-3842	244	4	𝑠	𝑠	PROPN
iajs-3842	244	5	!	!	PUNCT
iajs-3842	245	1	∞	∞	NUM
iajs-3842	245	2	𝑠=0	𝑠=0	PROPN
iajs-3842	245	3	(	(	PUNCT
iajs-3842	245	4	𝛽	𝛽	NOUN
iajs-3842	245	5	(	(	PUNCT
iajs-3842	245	6	𝛽	𝛽	NOUN
iajs-3842	245	7	−	−	PROPN
iajs-3842	245	8	𝑙𝑛𝑡)𝜆𝑠+1	𝑙𝑛𝑡)𝜆𝑠+1	NUM
iajs-3842	245	9	∫	∫	NOUN
iajs-3842	246	1	𝑦𝜆𝑠	𝑦𝜆𝑠	PROPN
iajs-3842	246	2	∞	∞	PROPN
iajs-3842	246	3	0	0	NUM
iajs-3842	246	4	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	247	1	+	+	CCONJ
iajs-3842	247	2	𝜆	𝜆	X
iajs-3842	247	3	(	(	PUNCT
iajs-3842	247	4	𝛽	𝛽	NOUN
iajs-3842	247	5	−	−	PROPN
iajs-3842	247	6	𝑙𝑛𝑡)𝜆𝑠+𝜆	𝑙𝑛𝑡)𝜆𝑠+𝜆	NOUN
iajs-3842	247	7	∫	∫	PROPN
iajs-3842	247	8	𝑦𝜆𝑠+𝜆−1	𝑦𝜆𝑠+𝜆−1	PROPN
iajs-3842	247	9	∞	∞	PROPN
iajs-3842	247	10	0	0	NUM
iajs-3842	247	11	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	247	12	+	+	CCONJ
iajs-3842	247	13	𝛽2	𝛽2	PROPN
iajs-3842	247	14	(	(	PUNCT
iajs-3842	247	15	𝛽2	𝛽2	NOUN
iajs-3842	247	16	+	+	NOUN
iajs-3842	247	17	1)(𝛽	1)(𝛽	NUM
iajs-3842	247	18	−	−	NOUN
iajs-3842	247	19	𝑙𝑛𝑡)𝜆𝑠+2	𝑙𝑛𝑡)𝜆𝑠+2	NUM
iajs-3842	247	20	∫	∫	PROPN
iajs-3842	247	21	𝑦𝜆𝑠+1	𝑦𝜆𝑠+1	PROPN
iajs-3842	247	22	∞	∞	PROPN
iajs-3842	247	23	0	0	NUM
iajs-3842	247	24	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	247	25	+	+	CCONJ
iajs-3842	247	26	𝛽𝜆	𝛽𝜆	X
iajs-3842	247	27	(	(	PUNCT
iajs-3842	247	28	𝛽2	𝛽2	PROPN
iajs-3842	247	29	+	+	CCONJ
iajs-3842	247	30	1)(𝛽	1)(𝛽	NUM
iajs-3842	247	31	−	−	NOUN
iajs-3842	248	1	𝑙𝑛𝑡)𝜆𝑠+𝜆+1	𝑙𝑛𝑡)𝜆𝑠+𝜆+1	NOUN
iajs-3842	248	2	∫	∫	PROPN
iajs-3842	248	3	𝑦𝜆𝑠+𝜆	𝑦𝜆𝑠+𝜆	NUM
iajs-3842	248	4	∞	∞	PROPN
iajs-3842	248	5	0	0	NUM
iajs-3842	248	6	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	248	7	−	−	PROPN
iajs-3842	248	8	𝛽	𝛽	PROPN
iajs-3842	248	9	(	(	PUNCT
iajs-3842	248	10	𝛽2	𝛽2	PROPN
iajs-3842	248	11	+	+	CCONJ
iajs-3842	248	12	1)(𝛽	1)(𝛽	NUM
iajs-3842	248	13	−	−	NOUN
iajs-3842	248	14	𝑙𝑛𝑡)𝜆𝑠+1	𝑙𝑛𝑡)𝜆𝑠+1	NUM
iajs-3842	248	15	∫	∫	NOUN
iajs-3842	248	16	𝑦𝜆𝑠	𝑦𝜆𝑠	PROPN
iajs-3842	248	17	∞	∞	PROPN
iajs-3842	248	18	0	0	NUM
iajs-3842	248	19	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	248	20	)	)	PUNCT
iajs-3842	248	21	ℳ𝑥(𝑡	ℳ𝑥(𝑡	NOUN
iajs-3842	248	22	)	)	PUNCT
iajs-3842	249	1	=	=	SYM
iajs-3842	249	2	∑	∑	PUNCT
iajs-3842	249	3	(	(	PUNCT
iajs-3842	249	4	−1)𝑠	−1)𝑠	X
iajs-3842	249	5	𝑠	𝑠	PROPN
iajs-3842	249	6	!	!	PUNCT
iajs-3842	250	1	∞	∞	NUM
iajs-3842	250	2	𝑠=0	𝑠=0	PROPN
iajs-3842	251	1	(	(	PUNCT
iajs-3842	251	2	𝛽	𝛽	NOUN
iajs-3842	251	3	∙	∙	PROPN
iajs-3842	251	4	𝛤(𝜆𝑠+1	𝛤(𝜆𝑠+1	PROPN
iajs-3842	251	5	)	)	PUNCT
iajs-3842	251	6	(	(	PUNCT
iajs-3842	251	7	𝛽	𝛽	NOUN
iajs-3842	251	8	−	−	PROPN
iajs-3842	251	9	𝑙𝑛𝑡)𝜆𝑠+1	𝑙𝑛𝑡)𝜆𝑠+1	NUM
iajs-3842	252	1	+	+	CCONJ
iajs-3842	252	2	𝜆	𝜆	ADP
iajs-3842	252	3	∙	∙	PROPN
iajs-3842	252	4	𝛤(𝜆𝑠+𝜆	𝛤(𝜆𝑠+𝜆	NUM
iajs-3842	252	5	)	)	PUNCT
iajs-3842	252	6	(	(	PUNCT
iajs-3842	252	7	𝛽	𝛽	NOUN
iajs-3842	252	8	−	−	PROPN
iajs-3842	252	9	𝑙𝑛𝑡)𝜆𝑠+𝜆	𝑙𝑛𝑡)𝜆𝑠+𝜆	NOUN
iajs-3842	252	10	+	+	NUM
iajs-3842	252	11	𝛽2	𝛽2	PROPN
iajs-3842	252	12	∙	∙	PROPN
iajs-3842	252	13	𝛤(𝜆𝑠+2	𝛤(𝜆𝑠+2	PROPN
iajs-3842	252	14	)	)	PUNCT
iajs-3842	252	15	(	(	PUNCT
iajs-3842	252	16	𝛽2	𝛽2	PROPN
iajs-3842	252	17	+	+	NOUN
iajs-3842	252	18	1)(𝛽	1)(𝛽	NUM
iajs-3842	252	19	−	−	NOUN
iajs-3842	252	20	𝑙𝑛𝑡)𝜆𝑠+2	𝑙𝑛𝑡)𝜆𝑠+2	PRON
iajs-3842	252	21	+	+	X
iajs-3842	252	22	𝛽𝜆	𝛽𝜆	ADP
iajs-3842	252	23	∙	∙	PROPN
iajs-3842	252	24	𝛤(𝜆𝑠+𝜆+1	𝛤(𝜆𝑠+𝜆+1	X
iajs-3842	252	25	)	)	PUNCT
iajs-3842	252	26	(	(	PUNCT
iajs-3842	252	27	𝛽2	𝛽2	PROPN
iajs-3842	252	28	+	+	CCONJ
iajs-3842	252	29	1)(𝛽	1)(𝛽	NUM
iajs-3842	252	30	−	−	NOUN
iajs-3842	252	31	𝑙𝑛𝑡)𝜆𝑠+𝜆+1	𝑙𝑛𝑡)𝜆𝑠+𝜆+1	NOUN
iajs-3842	252	32	−	−	PROPN
iajs-3842	252	33	𝛽	𝛽	NOUN
iajs-3842	252	34	∙	∙	PROPN
iajs-3842	252	35	𝛤(𝜆𝑠+1	𝛤(𝜆𝑠+1	PROPN
iajs-3842	252	36	)	)	PUNCT
iajs-3842	252	37	(	(	PUNCT
iajs-3842	252	38	𝛽2	𝛽2	PROPN
iajs-3842	252	39	+	+	NOUN
iajs-3842	252	40	1)(𝛽	1)(𝛽	NUM
iajs-3842	252	41	−	−	NOUN
iajs-3842	252	42	𝑙𝑛𝑡)𝜆𝑠+1	𝑙𝑛𝑡)𝜆𝑠+1	NUM
iajs-3842	252	43	)	)	PUNCT
iajs-3842	252	44	2.2.8	2.2.8	X
iajs-3842	252	45	.	.	PUNCT
iajs-3842	253	1	mean	mean	VERB
iajs-3842	253	2	time	time	NOUN
iajs-3842	253	3	to	to	ADP
iajs-3842	253	4	failure	failure	NOUN
iajs-3842	253	5	let	let	VERB
iajs-3842	253	6	𝑇	𝑇	PROPN
iajs-3842	253	7	denote	denote	VERB
iajs-3842	253	8	the	the	DET
iajs-3842	253	9	lifetime	lifetime	NOUN
iajs-3842	253	10	of	of	ADP
iajs-3842	253	11	a	a	DET
iajs-3842	253	12	component	component	NOUN
iajs-3842	253	13	,	,	PUNCT
iajs-3842	253	14	the𝑆(𝑆𝐻𝑊𝐷)(𝑥	the𝑆(𝑆𝐻𝑊𝐷)(𝑥	X
iajs-3842	253	15	)	)	PUNCT
iajs-3842	254	1	=	=	NOUN
iajs-3842	254	2	pr	pr	NOUN
iajs-3842	254	3	(	(	PUNCT
iajs-3842	254	4	𝑇	𝑇	PROPN
iajs-3842	254	5	>	>	SYM
iajs-3842	254	6	𝑥	𝑥	NOUN
iajs-3842	254	7	)	)	PUNCT
iajs-3842	255	1	[	[	X
iajs-3842	255	2	30	30	NUM
iajs-3842	255	3	]	]	X
iajs-3842	255	4	𝑆(𝑆𝐻𝑊𝐷)(𝑥	𝑆(𝑆𝐻𝑊𝐷)(𝑥	NOUN
iajs-3842	255	5	)	)	PUNCT
iajs-3842	255	6	=	=	SYM
iajs-3842	256	1	𝑃𝑟	𝑃𝑟	PROPN
iajs-3842	256	2	(	(	PUNCT
iajs-3842	256	3	𝑇	𝑇	PROPN
iajs-3842	256	4	>	>	SYM
iajs-3842	256	5	𝑥	𝑥	NOUN
iajs-3842	256	6	)	)	PUNCT
iajs-3842	256	7	since	since	SCONJ
iajs-3842	256	8	𝑆(𝑆𝐻𝑊𝐷)(𝑥	𝑆(𝑆𝐻𝑊𝐷)(𝑥	NOUN
iajs-3842	256	9	)	)	PUNCT
iajs-3842	256	10	→	→	SYM
iajs-3842	256	11	0	0	NUM
iajs-3842	256	12	at	at	ADP
iajs-3842	256	13	𝑡	𝑡	PROPN
iajs-3842	256	14	→	→	SYM
iajs-3842	256	15	∞	∞	PROPN
iajs-3842	256	16	,	,	PUNCT
iajs-3842	256	17	then	then	ADV
iajs-3842	256	18	is	be	AUX
iajs-3842	256	19	given	give	VERB
iajs-3842	256	20	by	by	ADP
iajs-3842	256	21	:	:	PUNCT
iajs-3842	256	22	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	PROPN
iajs-3842	256	23	=	=	SYM
iajs-3842	256	24	∫	∫	PROPN
iajs-3842	256	25	𝑆(𝑆𝐻𝑊𝐷)(𝑥	𝑆(𝑆𝐻𝑊𝐷)(𝑥	PROPN
iajs-3842	256	26	)	)	PUNCT
iajs-3842	256	27	∞	∞	NOUN
iajs-3842	256	28	0	0	NUM
iajs-3842	256	29	𝑑𝑥	𝑑𝑥	NOUN
iajs-3842	256	30	=	=	SYM
iajs-3842	256	31	∫	∫	PROPN
iajs-3842	256	32	(	(	PUNCT
iajs-3842	256	33	1	1	NUM
iajs-3842	256	34	+	+	CCONJ
iajs-3842	256	35	𝛽𝑥	𝛽𝑥	PROPN
iajs-3842	256	36	𝛽2	𝛽2	PROPN
iajs-3842	256	37	+	+	CCONJ
iajs-3842	256	38	1	1	NUM
iajs-3842	256	39	)	)	PUNCT
iajs-3842	256	40	𝑒−(𝛽𝑥+𝑥𝜆	𝑒−(𝛽𝑥+𝑥𝜆	NOUN
iajs-3842	256	41	)	)	PUNCT
iajs-3842	257	1	∞	∞	NUM
iajs-3842	257	2	0	0	NUM
iajs-3842	257	3	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	257	4	recall	recall	NOUN
iajs-3842	257	5	that	that	SCONJ
iajs-3842	257	6	,	,	PUNCT
iajs-3842	257	7	𝑒−	𝑒−	NOUN
iajs-3842	257	8	𝑥𝛽	𝑥𝛽	ADJ
iajs-3842	257	9	=	=	PRON
iajs-3842	257	10	∑	∑	PUNCT
iajs-3842	257	11	(	(	PUNCT
iajs-3842	257	12	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	257	13	𝑗	𝑗	PROPN
iajs-3842	257	14	!	!	PUNCT
iajs-3842	257	15	∞	∞	PROPN
iajs-3842	258	1	𝑗=0	𝑗=0	PROPN
iajs-3842	259	1	𝑥𝜆𝑗	𝑥𝜆𝑗	NOUN
iajs-3842	259	2	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	NOUN
iajs-3842	259	3	=	=	PRON
iajs-3842	259	4	∑	∑	PUNCT
iajs-3842	259	5	(	(	PUNCT
iajs-3842	259	6	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	259	7	𝑗	𝑗	PROPN
iajs-3842	259	8	!	!	PUNCT
iajs-3842	259	9	∞	∞	NUM
iajs-3842	259	10	𝑗=0	𝑗=0	PROPN
iajs-3842	260	1	(	(	PUNCT
iajs-3842	260	2	∫	∫	PROPN
iajs-3842	260	3	𝑥𝜆𝑗	𝑥𝜆𝑗	PROPN
iajs-3842	260	4	∞	∞	PROPN
iajs-3842	260	5	0	0	NUM
iajs-3842	261	1	∙	∙	NOUN
iajs-3842	261	2	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	X
iajs-3842	262	1	+	+	SYM
iajs-3842	262	2	𝛽	𝛽	PROPN
iajs-3842	262	3	𝛽2	𝛽2	NOUN
iajs-3842	262	4	+	+	CCONJ
iajs-3842	262	5	1	1	NUM
iajs-3842	262	6	∫	∫	NOUN
iajs-3842	262	7	𝑥𝜆𝑗+1	𝑥𝜆𝑗+1	ADP
iajs-3842	262	8	∞	∞	PROPN
iajs-3842	262	9	0	0	NUM
iajs-3842	262	10	∙	∙	PROPN
iajs-3842	262	11	𝑒−𝛽𝑥𝑑𝑥	𝑒−𝛽𝑥𝑑𝑥	NOUN
iajs-3842	262	12	)	)	PUNCT
iajs-3842	262	13	let	let	VERB
iajs-3842	262	14	𝛽𝑥	𝛽𝑥	NOUN
iajs-3842	262	15	=	=	VERB
iajs-3842	262	16	𝑦	𝑦	PROPN
iajs-3842	262	17	then	then	ADV
iajs-3842	262	18	𝑥	𝑥	VERB
iajs-3842	262	19	=	=	PUNCT
iajs-3842	262	20	𝑦	𝑦	SYM
iajs-3842	262	21	𝛽	𝛽	NOUN
iajs-3842	262	22	and	and	CCONJ
iajs-3842	262	23	𝑑𝑥	𝑑𝑥	VERB
iajs-3842	262	24	=	=	SYM
iajs-3842	262	25	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	262	26	𝛽	𝛽	NOUN
iajs-3842	262	27	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	NOUN
iajs-3842	262	28	=	=	PUNCT
iajs-3842	262	29	∑	∑	PUNCT
iajs-3842	262	30	(	(	PUNCT
iajs-3842	262	31	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	262	32	𝑗	𝑗	PROPN
iajs-3842	262	33	!	!	PUNCT
iajs-3842	262	34	∞	∞	NUM
iajs-3842	263	1	𝑗=0	𝑗=0	PROPN
iajs-3842	264	1	(	(	PUNCT
iajs-3842	264	2	∫	∫	PROPN
iajs-3842	264	3	(	(	PUNCT
iajs-3842	264	4	𝑦	𝑦	PROPN
iajs-3842	264	5	𝛽	𝛽	NOUN
iajs-3842	264	6	)	)	PUNCT
iajs-3842	264	7	𝜆𝑗	𝜆𝑗	X
iajs-3842	265	1	∞	∞	NOUN
iajs-3842	265	2	0	0	NUM
iajs-3842	266	1	∙	∙	PROPN
iajs-3842	266	2	𝑒−𝑦	𝑒−𝑦	ADJ
iajs-3842	266	3	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	266	4	𝛽	𝛽	PROPN
iajs-3842	266	5	+	+	ADP
iajs-3842	266	6	𝛽	𝛽	PROPN
iajs-3842	266	7	𝛽2	𝛽2	NOUN
iajs-3842	266	8	+	+	CCONJ
iajs-3842	266	9	1	1	NUM
iajs-3842	266	10	∫	∫	PROPN
iajs-3842	266	11	(	(	PUNCT
iajs-3842	266	12	𝑦	𝑦	NOUN
iajs-3842	266	13	𝛽	𝛽	NOUN
iajs-3842	266	14	)	)	PUNCT
iajs-3842	266	15	𝜆𝑗+1	𝜆𝑗+1	NUM
iajs-3842	267	1	∞	∞	NOUN
iajs-3842	267	2	0	0	NUM
iajs-3842	268	1	∙	∙	PROPN
iajs-3842	268	2	𝑒−𝑦	𝑒−𝑦	ADJ
iajs-3842	268	3	𝑑𝑦	𝑑𝑦	NOUN
iajs-3842	268	4	𝛽	𝛽	NOUN
iajs-3842	268	5	)	)	PUNCT
iajs-3842	268	6	=	=	PUNCT
iajs-3842	268	7	∑	∑	PUNCT
iajs-3842	268	8	(	(	PUNCT
iajs-3842	268	9	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	268	10	𝑗	𝑗	PROPN
iajs-3842	268	11	!	!	PUNCT
iajs-3842	269	1	∞	∞	NUM
iajs-3842	269	2	𝑗=0	𝑗=0	PUNCT
iajs-3842	270	1	(	(	PUNCT
iajs-3842	270	2	1	1	X
iajs-3842	270	3	𝛽𝜆𝑗+1	𝛽𝜆𝑗+1	ADP
iajs-3842	270	4	∫	∫	PROPN
iajs-3842	270	5	𝑦𝜆𝑗	𝑦𝜆𝑗	PROPN
iajs-3842	270	6	∞	∞	PROPN
iajs-3842	270	7	0	0	NUM
iajs-3842	270	8	∙	∙	PROPN
iajs-3842	270	9	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	271	1	+	+	CCONJ
iajs-3842	271	2	1	1	NUM
iajs-3842	271	3	(	(	PUNCT
iajs-3842	271	4	𝛽2	𝛽2	NOUN
iajs-3842	271	5	+	+	CCONJ
iajs-3842	271	6	1)𝛽𝜆𝑗+1	1)𝛽𝜆𝑗+1	NUM
iajs-3842	271	7	∫	∫	NOUN
iajs-3842	271	8	𝑦𝜆𝑗+1	𝑦𝜆𝑗+1	PROPN
iajs-3842	271	9	∞	∞	PROPN
iajs-3842	271	10	0	0	NUM
iajs-3842	272	1	∙	∙	PROPN
iajs-3842	272	2	𝑒−𝑦𝑑𝑦	𝑒−𝑦𝑑𝑦	NOUN
iajs-3842	272	3	)	)	PUNCT
iajs-3842	272	4	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	NOUN
iajs-3842	272	5	=	=	PUNCT
iajs-3842	272	6	∑	∑	PUNCT
iajs-3842	272	7	(	(	PUNCT
iajs-3842	272	8	−1)𝑗	−1)𝑗	PUNCT
iajs-3842	272	9	𝑗	𝑗	PROPN
iajs-3842	272	10	!	!	PUNCT
iajs-3842	273	1	∞	∞	NUM
iajs-3842	273	2	𝑗=0	𝑗=0	PUNCT
iajs-3842	274	1	(	(	PUNCT
iajs-3842	274	2	1	1	NUM
iajs-3842	274	3	𝛽𝜆𝑗+1	𝛽𝜆𝑗+1	ADP
iajs-3842	274	4	∙	∙	PROPN
iajs-3842	274	5	𝛤(𝜆𝑗+1	𝛤(𝜆𝑗+1	NUM
iajs-3842	274	6	)	)	PUNCT
iajs-3842	274	7	+	+	CCONJ
iajs-3842	274	8	1	1	NUM
iajs-3842	274	9	(	(	PUNCT
iajs-3842	274	10	𝛽2	𝛽2	NOUN
iajs-3842	274	11	+	+	CCONJ
iajs-3842	274	12	1)𝛽𝜆𝑗+1	1)𝛽𝜆𝑗+1	NUM
iajs-3842	274	13	∙	∙	PROPN
iajs-3842	274	14	𝛤(𝜆𝑗+2	𝛤(𝜆𝑗+2	NOUN
iajs-3842	274	15	)	)	PUNCT
iajs-3842	274	16	)	)	PUNCT
iajs-3842	274	17	3	3	X
iajs-3842	274	18	.	.	X
iajs-3842	274	19	conclusion	conclusion	NOUN
iajs-3842	274	20	a	a	DET
iajs-3842	274	21	new	new	ADJ
iajs-3842	274	22	statistical	statistical	ADJ
iajs-3842	274	23	lifetime	lifetime	NOUN
iajs-3842	274	24	distribution	distribution	NOUN
iajs-3842	274	25	was	be	AUX
iajs-3842	274	26	introduced	introduce	VERB
iajs-3842	274	27	,	,	PUNCT
iajs-3842	274	28	which	which	PRON
iajs-3842	274	29	is	be	AUX
iajs-3842	274	30	a	a	DET
iajs-3842	274	31	mixture	mixture	NOUN
iajs-3842	274	32	of	of	ADP
iajs-3842	274	33	shanker	shanker	NOUN
iajs-3842	274	34	and	and	CCONJ
iajs-3842	274	35	weibull	weibull	NOUN
iajs-3842	274	36	distribution	distribution	NOUN
iajs-3842	274	37	depending	depend	VERB
iajs-3842	274	38	on	on	ADP
iajs-3842	274	39	their	their	PRON
iajs-3842	274	40	survival	survival	NOUN
iajs-3842	274	41	functions	function	NOUN
iajs-3842	274	42	and	and	CCONJ
iajs-3842	274	43	is	be	AUX
iajs-3842	274	44	called	call	VERB
iajs-3842	274	45	"	"	PUNCT
iajs-3842	274	46	shanker	shanker	NOUN
iajs-3842	274	47	-	-	PUNCT
iajs-3842	274	48	weibull	weibull	NOUN
iajs-3842	274	49	distribution	distribution	NOUN
iajs-3842	274	50	"	"	PUNCT
iajs-3842	274	51	.	.	PUNCT
iajs-3842	275	1	in	in	ADP
iajs-3842	275	2	addition	addition	NOUN
iajs-3842	275	3	,	,	PUNCT
iajs-3842	275	4	the	the	DET
iajs-3842	275	5	shape	shape	NOUN
iajs-3842	275	6	of	of	ADP
iajs-3842	275	7	pdf	pdf	NOUN
iajs-3842	275	8	,	,	PUNCT
iajs-3842	275	9	cdf	cdf	PROPN
iajs-3842	275	10	and	and	CCONJ
iajs-3842	275	11	the	the	DET
iajs-3842	275	12	hazard	hazard	NOUN
iajs-3842	275	13	function	function	NOUN
iajs-3842	275	14	were	be	AUX
iajs-3842	275	15	discussed	discuss	VERB
iajs-3842	275	16	.	.	PUNCT
iajs-3842	276	1	in	in	ADP
iajs-3842	276	2	addition	addition	NOUN
iajs-3842	276	3	,	,	PUNCT
iajs-3842	276	4	the	the	DET
iajs-3842	276	5	basic	basic	ADJ
iajs-3842	276	6	statistical	statistical	ADJ
iajs-3842	276	7	and	and	CCONJ
iajs-3842	276	8	mathematical	mathematical	ADJ
iajs-3842	276	9	properties	property	NOUN
iajs-3842	276	10	of	of	ADP
iajs-3842	276	11	the	the	DET
iajs-3842	276	12	new	new	ADJ
iajs-3842	276	13	distribution	distribution	NOUN
iajs-3842	276	14	such	such	ADJ
iajs-3842	276	15	as	as	ADP
iajs-3842	276	16	mode	mode	NOUN
iajs-3842	276	17	,	,	PUNCT
iajs-3842	276	18	median	median	NOUN
iajs-3842	276	19	,	,	PUNCT
iajs-3842	276	20	the	the	DET
iajs-3842	276	21	rth	rth	NOUN
iajs-3842	276	22	moments	moment	NOUN
iajs-3842	276	23	around	around	ADP
iajs-3842	276	24	the	the	DET
iajs-3842	276	25	origin	origin	NOUN
iajs-3842	276	26	and	and	CCONJ
iajs-3842	276	27	the	the	DET
iajs-3842	276	28	moment	moment	NOUN
iajs-3842	276	29	generating	generate	VERB
iajs-3842	276	30	function	function	NOUN
iajs-3842	276	31	were	be	AUX
iajs-3842	276	32	described	describe	VERB
iajs-3842	276	33	.	.	PUNCT
iajs-3842	277	1	ihjpas	ihjpas	PROPN
iajs-3842	277	2	.	.	PUNCT
iajs-3842	278	1	2025,38(2	2025,38(2	NOUN
iajs-3842	278	2	)	)	PUNCT
iajs-3842	278	3	400	400	NUM
iajs-3842	278	4	acknowledgments	acknowledgment	NOUN
iajs-3842	278	5	our	our	PRON
iajs-3842	278	6	researcher	researcher	NOUN
iajs-3842	278	7	extends	extend	VERB
iajs-3842	278	8	his	his	PRON
iajs-3842	278	9	sincere	sincere	ADJ
iajs-3842	278	10	thanks	thank	NOUN
iajs-3842	278	11	to	to	ADP
iajs-3842	278	12	the	the	DET
iajs-3842	278	13	editor	editor	NOUN
iajs-3842	278	14	and	and	CCONJ
iajs-3842	278	15	members	member	NOUN
iajs-3842	278	16	of	of	ADP
iajs-3842	278	17	the	the	DET
iajs-3842	278	18	preparatory	preparatory	PROPN
iajs-3842	278	19	committee	committee	NOUN
iajs-3842	278	20	of	of	ADP
iajs-3842	278	21	the	the	DET
iajs-3842	278	22	ibn	ibn	PROPN
iajs-3842	278	23	al	al	PROPN
iajs-3842	278	24	-	-	PUNCT
iajs-3842	278	25	haitham	haitham	PROPN
iajs-3842	278	26	journal	journal	PROPN
iajs-3842	278	27	of	of	ADP
iajs-3842	278	28	pure	pure	ADJ
iajs-3842	278	29	and	and	CCONJ
iajs-3842	278	30	applied	applied	ADJ
iajs-3842	278	31	sciences	science	NOUN
iajs-3842	278	32	.	.	PUNCT
iajs-3842	279	1	conflict	conflict	NOUN
iajs-3842	279	2	of	of	ADP
iajs-3842	279	3	interest	interest	NOUN
iajs-3842	279	4	there	there	PRON
iajs-3842	279	5	are	be	VERB
iajs-3842	279	6	no	no	DET
iajs-3842	279	7	conflicts	conflict	NOUN
iajs-3842	279	8	of	of	ADP
iajs-3842	279	9	interest	interest	NOUN
iajs-3842	279	10	.	.	PUNCT
iajs-3842	280	1	funding	funding	NOUN
iajs-3842	280	2	there	there	PRON
iajs-3842	280	3	is	be	VERB
iajs-3842	280	4	no	no	DET
iajs-3842	280	5	funding	funding	NOUN
iajs-3842	280	6	for	for	ADP
iajs-3842	280	7	the	the	DET
iajs-3842	280	8	article	article	NOUN
iajs-3842	280	9	.	.	PUNCT
iajs-3842	281	1	references	reference	NOUN
iajs-3842	281	2	1	1	NUM
iajs-3842	281	3	.	.	PUNCT
iajs-3842	281	4	gupta	gupta	PROPN
iajs-3842	281	5	rd	rd	PROPN
iajs-3842	281	6	,	,	PUNCT
iajs-3842	281	7	kundu	kundu	PROPN
iajs-3842	281	8	d.	d.	PROPN
iajs-3842	281	9	a	a	DET
iajs-3842	281	10	new	new	ADJ
iajs-3842	281	11	class	class	NOUN
iajs-3842	281	12	of	of	ADP
iajs-3842	281	13	weighted	weight	VERB
iajs-3842	281	14	exponential	exponential	ADJ
iajs-3842	281	15	distributions	distribution	NOUN
iajs-3842	281	16	.	.	PUNCT
iajs-3842	282	1	statistics	statistic	NOUN
iajs-3842	282	2	.	.	PUNCT
iajs-3842	283	1	2009;43(6):621	2009;43(6):621	NUM
iajs-3842	283	2	–	–	PUNCT
iajs-3842	283	3	634	634	NUM
iajs-3842	283	4	.	.	PUNCT
iajs-3842	284	1	https://doi.org/10.1080/02331880802605346	https://doi.org/10.1080/02331880802605346	ADJ
iajs-3842	284	2	.	.	PUNCT
iajs-3842	285	1	2	2	X
iajs-3842	285	2	.	.	X
iajs-3842	285	3	khongthip	khongthip	NOUN
iajs-3842	285	4	p	p	NOUN
iajs-3842	285	5	,	,	PUNCT
iajs-3842	285	6	patummasut	patummasut	PROPN
iajs-3842	285	7	m	m	PROPN
iajs-3842	285	8	,	,	PUNCT
iajs-3842	285	9	bodhisuwan	bodhisuwan	PROPN
iajs-3842	285	10	w.	w.	PROPN
iajs-3842	285	11	the	the	DET
iajs-3842	285	12	discrete	discrete	ADJ
iajs-3842	285	13	weighted	weight	VERB
iajs-3842	285	14	exponential	exponential	ADJ
iajs-3842	285	15	distribution	distribution	NOUN
iajs-3842	285	16	and	and	CCONJ
iajs-3842	285	17	its	its	PRON
iajs-3842	285	18	applications	application	NOUN
iajs-3842	285	19	.	.	PUNCT
iajs-3842	286	1	songklanakarin	songklanakarin	PROPN
iajs-3842	286	2	journal	journal	PROPN
iajs-3842	286	3	of	of	ADP
iajs-3842	286	4	science	science	NOUN
iajs-3842	286	5	and	and	CCONJ
iajs-3842	286	6	technology.2018;40(5):1105–1114	technology.2018;40(5):1105–1114	NOUN
iajs-3842	286	7	.	.	PUNCT
iajs-3842	287	1	https://doi.org/10.14456/sjst-psu.2018.137	https://doi.org/10.14456/sjst-psu.2018.137	NOUN
iajs-3842	287	2	.	.	PUNCT
iajs-3842	288	1	3	3	NUM
iajs-3842	288	2	.	.	X
iajs-3842	288	3	shanker	shanker	PROPN
iajs-3842	288	4	r.	r.	PROPN
iajs-3842	288	5	a	a	DET
iajs-3842	288	6	quasi	quasi	NOUN
iajs-3842	288	7	shanker	shanker	NOUN
iajs-3842	288	8	distribution	distribution	NOUN
iajs-3842	288	9	and	and	CCONJ
iajs-3842	288	10	its	its	PRON
iajs-3842	288	11	applications	application	NOUN
iajs-3842	288	12	.	.	PUNCT
iajs-3842	289	1	biometrics	biometrics	PROPN
iajs-3842	289	2	&	&	CCONJ
iajs-3842	289	3	biostatistics	biostatistics	PROPN
iajs-3842	289	4	international	international	PROPN
iajs-3842	289	5	journal	journal	PROPN
iajs-3842	289	6	.	.	PUNCT
iajs-3842	290	1	2017;6(5):338–348	2017;6(5):338–348	X
iajs-3842	290	2	.	.	PUNCT
iajs-3842	291	1	https://doi.org/10.15406/bbij.2017.06.00156	https://doi.org/10.15406/bbij.2017.06.00156	PROPN
iajs-3842	291	2	.	.	PROPN
iajs-3842	292	1	4	4	X
iajs-3842	292	2	.	.	X
iajs-3842	292	3	cordeiro	cordeiro	PROPN
iajs-3842	292	4	gm	gm	PROPN
iajs-3842	292	5	,	,	PUNCT
iajs-3842	292	6	ortega	ortega	PROPN
iajs-3842	292	7	emm	emm	PROPN
iajs-3842	292	8	,	,	PUNCT
iajs-3842	292	9	lemonte	lemonte	PROPN
iajs-3842	292	10	aj	aj	PROPN
iajs-3842	292	11	.	.	PUNCT
iajs-3842	293	1	the	the	DET
iajs-3842	293	2	exponential	exponential	ADJ
iajs-3842	293	3	-	-	PUNCT
iajs-3842	293	4	weibull	weibull	NOUN
iajs-3842	293	5	lifetime	lifetime	NOUN
iajs-3842	293	6	distribution	distribution	NOUN
iajs-3842	293	7	.	.	PUNCT
iajs-3842	294	1	journal	journal	NOUN
iajs-3842	294	2	of	of	ADP
iajs-3842	294	3	statistical	statistical	ADJ
iajs-3842	294	4	computation	computation	NOUN
iajs-3842	294	5	and	and	CCONJ
iajs-3842	294	6	simulation	simulation	NOUN
iajs-3842	294	7	.	.	PUNCT
iajs-3842	295	1	2014;84(12):2592–2606	2014;84(12):2592–2606	X
iajs-3842	295	2	.	.	PUNCT
iajs-3842	296	1	https://doi.org/10.1080/00949655.2013.797982	https://doi.org/10.1080/00949655.2013.797982	PROPN
iajs-3842	296	2	.	.	PROPN
iajs-3842	297	1	5	5	X
iajs-3842	297	2	.	.	PUNCT
iajs-3842	297	3	merovci	merovci	PROPN
iajs-3842	297	4	f	f	X
iajs-3842	297	5	,	,	PUNCT
iajs-3842	297	6	elbatal	elbatal	ADJ
iajs-3842	297	7	i.	i.	PROPN
iajs-3842	297	8	weibull	weibull	PROPN
iajs-3842	297	9	rayleigh	rayleigh	PROPN
iajs-3842	297	10	distribution	distribution	PROPN
iajs-3842	297	11	:	:	PUNCT
iajs-3842	297	12	theory	theory	NOUN
iajs-3842	297	13	and	and	CCONJ
iajs-3842	297	14	applications	application	NOUN
iajs-3842	297	15	.	.	PUNCT
iajs-3842	298	1	applied	apply	VERB
iajs-3842	298	2	mathematics	mathematics	PROPN
iajs-3842	298	3	&	&	CCONJ
iajs-3842	298	4	information	information	NOUN
iajs-3842	298	5	sciences	sciences	PROPN
iajs-3842	298	6	.	.	PUNCT
iajs-3842	299	1	2015;9(4):2127–2136	2015;9(4):2127–2136	NOUN
iajs-3842	299	2	.	.	PUNCT
iajs-3842	300	1	https://doi.org/10.12785/amis/090445	https://doi.org/10.12785/amis/090445	NOUN
iajs-3842	300	2	.	.	PUNCT
iajs-3842	301	1	6	6	NUM
iajs-3842	301	2	.	.	X
iajs-3842	301	3	nasiru	nasiru	PROPN
iajs-3842	301	4	s.	s.	PROPN
iajs-3842	301	5	serial	serial	PROPN
iajs-3842	301	6	weibull	weibull	PROPN
iajs-3842	301	7	rayleigh	rayleigh	PROPN
iajs-3842	301	8	distribution	distribution	NOUN
iajs-3842	301	9	:	:	PUNCT
iajs-3842	301	10	theory	theory	NOUN
iajs-3842	301	11	and	and	CCONJ
iajs-3842	301	12	application	application	NOUN
iajs-3842	301	13	.	.	PUNCT
iajs-3842	302	1	international	international	ADJ
iajs-3842	302	2	journal	journal	PROPN
iajs-3842	302	3	of	of	ADP
iajs-3842	302	4	computer	computer	NOUN
iajs-3842	302	5	science	science	NOUN
iajs-3842	302	6	and	and	CCONJ
iajs-3842	302	7	mathematics.2016;7(3):239–244	mathematics.2016;7(3):239–244	PROPN
iajs-3842	302	8	.	.	PUNCT
iajs-3842	303	1	https://doi.org/10.1504/ijcsm.2016.078197	https://doi.org/10.1504/ijcsm.2016.078197	PROPN
iajs-3842	303	2	.	.	PROPN
iajs-3842	303	3	7	7	NUM
iajs-3842	303	4	.	.	PUNCT
iajs-3842	303	5	mohammed	mohammed	PROPN
iajs-3842	303	6	mj	mj	PROPN
iajs-3842	303	7	,	,	PUNCT
iajs-3842	303	8	hussein	hussein	PROPN
iajs-3842	303	9	ih	ih	PROPN
iajs-3842	303	10	.	.	PUNCT
iajs-3842	304	1	study	study	NOUN
iajs-3842	304	2	of	of	ADP
iajs-3842	304	3	new	new	ADJ
iajs-3842	304	4	mixture	mixture	NOUN
iajs-3842	304	5	distribution	distribution	NOUN
iajs-3842	304	6	.	.	PUNCT
iajs-3842	305	1	in	in	ADP
iajs-3842	305	2	:	:	PUNCT
iajs-3842	305	3	proceedings	proceeding	NOUN
iajs-3842	305	4	of	of	ADP
iajs-3842	305	5	the	the	DET
iajs-3842	305	6	international	international	ADJ
iajs-3842	305	7	conference	conference	NOUN
iajs-3842	305	8	on	on	ADP
iajs-3842	305	9	engineering	engineering	NOUN
iajs-3842	305	10	and	and	CCONJ
iajs-3842	305	11	applied	applied	ADJ
iajs-3842	305	12	sciences	science	NOUN
iajs-3842	305	13	.	.	PUNCT
iajs-3842	306	1	2018;14:1–8	2018;14:1–8	NUM
iajs-3842	306	2	.	.	PUNCT
iajs-3842	306	3	8	8	NUM
iajs-3842	306	4	.	.	PUNCT
iajs-3842	307	1	abdullah	abdullah	PROPN
iajs-3842	307	2	m	m	PROPN
iajs-3842	307	3	,	,	PUNCT
iajs-3842	307	4	akma	akma	NOUN
iajs-3842	307	5	n	n	CCONJ
iajs-3842	307	6	,	,	PUNCT
iajs-3842	307	7	shitan	shitan	PROPN
iajs-3842	307	8	m	m	PROPN
iajs-3842	307	9	,	,	PUNCT
iajs-3842	307	10	merovci	merovci	PROPN
iajs-3842	307	11	f.	f.	PROPN
iajs-3842	307	12	new	new	ADJ
iajs-3842	307	13	extension	extension	NOUN
iajs-3842	307	14	of	of	ADP
iajs-3842	307	15	burr	burr	NOUN
iajs-3842	307	16	type	type	NOUN
iajs-3842	307	17	x	x	NOUN
iajs-3842	307	18	distribution	distribution	NOUN
iajs-3842	307	19	properties	property	NOUN
iajs-3842	307	20	with	with	ADP
iajs-3842	307	21	application	application	NOUN
iajs-3842	307	22	.	.	PUNCT
iajs-3842	308	1	journal	journal	PROPN
iajs-3842	308	2	of	of	ADP
iajs-3842	308	3	king	king	PROPN
iajs-3842	308	4	saud	saud	PROPN
iajs-3842	308	5	university	university	PROPN
iajs-3842	308	6	–	–	PUNCT
iajs-3842	308	7	science	science	NOUN
iajs-3842	308	8	.	.	PUNCT
iajs-3842	309	1	2018;30(4):450–457	2018;30(4):450–457	X
iajs-3842	309	2	.	.	PUNCT
iajs-3842	310	1	https://doi.org/10.1016/j.jksus.2017.05.007	https://doi.org/10.1016/j.jksus.2017.05.007	NOUN
iajs-3842	310	2	.	.	PUNCT
iajs-3842	311	1	9	9	X
iajs-3842	311	2	.	.	PUNCT
iajs-3842	311	3	jalil	jalil	PROPN
iajs-3842	311	4	m	m	PROPN
iajs-3842	311	5	,	,	PUNCT
iajs-3842	311	6	hasan	hasan	PROPN
iajs-3842	311	7	mi	mi	PROPN
iajs-3842	311	8	.	.	PROPN
iajs-3842	312	1	some	some	DET
iajs-3842	312	2	estimation	estimation	NOUN
iajs-3842	312	3	methods	method	NOUN
iajs-3842	312	4	for	for	ADP
iajs-3842	312	5	new	new	ADJ
iajs-3842	312	6	mixture	mixture	NOUN
iajs-3842	312	7	distribution	distribution	NOUN
iajs-3842	312	8	with	with	ADP
iajs-3842	312	9	simulation	simulation	NOUN
iajs-3842	312	10	and	and	CCONJ
iajs-3842	312	11	application	application	NOUN
iajs-3842	312	12	.	.	PUNCT
iajs-3842	313	1	iop	iop	PROPN
iajs-3842	313	2	conference	conference	PROPN
iajs-3842	313	3	series	series	PROPN
iajs-3842	313	4	:	:	PUNCT
iajs-3842	313	5	materials	material	NOUN
iajs-3842	313	6	science	science	NOUN
iajs-3842	313	7	and	and	CCONJ
iajs-3842	313	8	engineering	engineering	NOUN
iajs-3842	313	9	.	.	PUNCT
iajs-3842	314	1	2019;571(1):012014	2019;571(1):012014	NUM
iajs-3842	314	2	.	.	PUNCT
iajs-3842	314	3	https://doi.org/10.1088/1757-899x/571/1/012014	https://doi.org/10.1088/1757-899x/571/1/012014	PROPN
iajs-3842	314	4	.	.	PROPN
iajs-3842	314	5	10	10	NUM
iajs-3842	314	6	.	.	PUNCT
iajs-3842	315	1	mohammed	mohammed	PROPN
iajs-3842	315	2	at	at	ADP
iajs-3842	315	3	,	,	PUNCT
iajs-3842	315	4	hussein	hussein	PROPN
iajs-3842	315	5	ih	ih	PROPN
iajs-3842	315	6	.	.	PUNCT
iajs-3842	316	1	density	density	NOUN
iajs-3842	316	2	estimation	estimation	NOUN
iajs-3842	316	3	for	for	ADP
iajs-3842	316	4	right	right	ADJ
iajs-3842	316	5	censored	censored	ADJ
iajs-3842	316	6	data	datum	NOUN
iajs-3842	316	7	using	use	VERB
iajs-3842	316	8	hybrid	hybrid	ADJ
iajs-3842	316	9	breslow	breslow	NOUN
iajs-3842	316	10	and	and	CCONJ
iajs-3842	316	11	semi	semi	ADJ
iajs-3842	316	12	-	-	ADJ
iajs-3842	316	13	symmetric	symmetric	ADJ
iajs-3842	316	14	wavelet	wavelet	NOUN
iajs-3842	316	15	.	.	PUNCT
iajs-3842	317	1	journal	journal	PROPN
iajs-3842	317	2	of	of	ADP
iajs-3842	317	3	engineering	engineering	NOUN
iajs-3842	317	4	and	and	CCONJ
iajs-3842	317	5	applied	apply	VERB
iajs-3842	317	6	sciences	science	NOUN
iajs-3842	317	7	.	.	PUNCT
iajs-3842	318	1	2019;14(1):1–8	2019;14(1):1–8	NOUN
iajs-3842	318	2	.	.	PUNCT
iajs-3842	319	1	11	11	NUM
iajs-3842	319	2	.	.	PUNCT
iajs-3842	319	3	hameed	hameed	PROPN
iajs-3842	319	4	ba	ba	PROPN
iajs-3842	319	5	,	,	PUNCT
iajs-3842	319	6	salman	salman	PROPN
iajs-3842	319	7	an	an	PROPN
iajs-3842	319	8	,	,	PUNCT
iajs-3842	319	9	kalaf	kalaf	PROPN
iajs-3842	319	10	ba	ba	PROPN
iajs-3842	319	11	.	.	PUNCT
iajs-3842	320	1	on	on	ADP
iajs-3842	320	2	estimation	estimation	NOUN
iajs-3842	320	3	of	of	ADP
iajs-3842	320	4	p(y	p(y	PROPN
iajs-3842	320	5	<	<	X
iajs-3842	320	6	x	x	X
iajs-3842	320	7	)	)	PUNCT
iajs-3842	320	8	in	in	ADP
iajs-3842	320	9	case	case	NOUN
iajs-3842	320	10	inverse	inverse	NOUN
iajs-3842	320	11	kumaraswamy	kumaraswamy	NOUN
iajs-3842	320	12	distribution	distribution	NOUN
iajs-3842	320	13	.	.	PUNCT
iajs-3842	321	1	ibn	ibn	PROPN
iajs-3842	321	2	al	al	PROPN
iajs-3842	321	3	-	-	PUNCT
iajs-3842	321	4	haitham	haitham	PROPN
iajs-3842	321	5	journal	journal	PROPN
iajs-3842	321	6	of	of	ADP
iajs-3842	321	7	pure	pure	ADJ
iajs-3842	321	8	and	and	CCONJ
iajs-3842	321	9	applied	applied	ADJ
iajs-3842	321	10	science	science	NOUN
iajs-3842	321	11	.	.	PUNCT
iajs-3842	322	1	2020;33(1):414–428	2020;33(1):414–428	X
iajs-3842	322	2	.	.	PUNCT
iajs-3842	323	1	https://doi.org/10.30526/36.4.2977	https://doi.org/10.30526/36.4.2977	X
iajs-3842	323	2	.	.	PROPN
iajs-3842	323	3	12	12	NUM
iajs-3842	323	4	.	.	PUNCT
iajs-3842	324	1	mohammed	mohammed	PROPN
iajs-3842	324	2	at	at	ADP
iajs-3842	324	3	,	,	PUNCT
iajs-3842	324	4	mohammed	mohammed	PROPN
iajs-3842	324	5	mj	mj	PROPN
iajs-3842	324	6	,	,	PUNCT
iajs-3842	324	7	salman	salman	PROPN
iajs-3842	324	8	md	md	PROPN
iajs-3842	324	9	,	,	PUNCT
iajs-3842	324	10	ibrahim	ibrahim	PROPN
iajs-3842	324	11	rw	rw	PROPN
iajs-3842	324	12	.	.	PUNCT
iajs-3842	325	1	the	the	DET
iajs-3842	325	2	inverse	inverse	ADJ
iajs-3842	325	3	exponential	exponential	NOUN
iajs-3842	325	4	rayleigh	rayleigh	NOUN
iajs-3842	325	5	distribution	distribution	NOUN
iajs-3842	325	6	and	and	CCONJ
iajs-3842	325	7	related	related	ADJ
iajs-3842	325	8	concepts	concept	NOUN
iajs-3842	325	9	.	.	PUNCT
iajs-3842	326	1	italian	italian	ADJ
iajs-3842	326	2	journal	journal	NOUN
iajs-3842	326	3	of	of	ADP
iajs-3842	326	4	pure	pure	ADJ
iajs-3842	326	5	and	and	CCONJ
iajs-3842	326	6	applied	applied	ADJ
iajs-3842	326	7	mathematics	mathematic	NOUN
iajs-3842	326	8	.	.	PUNCT
iajs-3842	327	1	2022;47:852	2022;47:852	NOUN
iajs-3842	327	2	–	–	PUNCT
iajs-3842	327	3	861	861	NUM
iajs-3842	327	4	.	.	NOUN
iajs-3842	327	5	13	13	NUM
iajs-3842	327	6	.	.	PUNCT
iajs-3842	328	1	wang	wang	PROPN
iajs-3842	328	2	fk	fk	INTJ
iajs-3842	328	3	.	.	PUNCT
iajs-3842	329	1	a	a	DET
iajs-3842	329	2	new	new	ADJ
iajs-3842	329	3	model	model	NOUN
iajs-3842	329	4	with	with	ADP
iajs-3842	329	5	bath	bath	NOUN
iajs-3842	329	6	tub	tub	NOUN
iajs-3842	329	7	-	-	PUNCT
iajs-3842	329	8	shaped	shape	VERB
iajs-3842	329	9	failure	failure	NOUN
iajs-3842	329	10	rate	rate	NOUN
iajs-3842	329	11	using	use	VERB
iajs-3842	329	12	an	an	DET
iajs-3842	329	13	additive	additive	ADJ
iajs-3842	329	14	burr	burr	NOUN
iajs-3842	329	15	xii	xii	NOUN
iajs-3842	329	16	distribution	distribution	NOUN
iajs-3842	329	17	.	.	PUNCT
iajs-3842	330	1	reliability	reliability	NOUN
iajs-3842	330	2	engineering	engineering	NOUN
iajs-3842	330	3	&	&	CCONJ
iajs-3842	330	4	system	system	NOUN
iajs-3842	330	5	safety	safety	NOUN
iajs-3842	330	6	.	.	PUNCT
iajs-3842	331	1	2000;70(3):305–312	2000;70(3):305–312	NUM
iajs-3842	331	2	.	.	PUNCT
iajs-3842	331	3	https://doi.org/10.1016/s09518320(00)00066-1	https://doi.org/10.1016/s09518320(00)00066-1	PROPN
iajs-3842	331	4	.	.	PUNCT
iajs-3842	332	1	14	14	NUM
iajs-3842	332	2	.	.	PUNCT
iajs-3842	333	1	shanker	shanker	PROPN
iajs-3842	333	2	r.	r.	PROPN
iajs-3842	333	3	akash	akash	PROPN
iajs-3842	333	4	distribution	distribution	NOUN
iajs-3842	333	5	and	and	CCONJ
iajs-3842	333	6	its	its	PRON
iajs-3842	333	7	applications	application	NOUN
iajs-3842	333	8	.	.	PUNCT
iajs-3842	334	1	international	international	ADJ
iajs-3842	334	2	journal	journal	NOUN
iajs-3842	334	3	of	of	ADP
iajs-3842	334	4	probability	probability	NOUN
iajs-3842	334	5	and	and	CCONJ
iajs-3842	334	6	statistics	statistic	NOUN
iajs-3842	334	7	.	.	PUNCT
iajs-3842	335	1	2015;4(3):65–75	2015;4(3):65–75	X
iajs-3842	335	2	.	.	PUNCT
iajs-3842	335	3	https://doi.org/10.5923/j.ijps.20150403.01	https://doi.org/10.5923/j.ijps.20150403.01	PROPN
iajs-3842	335	4	.	.	PUNCT
iajs-3842	336	1	https://doi.org/10.1080/02331880802605346	https://doi.org/10.1080/02331880802605346	ADJ
iajs-3842	336	2	.	.	PUNCT
iajs-3842	337	1	https://doi.org/10.1504/ijcsm.2016.078197	https://doi.org/10.1504/ijcsm.2016.078197	PROPN
iajs-3842	337	2	https://doi.org/10.1016/j.jksus.2017.05.007	https://doi.org/10.1016/j.jksus.2017.05.007	PRON
iajs-3842	337	3	https://doi.org/10.1088/1757-899x/571/1/012014	https://doi.org/10.1088/1757-899x/571/1/012014	VERB
iajs-3842	337	4	https://doi.org/10.30526/36.4.2977	https://doi.org/10.30526/36.4.2977	DET
iajs-3842	337	5	https://doi.org/10.1016/s0951-8320(00)00066-1	https://doi.org/10.1016/s0951-8320(00)00066-1	NOUN
iajs-3842	337	6	.	.	PUNCT
iajs-3842	338	1	https://doi.org/10.1016/s0951-8320(00)00066-1	https://doi.org/10.1016/s0951-8320(00)00066-1	PROPN
iajs-3842	338	2	.	.	PUNCT
iajs-3842	339	1	ihjpas	ihjpas	PROPN
iajs-3842	339	2	.	.	PUNCT
iajs-3842	340	1	2025,38(2	2025,38(2	PROPN
iajs-3842	340	2	)	)	PUNCT
iajs-3842	340	3	401	401	NUM
iajs-3842	340	4	15	15	NUM
iajs-3842	340	5	.	.	PUNCT
iajs-3842	341	1	kilany	kilany	PROPN
iajs-3842	341	2	nm	nm	PROPN
iajs-3842	341	3	.	.	PROPN
iajs-3842	341	4	weighted	weight	VERB
iajs-3842	341	5	lomax	lomax	PROPN
iajs-3842	341	6	distribution	distribution	NOUN
iajs-3842	341	7	.	.	PUNCT
iajs-3842	342	1	springerplus	springerplus	PROPN
iajs-3842	342	2	.	.	PUNCT
iajs-3842	342	3	2016;5:1862	2016;5:1862	NUM
iajs-3842	342	4	.	.	PUNCT
iajs-3842	343	1	https://doi.org/10.1186/s40064-016-3540-0	https://doi.org/10.1186/s40064-016-3540-0	NUM
iajs-3842	343	2	.	.	PUNCT
iajs-3842	344	1	16	16	NUM
iajs-3842	344	2	.	.	PUNCT
iajs-3842	345	1	oguntunde	oguntunde	PROPN
iajs-3842	345	2	pe	pe	PROPN
iajs-3842	345	3	,	,	PUNCT
iajs-3842	345	4	ilori	ilori	PROPN
iajs-3842	345	5	ka	ka	PROPN
iajs-3842	345	6	,	,	PUNCT
iajs-3842	345	7	okagbue	okagbue	PROPN
iajs-3842	345	8	hi	hi	INTJ
iajs-3842	345	9	.	.	PUNCT
iajs-3842	346	1	the	the	DET
iajs-3842	346	2	inverted	inverted	ADJ
iajs-3842	346	3	weighted	weight	VERB
iajs-3842	346	4	exponential	exponential	ADJ
iajs-3842	346	5	distribution	distribution	NOUN
iajs-3842	346	6	with	with	ADP
iajs-3842	346	7	applications	application	NOUN
iajs-3842	346	8	.	.	PUNCT
iajs-3842	347	1	international	international	ADJ
iajs-3842	347	2	journal	journal	PROPN
iajs-3842	347	3	of	of	ADP
iajs-3842	347	4	advanced	advanced	ADJ
iajs-3842	347	5	and	and	CCONJ
iajs-3842	347	6	applied	apply	VERB
iajs-3842	347	7	sciences	science	NOUN
iajs-3842	347	8	.	.	PUNCT
iajs-3842	348	1	2018;5(1):46–50	2018;5(1):46–50	NUM
iajs-3842	348	2	.	.	PUNCT
iajs-3842	349	1	https://doi.org/10.21833/ijaas.2018.01.007	https://doi.org/10.21833/ijaas.2018.01.007	NOUN
iajs-3842	349	2	.	.	PUNCT
iajs-3842	350	1	17	17	NUM
iajs-3842	350	2	.	.	PUNCT
iajs-3842	351	1	raheem	raheem	PROPN
iajs-3842	351	2	sh	sh	PROPN
iajs-3842	351	3	,	,	PUNCT
iajs-3842	351	4	mansor	mansor	PROPN
iajs-3842	351	5	hk	hk	PROPN
iajs-3842	351	6	,	,	PUNCT
iajs-3842	351	7	kalaf	kalaf	PROPN
iajs-3842	351	8	ba	ba	PROPN
iajs-3842	351	9	.	.	PUNCT
iajs-3842	352	1	a	a	DET
iajs-3842	352	2	comparison	comparison	NOUN
iajs-3842	352	3	for	for	ADP
iajs-3842	352	4	some	some	PRON
iajs-3842	352	5	of	of	ADP
iajs-3842	352	6	the	the	DET
iajs-3842	352	7	estimation	estimation	NOUN
iajs-3842	352	8	methods	method	NOUN
iajs-3842	352	9	of	of	ADP
iajs-3842	352	10	the	the	DET
iajs-3842	352	11	parallel	parallel	ADJ
iajs-3842	352	12	stress	stress	NOUN
iajs-3842	352	13	-	-	PUNCT
iajs-3842	352	14	strength	strength	NOUN
iajs-3842	352	15	model	model	NOUN
iajs-3842	352	16	in	in	ADP
iajs-3842	352	17	the	the	DET
iajs-3842	352	18	case	case	NOUN
iajs-3842	352	19	of	of	ADP
iajs-3842	352	20	inverse	inverse	NOUN
iajs-3842	352	21	rayleigh	rayleigh	NOUN
iajs-3842	352	22	distribution	distribution	NOUN
iajs-3842	352	23	.	.	PUNCT
iajs-3842	353	1	in	in	ADP
iajs-3842	353	2	:	:	PUNCT
iajs-3842	353	3	proceedings	proceeding	NOUN
iajs-3842	353	4	of	of	ADP
iajs-3842	353	5	the	the	DET
iajs-3842	353	6	first	first	ADJ
iajs-3842	353	7	international	international	ADJ
iajs-3842	353	8	conference	conference	NOUN
iajs-3842	353	9	on	on	ADP
iajs-3842	353	10	computer	computer	NOUN
iajs-3842	353	11	applications	application	NOUN
iajs-3842	353	12	and	and	CCONJ
iajs-3842	353	13	sciences	science	NOUN
iajs-3842	353	14	.	.	PUNCT
iajs-3842	353	15	ieee	ieee	PROPN
iajs-3842	353	16	;	;	PUNCT
iajs-3842	353	17	2019	2019	NUM
iajs-3842	353	18	.	.	PUNCT
iajs-3842	354	1	p.	p.	NOUN
iajs-3842	354	2	22–27	22–27	NUM
iajs-3842	354	3	.	.	PUNCT
iajs-3842	355	1	https://doi.org/10.1109/iopcas48143.2019.9073407	https://doi.org/10.1109/iopcas48143.2019.9073407	NOUN
iajs-3842	355	2	.	.	PUNCT
iajs-3842	356	1	18	18	NUM
iajs-3842	356	2	.	.	PUNCT
iajs-3842	357	1	dong	dong	PROPN
iajs-3842	357	2	j	j	PROPN
iajs-3842	357	3	,	,	PUNCT
iajs-3842	357	4	huang	huang	PROPN
iajs-3842	357	5	cx	cx	PROPN
iajs-3842	357	6	,	,	PUNCT
iajs-3842	357	7	ahmed	ahmed	PROPN
iajs-3842	357	8	s	s	PROPN
iajs-3842	357	9	,	,	PUNCT
iajs-3842	357	10	qasim	qasim	PROPN
iajs-3842	357	11	z.	z.	PROPN
iajs-3842	358	1	an	an	DET
iajs-3842	358	2	efficient	efficient	ADJ
iajs-3842	358	3	shrinkage	shrinkage	NOUN
iajs-3842	358	4	estimators	estimator	NOUN
iajs-3842	358	5	for	for	ADP
iajs-3842	358	6	generalized	generalized	ADJ
iajs-3842	358	7	inverse	inverse	NOUN
iajs-3842	358	8	rayleigh	rayleigh	NOUN
iajs-3842	358	9	distribution	distribution	NOUN
iajs-3842	358	10	based	base	VERB
iajs-3842	358	11	on	on	ADP
iajs-3842	358	12	bounded	bounded	ADJ
iajs-3842	358	13	and	and	CCONJ
iajs-3842	358	14	series	series	VERB
iajs-3842	358	15	stress	stress	NOUN
iajs-3842	358	16	-	-	PUNCT
iajs-3842	358	17	strength	strength	NOUN
iajs-3842	358	18	.	.	PUNCT
iajs-3842	359	1	journal	journal	PROPN
iajs-3842	359	2	of	of	ADP
iajs-3842	359	3	physics	physics	PROPN
iajs-3842	359	4	:	:	PUNCT
iajs-3842	359	5	conference	conference	NOUN
iajs-3842	359	6	series	series	NOUN
iajs-3842	359	7	.	.	PUNCT
iajs-3842	360	1	2021;1897(1):012054	2021;1897(1):012054	PROPN
iajs-3842	360	2	.	.	PUNCT
iajs-3842	361	1	https://doi.org/10.1088/1742-6596/1897/1/012054	https://doi.org/10.1088/1742-6596/1897/1/012054	PROPN
iajs-3842	361	2	.	.	PROPN
iajs-3842	362	1	19	19	NUM
iajs-3842	362	2	.	.	PUNCT
iajs-3842	363	1	mohammed	mohammed	PROPN
iajs-3842	363	2	,	,	PUNCT
iajs-3842	363	3	m.j	m.j	PROPN
iajs-3842	363	4	.	.	PROPN
iajs-3842	363	5	,	,	PUNCT
iajs-3842	363	6	&	&	CCONJ
iajs-3842	363	7	mohammed	mohammed	PROPN
iajs-3842	363	8	,	,	PUNCT
iajs-3842	363	9	a.t	a.t	PROPN
iajs-3842	363	10	.	.	PROPN
iajs-3842	363	11	(	(	PUNCT
iajs-3842	363	12	2021	2021	NUM
iajs-3842	363	13	)	)	PUNCT
iajs-3842	363	14	.	.	PUNCT
iajs-3842	364	1	parameter	parameter	PROPN
iajs-3842	364	2	estimation	estimation	NOUN
iajs-3842	364	3	of	of	ADP
iajs-3842	364	4	inverse	inverse	NOUN
iajs-3842	364	5	exponential	exponential	ADJ
iajs-3842	364	6	rayleigh	rayleigh	NOUN
iajs-3842	364	7	distribution	distribution	NOUN
iajs-3842	364	8	based	base	VERB
iajs-3842	364	9	on	on	ADP
iajs-3842	364	10	classical	classical	ADJ
iajs-3842	364	11	methods	method	NOUN
iajs-3842	364	12	.	.	PUNCT
iajs-3842	365	1	international	international	ADJ
iajs-3842	365	2	journal	journal	PROPN
iajs-3842	365	3	of	of	ADP
iajs-3842	365	4	nonlinear	nonlinear	ADJ
iajs-3842	365	5	analysis	analysis	NOUN
iajs-3842	365	6	and	and	CCONJ
iajs-3842	365	7	applications	application	NOUN
iajs-3842	365	8	,	,	PUNCT
iajs-3842	365	9	12(1	12(1	NUM
iajs-3842	365	10	)	)	PUNCT
iajs-3842	365	11	,	,	PUNCT
iajs-3842	365	12	935–944	935–944	NUM
iajs-3842	365	13	.	.	PUNCT
iajs-3842	366	1	https://doi.org/10.22075/ijnaa.2021.4948	https://doi.org/10.22075/ijnaa.2021.4948	PROPN
iajs-3842	366	2	.	.	PROPN
iajs-3842	366	3	20	20	NUM
iajs-3842	366	4	.	.	PUNCT
iajs-3842	367	1	mohammed	mohammed	PROPN
iajs-3842	367	2	mj	mj	PROPN
iajs-3842	367	3	,	,	PUNCT
iajs-3842	367	4	mohammed	mohammed	PROPN
iajs-3842	367	5	at	at	ADP
iajs-3842	367	6	.	.	PROPN
iajs-3842	368	1	parameter	parameter	PROPN
iajs-3842	368	2	estimation	estimation	NOUN
iajs-3842	368	3	of	of	ADP
iajs-3842	368	4	inverse	inverse	NOUN
iajs-3842	368	5	exponential	exponential	ADJ
iajs-3842	368	6	rayleigh	rayleigh	NOUN
iajs-3842	368	7	distribution	distribution	NOUN
iajs-3842	368	8	based	base	VERB
iajs-3842	368	9	on	on	ADP
iajs-3842	368	10	classical	classical	ADJ
iajs-3842	368	11	methods	method	NOUN
iajs-3842	368	12	.	.	PUNCT
iajs-3842	369	1	international	international	ADJ
iajs-3842	369	2	journal	journal	PROPN
iajs-3842	369	3	of	of	ADP
iajs-3842	369	4	nonlinear	nonlinear	ADJ
iajs-3842	369	5	analysis	analysis	NOUN
iajs-3842	369	6	and	and	CCONJ
iajs-3842	369	7	applications	application	NOUN
iajs-3842	369	8	.	.	PUNCT
iajs-3842	370	1	2021;12(1):935–944	2021;12(1):935–944	X
iajs-3842	370	2	.	.	PUNCT
iajs-3842	371	1	https://doi.org/10.22075/ijnaa.2021.4948	https://doi.org/10.22075/ijnaa.2021.4948	PROPN
iajs-3842	371	2	.	.	PROPN
iajs-3842	371	3	21	21	NUM
iajs-3842	371	4	.	.	PUNCT
iajs-3842	372	1	jabbar	jabbar	PROPN
iajs-3842	372	2	naa	naa	PROPN
iajs-3842	372	3	,	,	PUNCT
iajs-3842	372	4	kalaf	kalaf	PROPN
iajs-3842	372	5	ba	ba	PROPN
iajs-3842	372	6	,	,	PUNCT
iajs-3842	372	7	umar	umar	PROPN
iajs-3842	372	8	ym	ym	PROPN
iajs-3842	372	9	.	.	PUNCT
iajs-3842	373	1	truncated	truncated	ADJ
iajs-3842	373	2	inverse	inverse	NOUN
iajs-3842	373	3	generalized	generalize	VERB
iajs-3842	373	4	rayleigh	rayleigh	NOUN
iajs-3842	373	5	distribution	distribution	NOUN
iajs-3842	373	6	and	and	CCONJ
iajs-3842	373	7	some	some	DET
iajs-3842	373	8	properties	property	NOUN
iajs-3842	373	9	.	.	PUNCT
iajs-3842	374	1	ibn	ibn	PROPN
iajs-3842	374	2	al	al	PROPN
iajs-3842	374	3	-	-	PUNCT
iajs-3842	374	4	haitham	haitham	PROPN
iajs-3842	374	5	journal	journal	PROPN
iajs-3842	374	6	of	of	ADP
iajs-3842	374	7	pure	pure	ADJ
iajs-3842	374	8	and	and	CCONJ
iajs-3842	374	9	applied	applied	ADJ
iajs-3842	374	10	sciences	science	NOUN
iajs-3842	374	11	.	.	PUNCT
iajs-3842	375	1	2023;36(4):414–428	2023;36(4):414–428	NUM
iajs-3842	375	2	.	.	PUNCT
iajs-3842	376	1	https://doi.org/10.30526/36.4.2977	https://doi.org/10.30526/36.4.2977	X
iajs-3842	376	2	.	.	PROPN
iajs-3842	377	1	22	22	NUM
iajs-3842	377	2	.	.	PUNCT
iajs-3842	378	1	shamran	shamran	PROPN
iajs-3842	378	2	ma	ma	PROPN
iajs-3842	378	3	,	,	PUNCT
iajs-3842	378	4	mohammed	mohammed	PROPN
iajs-3842	378	5	aa	aa	PROPN
iajs-3842	378	6	,	,	PUNCT
iajs-3842	378	7	abdullah	abdullah	PROPN
iajs-3842	378	8	ih	ih	PROPN
iajs-3842	378	9	.	.	PUNCT
iajs-3842	378	10	comparison	comparison	NOUN
iajs-3842	378	11	between	between	ADP
iajs-3842	378	12	modified	modify	VERB
iajs-3842	378	13	weighted	weight	VERB
iajs-3842	378	14	pareto	pareto	ADJ
iajs-3842	378	15	distribution	distribution	NOUN
iajs-3842	378	16	and	and	CCONJ
iajs-3842	378	17	many	many	ADJ
iajs-3842	378	18	other	other	ADJ
iajs-3842	378	19	distributions	distribution	NOUN
iajs-3842	378	20	.	.	PUNCT
iajs-3842	379	1	baghdad	baghdad	PROPN
iajs-3842	379	2	science	science	PROPN
iajs-3842	379	3	journal	journal	PROPN
iajs-3842	379	4	.	.	PUNCT
iajs-3842	380	1	2023;20(4):1108–1115	2023;20(4):1108–1115	PROPN
iajs-3842	380	2	.	.	PUNCT
iajs-3842	381	1	https://doi.org/10.21123/bsj.2023.20.4.1108	https://doi.org/10.21123/bsj.2023.20.4.1108	PROPN
iajs-3842	381	2	.	.	PUNCT
iajs-3842	382	1	23	23	NUM
iajs-3842	382	2	.	.	PUNCT
iajs-3842	383	1	ramos	ramos	PROPN
iajs-3842	383	2	pl	pl	PROPN
iajs-3842	383	3	,	,	PUNCT
iajs-3842	383	4	louzada	louzada	PROPN
iajs-3842	383	5	f	f	PROPN
iajs-3842	383	6	,	,	PUNCT
iajs-3842	383	7	ramos	ramos	PROPN
iajs-3842	383	8	e	e	PROPN
iajs-3842	383	9	,	,	PUNCT
iajs-3842	383	10	dey	dey	PROPN
iajs-3842	383	11	s.	s.	PROPN
iajs-3842	384	1	the	the	DET
iajs-3842	384	2	fréchet	fréchet	PROPN
iajs-3842	384	3	distribution	distribution	NOUN
iajs-3842	384	4	:	:	PUNCT
iajs-3842	384	5	estimation	estimation	NOUN
iajs-3842	384	6	and	and	CCONJ
iajs-3842	384	7	application	application	NOUN
iajs-3842	384	8	—	—	PUNCT
iajs-3842	384	9	an	an	DET
iajs-3842	384	10	overview	overview	NOUN
iajs-3842	384	11	.	.	PUNCT
iajs-3842	385	1	journal	journal	NOUN
iajs-3842	385	2	of	of	ADP
iajs-3842	385	3	statistical	statistical	ADJ
iajs-3842	385	4	theory	theory	NOUN
iajs-3842	385	5	and	and	CCONJ
iajs-3842	385	6	practice	practice	NOUN
iajs-3842	385	7	.	.	PUNCT
iajs-3842	386	1	2020;14:23	2020;14:23	X
iajs-3842	386	2	.	.	PUNCT
iajs-3842	387	1	https://doi.org/10.1007/s42519-02000113-7	https://doi.org/10.1007/s42519-02000113-7	PROPN
iajs-3842	387	2	.	.	PUNCT
iajs-3842	388	1	24	24	NUM
iajs-3842	388	2	.	.	PUNCT
iajs-3842	388	3	hussein	hussein	PROPN
iajs-3842	388	4	lk	lk	PROPN
iajs-3842	388	5	,	,	PUNCT
iajs-3842	388	6	hussein	hussein	PROPN
iajs-3842	388	7	ih	ih	PROPN
iajs-3842	388	8	,	,	PUNCT
iajs-3842	388	9	rasheed	rasheed	VERB
iajs-3842	388	10	ha	ha	INTJ
iajs-3842	388	11	.	.	PUNCT
iajs-3842	389	1	a	a	DET
iajs-3842	389	2	class	class	NOUN
iajs-3842	389	3	of	of	ADP
iajs-3842	389	4	exponential	exponential	ADJ
iajs-3842	389	5	rayleigh	rayleigh	NOUN
iajs-3842	389	6	distribution	distribution	NOUN
iajs-3842	389	7	and	and	CCONJ
iajs-3842	389	8	new	new	ADJ
iajs-3842	389	9	modified	modify	VERB
iajs-3842	389	10	weighted	weight	VERB
iajs-3842	389	11	exponential	exponential	ADJ
iajs-3842	389	12	rayleigh	rayleigh	NOUN
iajs-3842	389	13	distribution	distribution	NOUN
iajs-3842	389	14	with	with	ADP
iajs-3842	389	15	statistical	statistical	ADJ
iajs-3842	389	16	properties	property	NOUN
iajs-3842	389	17	.	.	PUNCT
iajs-3842	390	1	ibn	ibn	PROPN
iajs-3842	390	2	al	al	PROPN
iajs-3842	390	3	-	-	PUNCT
iajs-3842	390	4	haitham	haitham	PROPN
iajs-3842	390	5	journal	journal	PROPN
iajs-3842	390	6	of	of	ADP
iajs-3842	390	7	pure	pure	ADJ
iajs-3842	390	8	and	and	CCONJ
iajs-3842	390	9	applied	applied	ADJ
iajs-3842	390	10	sciences	science	NOUN
iajs-3842	390	11	.	.	PUNCT
iajs-3842	391	1	2023;36(2):3044	2023;36(2):3044	NUM
iajs-3842	391	2	.	.	PUNCT
iajs-3842	392	1	https://doi.org/10.30526/36.2.3044	https://doi.org/10.30526/36.2.3044	PROPN
iajs-3842	392	2	.	.	PROPN
iajs-3842	392	3	25	25	NUM
iajs-3842	392	4	.	.	PUNCT
iajs-3842	393	1	carrasco	carrasco	PROPN
iajs-3842	393	2	jmf	jmf	PROPN
iajs-3842	393	3	,	,	PUNCT
iajs-3842	393	4	ortega	ortega	PROPN
iajs-3842	393	5	emm	emm	PROPN
iajs-3842	393	6	,	,	PUNCT
iajs-3842	393	7	cordeiro	cordeiro	PROPN
iajs-3842	393	8	gm	gm	PROPN
iajs-3842	393	9	.	.	PUNCT
iajs-3842	394	1	a	a	DET
iajs-3842	394	2	generalized	generalize	VERB
iajs-3842	394	3	modified	modify	VERB
iajs-3842	394	4	weibull	weibull	NOUN
iajs-3842	394	5	distribution	distribution	NOUN
iajs-3842	394	6	for	for	ADP
iajs-3842	394	7	lifetime	lifetime	NOUN
iajs-3842	394	8	modeling	modeling	NOUN
iajs-3842	394	9	.	.	PUNCT
iajs-3842	395	1	computational	computational	ADJ
iajs-3842	395	2	statistics	statistic	NOUN
iajs-3842	395	3	&	&	CCONJ
iajs-3842	395	4	data	datum	NOUN
iajs-3842	395	5	analysis	analysis	NOUN
iajs-3842	395	6	.	.	PUNCT
iajs-3842	396	1	2008;53(2):450–462	2008;53(2):450–462	X
iajs-3842	396	2	.	.	PUNCT
iajs-3842	397	1	https://doi.org/10.1016/j.csda.2008.08.023	https://doi.org/10.1016/j.csda.2008.08.023	NUM
iajs-3842	397	2	.	.	PUNCT
iajs-3842	398	1	26	26	NUM
iajs-3842	398	2	.	.	PUNCT
iajs-3842	398	3	abramowitz	abramowitz	PROPN
iajs-3842	398	4	m	m	PROPN
iajs-3842	398	5	,	,	PUNCT
iajs-3842	398	6	stegun	stegun	VERB
iajs-3842	398	7	ia	ia	PROPN
iajs-3842	398	8	.	.	PROPN
iajs-3842	398	9	handbook	handbook	PROPN
iajs-3842	398	10	of	of	ADP
iajs-3842	398	11	mathematical	mathematical	ADJ
iajs-3842	398	12	functions	function	NOUN
iajs-3842	398	13	:	:	PUNCT
iajs-3842	398	14	with	with	ADP
iajs-3842	398	15	formulas	formula	NOUN
iajs-3842	398	16	,	,	PUNCT
iajs-3842	398	17	graphs	graph	NOUN
iajs-3842	398	18	,	,	PUNCT
iajs-3842	398	19	and	and	CCONJ
iajs-3842	398	20	mathematical	mathematical	ADJ
iajs-3842	398	21	tables	table	NOUN
iajs-3842	398	22	.	.	PUNCT
iajs-3842	399	1	new	new	PROPN
iajs-3842	399	2	york	york	PROPN
iajs-3842	399	3	:	:	PUNCT
iajs-3842	399	4	dover	dover	PROPN
iajs-3842	399	5	publications	publication	NOUN
iajs-3842	399	6	;	;	PUNCT
iajs-3842	399	7	1965	1965	NUM
iajs-3842	399	8	.	.	PUNCT
iajs-3842	400	1	https://doi.org/10.1119/1.15378	https://doi.org/10.1119/1.15378	NOUN
iajs-3842	400	2	.	.	PUNCT
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iajs-3842	401	2	.	.	PUNCT
iajs-3842	402	1	linhart	linhart	PROPN
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iajs-3842	402	6	model	model	PROPN
iajs-3842	402	7	selection	selection	PROPN
iajs-3842	402	8	.	.	PUNCT
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iajs-3842	403	10	.	.	PUNCT
iajs-3842	404	1	28	28	NUM
iajs-3842	404	2	.	.	PUNCT
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iajs-3842	408	2	journal	journal	PROPN
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iajs-3842	408	5	.	.	PUNCT
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iajs-3842	412	4	reliability	reliability	NOUN
iajs-3842	412	5	data	datum	NOUN
iajs-3842	412	6	.	.	PUNCT
iajs-3842	413	1	new	new	PROPN
iajs-3842	413	2	york	york	PROPN
iajs-3842	413	3	:	:	PUNCT
iajs-3842	413	4	john	john	PROPN
iajs-3842	413	5	wiley	wiley	PROPN
iajs-3842	413	6	&	&	CCONJ
iajs-3842	413	7	sons	son	NOUN
iajs-3842	413	8	;	;	PUNCT
iajs-3842	413	9	1998	1998	NUM
iajs-3842	413	10	.	.	PUNCT
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iajs-3842	415	2	.	.	PUNCT
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iajs-3842	417	1	https://doi.org/10.1088/1742-6596/1897/1/012054	https://doi.org/10.1088/1742-6596/1897/1/012054	PROPN
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iajs-3842	417	7	https://doi.org/10.1007/s42519-020-00113-7	https://doi.org/10.1007/s42519-020-00113-7	CCONJ
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iajs-3842	417	11	https://www.jstor.org/stable/4615982	https://www.jstor.org/stable/4615982	VERB