id	sid	tid	token	lemma	pos
iajs-4031	1	1	493	493	NUM
iajs-4031	1	2	©	©	PROPN
iajs-4031	1	3	2025	2025	NUM
iajs-4031	1	4	the	the	DET
iajs-4031	1	5	author(s	author(s	NOUN
iajs-4031	1	6	)	)	PUNCT
iajs-4031	1	7	.	.	PUNCT
iajs-4031	2	1	published	publish	VERB
iajs-4031	2	2	by	by	ADP
iajs-4031	2	3	college	college	NOUN
iajs-4031	2	4	of	of	ADP
iajs-4031	2	5	education	education	NOUN
iajs-4031	2	6	for	for	ADP
iajs-4031	2	7	pure	pure	ADJ
iajs-4031	2	8	science	science	NOUN
iajs-4031	2	9	(	(	PUNCT
iajs-4031	2	10	ibn	ibn	PROPN
iajs-4031	2	11	al	al	PROPN
iajs-4031	2	12	-	-	PUNCT
iajs-4031	2	13	haitham	haitham	PROPN
iajs-4031	2	14	)	)	PUNCT
iajs-4031	2	15	,	,	PUNCT
iajs-4031	2	16	university	university	NOUN
iajs-4031	2	17	of	of	ADP
iajs-4031	2	18	baghdad	baghdad	PROPN
iajs-4031	2	19	.	.	PUNCT
iajs-4031	3	1	this	this	PRON
iajs-4031	3	2	is	be	AUX
iajs-4031	3	3	an	an	DET
iajs-4031	3	4	open	open	ADJ
iajs-4031	3	5	-	-	PUNCT
iajs-4031	3	6	access	access	NOUN
iajs-4031	3	7	article	article	NOUN
iajs-4031	3	8	distributed	distribute	VERB
iajs-4031	3	9	under	under	ADP
iajs-4031	3	10	the	the	DET
iajs-4031	3	11	terms	term	NOUN
iajs-4031	3	12	of	of	ADP
iajs-4031	3	13	the	the	DET
iajs-4031	3	14	creative	creative	ADJ
iajs-4031	3	15	commons	common	NOUN
iajs-4031	3	16	attribution	attribution	NOUN
iajs-4031	3	17	4.0	4.0	NUM
iajs-4031	3	18	international	international	ADJ
iajs-4031	3	19	license	license	NOUN
iajs-4031	3	20	right	right	NOUN
iajs-4031	3	21	truncated	truncate	VERB
iajs-4031	3	22	shankar	shankar	ADJ
iajs-4031	3	23	distribution	distribution	NOUN
iajs-4031	3	24	and	and	CCONJ
iajs-4031	3	25	its	its	PRON
iajs-4031	3	26	properties	property	NOUN
iajs-4031	3	27	bayda	bayda	VERB
iajs-4031	3	28	atiya	atiya	PROPN
iajs-4031	3	29	kalaf	kalaf	PROPN
iajs-4031	3	30	1	1	NUM
iajs-4031	3	31	*	*	NOUN
iajs-4031	3	32	,	,	PUNCT
iajs-4031	3	33	feras	feras	PROPN
iajs-4031	3	34	sh	sh	PROPN
iajs-4031	3	35	.	.	PROPN
iajs-4031	3	36	m.	m.	PROPN
iajs-4031	3	37	batah2	batah2	PROPN
iajs-4031	3	38	,	,	PUNCT
iajs-4031	3	39	and	and	CCONJ
iajs-4031	3	40	ahmed	ahmed	PROPN
iajs-4031	3	41	issa	issa	PROPN
iajs-4031	3	42	abdul	abdul	PROPN
iajs-4031	3	43	-	-	PUNCT
iajs-4031	3	44	nabi3	nabi3	PROPN
iajs-4031	3	45	1,3	1,3	NUM
iajs-4031	3	46	department	department	NOUN
iajs-4031	3	47	of	of	ADP
iajs-4031	3	48	mathematics	mathematics	PROPN
iajs-4031	3	49	,	,	PUNCT
iajs-4031	3	50	college	college	NOUN
iajs-4031	3	51	of	of	ADP
iajs-4031	3	52	education	education	NOUN
iajs-4031	3	53	for	for	ADP
iajs-4031	3	54	pure	pure	ADJ
iajs-4031	3	55	science	science	NOUN
iajs-4031	3	56	(	(	PUNCT
iajs-4031	3	57	ibn	ibn	NOUN
iajs-4031	3	58	al	al	PROPN
iajs-4031	3	59	haitham	haitham	PROPN
iajs-4031	3	60	)	)	PUNCT
iajs-4031	3	61	,	,	PUNCT
iajs-4031	3	62	university	university	NOUN
iajs-4031	3	63	of	of	ADP
iajs-4031	3	64	baghdad	baghdad	PROPN
iajs-4031	3	65	,	,	PUNCT
iajs-4031	3	66	baghdad	baghdad	PROPN
iajs-4031	3	67	,	,	PUNCT
iajs-4031	3	68	iraq	iraq	PROPN
iajs-4031	3	69	.	.	PUNCT
iajs-4031	4	1	2	2	NUM
iajs-4031	4	2	department	department	NOUN
iajs-4031	4	3	of	of	ADP
iajs-4031	4	4	mathematics	mathematic	NOUN
iajs-4031	4	5	,	,	PUNCT
iajs-4031	4	6	college	college	NOUN
iajs-4031	4	7	of	of	ADP
iajs-4031	4	8	education	education	NOUN
iajs-4031	4	9	for	for	ADP
iajs-4031	4	10	pure	pure	ADJ
iajs-4031	4	11	science	science	NOUN
iajs-4031	4	12	,	,	PUNCT
iajs-4031	4	13	university	university	NOUN
iajs-4031	4	14	of	of	ADP
iajs-4031	4	15	anbar	anbar	PROPN
iajs-4031	4	16	,	,	PUNCT
iajs-4031	4	17	anbar	anbar	NOUN
iajs-4031	4	18	,	,	PUNCT
iajs-4031	4	19	iraq	iraq	PROPN
iajs-4031	4	20	.	.	PUNCT
iajs-4031	5	1	*	*	PUNCT
iajs-4031	5	2	corresponding	correspond	VERB
iajs-4031	5	3	author	author	NOUN
iajs-4031	5	4	.	.	PUNCT
iajs-4031	6	1	received	receive	VERB
iajs-4031	6	2	:	:	PUNCT
iajs-4031	6	3	16	16	NUM
iajs-4031	6	4	july	july	PROPN
iajs-4031	6	5	2024	2024	NUM
iajs-4031	6	6	accepted:24	accepted:24	PROPN
iajs-4031	6	7	november	november	PROPN
iajs-4031	6	8	2024	2024	NUM
iajs-4031	6	9	published:20	published:20	NOUN
iajs-4031	6	10	january	january	PROPN
iajs-4031	6	11	2025	2025	NUM
iajs-4031	6	12	doi.org/10.30526/38.1.4031	doi.org/10.30526/38.1.4031	NOUN
iajs-4031	6	13	abstract	abstract	NOUN
iajs-4031	6	14	since	since	SCONJ
iajs-4031	6	15	the	the	DET
iajs-4031	6	16	importance	importance	NOUN
iajs-4031	6	17	of	of	ADP
iajs-4031	6	18	truncated	truncated	ADJ
iajs-4031	6	19	distributions	distribution	NOUN
iajs-4031	6	20	has	have	AUX
iajs-4031	6	21	increased	increase	VERB
iajs-4031	6	22	in	in	ADP
iajs-4031	6	23	many	many	ADJ
iajs-4031	6	24	scientific	scientific	ADJ
iajs-4031	6	25	fields	field	NOUN
iajs-4031	6	26	in	in	ADP
iajs-4031	6	27	recent	recent	ADJ
iajs-4031	6	28	years	year	NOUN
iajs-4031	6	29	and	and	CCONJ
iajs-4031	6	30	they	they	PRON
iajs-4031	6	31	provide	provide	VERB
iajs-4031	6	32	valuable	valuable	ADJ
iajs-4031	6	33	insights	insight	NOUN
iajs-4031	6	34	when	when	SCONJ
iajs-4031	6	35	dealing	deal	VERB
iajs-4031	6	36	with	with	ADP
iajs-4031	6	37	censored	censor	VERB
iajs-4031	6	38	or	or	CCONJ
iajs-4031	6	39	truncated	truncated	ADJ
iajs-4031	6	40	data	datum	NOUN
iajs-4031	6	41	,	,	PUNCT
iajs-4031	6	42	this	this	DET
iajs-4031	6	43	paper	paper	NOUN
iajs-4031	6	44	presents	present	VERB
iajs-4031	6	45	the	the	DET
iajs-4031	6	46	right	right	ADJ
iajs-4031	6	47	truncated	truncate	VERB
iajs-4031	6	48	shanker	shanker	NOUN
iajs-4031	6	49	distribution	distribution	NOUN
iajs-4031	6	50	as	as	ADP
iajs-4031	6	51	a	a	DET
iajs-4031	6	52	new	new	ADJ
iajs-4031	6	53	statistical	statistical	ADJ
iajs-4031	6	54	distribution	distribution	NOUN
iajs-4031	6	55	developed	develop	VERB
iajs-4031	6	56	for	for	ADP
iajs-4031	6	57	modelling	model	VERB
iajs-4031	6	58	right	right	ADJ
iajs-4031	6	59	truncated	truncated	ADJ
iajs-4031	6	60	data	datum	NOUN
iajs-4031	6	61	.	.	PUNCT
iajs-4031	7	1	the	the	DET
iajs-4031	7	2	distribution	distribution	NOUN
iajs-4031	7	3	is	be	AUX
iajs-4031	7	4	defined	define	VERB
iajs-4031	7	5	by	by	ADP
iajs-4031	7	6	specifying	specify	VERB
iajs-4031	7	7	its	its	PRON
iajs-4031	7	8	probability	probability	NOUN
iajs-4031	7	9	density	density	NOUN
iajs-4031	7	10	function	function	NOUN
iajs-4031	7	11	and	and	CCONJ
iajs-4031	7	12	cumulative	cumulative	ADJ
iajs-4031	7	13	distribution	distribution	NOUN
iajs-4031	7	14	function	function	NOUN
iajs-4031	7	15	under	under	ADP
iajs-4031	7	16	the	the	DET
iajs-4031	7	17	truncation	truncation	NOUN
iajs-4031	7	18	condition	condition	NOUN
iajs-4031	7	19	,	,	PUNCT
iajs-4031	7	20	the	the	DET
iajs-4031	7	21	survival	survival	NOUN
iajs-4031	7	22	function	function	NOUN
iajs-4031	7	23	and	and	CCONJ
iajs-4031	7	24	the	the	DET
iajs-4031	7	25	hazard	hazard	NOUN
iajs-4031	7	26	function	function	NOUN
iajs-4031	7	27	.	.	PUNCT
iajs-4031	8	1	in	in	ADP
iajs-4031	8	2	addition	addition	NOUN
iajs-4031	8	3	,	,	PUNCT
iajs-4031	8	4	some	some	DET
iajs-4031	8	5	properties	property	NOUN
iajs-4031	8	6	of	of	ADP
iajs-4031	8	7	the	the	DET
iajs-4031	8	8	right	right	ADJ
iajs-4031	8	9	truncated	truncate	VERB
iajs-4031	8	10	shanker	shanker	NOUN
iajs-4031	8	11	distribution	distribution	NOUN
iajs-4031	8	12	are	be	AUX
iajs-4031	8	13	derived	derive	VERB
iajs-4031	8	14	,	,	PUNCT
iajs-4031	8	15	such	such	ADJ
iajs-4031	8	16	as	as	ADP
iajs-4031	8	17	the	the	DET
iajs-4031	8	18	moments	moment	NOUN
iajs-4031	8	19	around	around	ADP
iajs-4031	8	20	the	the	DET
iajs-4031	8	21	origin	origin	NOUN
iajs-4031	8	22	,	,	PUNCT
iajs-4031	8	23	the	the	DET
iajs-4031	8	24	variance	variance	NOUN
iajs-4031	8	25	,	,	PUNCT
iajs-4031	8	26	the	the	DET
iajs-4031	8	27	coefficients	coefficient	NOUN
iajs-4031	8	28	of	of	ADP
iajs-4031	8	29	skewness	skewness	NOUN
iajs-4031	8	30	and	and	CCONJ
iajs-4031	8	31	kurtosis	kurtosis	NOUN
iajs-4031	8	32	,	,	PUNCT
iajs-4031	8	33	the	the	DET
iajs-4031	8	34	moment	moment	NOUN
iajs-4031	8	35	generating	generate	VERB
iajs-4031	8	36	function	function	NOUN
iajs-4031	8	37	,	,	PUNCT
iajs-4031	8	38	and	and	CCONJ
iajs-4031	8	39	the	the	DET
iajs-4031	8	40	mean	mean	ADJ
iajs-4031	8	41	time	time	NOUN
iajs-4031	8	42	to	to	ADP
iajs-4031	8	43	failure	failure	NOUN
iajs-4031	8	44	.	.	PUNCT
iajs-4031	9	1	our	our	PRON
iajs-4031	9	2	statistical	statistical	ADJ
iajs-4031	9	3	properties	property	NOUN
iajs-4031	9	4	show	show	VERB
iajs-4031	9	5	that	that	SCONJ
iajs-4031	9	6	the	the	DET
iajs-4031	9	7	new	new	ADJ
iajs-4031	9	8	distribution	distribution	NOUN
iajs-4031	9	9	has	have	VERB
iajs-4031	9	10	the	the	DET
iajs-4031	9	11	utility	utility	NOUN
iajs-4031	9	12	and	and	CCONJ
iajs-4031	9	13	flexibility	flexibility	NOUN
iajs-4031	9	14	to	to	PART
iajs-4031	9	15	effectively	effectively	ADV
iajs-4031	9	16	model	model	VERB
iajs-4031	9	17	truncated	truncate	VERB
iajs-4031	9	18	data	data	NOUN
iajs-4031	9	19	scenarios	scenario	NOUN
iajs-4031	9	20	.	.	PUNCT
iajs-4031	10	1	keywords	keyword	NOUN
iajs-4031	10	2	:	:	PUNCT
iajs-4031	10	3	truncated	truncated	ADJ
iajs-4031	10	4	distributions	distribution	NOUN
iajs-4031	10	5	,	,	PUNCT
iajs-4031	10	6	shanker	shanker	NOUN
iajs-4031	10	7	distribution	distribution	NOUN
iajs-4031	10	8	,	,	PUNCT
iajs-4031	10	9	probability	probability	NOUN
iajs-4031	10	10	density	density	NOUN
iajs-4031	10	11	function	function	NOUN
iajs-4031	10	12	,	,	PUNCT
iajs-4031	10	13	survival	survival	NOUN
iajs-4031	10	14	function	function	NOUN
iajs-4031	10	15	,	,	PUNCT
iajs-4031	10	16	moment	moment	NOUN
iajs-4031	10	17	generating	generate	VERB
iajs-4031	10	18	function	function	NOUN
iajs-4031	10	19	.	.	PUNCT
iajs-4031	11	1	1	1	X
iajs-4031	11	2	.	.	X
iajs-4031	11	3	introduction	introduction	NOUN
iajs-4031	11	4	over	over	ADP
iajs-4031	11	5	the	the	DET
iajs-4031	11	6	last	last	ADJ
iajs-4031	11	7	few	few	ADJ
iajs-4031	11	8	decades	decade	NOUN
iajs-4031	11	9	,	,	PUNCT
iajs-4031	11	10	there	there	PRON
iajs-4031	11	11	has	have	AUX
iajs-4031	11	12	been	be	AUX
iajs-4031	11	13	a	a	DET
iajs-4031	11	14	growing	grow	VERB
iajs-4031	11	15	interest	interest	NOUN
iajs-4031	11	16	in	in	ADP
iajs-4031	11	17	lifetime	lifetime	NOUN
iajs-4031	11	18	modeling	modeling	NOUN
iajs-4031	11	19	within	within	ADP
iajs-4031	11	20	distribution	distribution	NOUN
iajs-4031	11	21	theory	theory	NOUN
iajs-4031	11	22	,	,	PUNCT
iajs-4031	11	23	leading	lead	VERB
iajs-4031	11	24	to	to	ADP
iajs-4031	11	25	the	the	DET
iajs-4031	11	26	introduction	introduction	NOUN
iajs-4031	11	27	of	of	ADP
iajs-4031	11	28	new	new	ADJ
iajs-4031	11	29	models	model	NOUN
iajs-4031	11	30	by	by	ADP
iajs-4031	11	31	statisticians	statistician	NOUN
iajs-4031	11	32	.	.	PUNCT
iajs-4031	12	1	several	several	ADJ
iajs-4031	12	2	of	of	ADP
iajs-4031	12	3	these	these	DET
iajs-4031	12	4	models	model	NOUN
iajs-4031	12	5	have	have	AUX
iajs-4031	12	6	gained	gain	VERB
iajs-4031	12	7	popularity	popularity	NOUN
iajs-4031	12	8	and	and	CCONJ
iajs-4031	12	9	are	be	AUX
iajs-4031	12	10	widely	widely	ADV
iajs-4031	12	11	used	use	VERB
iajs-4031	12	12	in	in	ADP
iajs-4031	12	13	fields	field	NOUN
iajs-4031	12	14	such	such	ADJ
iajs-4031	12	15	as	as	ADP
iajs-4031	12	16	biology	biology	NOUN
iajs-4031	12	17	,	,	PUNCT
iajs-4031	12	18	engineering	engineering	NOUN
iajs-4031	12	19	,	,	PUNCT
iajs-4031	12	20	and	and	CCONJ
iajs-4031	12	21	agriculture[1	agriculture[1	NOUN
iajs-4031	12	22	]	]	PUNCT
iajs-4031	12	23	.	.	PUNCT
iajs-4031	13	1	many	many	ADJ
iajs-4031	13	2	new	new	ADJ
iajs-4031	13	3	statistical	statistical	ADJ
iajs-4031	13	4	distributions	distribution	NOUN
iajs-4031	13	5	have	have	AUX
iajs-4031	13	6	presented	present	VERB
iajs-4031	13	7	that	that	PRON
iajs-4031	13	8	are	be	AUX
iajs-4031	13	9	more	more	ADV
iajs-4031	13	10	flexible	flexible	ADJ
iajs-4031	13	11	in	in	ADP
iajs-4031	13	12	representing	represent	VERB
iajs-4031	13	13	data	data	NOUN
iajs-4031	13	14	-	-	PUNCT
iajs-4031	13	15	life	life	NOUN
iajs-4031	13	16	.	.	PUNCT
iajs-4031	14	1	lindley	lindley	NOUN
iajs-4031	14	2	distribution	distribution	NOUN
iajs-4031	14	3	developed	develop	VERB
iajs-4031	14	4	by	by	ADP
iajs-4031	14	5	lindley(2	lindley(2	PROPN
iajs-4031	14	6	)	)	PUNCT
iajs-4031	14	7	,	,	PUNCT
iajs-4031	14	8	and	and	CCONJ
iajs-4031	14	9	the	the	DET
iajs-4031	14	10	weighted	weighted	ADJ
iajs-4031	14	11	lindley	lindley	NOUN
iajs-4031	14	12	distribution	distribution	NOUN
iajs-4031	14	13	introduced	introduce	VERB
iajs-4031	14	14	by	by	ADP
iajs-4031	14	15	ghitany	ghitany	NOUN
iajs-4031	14	16	and	and	CCONJ
iajs-4031	14	17	atieh	atieh	NOUN
iajs-4031	14	18	(	(	PUNCT
iajs-4031	14	19	3	3	NUM
iajs-4031	14	20	)	)	PUNCT
iajs-4031	14	21	.	.	PUNCT
iajs-4031	15	1	nadarajahhaghighi	nadarajahhaghighi	PROPN
iajs-4031	15	2	distribution	distribution	NOUN
iajs-4031	15	3	(	(	PUNCT
iajs-4031	15	4	4	4	NUM
iajs-4031	15	5	)	)	PUNCT
iajs-4031	15	6	.	.	PUNCT
iajs-4031	16	1	the	the	DET
iajs-4031	16	2	modified	modify	VERB
iajs-4031	16	3	-	-	PUNCT
iajs-4031	16	4	lomax	lomax	NOUN
iajs-4031	16	5	distribution	distribution	NOUN
iajs-4031	16	6	(	(	PUNCT
iajs-4031	16	7	5	5	NUM
iajs-4031	16	8	)	)	PUNCT
iajs-4031	16	9	and	and	CCONJ
iajs-4031	16	10	komal	komal	ADJ
iajs-4031	16	11	distribution	distribution	NOUN
iajs-4031	16	12	(	(	PUNCT
iajs-4031	16	13	6	6	NUM
iajs-4031	16	14	)	)	PUNCT
iajs-4031	16	15	.	.	PUNCT
iajs-4031	17	1	the	the	DET
iajs-4031	17	2	concept	concept	NOUN
iajs-4031	17	3	of	of	ADP
iajs-4031	17	4	truncated	truncated	ADJ
iajs-4031	17	5	distributions	distribution	NOUN
iajs-4031	17	6	(	(	PUNCT
iajs-4031	17	7	td	td	NOUN
iajs-4031	17	8	)	)	PUNCT
iajs-4031	17	9	provides	provide	VERB
iajs-4031	17	10	a	a	DET
iajs-4031	17	11	more	more	ADV
iajs-4031	17	12	accurate	accurate	ADJ
iajs-4031	17	13	representation	representation	NOUN
iajs-4031	17	14	of	of	ADP
iajs-4031	17	15	phenomena	phenomenon	NOUN
iajs-4031	17	16	,	,	PUNCT
iajs-4031	17	17	while	while	SCONJ
iajs-4031	17	18	still	still	ADV
iajs-4031	17	19	maintaining	maintain	VERB
iajs-4031	17	20	a	a	DET
iajs-4031	17	21	level	level	NOUN
iajs-4031	17	22	of	of	ADP
iajs-4031	17	23	generality	generality	NOUN
iajs-4031	17	24	.	.	PUNCT
iajs-4031	18	1	therefore	therefore	ADV
iajs-4031	18	2	,	,	PUNCT
iajs-4031	18	3	truncated	truncated	ADJ
iajs-4031	18	4	distributions	distribution	NOUN
iajs-4031	18	5	are	be	AUX
iajs-4031	18	6	employed	employ	VERB
iajs-4031	18	7	when	when	SCONJ
iajs-4031	18	8	events	event	NOUN
iajs-4031	18	9	are	be	AUX
iajs-4031	18	10	restricted	restrict	VERB
iajs-4031	18	11	to	to	ADP
iajs-4031	18	12	values	value	NOUN
iajs-4031	18	13	that	that	PRON
iajs-4031	18	14	are	be	AUX
iajs-4031	18	15	either	either	CCONJ
iajs-4031	18	16	higher	high	ADJ
iajs-4031	18	17	or	or	CCONJ
iajs-4031	18	18	lower	low	ADJ
iajs-4031	18	19	than	than	ADP
iajs-4031	18	20	a	a	DET
iajs-4031	18	21	certain	certain	ADJ
iajs-4031	18	22	threshold	threshold	NOUN
iajs-4031	18	23	,	,	PUNCT
iajs-4031	18	24	or	or	CCONJ
iajs-4031	18	25	fall	fall	VERB
iajs-4031	18	26	within	within	ADP
iajs-4031	18	27	a	a	DET
iajs-4031	18	28	specific	specific	ADJ
iajs-4031	18	29	rang	rang	NOUN
iajs-4031	18	30	(	(	PUNCT
iajs-4031	18	31	7	7	X
iajs-4031	18	32	)	)	PUNCT
iajs-4031	18	33	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-4031	18	34	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-4031	18	35	https://doi.org/10.30526/38.1.3501	https://doi.org/10.30526/38.1.3501	NUM
iajs-4031	18	36	https://orcid.org/my-orcid?orcid=0000-0003-1136-0055	https://orcid.org/my-orcid?orcid=0000-0003-1136-0055	NOUN
iajs-4031	18	37	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4031	18	38	https://orcid.org/0000-0003-1254-3080	https://orcid.org/0000-0003-1254-3080	PROPN
iajs-4031	18	39	mailto:sairan.hamza@garmian.edu.krd	mailto:sairan.hamza@garmian.edu.krd	NOUN
iajs-4031	18	40	https://orcid.org/0000-0003-1254-3080	https://orcid.org/0000-0003-1254-3080	PROPN
iajs-4031	18	41	mailto:ahmad.e.an@ihcoedu.uobaghdad.edu.iq	mailto:ahmad.e.an@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-4031	18	42	ihjpas	ihjpas	PROPN
iajs-4031	18	43	.	.	PUNCT
iajs-4031	19	1	2025	2025	NUM
iajs-4031	19	2	,	,	PUNCT
iajs-4031	19	3	38	38	NUM
iajs-4031	19	4	(	(	PUNCT
iajs-4031	19	5	1	1	NUM
iajs-4031	19	6	)	)	PUNCT
iajs-4031	19	7	494	494	NUM
iajs-4031	19	8	truncated	truncate	VERB
iajs-4031	19	9	a	a	DET
iajs-4031	19	10	distribution	distribution	NOUN
iajs-4031	19	11	within	within	ADP
iajs-4031	19	12	a	a	DET
iajs-4031	19	13	specific	specific	ADJ
iajs-4031	19	14	duration	duration	NOUN
iajs-4031	19	15	is	be	AUX
iajs-4031	19	16	an	an	DET
iajs-4031	19	17	ideal	ideal	ADJ
iajs-4031	19	18	solution	solution	NOUN
iajs-4031	19	19	to	to	ADP
iajs-4031	19	20	the	the	DET
iajs-4031	19	21	problem	problem	NOUN
iajs-4031	19	22	of	of	ADP
iajs-4031	19	23	the	the	DET
iajs-4031	19	24	unavailability	unavailability	NOUN
iajs-4031	19	25	of	of	ADP
iajs-4031	19	26	information	information	NOUN
iajs-4031	19	27	during	during	ADP
iajs-4031	19	28	that	that	DET
iajs-4031	19	29	period	period	NOUN
iajs-4031	19	30	for	for	ADP
iajs-4031	19	31	some	some	DET
iajs-4031	19	32	reason	reason	NOUN
iajs-4031	19	33	singh	singh	PROPN
iajs-4031	19	34	et	et	PROPN
iajs-4031	19	35	al	al	PROPN
iajs-4031	19	36	(	(	PUNCT
iajs-4031	19	37	8)	8)	NUM
iajs-4031	19	38	explained	explain	VERB
iajs-4031	19	39	that	that	SCONJ
iajs-4031	19	40	a	a	DET
iajs-4031	19	41	td	td	NOUN
iajs-4031	19	42	arises	arise	VERB
iajs-4031	19	43	in	in	ADP
iajs-4031	19	44	practical	practical	ADJ
iajs-4031	19	45	statistics	statistic	NOUN
iajs-4031	19	46	when	when	SCONJ
iajs-4031	19	47	the	the	DET
iajs-4031	19	48	ability	ability	NOUN
iajs-4031	19	49	to	to	PART
iajs-4031	19	50	document	document	VERB
iajs-4031	19	51	or	or	CCONJ
iajs-4031	19	52	have	have	VERB
iajs-4031	19	53	knowledge	knowledge	NOUN
iajs-4031	19	54	of	of	ADP
iajs-4031	19	55	events	event	NOUN
iajs-4031	19	56	is	be	AUX
iajs-4031	19	57	restricted	restrict	VERB
iajs-4031	19	58	to	to	ADP
iajs-4031	19	59	values	value	NOUN
iajs-4031	19	60	that	that	PRON
iajs-4031	19	61	fall	fall	VERB
iajs-4031	19	62	either	either	CCONJ
iajs-4031	19	63	above	above	ADP
iajs-4031	19	64	or	or	CCONJ
iajs-4031	19	65	below	below	ADP
iajs-4031	19	66	a	a	DET
iajs-4031	19	67	given	give	VERB
iajs-4031	19	68	threshold	threshold	NOUN
iajs-4031	19	69	or	or	CCONJ
iajs-4031	19	70	within	within	ADP
iajs-4031	19	71	a	a	DET
iajs-4031	19	72	specified	specified	ADJ
iajs-4031	19	73	range.analyzing	range.analyze	VERB
iajs-4031	19	74	td	td	NOUN
iajs-4031	19	75	,	,	PUNCT
iajs-4031	19	76	its	its	PRON
iajs-4031	19	77	,	,	PUNCT
iajs-4031	19	78	parameters	parameter	NOUN
iajs-4031	19	79	estimation	estimation	NOUN
iajs-4031	19	80	and	and	CCONJ
iajs-4031	19	81	applications	application	NOUN
iajs-4031	19	82	considered	consider	VERB
iajs-4031	19	83	and	and	CCONJ
iajs-4031	19	84	studied	study	VERB
iajs-4031	19	85	by	by	ADP
iajs-4031	19	86	many	many	ADJ
iajs-4031	19	87	authors	author	NOUN
iajs-4031	19	88	.	.	PUNCT
iajs-4031	20	1	najarzadegan	najarzadegan	VERB
iajs-4031	20	2	and	and	CCONJ
iajs-4031	20	3	alamatsaz,(9	alamatsaz,(9	ADJ
iajs-4031	20	4	)	)	PUNCT
iajs-4031	20	5	derived	derive	VERB
iajs-4031	20	6	truncated	truncate	VERB
iajs-4031	20	7	weibull	weibull	PROPN
iajs-4031	20	8	-	-	PUNCT
iajs-4031	20	9	g	g	NOUN
iajs-4031	20	10	distribution	distribution	NOUN
iajs-4031	20	11	.	.	PUNCT
iajs-4031	21	1	abid	abid	PROPN
iajs-4031	21	2	and	and	CCONJ
iajs-4031	21	3	abdulrazak	abdulrazak	PROPN
iajs-4031	21	4	(	(	PUNCT
iajs-4031	21	5	10	10	NUM
iajs-4031	21	6	)	)	PUNCT
iajs-4031	21	7	presented	present	VERB
iajs-4031	21	8	[	[	X
iajs-4031	21	9	0,1	0,1	NUM
iajs-4031	21	10	]	]	PUNCT
iajs-4031	21	11	truncated	truncated	ADJ
iajs-4031	21	12	frechet	frechet	PROPN
iajs-4031	21	13	-	-	PUNCT
iajs-4031	21	14	weibull	weibull	PROPN
iajs-4031	21	15	distribution	distribution	NOUN
iajs-4031	21	16	.	.	PUNCT
iajs-4031	22	1	akbarinasab	akbarinasab	NOUN
iajs-4031	22	2	and	and	CCONJ
iajs-4031	22	3	arabpour	arabpour	PRON
iajs-4031	22	4	(	(	PUNCT
iajs-4031	22	5	11	11	NUM
iajs-4031	22	6	)	)	PUNCT
iajs-4031	22	7	discussed	discuss	VERB
iajs-4031	22	8	the	the	DET
iajs-4031	22	9	truncated	truncate	VERB
iajs-4031	22	10	log	log	NOUN
iajs-4031	22	11	-	-	PUNCT
iajs-4031	22	12	logistic	logistic	NOUN
iajs-4031	22	13	family	family	NOUN
iajs-4031	22	14	of	of	ADP
iajs-4031	22	15	distributions	distribution	NOUN
iajs-4031	22	16	.	.	PUNCT
iajs-4031	23	1	altawil	altawil	NOUN
iajs-4031	23	2	(	(	PUNCT
iajs-4031	23	3	12	12	NUM
iajs-4031	23	4	)	)	PUNCT
iajs-4031	23	5	proposed	propose	VERB
iajs-4031	23	6	the	the	DET
iajs-4031	23	7	[	[	X
iajs-4031	23	8	0,1	0,1	NUM
iajs-4031	23	9	]	]	PUNCT
iajs-4031	23	10	truncated	truncate	VERB
iajs-4031	23	11	lomax	lomax	PROPN
iajs-4031	23	12	–	–	PUNCT
iajs-4031	23	13	lomax	lomax	PROPN
iajs-4031	23	14	distribution	distribution	NOUN
iajs-4031	23	15	.	.	PUNCT
iajs-4031	24	1	gul	gul	PROPN
iajs-4031	24	2	et	et	PROPN
iajs-4031	24	3	al	al	PROPN
iajs-4031	24	4	(	(	PUNCT
iajs-4031	24	5	13	13	NUM
iajs-4031	24	6	)	)	PUNCT
iajs-4031	24	7	investigated	investigate	VERB
iajs-4031	24	8	weibull	weibull	PROPN
iajs-4031	24	9	-	-	PUNCT
iajs-4031	24	10	truncated	truncate	VERB
iajs-4031	24	11	exponential	exponential	ADJ
iajs-4031	24	12	distribution	distribution	NOUN
iajs-4031	24	13	.	.	PUNCT
iajs-4031	25	1	khaleel	khaleel	PROPN
iajs-4031	25	2	et	et	PROPN
iajs-4031	25	3	al	al	PROPN
iajs-4031	25	4	(	(	PUNCT
iajs-4031	25	5	14	14	NUM
iajs-4031	25	6	)	)	PUNCT
iajs-4031	25	7	presented	present	VERB
iajs-4031	25	8	[	[	X
iajs-4031	25	9	0,1	0,1	NUM
iajs-4031	25	10	]	]	PUNCT
iajs-4031	25	11	truncated	truncate	VERB
iajs-4031	25	12	inverse	inverse	NOUN
iajs-4031	25	13	weibull	weibull	PROPN
iajs-4031	25	14	rayleigh	rayleigh	PROPN
iajs-4031	25	15	distribution	distribution	NOUN
iajs-4031	25	16	.	.	PUNCT
iajs-4031	26	1	abbas	abbas	PROPN
iajs-4031	26	2	(	(	PUNCT
iajs-4031	26	3	15	15	NUM
iajs-4031	26	4	)	)	PUNCT
iajs-4031	26	5	propose	propose	VERB
iajs-4031	26	6	the	the	DET
iajs-4031	26	7	truncated	truncated	ADJ
iajs-4031	26	8	weibull	weibull	NOUN
iajs-4031	26	9	exponential	exponential	ADJ
iajs-4031	26	10	distribution	distribution	NOUN
iajs-4031	26	11	.	.	PUNCT
iajs-4031	27	1	hussein	hussein	PROPN
iajs-4031	27	2	(	(	PUNCT
iajs-4031	27	3	16	16	NUM
iajs-4031	27	4	)	)	PUNCT
iajs-4031	27	5	defined	define	VERB
iajs-4031	27	6	a	a	DET
iajs-4031	27	7	truncated	truncated	ADJ
iajs-4031	27	8	lindley	lindley	NOUN
iajs-4031	27	9	-	-	PUNCT
iajs-4031	27	10	generated	generate	VERB
iajs-4031	27	11	family	family	NOUN
iajs-4031	27	12	of	of	ADP
iajs-4031	27	13	distributions	distribution	NOUN
iajs-4031	27	14	.	.	PUNCT
iajs-4031	28	1	qasim	qasim	PROPN
iajs-4031	28	2	(	(	PUNCT
iajs-4031	28	3	17	17	NUM
iajs-4031	28	4	)	)	PUNCT
iajs-4031	28	5	presented	present	VERB
iajs-4031	28	6	the	the	DET
iajs-4031	28	7	left	left	ADJ
iajs-4031	28	8	truncated	truncate	VERB
iajs-4031	28	9	gumbel	gumbel	NOUN
iajs-4031	28	10	-	-	PUNCT
iajs-4031	28	11	exponential	exponential	NOUN
iajs-4031	28	12	distribution	distribution	NOUN
iajs-4031	28	13	.	.	PUNCT
iajs-4031	29	1	(	(	PUNCT
iajs-4031	29	2	18	18	NUM
iajs-4031	29	3	)	)	PUNCT
iajs-4031	29	4	investigated	investigate	VERB
iajs-4031	29	5	the	the	DET
iajs-4031	29	6	truncated	truncated	ADJ
iajs-4031	29	7	inverse	inverse	NOUN
iajs-4031	29	8	generalized	generalize	VERB
iajs-4031	29	9	rayleigh	rayleigh	NOUN
iajs-4031	29	10	distribution	distribution	NOUN
iajs-4031	29	11	.	.	PUNCT
iajs-4031	30	1	this	this	DET
iajs-4031	30	2	paper	paper	NOUN
iajs-4031	30	3	aims	aim	VERB
iajs-4031	30	4	to	to	PART
iajs-4031	30	5	precent	precent	VERB
iajs-4031	30	6	a	a	DET
iajs-4031	30	7	right	right	NOUN
iajs-4031	30	8	truncated	truncate	VERB
iajs-4031	30	9	for	for	ADP
iajs-4031	30	10	shanker	shanker	NOUN
iajs-4031	30	11	distribution	distribution	NOUN
iajs-4031	30	12	and	and	CCONJ
iajs-4031	30	13	discuss	discuss	VERB
iajs-4031	30	14	the	the	DET
iajs-4031	30	15	statistical	statistical	ADJ
iajs-4031	30	16	properties	property	NOUN
iajs-4031	30	17	.	.	PUNCT
iajs-4031	31	1	this	this	DET
iajs-4031	31	2	article	article	NOUN
iajs-4031	31	3	is	be	AUX
iajs-4031	31	4	organized	organize	VERB
iajs-4031	31	5	as	as	SCONJ
iajs-4031	31	6	follows	follow	VERB
iajs-4031	31	7	:	:	PUNCT
iajs-4031	31	8	section	section	NOUN
iajs-4031	31	9	2	2	NUM
iajs-4031	31	10	discusses	discuss	VERB
iajs-4031	31	11	the	the	DET
iajs-4031	31	12	right	right	ADJ
iajs-4031	31	13	truncated	truncate	VERB
iajs-4031	31	14	shanker	shanker	NOUN
iajs-4031	31	15	distribution	distribution	NOUN
iajs-4031	31	16	,	,	PUNCT
iajs-4031	31	17	section	section	NOUN
iajs-4031	31	18	3	3	NUM
iajs-4031	31	19	finds	find	VERB
iajs-4031	31	20	the	the	DET
iajs-4031	31	21	reliability	reliability	NOUN
iajs-4031	31	22	and	and	CCONJ
iajs-4031	31	23	the	the	DET
iajs-4031	31	24	hazard	hazard	NOUN
iajs-4031	31	25	functions	function	NOUN
iajs-4031	31	26	,	,	PUNCT
iajs-4031	31	27	section	section	NOUN
iajs-4031	31	28	4	4	NUM
iajs-4031	31	29	derives	derive	VERB
iajs-4031	31	30	some	some	PRON
iajs-4031	31	31	of	of	ADP
iajs-4031	31	32	the	the	DET
iajs-4031	31	33	statistical	statistical	ADJ
iajs-4031	31	34	properties	property	NOUN
iajs-4031	31	35	,	,	PUNCT
iajs-4031	31	36	and	and	CCONJ
iajs-4031	31	37	section	section	NOUN
iajs-4031	31	38	5	5	NUM
iajs-4031	31	39	presents	present	VERB
iajs-4031	31	40	the	the	DET
iajs-4031	31	41	mean	mean	ADJ
iajs-4031	31	42	time	time	NOUN
iajs-4031	31	43	to	to	ADP
iajs-4031	31	44	failure	failure	NOUN
iajs-4031	31	45	,	,	PUNCT
iajs-4031	31	46	finally	finally	ADV
iajs-4031	31	47	,	,	PUNCT
iajs-4031	31	48	section	section	NOUN
iajs-4031	31	49	6	6	NUM
iajs-4031	31	50	.	.	PUNCT
iajs-4031	32	1	provides	provide	VERB
iajs-4031	32	2	the	the	DET
iajs-4031	32	3	conclusion	conclusion	NOUN
iajs-4031	32	4	.	.	PUNCT
iajs-4031	33	1	2	2	X
iajs-4031	33	2	.	.	X
iajs-4031	33	3	right	right	ADJ
iajs-4031	33	4	truncated	truncate	VERB
iajs-4031	33	5	shanker	shanker	NOUN
iajs-4031	33	6	distribution	distribution	NOUN
iajs-4031	33	7	shanker	shanker	NOUN
iajs-4031	33	8	(	(	PUNCT
iajs-4031	33	9	19	19	NUM
iajs-4031	33	10	)	)	PUNCT
iajs-4031	33	11	,	,	PUNCT
iajs-4031	33	12	presented	present	VERB
iajs-4031	33	13	a	a	DET
iajs-4031	33	14	new	new	ADJ
iajs-4031	33	15	lifetime	lifetime	NOUN
iajs-4031	33	16	distribution	distribution	NOUN
iajs-4031	33	17	called	call	VERB
iajs-4031	33	18	the	the	DET
iajs-4031	33	19	"	"	PUNCT
iajs-4031	33	20	shanker	shanker	NOUN
iajs-4031	33	21	distribution	distribution	NOUN
iajs-4031	33	22	"	"	PUNCT
iajs-4031	33	23	,	,	PUNCT
iajs-4031	33	24	by	by	ADP
iajs-4031	33	25	mixture	mixture	NOUN
iajs-4031	33	26	''	''	PUNCT
iajs-4031	33	27	gamma(2,β	gamma(2,β	PROPN
iajs-4031	33	28	)	)	PUNCT
iajs-4031	33	29	distribution	distribution	NOUN
iajs-4031	33	30	''	''	PUNCT
iajs-4031	33	31	with	with	ADP
iajs-4031	33	32	''	''	PUNCT
iajs-4031	33	33	exponential	exponential	ADJ
iajs-4031	33	34	distribution	distribution	NOUN
iajs-4031	33	35	''	''	PUNCT
iajs-4031	33	36	the	the	DET
iajs-4031	33	37	pdf	pdf	NOUN
iajs-4031	33	38	and	and	CCONJ
iajs-4031	33	39	the	the	DET
iajs-4031	33	40	cdf	cdf	PROPN
iajs-4031	33	41	of	of	ADP
iajs-4031	33	42	shanker	shank	ADJ
iajs-4031	33	43	distribution	distribution	NOUN
iajs-4031	33	44	are	be	AUX
iajs-4031	33	45	respectively	respectively	ADV
iajs-4031	33	46	:	:	PUNCT
iajs-4031	33	47	𝑓𝑆𝐻(𝑥	𝑓𝑆𝐻(𝑥	NUM
iajs-4031	33	48	,	,	PUNCT
iajs-4031	33	49	𝜗	𝜗	NOUN
iajs-4031	33	50	)	)	PUNCT
iajs-4031	33	51	=	=	NOUN
iajs-4031	33	52	𝜗2	𝜗2	PROPN
iajs-4031	33	53	𝜗2	𝜗2	PROPN
iajs-4031	33	54	+	+	PROPN
iajs-4031	33	55	1	1	NUM
iajs-4031	33	56	(	(	PUNCT
iajs-4031	33	57	𝜗	𝜗	NOUN
iajs-4031	33	58	+	+	X
iajs-4031	33	59	𝑥)𝑒−𝜗𝑥	𝑥)𝑒−𝜗𝑥	NUM
iajs-4031	33	60	;	;	PUNCT
iajs-4031	33	61	𝑥	𝑥	PRON
iajs-4031	33	62	>	>	X
iajs-4031	33	63	0	0	NUM
iajs-4031	33	64	,	,	PUNCT
iajs-4031	33	65	𝜗	𝜗	X
iajs-4031	33	66	>	>	X
iajs-4031	33	67	0	0	PUNCT
iajs-4031	33	68	(	(	PUNCT
iajs-4031	33	69	1	1	NUM
iajs-4031	33	70	)	)	PUNCT
iajs-4031	33	71	𝐹𝑆𝐻(𝑥	𝐹𝑆𝐻(𝑥	NUM
iajs-4031	33	72	,	,	PUNCT
iajs-4031	33	73	𝜗	𝜗	NOUN
iajs-4031	33	74	)	)	PUNCT
iajs-4031	33	75	=	=	SYM
iajs-4031	33	76	1	1	NUM
iajs-4031	33	77	−	−	NOUN
iajs-4031	33	78	(	(	PUNCT
iajs-4031	33	79	𝜗2	𝜗2	PROPN
iajs-4031	33	80	+	+	PROPN
iajs-4031	33	81	1)+𝜗𝑥	1)+𝜗𝑥	NUM
iajs-4031	33	82	𝜗2	𝜗2	NOUN
iajs-4031	33	83	+	+	PROPN
iajs-4031	33	84	1	1	NUM
iajs-4031	33	85	𝑒−𝜗𝑥	𝑒−𝜗𝑥	NOUN
iajs-4031	33	86	;	;	PUNCT
iajs-4031	33	87	𝑥	𝑥	PROPN
iajs-4031	33	88	>	>	X
iajs-4031	33	89	0	0	NUM
iajs-4031	33	90	,	,	PUNCT
iajs-4031	33	91	𝜗	𝜗	X
iajs-4031	33	92	>	>	X
iajs-4031	33	93	0	0	PUNCT
iajs-4031	34	1	(	(	PUNCT
iajs-4031	34	2	2	2	NUM
iajs-4031	34	3	)	)	PUNCT
iajs-4031	34	4	while	while	SCONJ
iajs-4031	34	5	the	the	DET
iajs-4031	34	6	survival	survival	NOUN
iajs-4031	34	7	function	function	NOUN
iajs-4031	34	8	and	and	CCONJ
iajs-4031	34	9	hazard	hazard	NOUN
iajs-4031	34	10	rate	rate	NOUN
iajs-4031	34	11	are	be	AUX
iajs-4031	34	12	defined	define	VERB
iajs-4031	34	13	as	as	ADP
iajs-4031	34	14	:	:	PUNCT
iajs-4031	34	15	𝑆𝑆𝐻(𝑥	𝑆𝑆𝐻(𝑥	NUM
iajs-4031	34	16	,	,	PUNCT
iajs-4031	34	17	𝜗	𝜗	NOUN
iajs-4031	34	18	)	)	PUNCT
iajs-4031	34	19	=	=	SYM
iajs-4031	34	20	(	(	PUNCT
iajs-4031	34	21	𝜗2	𝜗2	PROPN
iajs-4031	34	22	+	+	PROPN
iajs-4031	34	23	1)+𝜗𝑥	1)+𝜗𝑥	NUM
iajs-4031	34	24	𝜗2	𝜗2	NOUN
iajs-4031	34	25	+	+	PROPN
iajs-4031	34	26	1	1	NUM
iajs-4031	34	27	𝑒−𝜗𝑥	𝑒−𝜗𝑥	NOUN
iajs-4031	34	28	(	(	PUNCT
iajs-4031	34	29	3	3	NUM
iajs-4031	34	30	)	)	PUNCT
iajs-4031	34	31	ℎ𝑠ℎ	ℎ𝑠ℎ	NOUN
iajs-4031	34	32	=	=	PUNCT
iajs-4031	34	33	𝜗2(𝜗2	𝜗2(𝜗2	X
iajs-4031	34	34	+	+	NOUN
iajs-4031	34	35	1	1	NUM
iajs-4031	34	36	)	)	PUNCT
iajs-4031	34	37	(	(	PUNCT
iajs-4031	34	38	𝜗2	𝜗2	PROPN
iajs-4031	34	39	+	+	PROPN
iajs-4031	34	40	1)+𝜗𝑥	1)+𝜗𝑥	NUM
iajs-4031	34	41	(	(	PUNCT
iajs-4031	34	42	4	4	NUM
iajs-4031	34	43	)	)	PUNCT
iajs-4031	34	44	let	let	VERB
iajs-4031	34	45	the	the	DET
iajs-4031	34	46	random	random	ADJ
iajs-4031	34	47	variable	variable	NOUN
iajs-4031	34	48	𝑋	𝑋	PROPN
iajs-4031	34	49	belong	belong	VERB
iajs-4031	34	50	to	to	ADP
iajs-4031	34	51	the	the	DET
iajs-4031	34	52	interval	interval	NOUN
iajs-4031	35	1	[	[	X
iajs-4031	35	2	0	0	NUM
iajs-4031	35	3	,	,	PUNCT
iajs-4031	35	4	1	1	NUM
iajs-4031	35	5	]	]	PUNCT
iajs-4031	35	6	,	,	PUNCT
iajs-4031	35	7	−∞	−∞	ADP
iajs-4031	35	8	<	<	X
iajs-4031	35	9	0	0	NUM
iajs-4031	35	10	≤	≤	NUM
iajs-4031	35	11	𝑥	𝑥	PUNCT
iajs-4031	35	12	≤	≤	NUM
iajs-4031	35	13	1	1	NUM
iajs-4031	35	14	<	<	X
iajs-4031	35	15	∞	∞	PROPN
iajs-4031	35	16	.	.	PUNCT
iajs-4031	36	1	then	then	ADV
iajs-4031	36	2	,	,	PUNCT
iajs-4031	36	3	the	the	DET
iajs-4031	36	4	conditional	conditional	ADJ
iajs-4031	36	5	on	on	ADP
iajs-4031	36	6	0	0	NUM
iajs-4031	36	7	≤	≤	NUM
iajs-4031	36	8	𝑥	𝑥	DET
iajs-4031	36	9	≤	≤	NUM
iajs-4031	36	10	1	1	NUM
iajs-4031	36	11	has	have	VERB
iajs-4031	36	12	a	a	DET
iajs-4031	36	13	truncated	truncate	VERB
iajs-4031	36	14	distribution	distribution	NOUN
iajs-4031	36	15	(	(	PUNCT
iajs-4031	36	16	20	20	NUM
iajs-4031	36	17	)	)	PUNCT
iajs-4031	36	18	.the	.the	PRON
iajs-4031	36	19	pdf	pdf	NOUN
iajs-4031	36	20	and	and	CCONJ
iajs-4031	36	21	the	the	DET
iajs-4031	36	22	cdf	cdf	PROPN
iajs-4031	36	23	for	for	ADP
iajs-4031	36	24	0	0	NUM
iajs-4031	36	25	≤	≤	NUM
iajs-4031	36	26	𝑥	𝑥	PRON
iajs-4031	36	27	≤	≤	NUM
iajs-4031	36	28	1	1	NUM
iajs-4031	36	29	where	where	SCONJ
iajs-4031	36	30	x	x	PRON
iajs-4031	36	31	is	be	AUX
iajs-4031	36	32	followed	follow	VERB
iajs-4031	36	33	shanker	shanker	NOUN
iajs-4031	36	34	distribution	distribution	NOUN
iajs-4031	36	35	are	be	AUX
iajs-4031	36	36	given	give	VERB
iajs-4031	36	37	by	by	ADP
iajs-4031	36	38	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	PROPN
iajs-4031	36	39	,	,	PUNCT
iajs-4031	36	40	𝜗	𝜗	NOUN
iajs-4031	36	41	)	)	PUNCT
iajs-4031	36	42	=	=	SYM
iajs-4031	36	43	𝑓𝑆𝐻(𝑥,𝜗	𝑓𝑆𝐻(𝑥,𝜗	PROPN
iajs-4031	36	44	)	)	PUNCT
iajs-4031	36	45	𝐹𝑠ℎ(1,𝜗	𝐹𝑠ℎ(1,𝜗	NOUN
iajs-4031	36	46	)	)	PUNCT
iajs-4031	36	47	(	(	PUNCT
iajs-4031	36	48	5	5	X
iajs-4031	36	49	)	)	PUNCT
iajs-4031	36	50	𝑊𝑅𝑇𝑆𝐻(𝑥	𝑊𝑅𝑇𝑆𝐻(𝑥	PROPN
iajs-4031	36	51	,	,	PUNCT
iajs-4031	36	52	𝜗	𝜗	NOUN
iajs-4031	36	53	)	)	PUNCT
iajs-4031	36	54	=	=	SYM
iajs-4031	36	55	𝐹𝑆𝐻(𝑥,𝜗	𝐹𝑆𝐻(𝑥,𝜗	ADJ
iajs-4031	36	56	)	)	PUNCT
iajs-4031	36	57	𝐹𝑠ℎ(1,𝜗	𝐹𝑠ℎ(1,𝜗	NOUN
iajs-4031	36	58	)	)	PUNCT
iajs-4031	36	59	(	(	PUNCT
iajs-4031	36	60	6	6	NUM
iajs-4031	36	61	)	)	PUNCT
iajs-4031	36	62	but	but	CCONJ
iajs-4031	36	63	𝐹𝑠ℎ(1	𝐹𝑠ℎ(1	NUM
iajs-4031	36	64	,	,	PUNCT
iajs-4031	36	65	𝜗	𝜗	NOUN
iajs-4031	36	66	)	)	PUNCT
iajs-4031	36	67	=	=	SYM
iajs-4031	36	68	(	(	PUNCT
iajs-4031	36	69	𝜗2	𝜗2	PROPN
iajs-4031	36	70	+	+	NOUN
iajs-4031	36	71	1)−[(𝜗2+𝜗+1	1)−[(𝜗2+𝜗+1	NOUN
iajs-4031	36	72	]	]	X
iajs-4031	36	73	𝜗2	𝜗2	PROPN
iajs-4031	36	74	+	+	ADJ
iajs-4031	36	75	1	1	NUM
iajs-4031	36	76	𝑒−𝜗	𝑒−𝜗	NOUN
iajs-4031	36	77	;	;	PUNCT
iajs-4031	36	78	,	,	PUNCT
iajs-4031	36	79	𝜗	𝜗	X
iajs-4031	36	80	>	>	X
iajs-4031	36	81	0	0	PUNCT
iajs-4031	37	1	(	(	PUNCT
iajs-4031	37	2	7	7	NUM
iajs-4031	37	3	)	)	PUNCT
iajs-4031	37	4	substituting(1	substituting(1	PROPN
iajs-4031	37	5	)	)	PUNCT
iajs-4031	37	6	and	and	CCONJ
iajs-4031	37	7	(	(	PUNCT
iajs-4031	37	8	7)in	7)in	NOUN
iajs-4031	37	9	(	(	PUNCT
iajs-4031	37	10	5	5	NUM
iajs-4031	37	11	)	)	PUNCT
iajs-4031	37	12	gives	give	VERB
iajs-4031	37	13	the	the	DET
iajs-4031	37	14	pdf	pdf	NOUN
iajs-4031	37	15	of	of	ADP
iajs-4031	37	16	right	right	ADJ
iajs-4031	37	17	truncated	truncate	VERB
iajs-4031	37	18	shanker	shanker	NOUN
iajs-4031	37	19	distribution	distribution	NOUN
iajs-4031	37	20	(	(	PUNCT
iajs-4031	37	21	rtshd	rtshd	NOUN
iajs-4031	37	22	)	)	PUNCT
iajs-4031	37	23	.	.	PUNCT
iajs-4031	38	1	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	VERB
iajs-4031	38	2	,	,	PUNCT
iajs-4031	38	3	𝜗	𝜗	NOUN
iajs-4031	38	4	)	)	PUNCT
iajs-4031	38	5	=	=	SYM
iajs-4031	39	1	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	PROPN
iajs-4031	39	2	𝜗2	𝜗2	PROPN
iajs-4031	39	3	+	+	PROPN
iajs-4031	39	4	1	1	NUM
iajs-4031	39	5	(	(	PUNCT
iajs-4031	39	6	𝜗2	𝜗2	PROPN
iajs-4031	39	7	+	+	NOUN
iajs-4031	39	8	1)−[(𝜗2+𝜗+1	1)−[(𝜗2+𝜗+1	NOUN
iajs-4031	39	9	]	]	X
iajs-4031	39	10	𝜗2	𝜗2	PROPN
iajs-4031	39	11	+	+	SYM
iajs-4031	39	12	1	1	NUM
iajs-4031	39	13	𝑒−𝜗	𝑒−𝜗	NOUN
iajs-4031	39	14	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	VERB
iajs-4031	39	15	,	,	PUNCT
iajs-4031	39	16	𝜗	𝜗	NOUN
iajs-4031	39	17	)	)	PUNCT
iajs-4031	39	18	=	=	SYM
iajs-4031	40	1	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	PROPN
iajs-4031	40	2	(	(	PUNCT
iajs-4031	40	3	𝜗2	𝜗2	PROPN
iajs-4031	40	4	+	+	ADJ
iajs-4031	40	5	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	40	6	(	(	PUNCT
iajs-4031	40	7	8)	8)	NUM
iajs-4031	40	8	ihjpas	ihjpa	NOUN
iajs-4031	40	9	.	.	PUNCT
iajs-4031	41	1	2025	2025	NUM
iajs-4031	41	2	,	,	PUNCT
iajs-4031	41	3	38	38	NUM
iajs-4031	41	4	(	(	PUNCT
iajs-4031	41	5	1	1	NUM
iajs-4031	41	6	)	)	PUNCT
iajs-4031	41	7	495	495	NUM
iajs-4031	41	8	and	and	CCONJ
iajs-4031	41	9	substitute	substitute	NOUN
iajs-4031	41	10	(	(	PUNCT
iajs-4031	41	11	2	2	NUM
iajs-4031	41	12	)	)	PUNCT
iajs-4031	41	13	and	and	CCONJ
iajs-4031	41	14	(	(	PUNCT
iajs-4031	41	15	7	7	X
iajs-4031	41	16	)	)	PUNCT
iajs-4031	41	17	in	in	ADP
iajs-4031	41	18	(	(	PUNCT
iajs-4031	41	19	6	6	NUM
iajs-4031	41	20	)	)	PUNCT
iajs-4031	41	21	gives	give	VERB
iajs-4031	41	22	the	the	DET
iajs-4031	41	23	c.d.f	c.d.f	NOUN
iajs-4031	41	24	of	of	ADP
iajs-4031	41	25	rtshd	rtshd	NOUN
iajs-4031	41	26	as	as	SCONJ
iajs-4031	41	27	follows	follow	VERB
iajs-4031	41	28	:	:	PUNCT
iajs-4031	41	29	𝑊𝑅𝑇𝑆𝐻(𝑥	𝑊𝑅𝑇𝑆𝐻(𝑥	VERB
iajs-4031	41	30	,	,	PUNCT
iajs-4031	41	31	𝜗	𝜗	NOUN
iajs-4031	41	32	)	)	PUNCT
iajs-4031	41	33	=	=	SYM
iajs-4031	41	34	(	(	PUNCT
iajs-4031	41	35	𝜗2	𝜗2	PROPN
iajs-4031	41	36	+	+	NOUN
iajs-4031	41	37	1)+[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	1)+[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	NOUN
iajs-4031	41	38	(	(	PUNCT
iajs-4031	41	39	𝜗2	𝜗2	PROPN
iajs-4031	41	40	+	+	ADJ
iajs-4031	41	41	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	41	42	(	(	PUNCT
iajs-4031	41	43	9	9	NUM
iajs-4031	41	44	)	)	SYM
iajs-4031	41	45	3	3	NUM
iajs-4031	41	46	.	.	X
iajs-4031	42	1	reliability	reliability	NOUN
iajs-4031	42	2	function	function	NOUN
iajs-4031	42	3	and	and	CCONJ
iajs-4031	42	4	hazard	hazard	NOUN
iajs-4031	42	5	function	function	NOUN
iajs-4031	42	6	according	accord	VERB
iajs-4031	42	7	to	to	ADP
iajs-4031	42	8	the	the	DET
iajs-4031	42	9	previous	previous	ADJ
iajs-4031	42	10	equations	equation	NOUN
iajs-4031	42	11	the	the	DET
iajs-4031	42	12	reliability	reliability	NOUN
iajs-4031	42	13	function	function	NOUN
iajs-4031	42	14	of	of	ADP
iajs-4031	42	15	(	(	PUNCT
iajs-4031	42	16	rtshd	rtshd	INTJ
iajs-4031	42	17	)	)	PUNCT
iajs-4031	42	18	can	can	AUX
iajs-4031	42	19	be	be	AUX
iajs-4031	42	20	derived	derive	VERB
iajs-4031	42	21	as	as	ADP
iajs-4031	42	22	follows	follow	VERB
iajs-4031	42	23	(	(	PUNCT
iajs-4031	42	24	21	21	NUM
iajs-4031	42	25	):	):	PUNCT
iajs-4031	42	26	𝑅𝑅𝑇𝑆𝐻(𝑥	𝑅𝑅𝑇𝑆𝐻(𝑥	NOUN
iajs-4031	42	27	,	,	PUNCT
iajs-4031	42	28	𝜗	𝜗	NOUN
iajs-4031	42	29	)	)	PUNCT
iajs-4031	42	30	=	=	SYM
iajs-4031	43	1	1	1	NUM
iajs-4031	43	2	−𝑊𝑅𝑇𝑆𝐻(𝑥	−𝑊𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	43	3	,	,	PUNCT
iajs-4031	43	4	𝜗	𝜗	NOUN
iajs-4031	43	5	)	)	PUNCT
iajs-4031	43	6	𝑅𝑅𝑇𝑆𝐻(𝑥	𝑅𝑅𝑇𝑆𝐻(𝑥	VERB
iajs-4031	43	7	,	,	PUNCT
iajs-4031	43	8	𝜗	𝜗	NOUN
iajs-4031	43	9	)	)	PUNCT
iajs-4031	43	10	=	=	SYM
iajs-4031	43	11	1	1	NUM
iajs-4031	43	12	−	−	NOUN
iajs-4031	43	13	(	(	PUNCT
iajs-4031	43	14	𝜗2	𝜗2	PROPN
iajs-4031	43	15	+	+	NOUN
iajs-4031	43	16	1)+[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	1)+[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	NOUN
iajs-4031	43	17	(	(	PUNCT
iajs-4031	43	18	𝜗2	𝜗2	PROPN
iajs-4031	43	19	+	+	ADJ
iajs-4031	43	20	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	43	21	(	(	PUNCT
iajs-4031	43	22	10	10	NUM
iajs-4031	43	23	)	)	PUNCT
iajs-4031	43	24	by	by	ADP
iajs-4031	43	25	simplifying	simplify	VERB
iajs-4031	43	26	(	(	PUNCT
iajs-4031	43	27	10	10	NUM
iajs-4031	43	28	)	)	PUNCT
iajs-4031	43	29	we	we	PRON
iajs-4031	43	30	obtain	obtain	VERB
iajs-4031	43	31	;	;	PUNCT
iajs-4031	43	32	𝑅𝑅𝑇𝑆𝐻(𝑥	𝑅𝑅𝑇𝑆𝐻(𝑥	NOUN
iajs-4031	43	33	,	,	PUNCT
iajs-4031	43	34	𝜗	𝜗	NOUN
iajs-4031	43	35	)	)	PUNCT
iajs-4031	43	36	=	=	SYM
iajs-4031	44	1	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	NOUN
iajs-4031	44	2	(	(	PUNCT
iajs-4031	44	3	𝜗2	𝜗2	PROPN
iajs-4031	44	4	+	+	ADJ
iajs-4031	44	5	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	44	6	(	(	PUNCT
iajs-4031	44	7	11	11	NUM
iajs-4031	44	8	)	)	PUNCT
iajs-4031	44	9	and	and	CCONJ
iajs-4031	44	10	the	the	DET
iajs-4031	44	11	hazard	hazard	NOUN
iajs-4031	44	12	rate	rate	NOUN
iajs-4031	44	13	function	function	NOUN
iajs-4031	44	14	is	be	AUX
iajs-4031	44	15	ℎ𝑅𝑇𝑆𝐻(𝑥	ℎ𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	44	16	,	,	PUNCT
iajs-4031	44	17	𝜗	𝜗	NOUN
iajs-4031	44	18	)	)	PUNCT
iajs-4031	44	19	=	=	PUNCT
iajs-4031	45	1	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	45	2	,	,	PUNCT
iajs-4031	45	3	𝜗	𝜗	NOUN
iajs-4031	45	4	)	)	PUNCT
iajs-4031	45	5	𝑆𝑅𝑇𝑆𝐻(𝑥	𝑆𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	45	6	,	,	PUNCT
iajs-4031	45	7	𝜗	𝜗	NOUN
iajs-4031	45	8	)	)	PUNCT
iajs-4031	45	9	=	=	SYM
iajs-4031	46	1	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	PROPN
iajs-4031	46	2	(	(	PUNCT
iajs-4031	46	3	𝜗2	𝜗2	PROPN
iajs-4031	46	4	+	+	PROPN
iajs-4031	46	5	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	46	6	×	×	NOUN
iajs-4031	46	7	(	(	PUNCT
iajs-4031	46	8	𝜗2	𝜗2	PROPN
iajs-4031	46	9	+	+	NOUN
iajs-4031	46	10	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	46	11	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	X
iajs-4031	46	12	then	then	ADV
iajs-4031	46	13	ℎ𝑅𝑇𝑆𝐻(𝑥	ℎ𝑅𝑇𝑆𝐻(𝑥	VERB
iajs-4031	46	14	,	,	PUNCT
iajs-4031	46	15	𝜗	𝜗	NOUN
iajs-4031	46	16	)	)	PUNCT
iajs-4031	46	17	=	=	PUNCT
iajs-4031	47	1	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	NUM
iajs-4031	47	2	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	X
iajs-4031	47	3	(	(	PUNCT
iajs-4031	47	4	12	12	NUM
iajs-4031	47	5	)	)	PUNCT
iajs-4031	47	6	4	4	NUM
iajs-4031	47	7	.	.	PUNCT
iajs-4031	48	1	statistical	statistical	ADJ
iajs-4031	48	2	properties	property	NOUN
iajs-4031	48	3	of	of	ADP
iajs-4031	48	4	right	right	ADJ
iajs-4031	48	5	truncated	truncate	VERB
iajs-4031	48	6	shanker	shanker	NOUN
iajs-4031	48	7	distribution	distribution	NOUN
iajs-4031	48	8	this	this	DET
iajs-4031	48	9	section	section	NOUN
iajs-4031	48	10	presents	present	VERB
iajs-4031	48	11	the	the	DET
iajs-4031	48	12	derivation	derivation	NOUN
iajs-4031	48	13	and	and	CCONJ
iajs-4031	48	14	calculation	calculation	NOUN
iajs-4031	48	15	of	of	ADP
iajs-4031	48	16	certain	certain	ADJ
iajs-4031	48	17	statistical	statistical	ADJ
iajs-4031	48	18	properties	property	NOUN
iajs-4031	48	19	of	of	ADP
iajs-4031	48	20	the	the	DET
iajs-4031	48	21	(	(	PUNCT
iajs-4031	48	22	rtshd	rtshd	NOUN
iajs-4031	48	23	)	)	PUNCT
iajs-4031	48	24	4.1	4.1	NUM
iajs-4031	48	25	.	.	PUNCT
iajs-4031	49	1	moments	moment	NOUN
iajs-4031	49	2	about	about	ADP
iajs-4031	49	3	origin	origin	NOUN
iajs-4031	49	4	moments	moment	NOUN
iajs-4031	49	5	about	about	ADP
iajs-4031	49	6	the	the	DET
iajs-4031	49	7	origin	origin	NOUN
iajs-4031	49	8	can	can	AUX
iajs-4031	49	9	be	be	AUX
iajs-4031	49	10	derived	derive	VERB
iajs-4031	49	11	as	as	ADP
iajs-4031	49	12	bellow	bellow	ADJ
iajs-4031	49	13	(	(	PUNCT
iajs-4031	49	14	22,23	22,23	NOUN
iajs-4031	49	15	):	):	PUNCT
iajs-4031	50	1	𝑀𝑘	𝑀𝑘	PROPN
iajs-4031	50	2	′	′	NUM
iajs-4031	50	3	(	(	PUNCT
iajs-4031	50	4	𝑥	𝑥	NOUN
iajs-4031	50	5	)	)	PUNCT
iajs-4031	50	6	=	=	SYM
iajs-4031	51	1	∫	∫	PROPN
iajs-4031	51	2	𝑥𝑘	𝑥𝑘	NOUN
iajs-4031	51	3	1	1	NUM
iajs-4031	51	4	0	0	NUM
iajs-4031	51	5	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	51	6	,	,	PUNCT
iajs-4031	51	7	𝜗)𝑑𝑥	𝜗)𝑑𝑥	PROPN
iajs-4031	51	8	=	=	SYM
iajs-4031	51	9	∫	∫	PROPN
iajs-4031	51	10	𝑥𝑘	𝑥𝑘	NOUN
iajs-4031	52	1	1	1	NUM
iajs-4031	52	2	0	0	NUM
iajs-4031	52	3	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	PROPN
iajs-4031	52	4	(	(	PUNCT
iajs-4031	52	5	𝜗2	𝜗2	PROPN
iajs-4031	52	6	+	+	NOUN
iajs-4031	52	7	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	52	8	𝑑𝑥	𝑑𝑥	VERB
iajs-4031	52	9	(	(	PUNCT
iajs-4031	52	10	12	12	NUM
iajs-4031	52	11	)	)	PUNCT
iajs-4031	52	12	=	=	SYM
iajs-4031	52	13	𝜗2	𝜗2	PROPN
iajs-4031	52	14	(	(	PUNCT
iajs-4031	52	15	𝜗2	𝜗2	PROPN
iajs-4031	52	16	+	+	PROPN
iajs-4031	52	17	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NUM
iajs-4031	53	1	∫	∫	PROPN
iajs-4031	53	2	𝑥𝑘	𝑥𝑘	NOUN
iajs-4031	53	3	1	1	NUM
iajs-4031	53	4	0	0	NUM
iajs-4031	53	5	(	(	PUNCT
iajs-4031	53	6	𝜗	𝜗	PROPN
iajs-4031	53	7	+	+	CCONJ
iajs-4031	53	8	𝑥)𝑒−𝜗𝑥𝑑𝑥	𝑥)𝑒−𝜗𝑥𝑑𝑥	PROPN
iajs-4031	53	9	(	(	PUNCT
iajs-4031	53	10	13	13	NUM
iajs-4031	53	11	)	)	PUNCT
iajs-4031	53	12	depending	depend	VERB
iajs-4031	53	13	on	on	ADP
iajs-4031	53	14	taylor	taylor	PROPN
iajs-4031	53	15	's	's	PART
iajs-4031	53	16	expansion	expansion	NOUN
iajs-4031	53	17	𝑒−𝜗𝑥	𝑒−𝜗𝑥	NOUN
iajs-4031	53	18	=	=	PUNCT
iajs-4031	53	19	∑	∑	PUNCT
iajs-4031	53	20	(	(	PUNCT
iajs-4031	53	21	−𝜗𝑥)𝑗	−𝜗𝑥)𝑗	NOUN
iajs-4031	53	22	𝑗	𝑗	PROPN
iajs-4031	53	23	!	!	PUNCT
iajs-4031	53	24	∞	∞	PROPN
iajs-4031	54	1	𝑗=0	𝑗=0	PROPN
iajs-4031	54	2	then	then	ADV
iajs-4031	54	3	equation(13	equation(13	NOUN
iajs-4031	54	4	)	)	PUNCT
iajs-4031	54	5	can	can	AUX
iajs-4031	54	6	be	be	AUX
iajs-4031	54	7	represented	represent	VERB
iajs-4031	54	8	by	by	ADP
iajs-4031	54	9	:	:	PUNCT
iajs-4031	54	10	𝑀𝑘	𝑀𝑘	PROPN
iajs-4031	54	11	′	′	NUM
iajs-4031	54	12	(	(	PUNCT
iajs-4031	54	13	𝑥	𝑥	NOUN
iajs-4031	54	14	)	)	PUNCT
iajs-4031	54	15	=	=	SYM
iajs-4031	54	16	𝜗2	𝜗2	PROPN
iajs-4031	54	17	(	(	PUNCT
iajs-4031	54	18	𝜗2	𝜗2	PROPN
iajs-4031	54	19	+	+	PROPN
iajs-4031	54	20	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	54	21	∑	∑	PUNCT
iajs-4031	54	22	(	(	PUNCT
iajs-4031	54	23	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	54	24	𝑗	𝑗	NOUN
iajs-4031	54	25	!	!	PUNCT
iajs-4031	54	26	∞	∞	PROPN
iajs-4031	55	1	𝑗=0	𝑗=0	PROPN
iajs-4031	56	1	∫	∫	PROPN
iajs-4031	56	2	𝑥𝑘+𝑗	𝑥𝑘+𝑗	PROPN
iajs-4031	56	3	1	1	NUM
iajs-4031	56	4	0	0	NUM
iajs-4031	56	5	(	(	PUNCT
iajs-4031	56	6	𝜗	𝜗	NOUN
iajs-4031	57	1	+	+	CCONJ
iajs-4031	57	2	𝑥)𝑑𝑥	𝑥)𝑑𝑥	PROPN
iajs-4031	57	3	=	=	SYM
iajs-4031	57	4	𝜗2	𝜗2	PROPN
iajs-4031	57	5	(	(	PUNCT
iajs-4031	57	6	𝜗2	𝜗2	PROPN
iajs-4031	57	7	+	+	PROPN
iajs-4031	57	8	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	57	9	∑	∑	PUNCT
iajs-4031	57	10	(	(	PUNCT
iajs-4031	57	11	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	57	12	𝑗	𝑗	PROPN
iajs-4031	57	13	!	!	PROPN
iajs-4031	57	14	∫	∫	PROPN
iajs-4031	57	15	(	(	PUNCT
iajs-4031	57	16	𝜗𝑥𝑘+𝑗	𝜗𝑥𝑘+𝑗	PROPN
iajs-4031	57	17	+	+	CCONJ
iajs-4031	57	18	𝑥𝑘+𝑗+1	𝑥𝑘+𝑗+1	ADV
iajs-4031	57	19	)	)	PUNCT
iajs-4031	57	20	1	1	NUM
iajs-4031	57	21	0	0	NUM
iajs-4031	58	1	𝑑𝑥∞	𝑑𝑥∞	PROPN
iajs-4031	58	2	𝑗=0	𝑗=0	PROPN
iajs-4031	59	1	then	then	ADV
iajs-4031	59	2	𝑀𝑘	𝑀𝑘	PROPN
iajs-4031	59	3	′	′	NUM
iajs-4031	59	4	(	(	PUNCT
iajs-4031	59	5	𝑥	𝑥	NOUN
iajs-4031	59	6	)	)	PUNCT
iajs-4031	59	7	=	=	SYM
iajs-4031	59	8	𝜗2	𝜗2	PROPN
iajs-4031	59	9	(	(	PUNCT
iajs-4031	59	10	𝜗2	𝜗2	PROPN
iajs-4031	59	11	+	+	PROPN
iajs-4031	59	12	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	59	13	∑	∑	PUNCT
iajs-4031	59	14	(	(	PUNCT
iajs-4031	59	15	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	59	16	𝑗	𝑗	NOUN
iajs-4031	59	17	!	!	PUNCT
iajs-4031	59	18	∞	∞	PROPN
iajs-4031	59	19	𝑗=0	𝑗=0	PUNCT
iajs-4031	60	1	(	(	PUNCT
iajs-4031	60	2	𝜗	𝜗	NUM
iajs-4031	60	3	𝑘+𝑗+1	𝑘+𝑗+1	NOUN
iajs-4031	60	4	+	+	CCONJ
iajs-4031	60	5	1	1	NUM
iajs-4031	60	6	𝑘+𝑗+2	𝑘+𝑗+2	NOUN
iajs-4031	60	7	)	)	PUNCT
iajs-4031	60	8	(	(	PUNCT
iajs-4031	60	9	14	14	NUM
iajs-4031	60	10	)	)	PUNCT
iajs-4031	60	11	substitute	substitute	NOUN
iajs-4031	60	12	k	k	NOUN
iajs-4031	60	13	by	by	ADP
iajs-4031	60	14	1,2,3,4	1,2,3,4	NUM
iajs-4031	60	15	respectively	respectively	ADV
iajs-4031	60	16	we	we	PRON
iajs-4031	60	17	get	get	VERB
iajs-4031	60	18	:	:	PUNCT
iajs-4031	60	19	𝑀1	𝑀1	PROPN
iajs-4031	60	20	′(𝑥	′(𝑥	NOUN
iajs-4031	60	21	)	)	PUNCT
iajs-4031	60	22	=	=	SYM
iajs-4031	60	23	𝐸(𝑋	𝐸(𝑋	NOUN
iajs-4031	60	24	)	)	PUNCT
iajs-4031	60	25	=	=	SYM
iajs-4031	60	26	𝜗2	𝜗2	PROPN
iajs-4031	60	27	(	(	PUNCT
iajs-4031	60	28	𝜗2	𝜗2	PROPN
iajs-4031	60	29	+	+	PROPN
iajs-4031	60	30	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	60	31	∑	∑	PUNCT
iajs-4031	60	32	(	(	PUNCT
iajs-4031	60	33	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	60	34	𝑗	𝑗	NOUN
iajs-4031	60	35	!	!	PUNCT
iajs-4031	60	36	∞	∞	PROPN
iajs-4031	60	37	𝑗=0	𝑗=0	PUNCT
iajs-4031	60	38	(	(	PUNCT
iajs-4031	60	39	𝜗	𝜗	SYM
iajs-4031	60	40	𝑗+2	𝑗+2	NUM
iajs-4031	60	41	+	+	CCONJ
iajs-4031	60	42	1	1	NUM
iajs-4031	60	43	𝑗+3	𝑗+3	NUM
iajs-4031	60	44	)	)	PUNCT
iajs-4031	60	45	(	(	PUNCT
iajs-4031	60	46	15	15	NUM
iajs-4031	60	47	)	)	PUNCT
iajs-4031	60	48	𝑀2	𝑀2	PROPN
iajs-4031	60	49	′(𝑥	′(𝑥	NUM
iajs-4031	60	50	)	)	PUNCT
iajs-4031	60	51	=	=	PUNCT
iajs-4031	60	52	𝐸(𝑋2	𝐸(𝑋2	NOUN
iajs-4031	60	53	)	)	PUNCT
iajs-4031	60	54	=	=	SYM
iajs-4031	60	55	𝜗2	𝜗2	PROPN
iajs-4031	60	56	(	(	PUNCT
iajs-4031	60	57	𝜗2	𝜗2	PROPN
iajs-4031	60	58	+	+	PROPN
iajs-4031	60	59	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	60	60	∑	∑	PUNCT
iajs-4031	60	61	(	(	PUNCT
iajs-4031	60	62	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	60	63	𝑗	𝑗	NOUN
iajs-4031	60	64	!	!	PUNCT
iajs-4031	60	65	∞	∞	PROPN
iajs-4031	60	66	𝑗=0	𝑗=0	PROPN
iajs-4031	60	67	(	(	PUNCT
iajs-4031	60	68	𝜗	𝜗	NOUN
iajs-4031	60	69	𝑗+3	𝑗+3	NUM
iajs-4031	60	70	+	+	NUM
iajs-4031	60	71	1	1	NUM
iajs-4031	60	72	𝑗+4	𝑗+4	NUM
iajs-4031	60	73	)	)	PUNCT
iajs-4031	60	74	(	(	PUNCT
iajs-4031	60	75	16	16	NUM
iajs-4031	60	76	)	)	PUNCT
iajs-4031	60	77	ihjpas	ihjpa	NOUN
iajs-4031	60	78	.	.	PUNCT
iajs-4031	61	1	2025	2025	NUM
iajs-4031	61	2	,	,	PUNCT
iajs-4031	61	3	38	38	NUM
iajs-4031	61	4	(	(	PUNCT
iajs-4031	61	5	1	1	NUM
iajs-4031	61	6	)	)	PUNCT
iajs-4031	61	7	496	496	NUM
iajs-4031	61	8	𝑀3	𝑀3	PROPN
iajs-4031	61	9	′(𝑥	′(𝑥	NOUN
iajs-4031	61	10	)	)	PUNCT
iajs-4031	61	11	=	=	SYM
iajs-4031	61	12	𝐸(𝑋3	𝐸(𝑋3	ADJ
iajs-4031	61	13	)	)	PUNCT
iajs-4031	61	14	=	=	SYM
iajs-4031	61	15	𝜗2	𝜗2	PROPN
iajs-4031	61	16	(	(	PUNCT
iajs-4031	61	17	𝜗2	𝜗2	PROPN
iajs-4031	61	18	+	+	PROPN
iajs-4031	61	19	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	61	20	∑	∑	PUNCT
iajs-4031	61	21	(	(	PUNCT
iajs-4031	61	22	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	61	23	𝑗	𝑗	NOUN
iajs-4031	61	24	!	!	PUNCT
iajs-4031	62	1	∞	∞	PROPN
iajs-4031	62	2	𝑗=0	𝑗=0	PUNCT
iajs-4031	63	1	(	(	PUNCT
iajs-4031	63	2	𝜗	𝜗	X
iajs-4031	63	3	𝑗+4	𝑗+4	X
iajs-4031	63	4	+	+	NOUN
iajs-4031	63	5	1	1	NUM
iajs-4031	63	6	𝑗+5	𝑗+5	NUM
iajs-4031	63	7	)	)	PUNCT
iajs-4031	63	8	(	(	PUNCT
iajs-4031	63	9	17	17	NUM
iajs-4031	63	10	)	)	PUNCT
iajs-4031	63	11	𝑀4	𝑀4	PROPN
iajs-4031	63	12	′(𝑥	′(𝑥	PROPN
iajs-4031	63	13	)	)	PUNCT
iajs-4031	63	14	=	=	SYM
iajs-4031	63	15	𝐸(𝑋4	𝐸(𝑋4	NOUN
iajs-4031	63	16	)	)	PUNCT
iajs-4031	63	17	=	=	SYM
iajs-4031	63	18	𝜗2	𝜗2	PROPN
iajs-4031	63	19	(	(	PUNCT
iajs-4031	63	20	𝜗2	𝜗2	PROPN
iajs-4031	63	21	+	+	PROPN
iajs-4031	63	22	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	63	23	∑	∑	PUNCT
iajs-4031	63	24	(	(	PUNCT
iajs-4031	63	25	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	63	26	𝑗	𝑗	NOUN
iajs-4031	63	27	!	!	PUNCT
iajs-4031	64	1	∞	∞	PROPN
iajs-4031	64	2	𝑗=0	𝑗=0	PUNCT
iajs-4031	65	1	(	(	PUNCT
iajs-4031	65	2	𝜗	𝜗	X
iajs-4031	65	3	𝑗+4	𝑗+4	X
iajs-4031	65	4	+	+	NOUN
iajs-4031	65	5	1	1	NUM
iajs-4031	65	6	𝑗+5	𝑗+5	NUM
iajs-4031	65	7	)	)	PUNCT
iajs-4031	65	8	(	(	PUNCT
iajs-4031	65	9	18	18	NUM
iajs-4031	65	10	)	)	PUNCT
iajs-4031	65	11	4.2	4.2	NUM
iajs-4031	65	12	.	.	PUNCT
iajs-4031	66	1	variance	variance	NOUN
iajs-4031	66	2	,	,	PUNCT
iajs-4031	66	3	skewness	skewness	NOUN
iajs-4031	66	4	and	and	CCONJ
iajs-4031	66	5	kurtosis	kurtosis	NOUN
iajs-4031	66	6	to	to	PART
iajs-4031	66	7	discuss	discuss	VERB
iajs-4031	66	8	more	more	ADJ
iajs-4031	66	9	properties	property	NOUN
iajs-4031	66	10	of	of	ADP
iajs-4031	66	11	the	the	DET
iajs-4031	66	12	truncated	truncate	VERB
iajs-4031	66	13	shanker	shanker	NOUN
iajs-4031	66	14	distribution	distribution	NOUN
iajs-4031	66	15	the	the	DET
iajs-4031	66	16	variance	variance	NOUN
iajs-4031	66	17	,	,	PUNCT
iajs-4031	66	18	skewness	skewness	NOUN
iajs-4031	66	19	and	and	CCONJ
iajs-4031	66	20	kurtosis	kurtosis	NOUN
iajs-4031	66	21	will	will	AUX
iajs-4031	66	22	be	be	AUX
iajs-4031	66	23	derived	derive	VERB
iajs-4031	66	24	respectively	respectively	ADV
iajs-4031	66	25	:	:	PUNCT
iajs-4031	66	26	𝑣𝑎𝑟(𝑥	𝑣𝑎𝑟(𝑥	NUM
iajs-4031	66	27	)	)	PUNCT
iajs-4031	66	28	=	=	SYM
iajs-4031	67	1	𝑀2	𝑀2	PROPN
iajs-4031	67	2	′	′	NUM
iajs-4031	67	3	(	(	PUNCT
iajs-4031	67	4	𝑥	𝑥	NOUN
iajs-4031	67	5	)	)	PUNCT
iajs-4031	67	6	−	−	PROPN
iajs-4031	67	7	(	(	PUNCT
iajs-4031	67	8	𝑀1	𝑀1	NOUN
iajs-4031	67	9	′(𝑥	′(𝑥	NUM
iajs-4031	67	10	)	)	PUNCT
iajs-4031	67	11	)	)	PUNCT
iajs-4031	67	12	2	2	NUM
iajs-4031	67	13	,	,	PUNCT
iajs-4031	67	14	then	then	ADV
iajs-4031	67	15	from	from	ADP
iajs-4031	67	16	equation	equation	NOUN
iajs-4031	67	17	(	(	PUNCT
iajs-4031	67	18	16	16	NUM
iajs-4031	67	19	)	)	PUNCT
iajs-4031	67	20	and	and	CCONJ
iajs-4031	67	21	(	(	PUNCT
iajs-4031	67	22	15	15	X
iajs-4031	67	23	)	)	PUNCT
iajs-4031	67	24	we	we	PRON
iajs-4031	67	25	get	get	VERB
iajs-4031	67	26	𝑣𝑎𝑟𝑅𝑇𝑆𝐻(𝑥	𝑣𝑎𝑟𝑅𝑇𝑆𝐻(𝑥	NUM
iajs-4031	67	27	)	)	PUNCT
iajs-4031	67	28	=	=	SYM
iajs-4031	67	29	𝜗2	𝜗2	PROPN
iajs-4031	67	30	(	(	PUNCT
iajs-4031	67	31	𝜗2	𝜗2	PROPN
iajs-4031	67	32	+	+	PROPN
iajs-4031	67	33	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	67	34	∑	∑	PUNCT
iajs-4031	67	35	(	(	PUNCT
iajs-4031	67	36	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	67	37	𝑗	𝑗	NOUN
iajs-4031	67	38	!	!	PUNCT
iajs-4031	68	1	∞	∞	PROPN
iajs-4031	68	2	𝑗=0	𝑗=0	PROPN
iajs-4031	69	1	(	(	PUNCT
iajs-4031	69	2	𝜗	𝜗	NOUN
iajs-4031	69	3	𝑗+3	𝑗+3	NUM
iajs-4031	69	4	+	+	NUM
iajs-4031	69	5	1	1	NUM
iajs-4031	69	6	𝑗+4	𝑗+4	NUM
iajs-4031	69	7	)	)	PUNCT
iajs-4031	69	8	−	−	PROPN
iajs-4031	69	9	(	(	PUNCT
iajs-4031	69	10	𝜗2	𝜗2	PROPN
iajs-4031	69	11	(	(	PUNCT
iajs-4031	69	12	𝜗2	𝜗2	PROPN
iajs-4031	69	13	+	+	PROPN
iajs-4031	69	14	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	69	15	∑	∑	PUNCT
iajs-4031	69	16	(	(	PUNCT
iajs-4031	69	17	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	69	18	𝑗	𝑗	NOUN
iajs-4031	69	19	!	!	PUNCT
iajs-4031	69	20	∞	∞	PROPN
iajs-4031	70	1	𝑗=0	𝑗=0	PUNCT
iajs-4031	70	2	(	(	PUNCT
iajs-4031	70	3	𝜗	𝜗	SYM
iajs-4031	70	4	𝑗+2	𝑗+2	NUM
iajs-4031	70	5	+	+	CCONJ
iajs-4031	70	6	1	1	NUM
iajs-4031	70	7	𝑗+3	𝑗+3	NUM
iajs-4031	70	8	)	)	PUNCT
iajs-4031	70	9	)	)	PUNCT
iajs-4031	70	10	2	2	NUM
iajs-4031	70	11	(	(	PUNCT
iajs-4031	70	12	19	19	NUM
iajs-4031	70	13	)	)	PUNCT
iajs-4031	70	14	the	the	DET
iajs-4031	70	15	formula	formula	NOUN
iajs-4031	70	16	of	of	ADP
iajs-4031	70	17	the	the	DET
iajs-4031	70	18	skewness	skewness	NOUN
iajs-4031	70	19	is	be	AUX
iajs-4031	70	20	𝑠𝑘	𝑠𝑘	NOUN
iajs-4031	70	21	=	=	SYM
iajs-4031	70	22	𝜇3	𝜇3	PROPN
iajs-4031	70	23	(	(	PUNCT
iajs-4031	70	24	𝜇2	𝜇2	PROPN
iajs-4031	70	25	)	)	PUNCT
iajs-4031	70	26	3	3	NUM
iajs-4031	70	27	2	2	NUM
iajs-4031	70	28	=	=	SYM
iajs-4031	70	29	𝐸(𝑥3)−3𝜇𝐸(𝑥2)+2𝜇3	𝐸(𝑥3)−3𝜇𝐸(𝑥2)+2𝜇3	PROPN
iajs-4031	70	30	(	(	PUNCT
iajs-4031	70	31	𝜎2	𝜎2	PROPN
iajs-4031	70	32	)	)	PUNCT
iajs-4031	70	33	3	3	NUM
iajs-4031	70	34	2	2	NUM
iajs-4031	70	35	so	so	ADV
iajs-4031	70	36	from	from	ADP
iajs-4031	70	37	equation	equation	NOUN
iajs-4031	70	38	(	(	PUNCT
iajs-4031	70	39	17),(15),(16	17),(15),(16	NUM
iajs-4031	70	40	)	)	PUNCT
iajs-4031	70	41	and	and	CCONJ
iajs-4031	70	42	(	(	PUNCT
iajs-4031	70	43	19	19	NUM
iajs-4031	70	44	)	)	PUNCT
iajs-4031	70	45	we	we	PRON
iajs-4031	70	46	find	find	VERB
iajs-4031	70	47	that	that	SCONJ
iajs-4031	70	48	:	:	PUNCT
iajs-4031	71	1	𝑠𝑘𝑅𝑇𝑆𝐻	𝑠𝑘𝑅𝑇𝑆𝐻	PROPN
iajs-4031	71	2	=	=	SYM
iajs-4031	71	3	{	{	PUNCT
iajs-4031	71	4	𝜗2	𝜗2	PROPN
iajs-4031	71	5	(	(	PUNCT
iajs-4031	71	6	𝜗2	𝜗2	PROPN
iajs-4031	71	7	+	+	PROPN
iajs-4031	71	8	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	71	9	∑	∑	PUNCT
iajs-4031	71	10	(	(	PUNCT
iajs-4031	71	11	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	71	12	𝑗	𝑗	NOUN
iajs-4031	71	13	!	!	PUNCT
iajs-4031	71	14	∞	∞	PROPN
iajs-4031	71	15	𝑗=0	𝑗=0	PUNCT
iajs-4031	72	1	(	(	PUNCT
iajs-4031	72	2	𝜗	𝜗	X
iajs-4031	72	3	𝑗+4	𝑗+4	X
iajs-4031	72	4	+	+	NOUN
iajs-4031	72	5	1	1	NUM
iajs-4031	72	6	𝑗+5	𝑗+5	NUM
iajs-4031	72	7	)	)	PUNCT
iajs-4031	72	8	−	−	PROPN
iajs-4031	73	1	3	3	NUM
iajs-4031	73	2	[	[	X
iajs-4031	73	3	(	(	PUNCT
iajs-4031	73	4	𝜗2	𝜗2	PROPN
iajs-4031	73	5	(	(	PUNCT
iajs-4031	73	6	𝜗2	𝜗2	PROPN
iajs-4031	73	7	+	+	PROPN
iajs-4031	73	8	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	73	9	∑	∑	PUNCT
iajs-4031	73	10	(	(	PUNCT
iajs-4031	73	11	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	73	12	𝑗	𝑗	NOUN
iajs-4031	73	13	!	!	PUNCT
iajs-4031	74	1	∞	∞	PROPN
iajs-4031	74	2	𝑗=0	𝑗=0	PUNCT
iajs-4031	75	1	(	(	PUNCT
iajs-4031	75	2	𝜗	𝜗	SYM
iajs-4031	75	3	𝑗+2	𝑗+2	NUM
iajs-4031	75	4	+	+	CCONJ
iajs-4031	75	5	1	1	NUM
iajs-4031	75	6	𝑗+3	𝑗+3	NUM
iajs-4031	75	7	)	)	PUNCT
iajs-4031	75	8	)	)	PUNCT
iajs-4031	76	1	×	×	NOUN
iajs-4031	76	2	(	(	PUNCT
iajs-4031	76	3	𝜗2	𝜗2	PROPN
iajs-4031	76	4	(	(	PUNCT
iajs-4031	76	5	𝜗2	𝜗2	PROPN
iajs-4031	76	6	+	+	PROPN
iajs-4031	76	7	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	76	8	∑	∑	PUNCT
iajs-4031	76	9	(	(	PUNCT
iajs-4031	76	10	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	76	11	𝑗	𝑗	NOUN
iajs-4031	76	12	!	!	PUNCT
iajs-4031	76	13	∞	∞	PROPN
iajs-4031	76	14	𝑗=0	𝑗=0	PROPN
iajs-4031	77	1	(	(	PUNCT
iajs-4031	77	2	𝜗	𝜗	NOUN
iajs-4031	77	3	𝑗+3	𝑗+3	NUM
iajs-4031	77	4	+	+	NUM
iajs-4031	77	5	1	1	NUM
iajs-4031	77	6	𝑗+4	𝑗+4	NUM
iajs-4031	77	7	)	)	PUNCT
iajs-4031	77	8	)	)	PUNCT
iajs-4031	78	1	]	]	PUNCT
iajs-4031	78	2	+	+	X
iajs-4031	78	3	2	2	NUM
iajs-4031	78	4	(	(	PUNCT
iajs-4031	78	5	𝜗2	𝜗2	PROPN
iajs-4031	78	6	(	(	PUNCT
iajs-4031	78	7	𝜗2	𝜗2	PROPN
iajs-4031	78	8	+	+	PROPN
iajs-4031	78	9	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	78	10	∑	∑	PUNCT
iajs-4031	78	11	(	(	PUNCT
iajs-4031	78	12	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	78	13	𝑗	𝑗	NOUN
iajs-4031	78	14	!	!	PUNCT
iajs-4031	79	1	∞	∞	PROPN
iajs-4031	79	2	𝑗=0	𝑗=0	PUNCT
iajs-4031	80	1	(	(	PUNCT
iajs-4031	80	2	𝜗	𝜗	SYM
iajs-4031	80	3	𝑗+2	𝑗+2	NUM
iajs-4031	80	4	+	+	CCONJ
iajs-4031	80	5	1	1	NUM
iajs-4031	80	6	𝑗+3	𝑗+3	NUM
iajs-4031	80	7	)	)	PUNCT
iajs-4031	80	8	)	)	PUNCT
iajs-4031	80	9	3	3	X
iajs-4031	80	10	}	}	PUNCT
iajs-4031	80	11	[	[	PUNCT
iajs-4031	80	12	𝜗2	𝜗2	PROPN
iajs-4031	80	13	(	(	PUNCT
iajs-4031	80	14	𝜗2	𝜗2	PROPN
iajs-4031	80	15	+	+	PROPN
iajs-4031	80	16	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	80	17	∑	∑	PUNCT
iajs-4031	80	18	(	(	PUNCT
iajs-4031	80	19	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	80	20	𝑗	𝑗	NOUN
iajs-4031	80	21	!	!	PUNCT
iajs-4031	80	22	∞	∞	PROPN
iajs-4031	80	23	𝑗=0	𝑗=0	PROPN
iajs-4031	80	24	(	(	PUNCT
iajs-4031	80	25	𝜗	𝜗	NOUN
iajs-4031	80	26	𝑗+3	𝑗+3	NUM
iajs-4031	80	27	+	+	NUM
iajs-4031	80	28	1	1	NUM
iajs-4031	80	29	𝑗+4	𝑗+4	NUM
iajs-4031	80	30	)	)	PUNCT
iajs-4031	80	31	−	−	PROPN
iajs-4031	80	32	(	(	PUNCT
iajs-4031	80	33	𝜗2	𝜗2	PROPN
iajs-4031	80	34	(	(	PUNCT
iajs-4031	80	35	𝜗2	𝜗2	PROPN
iajs-4031	80	36	+	+	PROPN
iajs-4031	80	37	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	80	38	∑	∑	PUNCT
iajs-4031	80	39	(	(	PUNCT
iajs-4031	80	40	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	80	41	𝑗	𝑗	NOUN
iajs-4031	80	42	!	!	PUNCT
iajs-4031	80	43	∞	∞	PROPN
iajs-4031	80	44	𝑗=0	𝑗=0	PUNCT
iajs-4031	80	45	(	(	PUNCT
iajs-4031	80	46	𝜗	𝜗	SYM
iajs-4031	80	47	𝑗+2	𝑗+2	NUM
iajs-4031	80	48	+	+	CCONJ
iajs-4031	80	49	1	1	NUM
iajs-4031	80	50	𝑗+3	𝑗+3	NUM
iajs-4031	80	51	)	)	PUNCT
iajs-4031	80	52	)	)	PUNCT
iajs-4031	80	53	2	2	NUM
iajs-4031	80	54	]	]	SYM
iajs-4031	80	55	3	3	NUM
iajs-4031	80	56	2	2	NUM
iajs-4031	80	57	)	)	PUNCT
iajs-4031	80	58	20	20	NUM
iajs-4031	80	59	)	)	PUNCT
iajs-4031	80	60	the	the	DET
iajs-4031	80	61	kurtosis	kurtosis	NOUN
iajs-4031	80	62	of	of	ADP
iajs-4031	80	63	right	right	ADJ
iajs-4031	80	64	truncated	truncate	VERB
iajs-4031	80	65	shanker	shanker	NOUN
iajs-4031	80	66	distribution	distribution	NOUN
iajs-4031	80	67	can	can	AUX
iajs-4031	80	68	be	be	AUX
iajs-4031	80	69	derived	derive	VERB
iajs-4031	80	70	by	by	ADP
iajs-4031	80	71	the	the	DET
iajs-4031	80	72	same	same	ADJ
iajs-4031	80	73	way	way	NOUN
iajs-4031	81	1	𝑘𝑟	𝑘𝑟	ADP
iajs-4031	82	1	=	=	NOUN
iajs-4031	83	1	𝜇3	𝜇3	PROPN
iajs-4031	84	1	(	(	PUNCT
iajs-4031	84	2	𝜇2)2	𝜇2)2	PROPN
iajs-4031	84	3	−	−	PROPN
iajs-4031	84	4	3	3	NUM
iajs-4031	84	5	=	=	SYM
iajs-4031	84	6	𝐸(𝑥4)−4𝜇𝐸(𝑥3)+6𝜇2𝐸(𝑥2)−3𝜇4	𝐸(𝑥4)−4𝜇𝐸(𝑥3)+6𝜇2𝐸(𝑥2)−3𝜇4	NOUN
iajs-4031	84	7	(	(	PUNCT
iajs-4031	84	8	𝜎2)2	𝜎2)2	NUM
iajs-4031	84	9	−	−	NUM
iajs-4031	84	10	3	3	NUM
iajs-4031	84	11	so	so	ADV
iajs-4031	84	12	𝑘𝑟𝑅𝑇𝑆𝐻	𝑘𝑟𝑅𝑇𝑆𝐻	PROPN
iajs-4031	84	13	=	=	PUNCT
iajs-4031	84	14	{	{	PUNCT
iajs-4031	84	15	𝜗2	𝜗2	PROPN
iajs-4031	84	16	(	(	PUNCT
iajs-4031	84	17	𝜗2	𝜗2	PROPN
iajs-4031	84	18	+	+	PROPN
iajs-4031	84	19	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	84	20	∑	∑	PUNCT
iajs-4031	84	21	(	(	PUNCT
iajs-4031	84	22	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	84	23	𝑗	𝑗	NOUN
iajs-4031	84	24	!	!	PUNCT
iajs-4031	84	25	∞	∞	PROPN
iajs-4031	84	26	𝑗=0	𝑗=0	PUNCT
iajs-4031	84	27	(	(	PUNCT
iajs-4031	84	28	𝜗	𝜗	X
iajs-4031	84	29	𝑗+4	𝑗+4	X
iajs-4031	84	30	+	+	NOUN
iajs-4031	84	31	1	1	NUM
iajs-4031	84	32	𝑗+5	𝑗+5	NUM
iajs-4031	84	33	)	)	PUNCT
iajs-4031	84	34	−4	−4	PROPN
iajs-4031	84	35	(	(	PUNCT
iajs-4031	84	36	𝜗2	𝜗2	PROPN
iajs-4031	84	37	(	(	PUNCT
iajs-4031	84	38	𝜗2	𝜗2	PROPN
iajs-4031	84	39	+	+	PROPN
iajs-4031	84	40	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	84	41	∑	∑	PUNCT
iajs-4031	84	42	(	(	PUNCT
iajs-4031	84	43	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	84	44	𝑗	𝑗	NOUN
iajs-4031	84	45	!	!	PUNCT
iajs-4031	84	46	∞	∞	PROPN
iajs-4031	84	47	𝑗=0	𝑗=0	PUNCT
iajs-4031	84	48	(	(	PUNCT
iajs-4031	84	49	𝜗	𝜗	SYM
iajs-4031	84	50	𝑗+2	𝑗+2	NUM
iajs-4031	84	51	+	+	CCONJ
iajs-4031	84	52	1	1	NUM
iajs-4031	84	53	𝑗+3	𝑗+3	NUM
iajs-4031	84	54	)	)	PUNCT
iajs-4031	84	55	)	)	PUNCT
iajs-4031	84	56	×	×	NOUN
iajs-4031	84	57	(	(	PUNCT
iajs-4031	84	58	𝜗2	𝜗2	PROPN
iajs-4031	84	59	(	(	PUNCT
iajs-4031	84	60	𝜗2	𝜗2	PROPN
iajs-4031	84	61	+	+	PROPN
iajs-4031	84	62	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	84	63	∑	∑	PUNCT
iajs-4031	84	64	(	(	PUNCT
iajs-4031	84	65	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	84	66	𝑗	𝑗	NOUN
iajs-4031	84	67	!	!	PUNCT
iajs-4031	84	68	∞	∞	PROPN
iajs-4031	84	69	𝑗=0	𝑗=0	PUNCT
iajs-4031	84	70	(	(	PUNCT
iajs-4031	84	71	𝜗	𝜗	X
iajs-4031	84	72	𝑗+4	𝑗+4	X
iajs-4031	84	73	+	+	NOUN
iajs-4031	84	74	1	1	NUM
iajs-4031	84	75	𝑗+5	𝑗+5	NUM
iajs-4031	84	76	)	)	PUNCT
iajs-4031	84	77	)	)	PUNCT
iajs-4031	85	1	+6	+6	PROPN
iajs-4031	85	2	(	(	PUNCT
iajs-4031	85	3	𝜗2	𝜗2	PROPN
iajs-4031	85	4	(	(	PUNCT
iajs-4031	85	5	𝜗2	𝜗2	PROPN
iajs-4031	85	6	+	+	PROPN
iajs-4031	85	7	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	85	8	∑	∑	PUNCT
iajs-4031	85	9	(	(	PUNCT
iajs-4031	85	10	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	85	11	𝑗	𝑗	NOUN
iajs-4031	85	12	!	!	PUNCT
iajs-4031	85	13	∞	∞	PROPN
iajs-4031	85	14	𝑗=0	𝑗=0	PUNCT
iajs-4031	85	15	(	(	PUNCT
iajs-4031	85	16	𝜗	𝜗	SYM
iajs-4031	85	17	𝑗+2	𝑗+2	NUM
iajs-4031	85	18	+	+	CCONJ
iajs-4031	85	19	1	1	NUM
iajs-4031	85	20	𝑗+3	𝑗+3	NUM
iajs-4031	85	21	)	)	PUNCT
iajs-4031	85	22	)	)	PUNCT
iajs-4031	85	23	2	2	NUM
iajs-4031	85	24	×	×	NOUN
iajs-4031	85	25	(	(	PUNCT
iajs-4031	85	26	𝜗2	𝜗2	PROPN
iajs-4031	85	27	(	(	PUNCT
iajs-4031	85	28	𝜗2	𝜗2	PROPN
iajs-4031	85	29	+	+	PROPN
iajs-4031	85	30	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	85	31	∑	∑	PUNCT
iajs-4031	85	32	(	(	PUNCT
iajs-4031	85	33	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	85	34	𝑗	𝑗	NOUN
iajs-4031	85	35	!	!	PUNCT
iajs-4031	85	36	∞	∞	PROPN
iajs-4031	85	37	𝑗=0	𝑗=0	PROPN
iajs-4031	85	38	(	(	PUNCT
iajs-4031	85	39	𝜗	𝜗	NOUN
iajs-4031	85	40	𝑗+3	𝑗+3	NUM
iajs-4031	85	41	+	+	NUM
iajs-4031	85	42	1	1	NUM
iajs-4031	85	43	𝑗+4	𝑗+4	NUM
iajs-4031	85	44	)	)	PUNCT
iajs-4031	85	45	)	)	PUNCT
iajs-4031	85	46	−3	−3	PROPN
iajs-4031	85	47	(	(	PUNCT
iajs-4031	85	48	𝜗2	𝜗2	PROPN
iajs-4031	85	49	(	(	PUNCT
iajs-4031	85	50	𝜗2	𝜗2	PROPN
iajs-4031	85	51	+	+	PROPN
iajs-4031	85	52	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	85	53	∑	∑	PUNCT
iajs-4031	85	54	(	(	PUNCT
iajs-4031	85	55	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	85	56	𝑗	𝑗	NOUN
iajs-4031	85	57	!	!	PUNCT
iajs-4031	85	58	∞	∞	PROPN
iajs-4031	85	59	𝑗=0	𝑗=0	PUNCT
iajs-4031	85	60	(	(	PUNCT
iajs-4031	85	61	𝜗	𝜗	SYM
iajs-4031	85	62	𝑗+2	𝑗+2	NUM
iajs-4031	85	63	+	+	CCONJ
iajs-4031	85	64	1	1	NUM
iajs-4031	85	65	𝑗+3	𝑗+3	NUM
iajs-4031	85	66	)	)	PUNCT
iajs-4031	85	67	)	)	PUNCT
iajs-4031	85	68	4	4	X
iajs-4031	85	69	}	}	PUNCT
iajs-4031	85	70	[	[	PUNCT
iajs-4031	85	71	𝜗2	𝜗2	PROPN
iajs-4031	85	72	(	(	PUNCT
iajs-4031	85	73	𝜗2	𝜗2	PROPN
iajs-4031	85	74	+	+	PROPN
iajs-4031	85	75	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	85	76	∑	∑	PUNCT
iajs-4031	85	77	(	(	PUNCT
iajs-4031	85	78	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	85	79	𝑗	𝑗	NOUN
iajs-4031	85	80	!	!	PUNCT
iajs-4031	85	81	∞	∞	PROPN
iajs-4031	85	82	𝑗=0	𝑗=0	PROPN
iajs-4031	85	83	(	(	PUNCT
iajs-4031	85	84	𝜗	𝜗	NOUN
iajs-4031	85	85	𝑗+3	𝑗+3	NUM
iajs-4031	85	86	+	+	NUM
iajs-4031	85	87	1	1	NUM
iajs-4031	85	88	𝑗+4	𝑗+4	NUM
iajs-4031	85	89	)	)	PUNCT
iajs-4031	85	90	−	−	PROPN
iajs-4031	85	91	(	(	PUNCT
iajs-4031	85	92	𝜗2	𝜗2	PROPN
iajs-4031	85	93	(	(	PUNCT
iajs-4031	85	94	𝜗2	𝜗2	PROPN
iajs-4031	85	95	+	+	PROPN
iajs-4031	85	96	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	85	97	∑	∑	PUNCT
iajs-4031	85	98	(	(	PUNCT
iajs-4031	85	99	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	85	100	𝑗	𝑗	NOUN
iajs-4031	85	101	!	!	PUNCT
iajs-4031	85	102	∞	∞	PROPN
iajs-4031	85	103	𝑗=0	𝑗=0	PUNCT
iajs-4031	85	104	(	(	PUNCT
iajs-4031	85	105	𝜗	𝜗	SYM
iajs-4031	85	106	𝑗+2	𝑗+2	NUM
iajs-4031	85	107	+	+	CCONJ
iajs-4031	85	108	1	1	NUM
iajs-4031	85	109	𝑗+3	𝑗+3	NUM
iajs-4031	85	110	)	)	PUNCT
iajs-4031	85	111	)	)	PUNCT
iajs-4031	85	112	2	2	NUM
iajs-4031	85	113	]	]	SYM
iajs-4031	85	114	2	2	NUM
iajs-4031	85	115	−	−	NOUN
iajs-4031	85	116	3	3	NUM
iajs-4031	85	117	(	(	PUNCT
iajs-4031	85	118	21	21	NUM
iajs-4031	85	119	)	)	PUNCT
iajs-4031	85	120	ihjpas	ihjpa	NOUN
iajs-4031	85	121	.	.	PUNCT
iajs-4031	86	1	2025	2025	NUM
iajs-4031	86	2	,	,	PUNCT
iajs-4031	86	3	38	38	NUM
iajs-4031	86	4	(	(	PUNCT
iajs-4031	86	5	1	1	NUM
iajs-4031	86	6	)	)	PUNCT
iajs-4031	86	7	497	497	NUM
iajs-4031	86	8	4.3	4.3	NUM
iajs-4031	86	9	.	.	PUNCT
iajs-4031	87	1	moment	moment	NOUN
iajs-4031	87	2	generating	generate	VERB
iajs-4031	87	3	function	function	NOUN
iajs-4031	87	4	mgf	mgf	PROPN
iajs-4031	87	5	in	in	ADP
iajs-4031	87	6	this	this	DET
iajs-4031	87	7	sub	sub	NOUN
iajs-4031	87	8	section	section	NOUN
iajs-4031	87	9	the	the	DET
iajs-4031	87	10	mgf	mgf	PROPN
iajs-4031	87	11	of	of	ADP
iajs-4031	87	12	the	the	DET
iajs-4031	87	13	right	right	ADJ
iajs-4031	87	14	truncated	truncate	VERB
iajs-4031	87	15	shanker	shanker	NOUN
iajs-4031	87	16	distribution	distribution	NOUN
iajs-4031	87	17	will	will	AUX
iajs-4031	87	18	be	be	AUX
iajs-4031	87	19	derived	derive	VERB
iajs-4031	87	20	as	as	ADP
iajs-4031	87	21	follow	follow	NOUN
iajs-4031	87	22	:	:	PUNCT
iajs-4031	87	23	ℳx(t	ℳx(t	NOUN
iajs-4031	87	24	)	)	PUNCT
iajs-4031	87	25	=	=	PUNCT
iajs-4031	88	1	e(etx	e(etx	CCONJ
iajs-4031	88	2	)	)	PUNCT
iajs-4031	88	3	=	=	SYM
iajs-4031	88	4	∫	∫	PROPN
iajs-4031	88	5	etx	etx	NOUN
iajs-4031	88	6	1	1	NUM
iajs-4031	88	7	0	0	NUM
iajs-4031	88	8	𝑤𝑅𝑇𝑆𝐻(𝑥	𝑤𝑅𝑇𝑆𝐻(𝑥	ADJ
iajs-4031	88	9	,	,	PUNCT
iajs-4031	88	10	𝜗)dx	𝜗)dx	PROPN
iajs-4031	88	11	;	;	PUNCT
iajs-4031	88	12	0	0	NUM
iajs-4031	88	13	≤	≤	NUM
iajs-4031	88	14	𝑥	𝑥	PUNCT
iajs-4031	88	15	≤	≤	NUM
iajs-4031	88	16	1	1	NUM
iajs-4031	88	17	(	(	PUNCT
iajs-4031	88	18	22	22	NUM
iajs-4031	88	19	)	)	PUNCT
iajs-4031	88	20	so	so	ADV
iajs-4031	88	21	from	from	ADP
iajs-4031	88	22	equation	equation	NOUN
iajs-4031	88	23	(	(	PUNCT
iajs-4031	88	24	5	5	NUM
iajs-4031	88	25	)	)	PUNCT
iajs-4031	88	26	ℳx(t	ℳx(t	NOUN
iajs-4031	88	27	)	)	PUNCT
iajs-4031	88	28	=	=	SYM
iajs-4031	88	29	∫	∫	PROPN
iajs-4031	88	30	etx	etx	NOUN
iajs-4031	88	31	1	1	NUM
iajs-4031	88	32	0	0	NUM
iajs-4031	89	1	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	𝜗2(𝜗+𝑥)𝑒−𝜗𝑥	PROPN
iajs-4031	89	2	(	(	PUNCT
iajs-4031	89	3	𝜗2	𝜗2	PROPN
iajs-4031	89	4	+	+	NOUN
iajs-4031	89	5	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	89	6	𝑑𝑥	𝑑𝑥	X
iajs-4031	89	7	=	=	SYM
iajs-4031	89	8	𝜗2	𝜗2	PROPN
iajs-4031	89	9	(	(	PUNCT
iajs-4031	89	10	𝜗2	𝜗2	PROPN
iajs-4031	89	11	+	+	PROPN
iajs-4031	89	12	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	PROPN
iajs-4031	89	13	∫	∫	NOUN
iajs-4031	89	14	(	(	PUNCT
iajs-4031	89	15	𝜗	𝜗	ADP
iajs-4031	89	16	+	+	CCONJ
iajs-4031	89	17	𝑥)𝑒−(𝜗−𝑡)𝑥	𝑥)𝑒−(𝜗−𝑡)𝑥	PROPN
iajs-4031	89	18	1	1	NUM
iajs-4031	89	19	0	0	NUM
iajs-4031	89	20	𝑑𝑥	𝑑𝑥	NOUN
iajs-4031	89	21	(	(	PUNCT
iajs-4031	89	22	23	23	NUM
iajs-4031	89	23	)	)	PUNCT
iajs-4031	89	24	but	but	CCONJ
iajs-4031	89	25	𝑒−(𝜗−𝑡)𝑥	𝑒−(𝜗−𝑡)𝑥	NOUN
iajs-4031	89	26	=	=	SYM
iajs-4031	89	27	∑	∑	PUNCT
iajs-4031	89	28	[	[	X
iajs-4031	89	29	−(𝜗−𝑡)𝑥]𝑗	−(𝜗−𝑡)𝑥]𝑗	X
iajs-4031	89	30	𝑗	𝑗	PROPN
iajs-4031	89	31	!	!	PUNCT
iajs-4031	89	32	∞	∞	PROPN
iajs-4031	90	1	𝑗=0	𝑗=0	PROPN
iajs-4031	90	2	(	(	PUNCT
iajs-4031	90	3	24	24	NUM
iajs-4031	90	4	)	)	PUNCT
iajs-4031	90	5	substitute	substitute	NOUN
iajs-4031	90	6	equation	equation	NOUN
iajs-4031	90	7	(	(	PUNCT
iajs-4031	90	8	24	24	NUM
iajs-4031	90	9	)	)	PUNCT
iajs-4031	90	10	in	in	ADP
iajs-4031	90	11	equation	equation	NOUN
iajs-4031	90	12	(	(	PUNCT
iajs-4031	90	13	23	23	NUM
iajs-4031	90	14	)	)	PUNCT
iajs-4031	90	15	ℳx(t	ℳx(t	NOUN
iajs-4031	90	16	)	)	PUNCT
iajs-4031	90	17	=	=	SYM
iajs-4031	90	18	𝜗2	𝜗2	PROPN
iajs-4031	90	19	(	(	PUNCT
iajs-4031	90	20	𝜗2	𝜗2	PROPN
iajs-4031	90	21	+	+	PROPN
iajs-4031	90	22	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	90	23	∑	∑	PUNCT
iajs-4031	91	1	[	[	X
iajs-4031	91	2	−(𝜗−𝑡)]𝑗	−(𝜗−𝑡)]𝑗	X
iajs-4031	91	3	𝑗	𝑗	NOUN
iajs-4031	91	4	!	!	PUNCT
iajs-4031	92	1	∞	∞	PROPN
iajs-4031	93	1	𝑗=0	𝑗=0	PROPN
iajs-4031	94	1	∫	∫	PROPN
iajs-4031	94	2	𝑥𝑗(𝜗	𝑥𝑗(𝜗	PROPN
iajs-4031	95	1	+	+	CCONJ
iajs-4031	95	2	𝑥	𝑥	X
iajs-4031	95	3	)	)	PUNCT
iajs-4031	95	4	1	1	NUM
iajs-4031	95	5	0	0	NUM
iajs-4031	95	6	𝑑𝑥	𝑑𝑥	VERB
iajs-4031	95	7	then	then	ADV
iajs-4031	95	8	ℳx(t	ℳx(t	NOUN
iajs-4031	95	9	)	)	PUNCT
iajs-4031	95	10	=	=	SYM
iajs-4031	95	11	𝜗2	𝜗2	PROPN
iajs-4031	95	12	(	(	PUNCT
iajs-4031	95	13	𝜗2	𝜗2	PROPN
iajs-4031	95	14	+	+	PROPN
iajs-4031	95	15	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	95	16	∑	∑	PUNCT
iajs-4031	96	1	[	[	X
iajs-4031	96	2	−(𝜗−𝑡)]𝑗	−(𝜗−𝑡)]𝑗	X
iajs-4031	96	3	𝑗	𝑗	INTJ
iajs-4031	96	4	!	!	PUNCT
iajs-4031	97	1	∞	∞	NUM
iajs-4031	97	2	𝑗=0	𝑗=0	PUNCT
iajs-4031	98	1	(	(	PUNCT
iajs-4031	98	2	𝜗	𝜗	X
iajs-4031	98	3	𝑗+1	𝑗+1	PUNCT
iajs-4031	99	1	+	+	CCONJ
iajs-4031	99	2	1	1	NUM
iajs-4031	99	3	𝑗+2	𝑗+2	NUM
iajs-4031	99	4	)	)	PUNCT
iajs-4031	99	5	(	(	PUNCT
iajs-4031	99	6	25	25	NUM
iajs-4031	99	7	)	)	PUNCT
iajs-4031	99	8	5	5	NUM
iajs-4031	99	9	.	.	PUNCT
iajs-4031	100	1	mean	mean	ADJ
iajs-4031	100	2	time	time	NOUN
iajs-4031	100	3	to	to	ADP
iajs-4031	100	4	failure	failure	NOUN
iajs-4031	100	5	𝑴𝑻𝑻𝑬	𝑴𝑻𝑻𝑬	ADP
iajs-4031	100	6	let	let	VERB
iajs-4031	100	7	𝑇	𝑇	PROPN
iajs-4031	100	8	denote	denote	VERB
iajs-4031	100	9	the	the	DET
iajs-4031	100	10	lifetime	lifetime	NOUN
iajs-4031	100	11	of	of	ADP
iajs-4031	100	12	a	a	DET
iajs-4031	100	13	component	component	NOUN
iajs-4031	100	14	so	so	ADV
iajs-4031	100	15	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	PROPN
iajs-4031	100	16	=	=	SYM
iajs-4031	100	17	∫	∫	PROPN
iajs-4031	101	1	𝑆(𝑅𝑇𝑆𝐻)(𝑥	𝑆(𝑅𝑇𝑆𝐻)(𝑥	NOUN
iajs-4031	101	2	)	)	PUNCT
iajs-4031	101	3	1	1	NUM
iajs-4031	101	4	0	0	NUM
iajs-4031	101	5	𝑑𝑥	𝑑𝑥	NOUN
iajs-4031	101	6	=	=	SYM
iajs-4031	101	7	∫	∫	NOUN
iajs-4031	101	8	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	−[(𝜗2+𝜗+1]𝑒−𝜗−[𝜗2+𝜗𝑥+1]𝑒−𝜗𝑥	X
iajs-4031	101	9	(	(	PUNCT
iajs-4031	101	10	𝜗2	𝜗2	PROPN
iajs-4031	101	11	+	+	PROPN
iajs-4031	101	12	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	101	13	1	1	NUM
iajs-4031	101	14	0	0	NUM
iajs-4031	101	15	𝑑𝑥	𝑑𝑥	NOUN
iajs-4031	101	16	(	(	PUNCT
iajs-4031	101	17	26	26	NUM
iajs-4031	101	18	)	)	PUNCT
iajs-4031	101	19	=	=	SYM
iajs-4031	101	20	1	1	NUM
iajs-4031	101	21	(	(	PUNCT
iajs-4031	101	22	𝜗2	𝜗2	PROPN
iajs-4031	101	23	+	+	PROPN
iajs-4031	101	24	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NUM
iajs-4031	101	25	∫	∫	NOUN
iajs-4031	101	26	(	(	PUNCT
iajs-4031	101	27	−[(𝜗2	−[(𝜗2	NOUN
iajs-4031	101	28	+	+	NUM
iajs-4031	101	29	𝜗	𝜗	PROPN
iajs-4031	101	30	+	+	NUM
iajs-4031	101	31	1]𝑒−𝜗	1]𝑒−𝜗	NUM
iajs-4031	101	32	−	−	NOUN
iajs-4031	102	1	[	[	X
iajs-4031	102	2	𝜗2	𝜗2	PROPN
iajs-4031	102	3	+	+	CCONJ
iajs-4031	102	4	𝜗𝑥	𝜗𝑥	X
iajs-4031	102	5	+	+	CCONJ
iajs-4031	102	6	1]𝑒−𝜗𝑥)𝑑𝑥	1]𝑒−𝜗𝑥)𝑑𝑥	NUM
iajs-4031	102	7	1	1	NUM
iajs-4031	102	8	0	0	NUM
iajs-4031	102	9	=	=	SYM
iajs-4031	102	10	1	1	NUM
iajs-4031	102	11	(	(	PUNCT
iajs-4031	102	12	𝜗2	𝜗2	PROPN
iajs-4031	102	13	+	+	NOUN
iajs-4031	102	14	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	103	1	[	[	X
iajs-4031	103	2	−[(𝜗2	−[(𝜗2	NOUN
iajs-4031	103	3	+	+	NUM
iajs-4031	103	4	𝜗	𝜗	PROPN
iajs-4031	103	5	+	+	NUM
iajs-4031	103	6	1]𝑒−𝜗	1]𝑒−𝜗	NUM
iajs-4031	103	7	−	−	PROPN
iajs-4031	103	8	∫	∫	PROPN
iajs-4031	103	9	(	(	PUNCT
iajs-4031	103	10	−[𝜗2	−[𝜗2	NOUN
iajs-4031	103	11	+	+	X
iajs-4031	103	12	𝜗𝑥	𝜗𝑥	NOUN
iajs-4031	103	13	+	+	CCONJ
iajs-4031	103	14	1]𝑒−𝜗𝑥)𝑑𝑥	1]𝑒−𝜗𝑥)𝑑𝑥	NUM
iajs-4031	103	15	1	1	NUM
iajs-4031	103	16	0	0	NUM
iajs-4031	103	17	]	]	PUNCT
iajs-4031	103	18	(	(	PUNCT
iajs-4031	103	19	27	27	NUM
iajs-4031	103	20	)	)	PUNCT
iajs-4031	103	21	recall	recall	VERB
iajs-4031	103	22	that	that	DET
iajs-4031	103	23	𝑒−𝜗𝑥	𝑒−𝜗𝑥	NOUN
iajs-4031	104	1	=	=	PUNCT
iajs-4031	104	2	∑	∑	PUNCT
iajs-4031	104	3	(	(	PUNCT
iajs-4031	104	4	−𝜗𝑥)𝑗	−𝜗𝑥)𝑗	NOUN
iajs-4031	104	5	𝑗	𝑗	PROPN
iajs-4031	104	6	!	!	PUNCT
iajs-4031	104	7	∞	∞	PROPN
iajs-4031	105	1	𝑗=0	𝑗=0	PROPN
iajs-4031	105	2	,	,	PUNCT
iajs-4031	105	3	then	then	ADV
iajs-4031	105	4	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	VERB
iajs-4031	105	5	=	=	SYM
iajs-4031	105	6	1	1	NUM
iajs-4031	105	7	(	(	PUNCT
iajs-4031	105	8	𝜗2	𝜗2	PROPN
iajs-4031	105	9	+	+	NOUN
iajs-4031	105	10	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	106	1	[	[	X
iajs-4031	106	2	−[(𝜗2	−[(𝜗2	NOUN
iajs-4031	106	3	+	+	NUM
iajs-4031	106	4	𝜗	𝜗	PROPN
iajs-4031	106	5	+	+	CCONJ
iajs-4031	106	6	1]𝑒−𝜗	1]𝑒−𝜗	NUM
iajs-4031	106	7	−	−	NOUN
iajs-4031	106	8	∑	∑	PROPN
iajs-4031	106	9	(	(	PUNCT
iajs-4031	106	10	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	106	11	𝑗	𝑗	NOUN
iajs-4031	106	12	!	!	PUNCT
iajs-4031	106	13	∞	∞	PROPN
iajs-4031	107	1	𝑗=0	𝑗=0	PROPN
iajs-4031	108	1	∫	∫	PROPN
iajs-4031	108	2	(	(	PUNCT
iajs-4031	108	3	−(𝑥)𝑗[𝜗2	−(𝑥)𝑗[𝜗2	NOUN
iajs-4031	108	4	+	+	CCONJ
iajs-4031	108	5	𝜗𝑥	𝜗𝑥	NOUN
iajs-4031	109	1	+	+	CCONJ
iajs-4031	109	2	1])𝑑𝑥	1])𝑑𝑥	NUM
iajs-4031	109	3	1	1	NUM
iajs-4031	109	4	0	0	NUM
iajs-4031	109	5	]	]	PUNCT
iajs-4031	109	6	𝑀𝑇𝑇𝐸	𝑀𝑇𝑇𝐸	NOUN
iajs-4031	109	7	=	=	SYM
iajs-4031	109	8	1	1	NUM
iajs-4031	109	9	(	(	PUNCT
iajs-4031	109	10	𝜗2	𝜗2	PROPN
iajs-4031	109	11	+	+	NOUN
iajs-4031	109	12	1)−[(𝜗2+𝜗+1]𝑒−𝜗	1)−[(𝜗2+𝜗+1]𝑒−𝜗	NOUN
iajs-4031	110	1	[	[	X
iajs-4031	110	2	−[(𝜗2	−[(𝜗2	NOUN
iajs-4031	110	3	+	+	NUM
iajs-4031	110	4	𝜗	𝜗	PROPN
iajs-4031	110	5	+	+	NUM
iajs-4031	110	6	1]𝑒−𝜗	1]𝑒−𝜗	NUM
iajs-4031	110	7	+	+	CCONJ
iajs-4031	110	8	∑	∑	PROPN
iajs-4031	110	9	(	(	PUNCT
iajs-4031	110	10	−𝜗)𝑗	−𝜗)𝑗	NOUN
iajs-4031	110	11	𝑗	𝑗	NOUN
iajs-4031	110	12	!	!	PUNCT
iajs-4031	110	13	∞	∞	NUM
iajs-4031	110	14	𝑗=0	𝑗=0	PUNCT
iajs-4031	111	1	[	[	X
iajs-4031	111	2	𝜗2+𝜗𝑥+1	𝜗2+𝜗𝑥+1	X
iajs-4031	111	3	]	]	X
iajs-4031	111	4	𝑗+1	𝑗+1	X
iajs-4031	111	5	]	]	PUNCT
iajs-4031	111	6	(	(	PUNCT
iajs-4031	111	7	28	28	NUM
iajs-4031	111	8	)	)	PUNCT
iajs-4031	111	9	6	6	NUM
iajs-4031	111	10	.	.	PUNCT
iajs-4031	111	11	conclusion	conclusion	NOUN
iajs-4031	111	12	a	a	DET
iajs-4031	111	13	new	new	ADJ
iajs-4031	111	14	lifetime	lifetime	NOUN
iajs-4031	111	15	truncated	truncate	VERB
iajs-4031	111	16	distribution	distribution	NOUN
iajs-4031	111	17	named	name	VERB
iajs-4031	111	18	,	,	PUNCT
iajs-4031	111	19	right	right	ADJ
iajs-4031	111	20	truncated	truncate	VERB
iajs-4031	111	21	shanker	shanker	NOUN
iajs-4031	111	22	distribution	distribution	NOUN
iajs-4031	111	23	was	be	AUX
iajs-4031	111	24	presented	present	VERB
iajs-4031	111	25	to	to	PART
iajs-4031	111	26	study	study	VERB
iajs-4031	111	27	the	the	DET
iajs-4031	111	28	shanker	shanker	NOUN
iajs-4031	111	29	distribution	distribution	NOUN
iajs-4031	111	30	when	when	SCONJ
iajs-4031	111	31	the	the	DET
iajs-4031	111	32	random	random	ADJ
iajs-4031	111	33	variable	variable	NOUN
iajs-4031	111	34	x	x	PUNCT
iajs-4031	111	35	belong	belong	VERB
iajs-4031	111	36	to	to	ADP
iajs-4031	111	37	the	the	DET
iajs-4031	111	38	interval	interval	NOUN
iajs-4031	112	1	[	[	X
iajs-4031	112	2	0,1	0,1	X
iajs-4031	112	3	]	]	PUNCT
iajs-4031	112	4	by	by	ADP
iajs-4031	112	5	driving	drive	VERB
iajs-4031	112	6	the	the	DET
iajs-4031	112	7	probability	probability	NOUN
iajs-4031	112	8	density	density	NOUN
iajs-4031	112	9	function	function	NOUN
iajs-4031	112	10	and	and	CCONJ
iajs-4031	112	11	cumulative	cumulative	ADJ
iajs-4031	112	12	distribution	distribution	NOUN
iajs-4031	112	13	function	function	VERB
iajs-4031	112	14	the	the	DET
iajs-4031	112	15	statistical	statistical	ADJ
iajs-4031	112	16	properties	property	NOUN
iajs-4031	112	17	including	include	VERB
iajs-4031	112	18	,	,	PUNCT
iajs-4031	112	19	hazard	hazard	NOUN
iajs-4031	112	20	rate	rate	NOUN
iajs-4031	112	21	function	function	NOUN
iajs-4031	112	22	,	,	PUNCT
iajs-4031	112	23	survival	survival	NOUN
iajs-4031	112	24	function	function	PROPN
iajs-4031	112	25	,	,	PUNCT
iajs-4031	112	26	moments	moment	NOUN
iajs-4031	112	27	,	,	PUNCT
iajs-4031	112	28	variance	variance	NOUN
iajs-4031	112	29	and	and	CCONJ
iajs-4031	112	30	coefficients	coefficient	NOUN
iajs-4031	112	31	of	of	ADP
iajs-4031	112	32	skewness	skewness	NOUN
iajs-4031	112	33	,	,	PUNCT
iajs-4031	112	34	and	and	CCONJ
iajs-4031	112	35	generating	generating	NOUN
iajs-4031	112	36	function	function	NOUN
iajs-4031	112	37	,	,	PUNCT
iajs-4031	112	38	have	have	AUX
iajs-4031	112	39	been	be	AUX
iajs-4031	112	40	provided	provide	VERB
iajs-4031	112	41	in	in	ADP
iajs-4031	112	42	addition	addition	NOUN
iajs-4031	112	43	to	to	PART
iajs-4031	112	44	mean	mean	VERB
iajs-4031	112	45	time	time	NOUN
iajs-4031	112	46	to	to	ADP
iajs-4031	112	47	failure	failure	NOUN
iajs-4031	112	48	to	to	PART
iajs-4031	112	49	know	know	VERB
iajs-4031	112	50	more	more	ADJ
iajs-4031	112	51	about	about	ADP
iajs-4031	112	52	the	the	DET
iajs-4031	112	53	behavior	behavior	NOUN
iajs-4031	112	54	of	of	ADP
iajs-4031	112	55	this	this	DET
iajs-4031	112	56	function	function	NOUN
iajs-4031	112	57	.	.	PUNCT
iajs-4031	113	1	acknowledgment	acknowledgment	NOUN
iajs-4031	113	2	the	the	DET
iajs-4031	113	3	authors	author	NOUN
iajs-4031	113	4	would	would	AUX
iajs-4031	113	5	like	like	VERB
iajs-4031	113	6	to	to	PART
iajs-4031	113	7	thank	thank	VERB
iajs-4031	113	8	the	the	DET
iajs-4031	113	9	referees	referee	NOUN
iajs-4031	113	10	for	for	ADP
iajs-4031	113	11	providing	provide	VERB
iajs-4031	113	12	very	very	ADV
iajs-4031	113	13	helpful	helpful	ADJ
iajs-4031	113	14	comments	comment	NOUN
iajs-4031	113	15	and	and	CCONJ
iajs-4031	113	16	ihjpas	ihjpa	NOUN
iajs-4031	113	17	.	.	PUNCT
iajs-4031	114	1	2025	2025	NUM
iajs-4031	114	2	,	,	PUNCT
iajs-4031	114	3	38	38	NUM
iajs-4031	114	4	(	(	PUNCT
iajs-4031	114	5	1	1	NUM
iajs-4031	114	6	)	)	PUNCT
iajs-4031	114	7	498	498	NUM
iajs-4031	114	8	suggestions	suggestion	NOUN
iajs-4031	114	9	that	that	PRON
iajs-4031	114	10	helped	help	VERB
iajs-4031	114	11	in	in	ADP
iajs-4031	114	12	improving	improve	VERB
iajs-4031	114	13	the	the	DET
iajs-4031	114	14	quality	quality	NOUN
iajs-4031	114	15	of	of	ADP
iajs-4031	114	16	the	the	DET
iajs-4031	114	17	paper	paper	NOUN
iajs-4031	114	18	.	.	PUNCT
iajs-4031	115	1	conflict	conflict	NOUN
iajs-4031	115	2	of	of	ADP
iajs-4031	115	3	interest	interest	NOUN
iajs-4031	115	4	bayda	bayda	VERB
iajs-4031	115	5	atiya	atiya	PROPN
iajs-4031	115	6	,	,	PUNCT
iajs-4031	115	7	the	the	DET
iajs-4031	115	8	manager	manager	NOUN
iajs-4031	115	9	,	,	PUNCT
iajs-4031	115	10	declared	declare	VERB
iajs-4031	115	11	that	that	SCONJ
iajs-4031	115	12	she	she	PRON
iajs-4031	115	13	was	be	AUX
iajs-4031	115	14	the	the	DET
iajs-4031	115	15	one	one	NUM
iajs-4031	115	16	at	at	ADP
iajs-4031	115	17	ihjpas	ihjpas	PROPN
iajs-4031	115	18	when	when	SCONJ
iajs-4031	115	19	submitting	submit	VERB
iajs-4031	115	20	the	the	DET
iajs-4031	115	21	manuscript	manuscript	NOUN
iajs-4031	115	22	.	.	PUNCT
iajs-4031	116	1	the	the	DET
iajs-4031	116	2	editor	editor	NOUN
iajs-4031	116	3	-	-	PUNCT
iajs-4031	116	4	in	in	ADP
iajs-4031	116	5	-	-	PUNCT
iajs-4031	116	6	chief	chief	NOUN
iajs-4031	116	7	of	of	ADP
iajs-4031	116	8	ihjpas	ihjpas	PROPN
iajs-4031	116	9	confirms	confirm	VERB
iajs-4031	116	10	that	that	SCONJ
iajs-4031	116	11	(	(	PUNCT
iajs-4031	116	12	bayda	bayda	PROPN
iajs-4031	116	13	atiya	atiya	PROPN
iajs-4031	116	14	)	)	PUNCT
iajs-4031	116	15	was	be	AUX
iajs-4031	116	16	excluded	exclude	VERB
iajs-4031	116	17	from	from	ADP
iajs-4031	116	18	any	any	DET
iajs-4031	116	19	decisions	decision	NOUN
iajs-4031	116	20	made	make	VERB
iajs-4031	116	21	regarding	regard	VERB
iajs-4031	116	22	this	this	DET
iajs-4031	116	23	paper	paper	NOUN
iajs-4031	116	24	.	.	PUNCT
iajs-4031	117	1	funding	funding	NOUN
iajs-4031	117	2	there	there	PRON
iajs-4031	117	3	is	be	VERB
iajs-4031	117	4	no	no	DET
iajs-4031	117	5	financial	financial	ADJ
iajs-4031	117	6	support	support	NOUN
iajs-4031	117	7	.	.	PUNCT
iajs-4031	118	1	references	reference	NOUN
iajs-4031	118	2	1	1	NUM
iajs-4031	118	3	.	.	PUNCT
iajs-4031	118	4	shukla	shukla	PROPN
iajs-4031	118	5	kk	kk	PROPN
iajs-4031	118	6	,	,	PUNCT
iajs-4031	118	7	shanker	shanker	PROPN
iajs-4031	118	8	r.	r.	PROPN
iajs-4031	118	9	truncated	truncate	VERB
iajs-4031	118	10	akash	akash	NOUN
iajs-4031	118	11	distribution	distribution	NOUN
iajs-4031	118	12	:	:	PUNCT
iajs-4031	118	13	properties	property	NOUN
iajs-4031	118	14	and	and	CCONJ
iajs-4031	118	15	applications	application	NOUN
iajs-4031	118	16	.	.	PUNCT
iajs-4031	119	1	biometrics	biometrics	PROPN
iajs-4031	119	2	&	&	CCONJ
iajs-4031	119	3	biostatistics	biostatistics	PROPN
iajs-4031	119	4	international	international	PROPN
iajs-4031	119	5	journal	journal	PROPN
iajs-4031	119	6	.	.	PUNCT
iajs-4031	120	1	2020;9(5):179–84	2020;9(5):179–84	NOUN
iajs-4031	120	2	.	.	PUNCT
iajs-4031	121	1	http://dx.doi.org/10.15406/bbij.2020.09.00317	http://dx.doi.org/10.15406/bbij.2020.09.00317	PROPN
iajs-4031	121	2	2	2	NUM
iajs-4031	121	3	.	.	PUNCT
iajs-4031	121	4	lindley	lindley	PROPN
iajs-4031	121	5	dv	dv	PROPN
iajs-4031	121	6	.	.	PROPN
iajs-4031	121	7	fiducial	fiducial	ADJ
iajs-4031	121	8	distributions	distribution	NOUN
iajs-4031	121	9	and	and	CCONJ
iajs-4031	121	10	bayes	bayes	PROPN
iajs-4031	121	11	’	'	PUNCT
iajs-4031	121	12	theorem	theorem	PROPN
iajs-4031	121	13	.	.	PROPN
iajs-4031	121	14	journal	journal	PROPN
iajs-4031	121	15	of	of	ADP
iajs-4031	121	16	the	the	DET
iajs-4031	121	17	royal	royal	ADJ
iajs-4031	121	18	statistical	statistical	ADJ
iajs-4031	121	19	society	society	NOUN
iajs-4031	121	20	,	,	PUNCT
iajs-4031	121	21	series	series	PROPN
iajs-4031	121	22	b.	b.	PROPN
iajs-4031	121	23	1958;20(1):102–7	1958;20(1):102–7	PROPN
iajs-4031	121	24	.	.	PUNCT
iajs-4031	122	1	https://doi.org/10.1111/j.2517-6161.1958.tb00278.x	https://doi.org/10.1111/j.2517-6161.1958.tb00278.x	PROPN
iajs-4031	122	2	3	3	X
iajs-4031	122	3	.	.	X
iajs-4031	122	4	ghitany	ghitany	VERB
iajs-4031	122	5	me	i	PRON
iajs-4031	122	6	,	,	PUNCT
iajs-4031	122	7	atieh	atieh	PROPN
iajs-4031	122	8	b	b	PROPN
iajs-4031	122	9	,	,	PUNCT
iajs-4031	122	10	nadarajah	nadarajah	PROPN
iajs-4031	122	11	s.	s.	PROPN
iajs-4031	122	12	lindley	lindley	PROPN
iajs-4031	122	13	distribution	distribution	NOUN
iajs-4031	122	14	and	and	CCONJ
iajs-4031	122	15	its	its	PRON
iajs-4031	122	16	applications	application	NOUN
iajs-4031	122	17	.	.	PUNCT
iajs-4031	123	1	mathematics	mathematic	NOUN
iajs-4031	123	2	and	and	CCONJ
iajs-4031	123	3	computers	computer	NOUN
iajs-4031	123	4	in	in	ADP
iajs-4031	123	5	simulation	simulation	NOUN
iajs-4031	123	6	.	.	PUNCT
iajs-4031	124	1	2008;78(4):493–506	2008;78(4):493–506	X
iajs-4031	124	2	.	.	PROPN
iajs-4031	124	3	https://doi.org/10.1016/j.matcom.2007.06.007	https://doi.org/10.1016/j.matcom.2007.06.007	PROPN
iajs-4031	124	4	4	4	NUM
iajs-4031	124	5	.	.	PUNCT
iajs-4031	124	6	nadarajah	nadarajah	PROPN
iajs-4031	124	7	s	s	PROPN
iajs-4031	124	8	,	,	PUNCT
iajs-4031	124	9	haghighi	haghighi	PROPN
iajs-4031	124	10	f.	f.	PROPN
iajs-4031	125	1	an	an	DET
iajs-4031	125	2	extension	extension	NOUN
iajs-4031	125	3	of	of	ADP
iajs-4031	125	4	the	the	DET
iajs-4031	125	5	exponential	exponential	ADJ
iajs-4031	125	6	distribution	distribution	NOUN
iajs-4031	125	7	.	.	PUNCT
iajs-4031	126	1	statistics	statistic	NOUN
iajs-4031	126	2	.	.	PUNCT
iajs-4031	127	1	2010;45(6):543–58	2010;45(6):543–58	NUM
iajs-4031	127	2	.	.	PUNCT
iajs-4031	128	1	https://doi.org/10.1080/02331881003678678	https://doi.org/10.1080/02331881003678678	NUM
iajs-4031	128	2	5	5	NUM
iajs-4031	128	3	.	.	X
iajs-4031	128	4	alnssyan	alnssyan	PROPN
iajs-4031	128	5	b.	b.	PROPN
iajs-4031	129	1	the	the	DET
iajs-4031	129	2	modified	modify	VERB
iajs-4031	129	3	-	-	PUNCT
iajs-4031	129	4	lomax	lomax	NOUN
iajs-4031	129	5	distribution	distribution	NOUN
iajs-4031	129	6	:	:	PUNCT
iajs-4031	129	7	properties	property	NOUN
iajs-4031	129	8	,	,	PUNCT
iajs-4031	129	9	estimation	estimation	NOUN
iajs-4031	129	10	methods	method	NOUN
iajs-4031	129	11	,	,	PUNCT
iajs-4031	129	12	and	and	CCONJ
iajs-4031	129	13	application	application	NOUN
iajs-4031	129	14	.	.	PUNCT
iajs-4031	130	1	symmetry	symmetry	NOUN
iajs-4031	130	2	.	.	PUNCT
iajs-4031	131	1	2023;15(7):1367	2023;15(7):1367	NUM
iajs-4031	131	2	.	.	PUNCT
iajs-4031	132	1	https://doi.org/10.3390/sym15071367	https://doi.org/10.3390/sym15071367	NOUN
iajs-4031	132	2	6	6	NUM
iajs-4031	132	3	.	.	PUNCT
iajs-4031	133	1	shanker	shanker	PROPN
iajs-4031	133	2	r.	r.	PROPN
iajs-4031	133	3	komal	komal	PROPN
iajs-4031	133	4	distribution	distribution	NOUN
iajs-4031	133	5	with	with	ADP
iajs-4031	133	6	properties	property	NOUN
iajs-4031	133	7	and	and	CCONJ
iajs-4031	133	8	application	application	NOUN
iajs-4031	133	9	in	in	ADP
iajs-4031	133	10	survival	survival	NOUN
iajs-4031	133	11	analysis	analysis	NOUN
iajs-4031	133	12	.	.	PUNCT
iajs-4031	134	1	biometrics	biometrics	PROPN
iajs-4031	134	2	&	&	CCONJ
iajs-4031	134	3	biostatistics	biostatistics	PROPN
iajs-4031	134	4	international	international	PROPN
iajs-4031	134	5	journal	journal	NOUN
iajs-4031	134	6	.	.	PUNCT
iajs-4031	135	1	2023;12(2):40–4	2023;12(2):40–4	X
iajs-4031	135	2	.	.	PUNCT
iajs-4031	136	1	http://dx.doi.org/10.15406/bbij.2023.12.00381	http://dx.doi.org/10.15406/bbij.2023.12.00381	PROPN
iajs-4031	136	2	7	7	NUM
iajs-4031	136	3	.	.	PUNCT
iajs-4031	136	4	jawitz	jawitz	PROPN
iajs-4031	136	5	jw	jw	PROPN
iajs-4031	136	6	.	.	PROPN
iajs-4031	136	7	moments	moment	NOUN
iajs-4031	136	8	of	of	ADP
iajs-4031	136	9	truncated	truncated	ADJ
iajs-4031	136	10	continuous	continuous	ADJ
iajs-4031	136	11	univariate	univariate	ADJ
iajs-4031	136	12	distributions	distribution	NOUN
iajs-4031	136	13	.	.	PUNCT
iajs-4031	137	1	advances	advance	NOUN
iajs-4031	137	2	in	in	ADP
iajs-4031	137	3	water	water	NOUN
iajs-4031	137	4	resources	resource	NOUN
iajs-4031	137	5	.	.	PUNCT
iajs-4031	138	1	2004;27(3):269–81	2004;27(3):269–81	NUM
iajs-4031	138	2	.	.	PUNCT
iajs-4031	138	3	http://dx.doi.org/10.1016/j.advwatres.203.12.002	http://dx.doi.org/10.1016/j.advwatres.203.12.002	NOUN
iajs-4031	138	4	8	8	NUM
iajs-4031	138	5	.	.	X
iajs-4031	139	1	singh	singh	PROPN
iajs-4031	139	2	sk	sk	PROPN
iajs-4031	139	3	,	,	PUNCT
iajs-4031	139	4	singh	singh	PROPN
iajs-4031	139	5	u	u	PROPN
iajs-4031	139	6	,	,	PUNCT
iajs-4031	139	7	sharma	sharma	PROPN
iajs-4031	139	8	vk	vk	PROPN
iajs-4031	139	9	.	.	PUNCT
iajs-4031	140	1	the	the	DET
iajs-4031	140	2	truncated	truncated	ADJ
iajs-4031	140	3	lindley	lindley	NOUN
iajs-4031	140	4	distribution	distribution	NOUN
iajs-4031	140	5	:	:	PUNCT
iajs-4031	140	6	inference	inference	NOUN
iajs-4031	140	7	and	and	CCONJ
iajs-4031	140	8	application	application	NOUN
iajs-4031	140	9	.	.	PUNCT
iajs-4031	141	1	journal	journal	PROPN
iajs-4031	141	2	of	of	ADP
iajs-4031	141	3	statistics	statistic	NOUN
iajs-4031	141	4	applications	application	NOUN
iajs-4031	141	5	and	and	CCONJ
iajs-4031	141	6	probability	probability	NOUN
iajs-4031	141	7	.	.	PUNCT
iajs-4031	142	1	2014;3(2):2019–28	2014;3(2):2019–28	X
iajs-4031	142	2	.	.	PUNCT
iajs-4031	143	1	http://dx.doi.org/10.12785/jsap/030212	http://dx.doi.org/10.12785/jsap/030212	ADJ
iajs-4031	143	2	9	9	NUM
iajs-4031	143	3	.	.	PUNCT
iajs-4031	144	1	najarzadegan	najarzadegan	PROPN
iajs-4031	144	2	h	h	NOUN
iajs-4031	144	3	,	,	PUNCT
iajs-4031	144	4	alamatsaz	alamatsaz	PROPN
iajs-4031	144	5	mh	mh	PROPN
iajs-4031	144	6	,	,	PUNCT
iajs-4031	144	7	saied	saie	VERB
iajs-4031	145	1	h.	h.	PROPN
iajs-4031	145	2	truncated	truncate	VERB
iajs-4031	145	3	weibull	weibull	PROPN
iajs-4031	145	4	-	-	PUNCT
iajs-4031	145	5	g	g	NOUN
iajs-4031	145	6	more	more	ADV
iajs-4031	145	7	flexible	flexible	ADJ
iajs-4031	145	8	and	and	CCONJ
iajs-4031	145	9	more	more	ADV
iajs-4031	145	10	reliable	reliable	ADJ
iajs-4031	145	11	than	than	ADP
iajs-4031	145	12	beta	beta	NOUN
iajs-4031	145	13	-	-	PUNCT
iajs-4031	145	14	g	g	NOUN
iajs-4031	145	15	distribution	distribution	NOUN
iajs-4031	145	16	.	.	PUNCT
iajs-4031	146	1	international	international	ADJ
iajs-4031	146	2	journal	journal	PROPN
iajs-4031	146	3	of	of	ADP
iajs-4031	146	4	statistics	statistic	NOUN
iajs-4031	146	5	and	and	CCONJ
iajs-4031	146	6	probability	probability	NOUN
iajs-4031	146	7	.	.	PUNCT
iajs-4031	147	1	2017;6:1–17	2017;6:1–17	NUM
iajs-4031	147	2	.	.	PUNCT
iajs-4031	147	3	http://dx.doi.org/10.5539/ijsp.v6n5p1	http://dx.doi.org/10.5539/ijsp.v6n5p1	PROPN
iajs-4031	147	4	10	10	NUM
iajs-4031	147	5	.	.	PUNCT
iajs-4031	148	1	abid	abid	PROPN
iajs-4031	148	2	s	s	PROPN
iajs-4031	148	3	,	,	PUNCT
iajs-4031	148	4	abdulrazak	abdulrazak	ADJ
iajs-4031	148	5	.	.	PUNCT
iajs-4031	149	1	[	[	X
iajs-4031	149	2	0	0	NUM
iajs-4031	149	3	,	,	PUNCT
iajs-4031	149	4	1	1	NUM
iajs-4031	149	5	]	]	PUNCT
iajs-4031	149	6	truncated	truncated	ADJ
iajs-4031	149	7	frechet	frechet	PROPN
iajs-4031	149	8	-	-	PUNCT
iajs-4031	149	9	weibull	weibull	PROPN
iajs-4031	149	10	and	and	CCONJ
iajs-4031	149	11	frechet	frechet	NOUN
iajs-4031	149	12	distributions	distribution	NOUN
iajs-4031	149	13	.	.	PUNCT
iajs-4031	150	1	international	international	ADJ
iajs-4031	150	2	journal	journal	PROPN
iajs-4031	150	3	of	of	ADP
iajs-4031	150	4	research	research	NOUN
iajs-4031	150	5	in	in	ADP
iajs-4031	150	6	industrial	industrial	ADJ
iajs-4031	150	7	engineering	engineering	NOUN
iajs-4031	150	8	.	.	PUNCT
iajs-4031	151	1	2018;7:106–35	2018;7:106–35	NUM
iajs-4031	151	2	.	.	NOUN
iajs-4031	151	3	https://doi.org/10.22105/riej.2018.100865.1020	https://doi.org/10.22105/riej.2018.100865.1020	NUM
iajs-4031	151	4	11	11	NUM
iajs-4031	151	5	.	.	PUNCT
iajs-4031	151	6	akbarinasab	akbarinasab	PROPN
iajs-4031	151	7	m	m	PROPN
iajs-4031	151	8	,	,	PUNCT
iajs-4031	151	9	arabpour	arabpour	PROPN
iajs-4031	151	10	ar	ar	PROPN
iajs-4031	151	11	,	,	PUNCT
iajs-4031	151	12	mahdavi	mahdavi	PROPN
iajs-4031	151	13	a.	a.	PROPN
iajs-4031	151	14	truncated	truncate	VERB
iajs-4031	151	15	log	log	NOUN
iajs-4031	151	16	-	-	PUNCT
iajs-4031	151	17	logistic	logistic	NOUN
iajs-4031	151	18	family	family	NOUN
iajs-4031	151	19	of	of	ADP
iajs-4031	151	20	distributions	distribution	NOUN
iajs-4031	151	21	.	.	PUNCT
iajs-4031	152	1	journal	journal	NOUN
iajs-4031	152	2	of	of	ADP
iajs-4031	152	3	biostatistics	biostatistic	NOUN
iajs-4031	152	4	and	and	CCONJ
iajs-4031	152	5	epidemiology	epidemiology	NOUN
iajs-4031	152	6	.	.	PUNCT
iajs-4031	153	1	2019;5(2):137–47	2019;5(2):137–47	X
iajs-4031	153	2	.	.	PUNCT
iajs-4031	154	1	https://doi.org/10.18502/jbe.v5i2.2345	https://doi.org/10.18502/jbe.v5i2.2345	PROPN
iajs-4031	154	2	12	12	NUM
iajs-4031	154	3	.	.	PUNCT
iajs-4031	155	1	altawil	altawil	PROPN
iajs-4031	155	2	j.	j.	PROPN
iajs-4031	156	1	[	[	X
iajs-4031	156	2	0,1	0,1	NUM
iajs-4031	156	3	]	]	PUNCT
iajs-4031	156	4	truncated	truncated	ADJ
iajs-4031	156	5	lomax	lomax	PROPN
iajs-4031	156	6	–	–	PUNCT
iajs-4031	156	7	lomax	lomax	PROPN
iajs-4031	156	8	distribution	distribution	NOUN
iajs-4031	156	9	with	with	ADP
iajs-4031	156	10	properties	property	NOUN
iajs-4031	156	11	.	.	PUNCT
iajs-4031	157	1	journal	journal	PROPN
iajs-4031	157	2	of	of	ADP
iajs-4031	157	3	kufa	kufa	PROPN
iajs-4031	157	4	for	for	ADP
iajs-4031	157	5	mathematics	mathematic	NOUN
iajs-4031	157	6	and	and	CCONJ
iajs-4031	157	7	computer	computer	NOUN
iajs-4031	157	8	.	.	PUNCT
iajs-4031	158	1	2021;8(1):1–8	2021;8(1):1–8	NUM
iajs-4031	158	2	.	.	PUNCT
iajs-4031	159	1	https://doi.org/10.31642/jokmc/2018/08010	https://doi.org/10.31642/jokmc/2018/08010	PROPN
iajs-4031	159	2	13	13	NUM
iajs-4031	159	3	.	.	PUNCT
iajs-4031	160	1	gul	gul	PROPN
iajs-4031	160	2	a	a	PROPN
iajs-4031	160	3	,	,	PUNCT
iajs-4031	160	4	mohsin	mohsin	PROPN
iajs-4031	160	5	m	m	PROPN
iajs-4031	160	6	,	,	PUNCT
iajs-4031	160	7	adil	adil	PROPN
iajs-4031	160	8	m	m	PROPN
iajs-4031	160	9	,	,	PUNCT
iajs-4031	160	10	ali	ali	PROPN
iajs-4031	160	11	m.	m.	PROPN
iajs-4031	160	12	a	a	DET
iajs-4031	160	13	modified	modify	VERB
iajs-4031	160	14	truncated	truncate	VERB
iajs-4031	160	15	distribution	distribution	NOUN
iajs-4031	160	16	for	for	ADP
iajs-4031	160	17	modeling	model	VERB
iajs-4031	160	18	the	the	DET
iajs-4031	160	19	heavy	heavy	ADJ
iajs-4031	160	20	tail	tail	NOUN
iajs-4031	160	21	,	,	PUNCT
iajs-4031	160	22	engineering	engineering	NOUN
iajs-4031	160	23	and	and	CCONJ
iajs-4031	160	24	environmental	environmental	ADJ
iajs-4031	160	25	sciences	sciences	PROPN
iajs-4031	160	26	data	datum	NOUN
iajs-4031	160	27	.	.	PUNCT
iajs-4031	161	1	plos	plos	PROPN
iajs-4031	161	2	one	one	NUM
iajs-4031	161	3	.	.	PUNCT
iajs-4031	161	4	2021;16(4	2021;16(4	NUM
iajs-4031	161	5	)	)	PUNCT
iajs-4031	161	6	.	.	PUNCT
iajs-4031	162	1	https://doi.org/10.1371/journal.pone.0249001	https://doi.org/10.1371/journal.pone.0249001	PROPN
iajs-4031	162	2	14	14	NUM
iajs-4031	162	3	.	.	PUNCT
iajs-4031	163	1	khaleel	khaleel	PROPN
iajs-4031	163	2	ma	ma	PROPN
iajs-4031	163	3	,	,	PUNCT
iajs-4031	163	4	abdulwahab	abdulwahab	PROPN
iajs-4031	163	5	ma	ma	PROPN
iajs-4031	163	6	,	,	PUNCT
iajs-4031	163	7	gaftan	gaftan	PROPN
iajs-4031	163	8	am	am	NOUN
iajs-4031	163	9	,	,	PUNCT
iajs-4031	163	10	abdal	abdal	ADJ
iajs-4031	163	11	-	-	PUNCT
iajs-4031	163	12	hammed	ham	VERB
iajs-4031	163	13	mk	mk	PROPN
iajs-4031	163	14	.	.	PUNCT
iajs-4031	164	1	a	a	DET
iajs-4031	164	2	new	new	ADJ
iajs-4031	164	3	[	[	X
iajs-4031	164	4	0	0	NUM
iajs-4031	164	5	,	,	PUNCT
iajs-4031	164	6	1	1	NUM
iajs-4031	164	7	]	]	PUNCT
iajs-4031	164	8	truncated	truncate	VERB
iajs-4031	164	9	inverse	inverse	NOUN
iajs-4031	164	10	weibull	weibull	PROPN
iajs-4031	164	11	rayleigh	rayleigh	PROPN
iajs-4031	164	12	distribution	distribution	NOUN
iajs-4031	164	13	properties	property	NOUN
iajs-4031	164	14	with	with	ADP
iajs-4031	164	15	application	application	NOUN
iajs-4031	164	16	to	to	ADP
iajs-4031	164	17	covid-19	covid-19	PROPN
iajs-4031	164	18	.	.	PUNCT
iajs-4031	164	19	international	international	PROPN
iajs-4031	164	20	journal	journal	PROPN
iajs-4031	164	21	of	of	ADP
iajs-4031	164	22	nonlinear	nonlinear	ADJ
iajs-4031	164	23	analysis	analysis	NOUN
iajs-4031	164	24	and	and	CCONJ
iajs-4031	164	25	applications	application	NOUN
iajs-4031	164	26	.	.	PUNCT
iajs-4031	165	1	2022;13(1):2933–46	2022;13(1):2933–46	NOUN
iajs-4031	165	2	.	.	PUNCT
iajs-4031	166	1	15	15	NUM
iajs-4031	166	2	.	.	PUNCT
iajs-4031	167	1	abbas	abbas	PROPN
iajs-4031	167	2	s	s	PART
iajs-4031	167	3	,	,	PUNCT
iajs-4031	167	4	farooq	farooq	PROPN
iajs-4031	167	5	m	m	PROPN
iajs-4031	167	6	,	,	PUNCT
iajs-4031	167	7	darwish	darwish	PROPN
iajs-4031	167	8	ja	ja	PROPN
iajs-4031	167	9	,	,	PUNCT
iajs-4031	167	10	shahbaz	shahbaz	PROPN
iajs-4031	167	11	sh	sh	PROPN
iajs-4031	167	12	,	,	PUNCT
iajs-4031	167	13	shahbaz	shahbaz	PROPN
iajs-4031	167	14	mq	mq	PROPN
iajs-4031	167	15	.	.	PROPN
iajs-4031	167	16	truncated	truncate	VERB
iajs-4031	167	17	weibull	weibull	PROPN
iajs-4031	167	18	–	–	PUNCT
iajs-4031	167	19	exponential	exponential	ADJ
iajs-4031	167	20	distribution	distribution	NOUN
iajs-4031	167	21	:	:	PUNCT
iajs-4031	167	22	methods	method	NOUN
iajs-4031	167	23	and	and	CCONJ
iajs-4031	167	24	applications	application	NOUN
iajs-4031	167	25	.	.	PUNCT
iajs-4031	168	1	scientific	scientific	ADJ
iajs-4031	168	2	reports	report	NOUN
iajs-4031	168	3	.	.	PUNCT
iajs-4031	169	1	2023;13(1	2023;13(1	NUM
iajs-4031	169	2	)	)	PUNCT
iajs-4031	169	3	.	.	PUNCT
iajs-4031	170	1	https://doi.org/10.1038/s41598023-48288-x	https://doi.org/10.1038/s41598023-48288-x	PROPN
iajs-4031	171	1	16	16	NUM
iajs-4031	171	2	.	.	PUNCT
iajs-4031	172	1	hussein	hussein	PROPN
iajs-4031	172	2	lk	lk	PROPN
iajs-4031	172	3	,	,	PUNCT
iajs-4031	172	4	abdullah	abdullah	PROPN
iajs-4031	172	5	rasheed	rasheed	PROPN
iajs-4031	172	6	h	h	PROPN
iajs-4031	172	7	,	,	PUNCT
iajs-4031	172	8	hasan	hasan	PROPN
iajs-4031	172	9	hussein	hussein	PROPN
iajs-4031	172	10	i.	i.	PROPN
iajs-4031	172	11	a	a	DET
iajs-4031	172	12	class	class	NOUN
iajs-4031	172	13	of	of	ADP
iajs-4031	172	14	exponential	exponential	ADJ
iajs-4031	172	15	rayleigh	rayleigh	NOUN
iajs-4031	172	16	distribution	distribution	NOUN
iajs-4031	172	17	and	and	CCONJ
iajs-4031	172	18	new	new	ADJ
iajs-4031	172	19	modified	modify	VERB
iajs-4031	172	20	weighted	weight	VERB
iajs-4031	172	21	exponential	exponential	ADJ
iajs-4031	172	22	rayleigh	rayleigh	NOUN
iajs-4031	172	23	distribution	distribution	NOUN
iajs-4031	172	24	with	with	ADP
iajs-4031	172	25	statistical	statistical	ADJ
iajs-4031	172	26	properties	property	NOUN
iajs-4031	172	27	.	.	PUNCT
iajs-4031	173	1	ibn	ibn	PROPN
iajs-4031	173	2	alhaitham	alhaitham	PROPN
iajs-4031	173	3	journal	journal	NOUN
iajs-4031	173	4	for	for	ADP
iajs-4031	173	5	pure	pure	ADJ
iajs-4031	173	6	and	and	CCONJ
iajs-4031	173	7	applied	applied	ADJ
iajs-4031	173	8	sciences	science	NOUN
iajs-4031	173	9	.	.	PUNCT
iajs-4031	174	1	2023;36(2):390–406	2023;36(2):390–406	NUM
iajs-4031	174	2	.	.	PUNCT
iajs-4031	175	1	https://doi.org/10.30526/36.2.3044	https://doi.org/10.30526/36.2.3044	AUX
iajs-4031	175	2	http://dx.doi.org/10.15406/bbij.2020.09.00317	http://dx.doi.org/10.15406/bbij.2020.09.00317	PROPN
iajs-4031	175	3	https://doi.org/10.1111/j.2517-6161.1958.tb00278.x	https://doi.org/10.1111/j.2517-6161.1958.tb00278.x	PROPN
iajs-4031	175	4	https://doi.org/10.1016/j.matcom.2007.06.007	https://doi.org/10.1016/j.matcom.2007.06.007	PROPN
iajs-4031	175	5	https://doi.org/10.1080/02331881003678678	https://doi.org/10.1080/02331881003678678	X
iajs-4031	175	6	https://doi.org/10.3390/sym15071367	https://doi.org/10.3390/sym15071367	NOUN
iajs-4031	175	7	http://dx.doi.org/10.15406/bbij.2023.12.00381	http://dx.doi.org/10.15406/bbij.2023.12.00381	PROPN
iajs-4031	175	8	http://dx.doi.org/10.1016/j.advwatres.203.12.002	http://dx.doi.org/10.1016/j.advwatres.203.12.002	NOUN
iajs-4031	175	9	http://dx.doi.org/10.12785/jsap/030212	http://dx.doi.org/10.12785/jsap/030212	ADJ
iajs-4031	175	10	http://dx.doi.org/10.5539/ijsp.v6n5p1	http://dx.doi.org/10.5539/ijsp.v6n5p1	VERB
iajs-4031	175	11	https://doi.org/10.22105/riej.2018.100865.1020	https://doi.org/10.22105/riej.2018.100865.1020	PROPN
iajs-4031	175	12	https://doi.org/10.18502/jbe.v5i2.2345	https://doi.org/10.18502/jbe.v5i2.2345	PROPN
iajs-4031	175	13	https://doi.org/10.31642/jokmc/2018/08010	https://doi.org/10.31642/jokmc/2018/08010	NOUN
iajs-4031	175	14	https://doi.org/10.1371/journal.pone.0249001	https://doi.org/10.1371/journal.pone.0249001	PROPN
iajs-4031	175	15	https://doi.org/10.1038/s41598-023-48288-x	https://doi.org/10.1038/s41598-023-48288-x	PROPN
iajs-4031	175	16	https://doi.org/10.1038/s41598-023-48288-x	https://doi.org/10.1038/s41598-023-48288-x	PROPN
iajs-4031	175	17	https://doi.org/10.30526/36.2.3044	https://doi.org/10.30526/36.2.3044	PROPN
iajs-4031	175	18	ihjpas	ihjpas	PROPN
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iajs-4031	176	2	,	,	PUNCT
iajs-4031	176	3	38	38	NUM
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iajs-4031	176	5	1	1	NUM
iajs-4031	176	6	)	)	PUNCT
iajs-4031	176	7	499	499	NUM
iajs-4031	176	8	17	17	NUM
iajs-4031	176	9	.	.	PUNCT
iajs-4031	177	1	qasim	qasim	PROPN
iajs-4031	177	2	ba	ba	PROPN
iajs-4031	177	3	.	.	PUNCT
iajs-4031	178	1	a	a	DET
iajs-4031	178	2	new	new	ADJ
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iajs-4031	178	6	-	-	PUNCT
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iajs-4031	178	8	distribution	distribution	NOUN
iajs-4031	178	9	:	:	PUNCT
iajs-4031	178	10	properties	property	NOUN
iajs-4031	178	11	and	and	CCONJ
iajs-4031	178	12	estimation	estimation	NOUN
iajs-4031	178	13	.	.	PUNCT
iajs-4031	179	1	aip	aip	PROPN
iajs-4031	179	2	conference	conference	NOUN
iajs-4031	179	3	proceedings	proceeding	NOUN
iajs-4031	179	4	.	.	PUNCT
iajs-4031	180	1	2023	2023	NUM
iajs-4031	180	2	.	.	PUNCT
iajs-4031	181	1	https://doi.org/10.1063/5.0118651	https://doi.org/10.1063/5.0118651	ADV
iajs-4031	181	2	18	18	NUM
iajs-4031	181	3	.	.	PUNCT
iajs-4031	182	1	kalaf	kalaf	PROPN
iajs-4031	182	2	ba	ba	PROPN
iajs-4031	182	3	,	,	PUNCT
iajs-4031	182	4	abdul	abdul	PROPN
iajs-4031	182	5	ameer	ameer	PROPN
iajs-4031	182	6	jn	jn	PROPN
iajs-4031	182	7	,	,	PUNCT
iajs-4031	182	8	madaki	madaki	PROPN
iajs-4031	182	9	uy	uy	PROPN
iajs-4031	182	10	.	.	PUNCT
iajs-4031	183	1	truncated	truncated	ADJ
iajs-4031	183	2	inverse	inverse	NOUN
iajs-4031	183	3	generalized	generalize	VERB
iajs-4031	183	4	rayleigh	rayleigh	NOUN
iajs-4031	183	5	distribution	distribution	NOUN
iajs-4031	183	6	and	and	CCONJ
iajs-4031	183	7	some	some	DET
iajs-4031	183	8	properties	property	NOUN
iajs-4031	183	9	.	.	PUNCT
iajs-4031	184	1	ibn	ibn	PROPN
iajs-4031	184	2	al	al	PROPN
iajs-4031	184	3	-	-	PUNCT
iajs-4031	184	4	haitham	haitham	PROPN
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iajs-4031	184	7	pure	pure	ADJ
iajs-4031	184	8	and	and	CCONJ
iajs-4031	184	9	applied	applied	ADJ
iajs-4031	184	10	sciences	science	NOUN
iajs-4031	184	11	.	.	PUNCT
iajs-4031	185	1	2023;36(4):414–28	2023;36(4):414–28	NUM
iajs-4031	185	2	.	.	PUNCT
iajs-4031	186	1	https://doi.org/10.30526/36.4.2977	https://doi.org/10.30526/36.4.2977	X
iajs-4031	186	2	19	19	NUM
iajs-4031	186	3	.	.	PUNCT
iajs-4031	186	4	shanker	shanker	PROPN
iajs-4031	186	5	r.	r.	PROPN
iajs-4031	186	6	shanker	shanker	PROPN
iajs-4031	186	7	distribution	distribution	NOUN
iajs-4031	186	8	and	and	CCONJ
iajs-4031	186	9	its	its	PRON
iajs-4031	186	10	applications	application	NOUN
iajs-4031	186	11	.	.	PUNCT
iajs-4031	187	1	international	international	ADJ
iajs-4031	187	2	journal	journal	PROPN
iajs-4031	187	3	of	of	ADP
iajs-4031	187	4	statistics	statistic	NOUN
iajs-4031	187	5	and	and	CCONJ
iajs-4031	187	6	applications	application	NOUN
iajs-4031	187	7	.	.	PUNCT
iajs-4031	188	1	2015;5(6):338–48	2015;5(6):338–48	NUM
iajs-4031	188	2	.	.	PUNCT
iajs-4031	188	3	http://dx.doi.org/10.5923/j.statistics.20150506.08	http://dx.doi.org/10.5923/j.statistics.20150506.08	NOUN
iajs-4031	188	4	20	20	NUM
iajs-4031	188	5	.	.	PUNCT
iajs-4031	189	1	aryuyuen	aryuyuen	PROPN
iajs-4031	189	2	s	s	PROPN
iajs-4031	189	3	,	,	PUNCT
iajs-4031	189	4	bodhisuwan	bodhisuwan	PROPN
iajs-4031	189	5	w.	w.	PROPN
iajs-4031	189	6	the	the	DET
iajs-4031	189	7	truncated	truncate	VERB
iajs-4031	189	8	power	power	NOUN
iajs-4031	189	9	lomax	lomax	PROPN
iajs-4031	189	10	distribution	distribution	NOUN
iajs-4031	189	11	:	:	PUNCT
iajs-4031	189	12	properties	property	NOUN
iajs-4031	189	13	and	and	CCONJ
iajs-4031	189	14	applications	application	NOUN
iajs-4031	189	15	.	.	PUNCT
iajs-4031	190	1	walailak	walailak	ADJ
iajs-4031	190	2	journal	journal	NOUN
iajs-4031	190	3	of	of	ADP
iajs-4031	190	4	science	science	NOUN
iajs-4031	190	5	and	and	CCONJ
iajs-4031	190	6	technology	technology	NOUN
iajs-4031	190	7	.	.	PUNCT
iajs-4031	191	1	2019;16(9):655–68	2019;16(9):655–68	X
iajs-4031	191	2	.	.	PUNCT
iajs-4031	192	1	https://doi.org/10.48048/wjst.2019.4542	https://doi.org/10.48048/wjst.2019.4542	PROPN
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iajs-4031	192	3	.	.	PUNCT
iajs-4031	193	1	mohammed	mohammed	PROPN
iajs-4031	193	2	mj	mj	PROPN
iajs-4031	193	3	,	,	PUNCT
iajs-4031	193	4	hussein	hussein	PROPN
iajs-4031	193	5	ih	ih	PRON
iajs-4031	193	6	.	.	PUNCT
iajs-4031	194	1	some	some	DET
iajs-4031	194	2	estimation	estimation	NOUN
iajs-4031	194	3	methods	method	NOUN
iajs-4031	194	4	for	for	ADP
iajs-4031	194	5	new	new	ADJ
iajs-4031	194	6	mixture	mixture	NOUN
iajs-4031	194	7	distribution	distribution	NOUN
iajs-4031	194	8	with	with	ADP
iajs-4031	194	9	simulation	simulation	NOUN
iajs-4031	194	10	and	and	CCONJ
iajs-4031	194	11	application	application	NOUN
iajs-4031	194	12	.	.	PUNCT
iajs-4031	195	1	iop	iop	PROPN
iajs-4031	195	2	conference	conference	PROPN
iajs-4031	195	3	series	series	PROPN
iajs-4031	195	4	:	:	PUNCT
iajs-4031	195	5	materials	material	NOUN
iajs-4031	195	6	science	science	NOUN
iajs-4031	195	7	and	and	CCONJ
iajs-4031	195	8	engineering	engineering	NOUN
iajs-4031	195	9	.	.	PUNCT
iajs-4031	196	1	2019;571(1	2019;571(1	NUM
iajs-4031	196	2	)	)	PUNCT
iajs-4031	196	3	.	.	PUNCT
iajs-4031	197	1	https://doi.org/10.1088/1757-899x/571/1/012014	https://doi.org/10.1088/1757-899x/571/1/012014	PROPN
iajs-4031	197	2	22	22	NUM
iajs-4031	197	3	.	.	PUNCT
iajs-4031	198	1	shanker	shanker	NOUN
iajs-4031	198	2	r	r	PROPN
iajs-4031	198	3	,	,	PUNCT
iajs-4031	198	4	upadhyay	upadhyay	PROPN
iajs-4031	198	5	r	r	PROPN
iajs-4031	198	6	,	,	PUNCT
iajs-4031	198	7	shukla	shukla	NOUN
iajs-4031	198	8	kk	kk	PROPN
iajs-4031	198	9	.	.	PUNCT
iajs-4031	199	1	a	a	DET
iajs-4031	199	2	quasi	quasi	X
iajs-4031	199	3	suja	suja	PROPN
iajs-4031	199	4	distribution	distribution	NOUN
iajs-4031	199	5	.	.	PUNCT
iajs-4031	200	1	reliability	reliability	NOUN
iajs-4031	200	2	:	:	PUNCT
iajs-4031	200	3	theory	theory	NOUN
iajs-4031	200	4	&	&	CCONJ
iajs-4031	200	5	applications	application	NOUN
iajs-4031	200	6	.	.	PUNCT
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iajs-4031	201	2	.	.	PROPN
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iajs-4031	201	4	.	.	PUNCT
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iajs-4031	202	2	,	,	PUNCT
iajs-4031	202	3	a.	a.	PROPN
iajs-4031	202	4	,	,	PUNCT
iajs-4031	202	5	kalaf	kalaf	PROPN
iajs-4031	202	6	,	,	PUNCT
iajs-4031	202	7	b.	b.	PROPN
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iajs-4031	202	14	on	on	ADP
iajs-4031	202	15	the	the	DET
iajs-4031	202	16	log	log	NOUN
iajs-4031	202	17	-	-	PUNCT
iajs-4031	202	18	logistic	logistic	ADJ
iajs-4031	202	19	distribution	distribution	NOUN
iajs-4031	202	20	.	.	PUNCT
iajs-4031	203	1	international	international	ADJ
iajs-4031	203	2	journal	journal	PROPN
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iajs-4031	203	5	analysis	analysis	NOUN
iajs-4031	203	6	and	and	CCONJ
iajs-4031	203	7	applications	application	NOUN
iajs-4031	203	8	,	,	PUNCT
iajs-4031	203	9	2022	2022	NUM
iajs-4031	203	10	;	;	PUNCT
iajs-4031	203	11	13(1	13(1	NUM
iajs-4031	203	12	):	):	PUNCT
iajs-4031	203	13	127	127	NUM
iajs-4031	203	14	-	-	SYM
iajs-4031	203	15	141	141	NUM
iajs-4031	203	16	.	.	PUNCT
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iajs-4031	204	4	http://dx.doi.org/10.5923/j.statistics.20150506.08	http://dx.doi.org/10.5923/j.statistics.20150506.08	NOUN
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