id	sid	tid	token	lemma	pos
cana-4617	1	1	communications	communication	NOUN
cana-4617	1	2	on	on	ADP
cana-4617	1	3	applied	apply	VERB
cana-4617	1	4	nonlinear	nonlinear	ADJ
cana-4617	1	5	analysis	analysis	NOUN
cana-4617	1	6	issn	issn	NOUN
cana-4617	1	7	:	:	PUNCT
cana-4617	1	8	1074	1074	NUM
cana-4617	1	9	-	-	PUNCT
cana-4617	1	10	133x	133x	NUM
cana-4617	1	11	vol	vol	NOUN
cana-4617	1	12	32	32	NUM
cana-4617	1	13	no	no	NOUN
cana-4617	1	14	.	.	PUNCT
cana-4617	2	1	9s	9s	NUM
cana-4617	2	2	(	(	PUNCT
cana-4617	2	3	2025	2025	NUM
cana-4617	2	4	)	)	PUNCT
cana-4617	2	5	3020	3020	NUM
cana-4617	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	2	7	recurrence	recurrence	NOUN
cana-4617	2	8	relations	relation	NOUN
cana-4617	2	9	for	for	ADP
cana-4617	2	10	moments	moment	NOUN
cana-4617	2	11	of	of	ADP
cana-4617	2	12	generalized	generalized	ADJ
cana-4617	2	13	order	order	NOUN
cana-4617	2	14	statistics	statistic	NOUN
cana-4617	2	15	from	from	ADP
cana-4617	2	16	area	area	NOUN
cana-4617	2	17	-	-	PUNCT
cana-4617	2	18	biased	bias	VERB
cana-4617	2	19	rayleigh	rayleigh	NOUN
cana-4617	2	20	distribution	distribution	NOUN
cana-4617	2	21	and	and	CCONJ
cana-4617	2	22	its	its	PRON
cana-4617	2	23	characterization	characterization	NOUN
cana-4617	2	24	a.	a.	NOUN
cana-4617	2	25	a.	a.	NOUN
cana-4617	2	26	a	a	PROPN
cana-4617	2	27	-	-	PUNCT
cana-4617	2	28	rahman1	rahman1	NOUN
cana-4617	2	29	,	,	PUNCT
cana-4617	2	30	i.	i.	PROPN
cana-4617	2	31	b.	b.	PROPN
cana-4617	2	32	abdul	abdul	PROPN
cana-4617	2	33	-	-	PUNCT
cana-4617	2	34	moniem	moniem	ADJ
cana-4617	2	35	2	2	NUM
cana-4617	2	36	,	,	PUNCT
cana-4617	2	37	m.	m.	PROPN
cana-4617	2	38	b.	b.	PROPN
cana-4617	2	39	moemen	moemen	PROPN
cana-4617	2	40	1	1	NUM
cana-4617	2	41	*	*	SYM
cana-4617	2	42	1	1	NUM
cana-4617	2	43	.	.	PUNCT
cana-4617	3	1	department	department	NOUN
cana-4617	3	2	of	of	ADP
cana-4617	3	3	mathematical	mathematical	ADJ
cana-4617	3	4	statistics	statistic	NOUN
cana-4617	3	5	,	,	PUNCT
cana-4617	3	6	faculty	faculty	NOUN
cana-4617	3	7	of	of	ADP
cana-4617	3	8	graduate	graduate	ADJ
cana-4617	3	9	studies	study	NOUN
cana-4617	3	10	for	for	ADP
cana-4617	3	11	statistical	statistical	ADJ
cana-4617	3	12	research	research	NOUN
cana-4617	3	13	,	,	PUNCT
cana-4617	3	14	cairo	cairo	PROPN
cana-4617	3	15	university	university	PROPN
cana-4617	3	16	,	,	PUNCT
cana-4617	3	17	egypt	egypt	PROPN
cana-4617	3	18	.	.	PUNCT
cana-4617	4	1	2	2	X
cana-4617	4	2	.	.	X
cana-4617	4	3	department	department	NOUN
cana-4617	4	4	of	of	ADP
cana-4617	4	5	statistics	statistic	NOUN
cana-4617	4	6	,	,	PUNCT
cana-4617	4	7	higher	high	ADJ
cana-4617	4	8	institute	institute	PROPN
cana-4617	4	9	of	of	ADP
cana-4617	4	10	management	management	NOUN
cana-4617	4	11	sciences	sciences	PROPN
cana-4617	4	12	in	in	ADP
cana-4617	4	13	sohag	sohag	NOUN
cana-4617	4	14	,	,	PUNCT
cana-4617	4	15	sohag	sohag	NOUN
cana-4617	4	16	,	,	PUNCT
cana-4617	4	17	egypt	egypt	PROPN
cana-4617	4	18	.	.	PUNCT
cana-4617	4	19	,	,	PUNCT
cana-4617	5	1	*	*	PUNCT
cana-4617	5	2	corresponding	correspond	VERB
cana-4617	5	3	author	author	NOUN
cana-4617	5	4	:	:	PUNCT
cana-4617	5	5	mo.baha2010@gmail.com	mo.baha2010@gmail.com	PROPN
cana-4617	5	6	article	article	PROPN
cana-4617	5	7	history	history	NOUN
cana-4617	5	8	:	:	PUNCT
cana-4617	5	9	received	receive	VERB
cana-4617	5	10	:	:	PUNCT
cana-4617	5	11	12	12	NUM
cana-4617	5	12	-	-	SYM
cana-4617	5	13	01	01	NUM
cana-4617	5	14	-	-	PUNCT
cana-4617	5	15	2025	2025	NUM
cana-4617	5	16	revised	revise	VERB
cana-4617	5	17	:	:	PUNCT
cana-4617	5	18	15	15	NUM
cana-4617	5	19	-	-	NUM
cana-4617	5	20	02	02	NUM
cana-4617	5	21	-	-	PUNCT
cana-4617	5	22	2025	2025	NUM
cana-4617	5	23	accepted	accept	VERB
cana-4617	5	24	:	:	PUNCT
cana-4617	5	25	01	01	NUM
cana-4617	5	26	-	-	SYM
cana-4617	5	27	03	03	NUM
cana-4617	5	28	-	-	PUNCT
cana-4617	5	29	2025	2025	NUM
cana-4617	5	30	abstract	abstract	NOUN
cana-4617	5	31	:	:	PUNCT
cana-4617	5	32	in	in	ADP
cana-4617	5	33	this	this	DET
cana-4617	5	34	paper	paper	NOUN
cana-4617	5	35	,	,	PUNCT
cana-4617	5	36	the	the	DET
cana-4617	5	37	derivation	derivation	NOUN
cana-4617	5	38	of	of	ADP
cana-4617	5	39	recurrence	recurrence	NOUN
cana-4617	5	40	relations	relation	NOUN
cana-4617	5	41	for	for	ADP
cana-4617	5	42	single	single	ADJ
cana-4617	5	43	and	and	CCONJ
cana-4617	5	44	product	product	NOUN
cana-4617	5	45	moments	moment	NOUN
cana-4617	5	46	from	from	ADP
cana-4617	5	47	generalized	generalized	ADJ
cana-4617	5	48	order	order	NOUN
cana-4617	5	49	statistics	statistic	NOUN
cana-4617	5	50	using	use	VERB
cana-4617	5	51	the	the	DET
cana-4617	5	52	area	area	NOUN
cana-4617	5	53	-	-	PUNCT
cana-4617	5	54	biased	bias	VERB
cana-4617	5	55	rayleigh	rayleigh	NOUN
cana-4617	5	56	distribution	distribution	NOUN
cana-4617	5	57	is	be	AUX
cana-4617	5	58	presented	present	VERB
cana-4617	5	59	.	.	PUNCT
cana-4617	6	1	this	this	PRON
cana-4617	6	2	includes	include	VERB
cana-4617	6	3	specific	specific	ADJ
cana-4617	6	4	cases	case	NOUN
cana-4617	6	5	for	for	ADP
cana-4617	6	6	order	order	NOUN
cana-4617	6	7	statistics	statistic	NOUN
cana-4617	6	8	and	and	CCONJ
cana-4617	6	9	records	record	NOUN
cana-4617	6	10	.	.	PUNCT
cana-4617	7	1	additionally	additionally	ADV
cana-4617	7	2	,	,	PUNCT
cana-4617	7	3	the	the	DET
cana-4617	7	4	area	area	NOUN
cana-4617	7	5	-	-	PUNCT
cana-4617	7	6	biased	bias	VERB
cana-4617	7	7	rayleigh	rayleigh	NOUN
cana-4617	7	8	distribution	distribution	NOUN
cana-4617	7	9	is	be	AUX
cana-4617	7	10	characterized	characterize	VERB
cana-4617	7	11	through	through	ADP
cana-4617	7	12	a	a	DET
cana-4617	7	13	recurrence	recurrence	NOUN
cana-4617	7	14	relation	relation	NOUN
cana-4617	7	15	for	for	ADP
cana-4617	7	16	single	single	ADJ
cana-4617	7	17	moments	moment	NOUN
cana-4617	7	18	.	.	PUNCT
cana-4617	8	1	keywords	keyword	NOUN
cana-4617	8	2	:	:	PUNCT
cana-4617	8	3	generalized	generalized	ADJ
cana-4617	8	4	order	order	NOUN
cana-4617	8	5	statistics	statistic	NOUN
cana-4617	8	6	-single	-single	NOUN
cana-4617	8	7	and	and	CCONJ
cana-4617	8	8	product	product	NOUN
cana-4617	8	9	moments	moment	NOUN
cana-4617	8	10	recurrence	recurrence	PROPN
cana-4617	8	11	relations	relation	NOUN
cana-4617	8	12	area	area	NOUN
cana-4617	8	13	biased	bias	VERB
cana-4617	8	14	rayleigh	rayleigh	NOUN
cana-4617	8	15	distribution	distribution	NOUN
cana-4617	8	16	characterization	characterization	NOUN
cana-4617	8	17	.	.	PUNCT
cana-4617	9	1	1	1	X
cana-4617	9	2	.	.	X
cana-4617	9	3	introduction	introduction	NOUN
cana-4617	9	4	recurrence	recurrence	NOUN
cana-4617	9	5	relations	relation	NOUN
cana-4617	9	6	are	be	AUX
cana-4617	9	7	mathematical	mathematical	ADJ
cana-4617	9	8	formulas	formula	NOUN
cana-4617	9	9	that	that	PRON
cana-4617	9	10	link	link	VERB
cana-4617	9	11	each	each	DET
cana-4617	9	12	term	term	NOUN
cana-4617	9	13	in	in	ADP
cana-4617	9	14	a	a	DET
cana-4617	9	15	series	series	NOUN
cana-4617	9	16	to	to	ADP
cana-4617	9	17	the	the	DET
cana-4617	9	18	preceding	precede	VERB
cana-4617	9	19	terms	term	NOUN
cana-4617	9	20	,	,	PUNCT
cana-4617	9	21	thereby	thereby	ADV
cana-4617	9	22	simplifying	simplify	VERB
cana-4617	9	23	calculations	calculation	NOUN
cana-4617	9	24	and	and	CCONJ
cana-4617	9	25	revealing	reveal	VERB
cana-4617	9	26	data	datum	NOUN
cana-4617	9	27	patterns	pattern	NOUN
cana-4617	9	28	.	.	PUNCT
cana-4617	10	1	these	these	DET
cana-4617	10	2	relations	relation	NOUN
cana-4617	10	3	find	find	VERB
cana-4617	10	4	applications	application	NOUN
cana-4617	10	5	in	in	ADP
cana-4617	10	6	moments	moment	NOUN
cana-4617	10	7	of	of	ADP
cana-4617	10	8	order	order	NOUN
cana-4617	10	9	statistics	statistic	NOUN
cana-4617	10	10	and	and	CCONJ
cana-4617	10	11	generalized	generalized	ADJ
cana-4617	10	12	order	order	NOUN
cana-4617	10	13	statistics	statistic	NOUN
cana-4617	10	14	,	,	PUNCT
cana-4617	10	15	such	such	ADJ
cana-4617	10	16	as	as	ADP
cana-4617	10	17	parameter	parameter	NOUN
cana-4617	10	18	estimation	estimation	NOUN
cana-4617	10	19	,	,	PUNCT
cana-4617	10	20	hypothesis	hypothesis	NOUN
cana-4617	10	21	testing	testing	NOUN
cana-4617	10	22	,	,	PUNCT
cana-4617	10	23	and	and	CCONJ
cana-4617	10	24	deriving	derive	VERB
cana-4617	10	25	conclusions	conclusion	NOUN
cana-4617	10	26	about	about	ADP
cana-4617	10	27	the	the	DET
cana-4617	10	28	underlying	underlie	VERB
cana-4617	10	29	distribution	distribution	NOUN
cana-4617	10	30	.	.	PUNCT
cana-4617	11	1	many	many	ADJ
cana-4617	11	2	researchers	researcher	NOUN
cana-4617	11	3	have	have	AUX
cana-4617	11	4	employed	employ	VERB
cana-4617	11	5	the	the	DET
cana-4617	11	6	generalized	generalize	VERB
cana-4617	11	7	order	order	NOUN
cana-4617	11	8	statistics	statistic	NOUN
cana-4617	11	9	(	(	PUNCT
cana-4617	11	10	gos	gos	PROPN
cana-4617	11	11	)	)	PUNCT
cana-4617	11	12	in	in	ADP
cana-4617	11	13	their	their	PRON
cana-4617	11	14	research	research	NOUN
cana-4617	11	15	,	,	PUNCT
cana-4617	11	16	such	such	ADJ
cana-4617	11	17	as	as	ADP
cana-4617	11	18	kamps	kamps	PROPN
cana-4617	11	19	and	and	CCONJ
cana-4617	11	20	gather	gather	PROPN
cana-4617	11	21	(	(	PUNCT
cana-4617	11	22	1997	1997	NUM
cana-4617	11	23	)	)	PUNCT
cana-4617	11	24	,	,	PUNCT
cana-4617	11	25	keseling	kesele	VERB
cana-4617	11	26	(	(	PUNCT
cana-4617	11	27	1999	1999	NUM
cana-4617	11	28	)	)	PUNCT
cana-4617	11	29	,	,	PUNCT
cana-4617	11	30	cramer	cramer	PROPN
cana-4617	11	31	and	and	CCONJ
cana-4617	11	32	kamps	kamps	PROPN
cana-4617	11	33	(	(	PUNCT
cana-4617	11	34	2000	2000	NUM
cana-4617	11	35	)	)	PUNCT
cana-4617	11	36	,	,	PUNCT
cana-4617	11	37	ahsanullah	ahsanullah	PROPN
cana-4617	11	38	(	(	PUNCT
cana-4617	11	39	2000	2000	NUM
cana-4617	11	40	)	)	PUNCT
cana-4617	11	41	,	,	PUNCT
cana-4617	11	42	pawlas	pawla	NOUN
cana-4617	11	43	and	and	CCONJ
cana-4617	11	44	szynal	szynal	ADJ
cana-4617	11	45	(	(	PUNCT
cana-4617	11	46	2001	2001	NUM
cana-4617	11	47	)	)	PUNCT
cana-4617	11	48	,	,	PUNCT
cana-4617	11	49	ahmed	ahmed	PROPN
cana-4617	11	50	(	(	PUNCT
cana-4617	11	51	2007	2007	NUM
cana-4617	11	52	)	)	PUNCT
cana-4617	11	53	,	,	PUNCT
cana-4617	11	54	ahmed	ahmed	PROPN
cana-4617	11	55	and	and	CCONJ
cana-4617	11	56	fawzy	fawzy	PROPN
cana-4617	11	57	(	(	PUNCT
cana-4617	11	58	2003	2003	NUM
cana-4617	11	59	)	)	PUNCT
cana-4617	11	60	,	,	PUNCT
cana-4617	11	61	khan	khan	PROPN
cana-4617	11	62	et	et	PROPN
cana-4617	11	63	al	al	PROPN
cana-4617	11	64	.	.	PROPN
cana-4617	12	1	(	(	PUNCT
cana-4617	12	2	2007	2007	NUM
cana-4617	12	3	)	)	PUNCT
cana-4617	12	4	,	,	PUNCT
cana-4617	12	5	al	al	PROPN
cana-4617	12	6	-	-	PUNCT
cana-4617	12	7	hussaini	hussaini	PROPN
cana-4617	12	8	et	et	PROPN
cana-4617	12	9	al	al	PROPN
cana-4617	12	10	.	.	PROPN
cana-4617	13	1	(	(	PUNCT
cana-4617	13	2	2005	2005	NUM
cana-4617	13	3	)	)	PUNCT
cana-4617	13	4	,	,	PUNCT
cana-4617	13	5	kumar	kumar	PROPN
cana-4617	13	6	(	(	PUNCT
cana-4617	13	7	2011	2011	NUM
cana-4617	13	8	)	)	PUNCT
cana-4617	13	9	,	,	PUNCT
cana-4617	13	10	mahmoud	mahmoud	PROPN
cana-4617	13	11	and	and	CCONJ
cana-4617	13	12	ghazal	ghazal	PROPN
cana-4617	13	13	(	(	PUNCT
cana-4617	13	14	2012	2012	NUM
cana-4617	13	15	)	)	PUNCT
cana-4617	13	16	.	.	PUNCT
cana-4617	14	1	recently	recently	ADV
cana-4617	14	2	,	,	PUNCT
cana-4617	14	3	abdul	abdul	PROPN
cana-4617	14	4	-	-	PUNCT
cana-4617	14	5	moniem	moniem	PROPN
cana-4617	14	6	[	[	X
cana-4617	14	7	(	(	PUNCT
cana-4617	14	8	2014	2014	NUM
cana-4617	14	9	,	,	PUNCT
cana-4617	14	10	2019	2019	NUM
cana-4617	14	11	,	,	PUNCT
cana-4617	14	12	2022	2022	NUM
cana-4617	14	13	)	)	PUNCT
cana-4617	14	14	]	]	PUNCT
cana-4617	14	15	has	have	AUX
cana-4617	14	16	contributed	contribute	VERB
cana-4617	14	17	significantly	significantly	ADV
cana-4617	14	18	to	to	ADP
cana-4617	14	19	this	this	DET
cana-4617	14	20	field	field	NOUN
cana-4617	14	21	,	,	PUNCT
cana-4617	14	22	presenting	present	VERB
cana-4617	14	23	various	various	ADJ
cana-4617	14	24	studies	study	NOUN
cana-4617	14	25	on	on	ADP
cana-4617	14	26	recurrence	recurrence	NOUN
cana-4617	14	27	relations	relation	NOUN
cana-4617	14	28	for	for	ADP
cana-4617	14	29	moments	moment	NOUN
cana-4617	14	30	of	of	ADP
cana-4617	14	31	generalized	generalized	ADJ
cana-4617	14	32	order	order	NOUN
cana-4617	14	33	statistics	statistic	NOUN
cana-4617	14	34	from	from	ADP
cana-4617	14	35	different	different	ADJ
cana-4617	14	36	distributions	distribution	NOUN
cana-4617	14	37	,	,	PUNCT
cana-4617	14	38	extending	extend	VERB
cana-4617	14	39	well	well	ADV
cana-4617	14	40	-	-	PUNCT
cana-4617	14	41	known	know	VERB
cana-4617	14	42	life	life	NOUN
cana-4617	14	43	distribution	distribution	NOUN
cana-4617	14	44	families	family	NOUN
cana-4617	14	45	,	,	PUNCT
cana-4617	14	46	and	and	CCONJ
cana-4617	14	47	exploring	explore	VERB
cana-4617	14	48	new	new	ADJ
cana-4617	14	49	characterizations	characterization	NOUN
cana-4617	14	50	of	of	ADP
cana-4617	14	51	these	these	DET
cana-4617	14	52	extended	extended	ADJ
cana-4617	14	53	distributions	distribution	NOUN
cana-4617	14	54	.	.	PUNCT
cana-4617	15	1	these	these	DET
cana-4617	15	2	studies	study	NOUN
cana-4617	15	3	have	have	AUX
cana-4617	15	4	resulted	result	VERB
cana-4617	15	5	in	in	ADP
cana-4617	15	6	deriving	derive	VERB
cana-4617	15	7	new	new	ADJ
cana-4617	15	8	recurrence	recurrence	NOUN
cana-4617	15	9	relations	relation	NOUN
cana-4617	15	10	for	for	ADP
cana-4617	15	11	moments	moment	NOUN
cana-4617	15	12	,	,	PUNCT
cana-4617	15	13	particularly	particularly	ADV
cana-4617	15	14	in	in	ADP
cana-4617	15	15	the	the	DET
cana-4617	15	16	context	context	NOUN
cana-4617	15	17	of	of	ADP
cana-4617	15	18	weighted	weight	VERB
cana-4617	15	19	distributions	distribution	NOUN
cana-4617	15	20	such	such	ADJ
cana-4617	15	21	as	as	ADP
cana-4617	15	22	the	the	DET
cana-4617	15	23	length	length	NOUN
cana-4617	15	24	-	-	PUNCT
cana-4617	15	25	biased	bias	VERB
cana-4617	15	26	maxwell	maxwell	NOUN
cana-4617	15	27	distribution	distribution	NOUN
cana-4617	15	28	and	and	CCONJ
cana-4617	15	29	extended	extended	ADJ
cana-4617	15	30	distributions	distribution	NOUN
cana-4617	15	31	like	like	ADP
cana-4617	15	32	those	those	PRON
cana-4617	15	33	based	base	VERB
cana-4617	15	34	on	on	ADP
cana-4617	15	35	the	the	DET
cana-4617	15	36	marshall	marshall	PROPN
cana-4617	15	37	–	–	PUNCT
cana-4617	15	38	olkin	olkin	NOUN
cana-4617	15	39	family	family	NOUN
cana-4617	15	40	.	.	PUNCT
cana-4617	16	1	additionally	additionally	ADV
cana-4617	16	2	,	,	PUNCT
cana-4617	16	3	these	these	DET
cana-4617	16	4	works	work	NOUN
cana-4617	16	5	have	have	AUX
cana-4617	16	6	enhanced	enhance	VERB
cana-4617	16	7	the	the	DET
cana-4617	16	8	understanding	understanding	NOUN
cana-4617	16	9	of	of	ADP
cana-4617	16	10	life	life	NOUN
cana-4617	16	11	distribution	distribution	NOUN
cana-4617	16	12	properties	property	NOUN
cana-4617	16	13	and	and	CCONJ
cana-4617	16	14	provided	provide	VERB
cana-4617	16	15	novel	novel	ADJ
cana-4617	16	16	characterizations	characterization	NOUN
cana-4617	16	17	that	that	PRON
cana-4617	16	18	improve	improve	VERB
cana-4617	16	19	the	the	DET
cana-4617	16	20	applicability	applicability	NOUN
cana-4617	16	21	of	of	ADP
cana-4617	16	22	these	these	DET
cana-4617	16	23	statistical	statistical	ADJ
cana-4617	16	24	models	model	NOUN
cana-4617	16	25	in	in	ADP
cana-4617	16	26	various	various	ADJ
cana-4617	16	27	practical	practical	ADJ
cana-4617	16	28	scenarios	scenario	NOUN
cana-4617	16	29	.	.	PUNCT
cana-4617	17	1	mohsin	mohsin	PROPN
cana-4617	17	2	et	et	PROPN
cana-4617	17	3	al	al	PROPN
cana-4617	17	4	.	.	PROPN
cana-4617	18	1	(	(	PUNCT
cana-4617	18	2	2010	2010	NUM
cana-4617	18	3	)	)	PUNCT
cana-4617	18	4	further	far	ADV
cana-4617	18	5	contributed	contribute	VERB
cana-4617	18	6	by	by	ADP
cana-4617	18	7	deriving	derive	VERB
cana-4617	18	8	a	a	DET
cana-4617	18	9	recurrence	recurrence	NOUN
cana-4617	18	10	relation	relation	NOUN
cana-4617	18	11	for	for	ADP
cana-4617	18	12	single	single	ADJ
cana-4617	18	13	moments	moment	NOUN
cana-4617	18	14	of	of	ADP
cana-4617	18	15	generalized	generalized	ADJ
cana-4617	18	16	order	order	NOUN
cana-4617	18	17	statistics	statistic	NOUN
cana-4617	18	18	from	from	ADP
cana-4617	18	19	the	the	DET
cana-4617	18	20	rayleigh	rayleigh	PROPN
cana-4617	18	21	distribution	distribution	NOUN
cana-4617	18	22	,	,	PUNCT
cana-4617	18	23	enhancing	enhance	VERB
cana-4617	18	24	understanding	understanding	NOUN
cana-4617	18	25	of	of	ADP
cana-4617	18	26	distribution	distribution	NOUN
cana-4617	18	27	properties	property	NOUN
cana-4617	18	28	and	and	CCONJ
cana-4617	18	29	offering	offer	VERB
cana-4617	18	30	new	new	ADJ
cana-4617	18	31	characterizations	characterization	NOUN
cana-4617	18	32	for	for	ADP
cana-4617	18	33	practical	practical	ADJ
cana-4617	18	34	applications	application	NOUN
cana-4617	18	35	.	.	PUNCT
cana-4617	19	1	mailto:mo.baha2010@gmail.com	mailto:mo.baha2010@gmail.com	PROPN
cana-4617	19	2	communications	communication	NOUN
cana-4617	19	3	on	on	ADP
cana-4617	19	4	applied	apply	VERB
cana-4617	19	5	nonlinear	nonlinear	ADJ
cana-4617	19	6	analysis	analysis	NOUN
cana-4617	19	7	issn	issn	NOUN
cana-4617	19	8	:	:	PUNCT
cana-4617	19	9	1074	1074	NUM
cana-4617	19	10	-	-	PUNCT
cana-4617	19	11	133x	133x	NUM
cana-4617	19	12	vol	vol	NOUN
cana-4617	19	13	32	32	NUM
cana-4617	19	14	no	no	NOUN
cana-4617	19	15	.	.	PUNCT
cana-4617	20	1	9s	9s	NUM
cana-4617	20	2	(	(	PUNCT
cana-4617	20	3	2025	2025	NUM
cana-4617	20	4	)	)	PUNCT
cana-4617	20	5	3021	3021	NUM
cana-4617	20	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	20	7	a	a	DET
cana-4617	20	8	random	random	ADJ
cana-4617	20	9	variable	variable	NOUN
cana-4617	20	10	(	(	PUNCT
cana-4617	20	11	rv	rv	NOUN
cana-4617	20	12	)	)	PUNCT
cana-4617	20	13	z	z	NOUN
cana-4617	20	14	is	be	AUX
cana-4617	20	15	considered	consider	VERB
cana-4617	20	16	to	to	PART
cana-4617	20	17	have	have	VERB
cana-4617	20	18	area	area	NOUN
cana-4617	20	19	-	-	PUNCT
cana-4617	20	20	biased	bias	VERB
cana-4617	20	21	rayleigh	rayleigh	NOUN
cana-4617	20	22	distribution	distribution	NOUN
cana-4617	20	23	(	(	PUNCT
cana-4617	20	24	abrd	abrd	ADV
cana-4617	20	25	)	)	PUNCT
cana-4617	20	26	if	if	SCONJ
cana-4617	20	27	its	its	PRON
cana-4617	20	28	probability	probability	NOUN
cana-4617	20	29	density	density	NOUN
cana-4617	20	30	function	function	NOUN
cana-4617	20	31	(	(	PUNCT
cana-4617	20	32	pdf	pdf	NOUN
cana-4617	20	33	)	)	PUNCT
cana-4617	20	34	has	have	VERB
cana-4617	20	35	the	the	DET
cana-4617	20	36	following	follow	VERB
cana-4617	20	37	form	form	NOUN
cana-4617	20	38	:	:	PUNCT
cana-4617	20	39	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	20	40	)	)	PUNCT
cana-4617	21	1	=	=	SYM
cana-4617	21	2	2𝑧3	2𝑧3	NUM
cana-4617	21	3	𝛽4	𝛽4	PROPN
cana-4617	21	4	𝐞𝐱𝐩	𝐞𝐱𝐩	NOUN
cana-4617	21	5	(	(	PUNCT
cana-4617	21	6	−	−	PROPN
cana-4617	21	7	𝑧2	𝑧2	PROPN
cana-4617	21	8	𝛽2	𝛽2	PROPN
cana-4617	21	9	)	)	PUNCT
cana-4617	21	10	;	;	PUNCT
cana-4617	21	11	𝛽	𝛽	X
cana-4617	21	12	>	>	X
cana-4617	21	13	0	0	NUM
cana-4617	21	14	,	,	PUNCT
cana-4617	21	15	𝑧	𝑧	PRON
cana-4617	21	16	≥	≥	NUM
cana-4617	21	17	0	0	NUM
cana-4617	21	18	(	(	PUNCT
cana-4617	21	19	1	1	X
cana-4617	21	20	)	)	PUNCT
cana-4617	21	21	the	the	DET
cana-4617	21	22	survival	survival	NOUN
cana-4617	21	23	function	function	NOUN
cana-4617	21	24	(	(	PUNCT
cana-4617	21	25	sf	sf	NOUN
cana-4617	21	26	)	)	PUNCT
cana-4617	21	27	corresponding	correspond	VERB
cana-4617	21	28	to	to	ADP
cana-4617	21	29	equation	equation	NOUN
cana-4617	21	30	(	(	PUNCT
cana-4617	21	31	1	1	X
cana-4617	21	32	)	)	PUNCT
cana-4617	21	33	is	be	AUX
cana-4617	21	34	expressed	express	VERB
cana-4617	21	35	as	as	ADP
cana-4617	21	36	:	:	PUNCT
cana-4617	21	37	�	�	NOUN
cana-4617	21	38	̅	̅	NOUN
cana-4617	21	39	�	�	NOUN
cana-4617	21	40	(𝑧	(𝑧	NOUN
cana-4617	21	41	)	)	PUNCT
cana-4617	21	42	=	=	PUNCT
cana-4617	21	43	(	(	PUNCT
cana-4617	21	44	1	1	NUM
cana-4617	21	45	+	+	NUM
cana-4617	21	46	𝑧2	𝑧2	PROPN
cana-4617	21	47	𝛽2	𝛽2	PROPN
cana-4617	21	48	)	)	PUNCT
cana-4617	21	49	𝐞𝐱𝐩	𝐞𝐱𝐩	NOUN
cana-4617	21	50	(	(	PUNCT
cana-4617	21	51	−	−	PROPN
cana-4617	21	52	𝑧2	𝑧2	PROPN
cana-4617	21	53	𝛽2	𝛽2	PROPN
cana-4617	21	54	)	)	PUNCT
cana-4617	21	55	;	;	PUNCT
cana-4617	21	56	𝛽	𝛽	X
cana-4617	21	57	>	>	X
cana-4617	21	58	0	0	NUM
cana-4617	21	59	,	,	PUNCT
cana-4617	21	60	𝑧	𝑧	PRON
cana-4617	21	61	≥	≥	NUM
cana-4617	21	62	0	0	NUM
cana-4617	21	63	(	(	PUNCT
cana-4617	21	64	2	2	X
cana-4617	21	65	)	)	PUNCT
cana-4617	21	66	substituting	substitute	VERB
cana-4617	21	67	from	from	ADP
cana-4617	21	68	(	(	PUNCT
cana-4617	21	69	2	2	NUM
cana-4617	21	70	)	)	PUNCT
cana-4617	21	71	in	in	ADP
cana-4617	21	72	(	(	PUNCT
cana-4617	21	73	1	1	NUM
cana-4617	21	74	)	)	PUNCT
cana-4617	21	75	,	,	PUNCT
cana-4617	21	76	we	we	PRON
cana-4617	21	77	get	get	VERB
cana-4617	21	78	:	:	PUNCT
cana-4617	21	79	�	�	NOUN
cana-4617	21	80	̅	̅	NOUN
cana-4617	21	81	�	�	NOUN
cana-4617	21	82	(𝑧	(𝑧	NOUN
cana-4617	21	83	)	)	PUNCT
cana-4617	21	84	=	=	SYM
cana-4617	21	85	(	(	PUNCT
cana-4617	21	86	𝛽2	𝛽2	ADJ
cana-4617	21	87	2𝑧	2𝑧	NOUN
cana-4617	21	88	+	+	CCONJ
cana-4617	21	89	𝛽4	𝛽4	PROPN
cana-4617	21	90	2𝑧3	2𝑧3	NUM
cana-4617	21	91	)	)	PUNCT
cana-4617	21	92	𝑓(𝑧	𝑓(𝑧	PROPN
cana-4617	21	93	)	)	PUNCT
cana-4617	21	94	(	(	PUNCT
cana-4617	21	95	3	3	X
cana-4617	21	96	)	)	PUNCT
cana-4617	21	97	bashir	bashir	NOUN
cana-4617	21	98	and	and	CCONJ
cana-4617	21	99	rasul	rasul	PROPN
cana-4617	21	100	,	,	PUNCT
cana-4617	21	101	(	(	PUNCT
cana-4617	21	102	2018	2018	NUM
cana-4617	21	103	)	)	PUNCT
cana-4617	21	104	provided	provide	VERB
cana-4617	21	105	further	further	ADJ
cana-4617	21	106	details	detail	NOUN
cana-4617	21	107	on	on	ADP
cana-4617	21	108	this	this	DET
cana-4617	21	109	distribution	distribution	NOUN
cana-4617	21	110	and	and	CCONJ
cana-4617	21	111	its	its	PRON
cana-4617	21	112	applications	application	NOUN
cana-4617	21	113	.	.	PUNCT
cana-4617	22	1	kamps	kamps	X
cana-4617	22	2	(	(	PUNCT
cana-4617	22	3	1995	1995	NUM
cana-4617	22	4	)	)	PUNCT
cana-4617	22	5	developed	develop	VERB
cana-4617	22	6	the	the	DET
cana-4617	22	7	concept	concept	NOUN
cana-4617	22	8	of	of	ADP
cana-4617	22	9	generalized	generalized	ADJ
cana-4617	22	10	order	order	NOUN
cana-4617	22	11	statistics	statistic	NOUN
cana-4617	22	12	(	(	PUNCT
cana-4617	22	13	gos	gos	PROPN
cana-4617	22	14	)	)	PUNCT
cana-4617	22	15	,	,	PUNCT
cana-4617	22	16	which	which	PRON
cana-4617	22	17	encompasses	encompass	VERB
cana-4617	22	18	various	various	ADJ
cana-4617	22	19	order	order	NOUN
cana-4617	22	20	models	model	NOUN
cana-4617	22	21	of	of	ADP
cana-4617	22	22	random	random	ADJ
cana-4617	22	23	variables	variable	NOUN
cana-4617	22	24	.	.	PUNCT
cana-4617	23	1	for	for	ADP
cana-4617	23	2	simplicity	simplicity	NOUN
cana-4617	23	3	,	,	PUNCT
cana-4617	23	4	let	let	VERB
cana-4617	23	5	,	,	PUNCT
cana-4617	23	6	f	f	PROPN
cana-4617	23	7	throughout	throughout	PART
cana-4617	23	8	represent	represent	VERB
cana-4617	23	9	a	a	DET
cana-4617	23	10	continuous	continuous	ADJ
cana-4617	23	11	distribution	distribution	NOUN
cana-4617	23	12	function	function	NOUN
cana-4617	23	13	with	with	ADP
cana-4617	23	14	a	a	DET
cana-4617	23	15	density	density	NOUN
cana-4617	23	16	function	function	NOUN
cana-4617	23	17	f.	f.	NOUN
cana-4617	24	1	the	the	DET
cana-4617	24	2	random	random	ADJ
cana-4617	24	3	variables	variable	NOUN
cana-4617	24	4	𝑍(1	𝑍(1	PUNCT
cana-4617	24	5	,	,	PUNCT
cana-4617	24	6	𝑛	𝑛	PROPN
cana-4617	24	7	,	,	PUNCT
cana-4617	24	8	�	�	PROPN
cana-4617	24	9	̃	̃	PROPN
cana-4617	24	10	�	�	PROPN
cana-4617	24	11	,	,	PUNCT
cana-4617	24	12	𝑘	𝑘	NOUN
cana-4617	24	13	)	)	PUNCT
cana-4617	24	14	,	,	PUNCT
cana-4617	24	15	.	.	PUNCT
cana-4617	24	16	.	.	PUNCT
cana-4617	24	17	.	.	PUNCT
cana-4617	25	1	,	,	PUNCT
cana-4617	25	2	𝑍(𝑛	𝑍(𝑛	PROPN
cana-4617	25	3	,	,	PUNCT
cana-4617	25	4	𝑛	𝑛	PROPN
cana-4617	25	5	,	,	PUNCT
cana-4617	25	6	�	�	PROPN
cana-4617	25	7	̃	̃	PROPN
cana-4617	25	8	�	�	PROPN
cana-4617	25	9	,	,	PUNCT
cana-4617	25	10	𝑘	𝑘	NOUN
cana-4617	25	11	)	)	PUNCT
cana-4617	25	12	are	be	AUX
cana-4617	25	13	referred	refer	VERB
cana-4617	25	14	to	to	ADP
cana-4617	25	15	as	as	ADP
cana-4617	25	16	generalized	generalize	VERB
cana-4617	25	17	order	order	NOUN
cana-4617	25	18	statistics	statistic	NOUN
cana-4617	25	19	based	base	VERB
cana-4617	25	20	on	on	ADP
cana-4617	25	21	f	f	NUM
cana-4617	25	22	,	,	PUNCT
cana-4617	25	23	if	if	SCONJ
cana-4617	25	24	their	their	PRON
cana-4617	25	25	joint	joint	ADJ
cana-4617	25	26	probability	probability	NOUN
cana-4617	25	27	density	density	NOUN
cana-4617	25	28	function	function	NOUN
cana-4617	25	29	takes	take	VERB
cana-4617	25	30	the	the	DET
cana-4617	25	31	following	follow	VERB
cana-4617	25	32	form	form	NOUN
cana-4617	25	33	𝑘	𝑘	X
cana-4617	25	34	(	(	PUNCT
cana-4617	25	35	∏	∏	X
cana-4617	25	36	𝛾𝑗	𝛾𝑗	INTJ
cana-4617	25	37	𝑛−1	𝑛−1	NUM
cana-4617	25	38	𝑗=1	𝑗=1	PROPN
cana-4617	25	39	)	)	PUNCT
cana-4617	25	40	(	(	PUNCT
cana-4617	25	41	∏[	∏[	NOUN
cana-4617	25	42	�	�	PROPN
cana-4617	25	43	̅	̅	NOUN
cana-4617	25	44	�	�	NOUN
cana-4617	25	45	(𝑧𝑖)]𝑚𝑖	(𝑧𝑖)]𝑚𝑖	NOUN
cana-4617	25	46	𝑛−1	𝑛−1	PROPN
cana-4617	25	47	𝑖=1	𝑖=1	PROPN
cana-4617	25	48	𝑓(𝑧𝑖	𝑓(𝑧𝑖	NUM
cana-4617	25	49	)	)	PUNCT
cana-4617	25	50	)	)	PUNCT
cana-4617	26	1	[	[	X
cana-4617	26	2	�	�	NOUN
cana-4617	26	3	̅	̅	NOUN
cana-4617	26	4	�	�	NOUN
cana-4617	26	5	(𝑧𝑛)]𝑘−1𝑓(𝑧𝑛	(𝑧𝑛)]𝑘−1𝑓(𝑧𝑛	NUM
cana-4617	26	6	)	)	PUNCT
cana-4617	26	7	,	,	PUNCT
cana-4617	26	8	for	for	ADP
cana-4617	26	9	�	�	PROPN
cana-4617	26	10	̅	̅	NOUN
cana-4617	26	11	�	�	NOUN
cana-4617	26	12	−1(1	−1(1	ADJ
cana-4617	26	13	)	)	PUNCT
cana-4617	26	14	>	>	X
cana-4617	26	15	𝑧1	𝑧1	PROPN
cana-4617	26	16	≥	≥	PROPN
cana-4617	26	17	𝑧2	𝑧2	NOUN
cana-4617	26	18	≥.	≥.	NOUN
cana-4617	26	19	.	.	PUNCT
cana-4617	26	20	.	.	PUNCT
cana-4617	27	1	≥	≥	X
cana-4617	27	2	𝑧𝑛	𝑧𝑛	ADP
cana-4617	27	3	>	>	X
cana-4617	27	4	�	�	PROPN
cana-4617	27	5	̅	̅	NOUN
cana-4617	27	6	�	�	NOUN
cana-4617	27	7	−1(0	−1(0	NOUN
cana-4617	27	8	)	)	PUNCT
cana-4617	27	9	,	,	PUNCT
cana-4617	27	10	with	with	ADP
cana-4617	27	11	parameters	parameter	NOUN
cana-4617	27	12	𝑛	𝑛	PRON
cana-4617	27	13	∈	∈	PROPN
cana-4617	27	14	𝑁	𝑁	PROPN
cana-4617	27	15	,	,	PUNCT
cana-4617	27	16	𝑛	𝑛	DET
cana-4617	27	17	≥	≥	NOUN
cana-4617	27	18	2	2	NUM
cana-4617	27	19	,	,	PUNCT
cana-4617	27	20	𝑘	𝑘	ADJ
cana-4617	27	21	>	>	X
cana-4617	27	22	0	0	NUM
cana-4617	27	23	,	,	PUNCT
cana-4617	27	24	�	�	PROPN
cana-4617	27	25	̃	̃	NOUN
cana-4617	27	26	�	�	NOUN
cana-4617	27	27	=	=	SYM
cana-4617	27	28	(	(	PUNCT
cana-4617	27	29	𝑚1	𝑚1	PROPN
cana-4617	27	30	,	,	PUNCT
cana-4617	27	31	𝑚2	𝑚2	NOUN
cana-4617	27	32	,	,	PUNCT
cana-4617	27	33	.	.	PUNCT
cana-4617	27	34	.	.	PUNCT
cana-4617	28	1	.	.	PUNCT
cana-4617	29	1	,	,	PUNCT
cana-4617	29	2	𝑚𝑛−1	𝑚𝑛−1	NOUN
cana-4617	29	3	)	)	PUNCT
cana-4617	29	4	∈	∈	NOUN
cana-4617	30	1	𝑅𝑛−1	𝑅𝑛−1	NOUN
cana-4617	30	2	,	,	PUNCT
cana-4617	30	3	𝑀𝑟	𝑀𝑟	PROPN
cana-4617	30	4	=	=	PUNCT
cana-4617	30	5	∑	∑	PUNCT
cana-4617	30	6	𝑚𝑖	𝑚𝑖	NUM
cana-4617	30	7	𝑛=1	𝑛=1	PRON
cana-4617	30	8	𝑖=𝑟	𝑖=𝑟	PROPN
cana-4617	30	9	,	,	PUNCT
cana-4617	30	10	such	such	ADJ
cana-4617	30	11	that	that	PRON
cana-4617	30	12	𝛾𝑟	𝛾𝑟	ADP
cana-4617	30	13	=	=	PUNCT
cana-4617	30	14	𝑘	𝑘	PROPN
cana-4617	30	15	+	+	NOUN
cana-4617	30	16	𝑛	𝑛	DET
cana-4617	30	17	−	−	NOUN
cana-4617	30	18	𝑟	𝑟	NOUN
cana-4617	30	19	+	+	CCONJ
cana-4617	30	20	𝑀𝑟	𝑀𝑟	PROPN
cana-4617	30	21	>	>	X
cana-4617	30	22	0	0	NUM
cana-4617	30	23	,	,	PUNCT
cana-4617	30	24	for	for	ADP
cana-4617	30	25	all	all	DET
cana-4617	30	26	𝑟	𝑟	PRON
cana-4617	30	27	∈	∈	PROPN
cana-4617	30	28	{	{	PUNCT
cana-4617	30	29	1,2	1,2	NUM
cana-4617	30	30	,	,	PUNCT
cana-4617	30	31	.	.	PUNCT
cana-4617	30	32	.	.	PUNCT
cana-4617	30	33	.	.	PUNCT
cana-4617	31	1	,	,	PUNCT
cana-4617	31	2	𝑛	𝑛	DET
cana-4617	31	3	−	−	PROPN
cana-4617	31	4	1}.for	1}.for	NUM
cana-4617	31	5	𝛾𝑖	𝛾𝑖	NOUN
cana-4617	31	6	≠	≠	PROPN
cana-4617	31	7	𝛾𝑗	𝛾𝑗	INTJ
cana-4617	31	8	,	,	PUNCT
cana-4617	31	9	𝑖	𝑖	PROPN
cana-4617	31	10	≠	≠	NOUN
cana-4617	31	11	𝑗	𝑗	PRON
cana-4617	31	12	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-4617	31	13	𝑎𝑙𝑙	𝑎𝑙𝑙	X
cana-4617	31	14	𝑖	𝑖	SYM
cana-4617	31	15	,	,	PUNCT
cana-4617	31	16	𝑗	𝑗	PROPN
cana-4617	31	17	∈	∈	NOUN
cana-4617	31	18	(	(	PUNCT
cana-4617	31	19	1,2	1,2	NUM
cana-4617	31	20	,	,	PUNCT
cana-4617	31	21	.	.	PUNCT
cana-4617	31	22	.	.	PUNCT
cana-4617	32	1	.	.	PUNCT
cana-4617	33	1	,	,	PUNCT
cana-4617	33	2	𝑛	𝑛	PRON
cana-4617	33	3	−	−	NOUN
cana-4617	33	4	1	1	NUM
cana-4617	33	5	)	)	PUNCT
cana-4617	33	6	the	the	DET
cana-4617	33	7	probability	probability	NOUN
cana-4617	33	8	density	density	NOUN
cana-4617	33	9	function	function	NOUN
cana-4617	33	10	(	(	PUNCT
cana-4617	33	11	pdf	pdf	NOUN
cana-4617	33	12	)	)	PUNCT
cana-4617	33	13	of	of	ADP
cana-4617	33	14	𝑍(𝑟	𝑍(𝑟	ADJ
cana-4617	33	15	,	,	PUNCT
cana-4617	33	16	𝑛	𝑛	PROPN
cana-4617	33	17	,	,	PUNCT
cana-4617	33	18	�	�	PROPN
cana-4617	33	19	̃	̃	PROPN
cana-4617	33	20	�	�	PROPN
cana-4617	33	21	,	,	PUNCT
cana-4617	33	22	𝑘	𝑘	NOUN
cana-4617	33	23	)	)	PUNCT
cana-4617	33	24	is	be	AUX
cana-4617	33	25	expressed	express	VERB
cana-4617	33	26	(	(	PUNCT
cana-4617	33	27	by	by	ADP
cana-4617	33	28	cramer	cramer	PROPN
cana-4617	33	29	and	and	CCONJ
cana-4617	33	30	kamps.(2000	kamps.(2000	ADJ
cana-4617	33	31	)	)	PUNCT
cana-4617	33	32	)	)	PUNCT
cana-4617	33	33	as	as	SCONJ
cana-4617	33	34	follows	follow	VERB
cana-4617	33	35	𝑓𝑍(𝑟,𝑛,	𝑓𝑍(𝑟,𝑛,	PROPN
cana-4617	33	36	�	�	PROPN
cana-4617	33	37	̃	̃	PROPN
cana-4617	33	38	�	�	NOUN
cana-4617	33	39	,𝑘)(𝑧	,𝑘)(𝑧	NOUN
cana-4617	33	40	)	)	PUNCT
cana-4617	33	41	=	=	SYM
cana-4617	33	42	𝐶𝑟−1𝑓(𝑧	𝐶𝑟−1𝑓(𝑧	ADJ
cana-4617	33	43	)	)	PUNCT
cana-4617	33	44	∑	∑	PUNCT
cana-4617	34	1	𝑎𝑖(𝑟)𝑟	𝑎𝑖(𝑟)𝑟	ADJ
cana-4617	34	2	𝑖=1	𝑖=1	PROPN
cana-4617	34	3	[	[	X
cana-4617	34	4	�	�	NOUN
cana-4617	34	5	̅	̅	NOUN
cana-4617	34	6	�	�	NOUN
cana-4617	34	7	(𝑧)]𝛾𝑖−1	(𝑧)]𝛾𝑖−1	PUNCT
cana-4617	34	8	(	(	PUNCT
cana-4617	34	9	4	4	NUM
cana-4617	34	10	)	)	PUNCT
cana-4617	34	11	the	the	DET
cana-4617	34	12	joint	joint	ADJ
cana-4617	34	13	pdf	pdf	NOUN
cana-4617	34	14	for	for	ADP
cana-4617	34	15	𝑍(𝑟	𝑍(𝑟	PROPN
cana-4617	34	16	,	,	PUNCT
cana-4617	34	17	𝑛	𝑛	PROPN
cana-4617	34	18	,	,	PUNCT
cana-4617	34	19	�	�	PROPN
cana-4617	34	20	̃	̃	PROPN
cana-4617	34	21	�	�	PROPN
cana-4617	34	22	,	,	PUNCT
cana-4617	34	23	𝑘	𝑘	NOUN
cana-4617	34	24	)	)	PUNCT
cana-4617	34	25	and	and	CCONJ
cana-4617	34	26	𝑍(𝑠	𝑍(𝑠	NUM
cana-4617	34	27	,	,	PUNCT
cana-4617	34	28	𝑛	𝑛	PROPN
cana-4617	34	29	,	,	PUNCT
cana-4617	34	30	�	�	PROPN
cana-4617	34	31	̃	̃	PROPN
cana-4617	34	32	�	�	PROPN
cana-4617	34	33	,	,	PUNCT
cana-4617	34	34	𝑘	𝑘	NOUN
cana-4617	34	35	)	)	PUNCT
cana-4617	34	36	,	,	PUNCT
cana-4617	34	37	1	1	NUM
cana-4617	34	38	≤	≤	NUM
cana-4617	34	39	𝑟	𝑟	PRON
cana-4617	34	40	<	<	X
cana-4617	34	41	𝑠	𝑠	X
cana-4617	34	42	≤	≤	ADV
cana-4617	34	43	𝑛	𝑛	PROPN
cana-4617	34	44	is	be	AUX
cana-4617	34	45	given	give	VERB
cana-4617	34	46	as	as	ADP
cana-4617	34	47	𝑓𝑍(𝑟,𝑛,	𝑓𝑍(𝑟,𝑛,	NOUN
cana-4617	34	48	�	�	PROPN
cana-4617	34	49	̃	̃	PROPN
cana-4617	34	50	�	�	PROPN
cana-4617	34	51	,𝑘),𝑍(𝑠,𝑛,	,𝑘),𝑍(𝑠,𝑛,	PUNCT
cana-4617	34	52	�	�	PROPN
cana-4617	34	53	̃	̃	PROPN
cana-4617	34	54	�	�	NOUN
cana-4617	34	55	,𝑘)(𝑧	,𝑘)(𝑧	NOUN
cana-4617	34	56	,	,	PUNCT
cana-4617	34	57	𝑡	𝑡	PROPN
cana-4617	34	58	)	)	PUNCT
cana-4617	35	1	=	=	SYM
cana-4617	35	2	𝐶𝑠−1	𝐶𝑠−1	PROPN
cana-4617	35	3	(	(	PUNCT
cana-4617	35	4	∑	∑	PROPN
cana-4617	35	5	𝑎𝑖	𝑎𝑖	INTJ
cana-4617	35	6	(	(	PUNCT
cana-4617	35	7	𝑟)(𝑠)𝑠	𝑟)(𝑠)𝑠	NUM
cana-4617	35	8	𝑖=𝑟+1	𝑖=𝑟+1	PRON
cana-4617	35	9	[	[	PUNCT
cana-4617	35	10	𝐹(𝑡	𝐹(𝑡	NUM
cana-4617	35	11	)	)	PUNCT
cana-4617	35	12	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	35	13	)	)	PUNCT
cana-4617	35	14	]	]	PUNCT
cana-4617	35	15	𝛾𝑖	𝛾𝑖	CCONJ
cana-4617	35	16	)	)	PUNCT
cana-4617	35	17	(	(	PUNCT
cana-4617	35	18	∑	∑	PUNCT
cana-4617	35	19	𝑎𝑖(𝑟)𝑟	𝑎𝑖(𝑟)𝑟	ADJ
cana-4617	35	20	𝑖=1	𝑖=1	PROPN
cana-4617	36	1	[	[	X
cana-4617	36	2	�	�	NOUN
cana-4617	36	3	̅	̅	NOUN
cana-4617	36	4	�	�	NOUN
cana-4617	36	5	(𝑧)]𝛾𝑖	(𝑧)]𝛾𝑖	NOUN
cana-4617	36	6	)	)	PUNCT
cana-4617	36	7	𝑓(𝑧)𝑓(𝑡	𝑓(𝑧)𝑓(𝑡	NUM
cana-4617	36	8	)	)	PUNCT
cana-4617	36	9	𝐹(𝑧)𝐹(𝑡	𝐹(𝑧)𝐹(𝑡	NUM
cana-4617	36	10	)	)	PUNCT
cana-4617	36	11	,	,	PUNCT
cana-4617	36	12	(	(	PUNCT
cana-4617	36	13	5	5	X
cana-4617	36	14	)	)	PUNCT
cana-4617	36	15	where	where	SCONJ
cana-4617	36	16	𝑧	𝑧	PRON
cana-4617	36	17	<	<	X
cana-4617	36	18	𝑡	𝑡	NOUN
cana-4617	36	19	and	and	CCONJ
cana-4617	36	20	communications	communication	NOUN
cana-4617	36	21	on	on	ADP
cana-4617	36	22	applied	apply	VERB
cana-4617	36	23	nonlinear	nonlinear	ADJ
cana-4617	36	24	analysis	analysis	NOUN
cana-4617	36	25	issn	issn	NOUN
cana-4617	36	26	:	:	PUNCT
cana-4617	36	27	1074	1074	NUM
cana-4617	36	28	-	-	PUNCT
cana-4617	36	29	133x	133x	NUM
cana-4617	36	30	vol	vol	NOUN
cana-4617	36	31	32	32	NUM
cana-4617	36	32	no	no	NOUN
cana-4617	36	33	.	.	PUNCT
cana-4617	37	1	9s	9s	NUM
cana-4617	37	2	(	(	PUNCT
cana-4617	37	3	2025	2025	NUM
cana-4617	37	4	)	)	PUNCT
cana-4617	37	5	3022	3022	NUM
cana-4617	37	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	37	7	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NOUN
cana-4617	37	8	)	)	PUNCT
cana-4617	38	1	=	=	SYM
cana-4617	38	2	∏	∏	PROPN
cana-4617	38	3	1	1	NUM
cana-4617	38	4	𝛾𝑗	𝛾𝑗	INTJ
cana-4617	38	5	−	−	PROPN
cana-4617	38	6	𝛾𝑖	𝛾𝑖	NOUN
cana-4617	38	7	𝑟	𝑟	X
cana-4617	38	8	𝑗=1	𝑗=1	PROPN
cana-4617	38	9	𝑗≠𝑖	𝑗≠𝑖	X
cana-4617	38	10	,	,	PUNCT
cana-4617	38	11	1	1	NUM
cana-4617	38	12	≤	≤	NUM
cana-4617	38	13	𝑖	𝑖	SYM
cana-4617	38	14	≤	≤	NUM
cana-4617	38	15	𝑟	𝑟	PRON
cana-4617	38	16	≤	≤	NUM
cana-4617	38	17	𝑛	𝑛	PRON
cana-4617	38	18	,	,	PUNCT
cana-4617	38	19	𝑎𝑖	𝑎𝑖	X
cana-4617	38	20	(	(	PUNCT
cana-4617	38	21	𝑟	𝑟	NOUN
cana-4617	38	22	)	)	PUNCT
cana-4617	38	23	(	(	PUNCT
cana-4617	38	24	𝑠	𝑠	X
cana-4617	38	25	)	)	PUNCT
cana-4617	38	26	=	=	SYM
cana-4617	38	27	∏	∏	PROPN
cana-4617	38	28	1	1	NUM
cana-4617	38	29	𝛾𝑗	𝛾𝑗	INTJ
cana-4617	38	30	−	−	PROPN
cana-4617	38	31	𝛾𝑖	𝛾𝑖	INTJ
cana-4617	38	32	,	,	PUNCT
cana-4617	38	33	𝑟	𝑟	X
cana-4617	38	34	+	+	CCONJ
cana-4617	38	35	1	1	NUM
cana-4617	38	36	≤	≤	NUM
cana-4617	38	37	𝑖	𝑖	SYM
cana-4617	38	38	≤	≤	NUM
cana-4617	38	39	𝑠	𝑠	PRON
cana-4617	38	40	≤	≤	NUM
cana-4617	38	41	𝑛	𝑛	PRON
cana-4617	38	42	.	.	PUNCT
cana-4617	39	1	𝑠	𝑠	INTJ
cana-4617	39	2	𝑗=𝑟+1	𝑗=𝑟+1	PRON
cana-4617	39	3	𝑗≠𝑖	𝑗≠𝑖	PROPN
cana-4617	40	1	it	it	PRON
cana-4617	40	2	should	should	AUX
cana-4617	40	3	be	be	AUX
cana-4617	40	4	noted	note	VERB
cana-4617	40	5	that	that	SCONJ
cana-4617	40	6	when	when	SCONJ
cana-4617	40	7	𝑚1	𝑚1	NOUN
cana-4617	40	8	=	=	SYM
cana-4617	40	9	𝑚2	𝑚2	PROPN
cana-4617	40	10	=	=	NOUN
cana-4617	40	11	.	.	PUNCT
cana-4617	40	12	.	.	PUNCT
cana-4617	40	13	.	.	PUNCT
cana-4617	41	1	=	=	PUNCT
cana-4617	41	2	𝑚𝑛−1	𝑚𝑛−1	PROPN
cana-4617	41	3	=	=	PUNCT
cana-4617	41	4	𝑚	𝑚	ADP
cana-4617	41	5	≠	≠	PROPN
cana-4617	41	6	−1	−1	NOUN
cana-4617	41	7	,	,	PUNCT
cana-4617	41	8	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NUM
cana-4617	41	9	)	)	PUNCT
cana-4617	41	10	=	=	PRON
cana-4617	42	1	(	(	PUNCT
cana-4617	42	2	−1)𝑟−𝑖	−1)𝑟−𝑖	X
cana-4617	42	3	(	(	PUNCT
cana-4617	42	4	𝑚	𝑚	PROPN
cana-4617	42	5	+	+	NOUN
cana-4617	42	6	1)𝑟−1(𝑟	1)𝑟−1(𝑟	NUM
cana-4617	42	7	−	−	NUM
cana-4617	42	8	1	1	NUM
cana-4617	42	9	)	)	PUNCT
cana-4617	42	10	!	!	PUNCT
cana-4617	43	1	(	(	PUNCT
cana-4617	43	2	𝑟	𝑟	X
cana-4617	43	3	−	−	ADP
cana-4617	43	4	1	1	NUM
cana-4617	43	5	𝑟	𝑟	NOUN
cana-4617	43	6	−	−	PROPN
cana-4617	43	7	𝑖	𝑖	SYM
cana-4617	43	8	)	)	PUNCT
cana-4617	43	9	,	,	PUNCT
cana-4617	43	10	(	(	PUNCT
cana-4617	43	11	6	6	NUM
cana-4617	43	12	)	)	PUNCT
cana-4617	43	13	and	and	CCONJ
cana-4617	43	14	𝑎𝑖	𝑎𝑖	PRON
cana-4617	43	15	(	(	PUNCT
cana-4617	43	16	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	43	17	)	)	PUNCT
cana-4617	43	18	=	=	SYM
cana-4617	43	19	(	(	PUNCT
cana-4617	43	20	−1)𝑠−𝑖	−1)𝑠−𝑖	PROPN
cana-4617	43	21	(	(	PUNCT
cana-4617	43	22	𝑚	𝑚	PROPN
cana-4617	43	23	+	+	PROPN
cana-4617	43	24	1)𝑠−𝑟−1(𝑠	1)𝑠−𝑟−1(𝑠	PROPN
cana-4617	43	25	−	−	NOUN
cana-4617	44	1	𝑟	𝑟	SYM
cana-4617	45	1	−	−	PROPN
cana-4617	45	2	1	1	NUM
cana-4617	45	3	)	)	PUNCT
cana-4617	45	4	!	!	PUNCT
cana-4617	46	1	(	(	PUNCT
cana-4617	46	2	𝑠	𝑠	INTJ
cana-4617	46	3	−	−	NOUN
cana-4617	46	4	𝑟	𝑟	PRON
cana-4617	46	5	−	−	PROPN
cana-4617	46	6	1	1	NUM
cana-4617	46	7	𝑠	𝑠	INTJ
cana-4617	46	8	−	−	PROPN
cana-4617	46	9	𝑖	𝑖	SYM
cana-4617	46	10	)	)	PUNCT
cana-4617	46	11	(	(	PUNCT
cana-4617	46	12	7	7	X
cana-4617	46	13	)	)	PUNCT
cana-4617	46	14	therefore	therefore	ADV
cana-4617	46	15	,	,	PUNCT
cana-4617	46	16	the	the	DET
cana-4617	46	17	pdf	pdf	NOUN
cana-4617	46	18	of	of	ADP
cana-4617	46	19	𝑍(𝑟	𝑍(𝑟	PROPN
cana-4617	46	20	,	,	PUNCT
cana-4617	46	21	𝑛	𝑛	PROPN
cana-4617	46	22	,	,	PUNCT
cana-4617	46	23	�	�	PROPN
cana-4617	46	24	̃	̃	PROPN
cana-4617	46	25	�	�	PROPN
cana-4617	46	26	,	,	PUNCT
cana-4617	46	27	𝑘	𝑘	NOUN
cana-4617	46	28	)	)	PUNCT
cana-4617	46	29	given	give	VERB
cana-4617	46	30	in	in	ADP
cana-4617	46	31	(	(	PUNCT
cana-4617	46	32	4	4	NUM
cana-4617	46	33	)	)	PUNCT
cana-4617	46	34	reduces	reduce	VERB
cana-4617	46	35	to	to	PART
cana-4617	46	36	𝑓𝑍(𝑟,𝑛,𝑚,𝑘)(𝑧	𝑓𝑍(𝑟,𝑛,𝑚,𝑘)(𝑧	VERB
cana-4617	46	37	)	)	PUNCT
cana-4617	47	1	=	=	SYM
cana-4617	47	2	𝐶𝑟−1	𝐶𝑟−1	PROPN
cana-4617	47	3	(	(	PUNCT
cana-4617	47	4	𝑟−1	𝑟−1	PROPN
cana-4617	47	5	)	)	PUNCT
cana-4617	47	6	!	!	PUNCT
cana-4617	48	1	[	[	X
cana-4617	48	2	�	�	NOUN
cana-4617	48	3	̅	̅	NOUN
cana-4617	48	4	�	�	NOUN
cana-4617	48	5	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	48	6	𝑟−1	𝑟−1	PROPN
cana-4617	48	7	[	[	X
cana-4617	48	8	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	48	9	)	)	PUNCT
cana-4617	48	10	]	]	PUNCT
cana-4617	48	11	(	(	PUNCT
cana-4617	48	12	8)	8)	NUM
cana-4617	48	13	and	and	CCONJ
cana-4617	48	14	joint	joint	ADJ
cana-4617	48	15	pdf	pdf	NOUN
cana-4617	48	16	of	of	ADP
cana-4617	48	17	𝑍(𝑟	𝑍(𝑟	PROPN
cana-4617	48	18	,	,	PUNCT
cana-4617	48	19	𝑛	𝑛	PROPN
cana-4617	48	20	,	,	PUNCT
cana-4617	48	21	�	�	PROPN
cana-4617	48	22	̃	̃	PROPN
cana-4617	48	23	�	�	PROPN
cana-4617	48	24	,	,	PUNCT
cana-4617	48	25	𝑘	𝑘	NOUN
cana-4617	48	26	)	)	PUNCT
cana-4617	48	27	and	and	CCONJ
cana-4617	48	28	𝑍(𝑠	𝑍(𝑠	NUM
cana-4617	48	29	,	,	PUNCT
cana-4617	48	30	𝑛	𝑛	PROPN
cana-4617	48	31	,	,	PUNCT
cana-4617	48	32	�	�	PROPN
cana-4617	48	33	̃	̃	PROPN
cana-4617	48	34	�	�	PROPN
cana-4617	48	35	,	,	PUNCT
cana-4617	48	36	𝑘	𝑘	NOUN
cana-4617	48	37	)	)	PUNCT
cana-4617	48	38	given	give	VERB
cana-4617	48	39	in	in	ADP
cana-4617	48	40	(	(	PUNCT
cana-4617	48	41	5	5	NUM
cana-4617	48	42	)	)	PUNCT
cana-4617	48	43	reduces	reduce	VERB
cana-4617	48	44	to	to	PART
cana-4617	48	45	𝑓𝑍(𝑟,𝑛,𝑚,𝑘),𝑍(𝑠,𝑛,𝑚,𝑘)(𝑧	𝑓𝑍(𝑟,𝑛,𝑚,𝑘),𝑍(𝑠,𝑛,𝑚,𝑘)(𝑧	VERB
cana-4617	48	46	,	,	PUNCT
cana-4617	48	47	𝑡	𝑡	NOUN
cana-4617	48	48	)	)	PUNCT
cana-4617	48	49	=	=	SYM
cana-4617	48	50	𝐶𝑠−1	𝐶𝑠−1	PROPN
cana-4617	48	51	(	(	PUNCT
cana-4617	48	52	𝑟	𝑟	NOUN
cana-4617	48	53	−	−	PROPN
cana-4617	48	54	1	1	NUM
cana-4617	48	55	)	)	PUNCT
cana-4617	48	56	!	!	PUNCT
cana-4617	49	1	(	(	PUNCT
cana-4617	49	2	𝑠	𝑠	INTJ
cana-4617	49	3	−	−	NOUN
cana-4617	49	4	𝑟	𝑟	PRON
cana-4617	49	5	−	−	PROPN
cana-4617	49	6	1	1	NUM
cana-4617	49	7	)	)	PUNCT
cana-4617	49	8	!	!	PUNCT
cana-4617	50	1	[	[	X
cana-4617	50	2	�	�	NOUN
cana-4617	50	3	̅	̅	NOUN
cana-4617	50	4	�	�	NOUN
cana-4617	50	5	(𝑧)]𝑚𝑓(𝑧)𝑔𝑚	(𝑧)]𝑚𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	50	6	𝑟−1[𝐹(𝑧	𝑟−1[𝐹(𝑧	NUM
cana-4617	50	7	)	)	PUNCT
cana-4617	50	8	]	]	PUNCT
cana-4617	50	9	×	×	NOUN
cana-4617	50	10	{	{	PUNCT
cana-4617	50	11	ℎ𝑚[𝐹(𝑡	ℎ𝑚[𝐹(𝑡	NOUN
cana-4617	50	12	)	)	PUNCT
cana-4617	50	13	]	]	PUNCT
cana-4617	51	1	−	−	PUNCT
cana-4617	51	2	ℎ𝑚[𝐹(𝑧)]}𝑠−𝑟−1[	ℎ𝑚[𝐹(𝑧)]}𝑠−𝑟−1[	SYM
cana-4617	51	3	�	�	NOUN
cana-4617	51	4	̅	̅	NOUN
cana-4617	51	5	�	�	NOUN
cana-4617	51	6	(𝑡)]𝛾𝑠−1𝑓(𝑡	(𝑡)]𝛾𝑠−1𝑓(𝑡	NUM
cana-4617	51	7	)	)	PUNCT
cana-4617	51	8	,	,	PUNCT
cana-4617	51	9	𝑧	𝑧	X
cana-4617	51	10	<	<	X
cana-4617	51	11	𝑡	𝑡	X
cana-4617	51	12	(	(	PUNCT
cana-4617	51	13	9	9	NUM
cana-4617	51	14	)	)	PUNCT
cana-4617	51	15	whereas	whereas	SCONJ
cana-4617	51	16	𝐶𝑟−1	𝐶𝑟−1	PROPN
cana-4617	51	17	=	=	SYM
cana-4617	51	18	∏	∏	PROPN
cana-4617	51	19	𝛾𝑖	𝛾𝑖	NOUN
cana-4617	51	20	𝑟	𝑟	NOUN
cana-4617	51	21	𝑖=1	𝑖=1	PUNCT
cana-4617	51	22	,	,	PUNCT
cana-4617	51	23	𝛾𝑖	𝛾𝑖	ADV
cana-4617	51	24	=	=	SYM
cana-4617	51	25	𝑘	𝑘	PROPN
cana-4617	51	26	+	+	CCONJ
cana-4617	51	27	(	(	PUNCT
cana-4617	51	28	𝑛	𝑛	PRON
cana-4617	51	29	−	−	PROPN
cana-4617	51	30	𝑖)(𝑚	𝑖)(𝑚	PUNCT
cana-4617	51	31	+	+	CCONJ
cana-4617	51	32	1	1	NUM
cana-4617	51	33	)	)	PUNCT
cana-4617	51	34	,	,	PUNCT
cana-4617	51	35	ℎ𝑚(𝑧	ℎ𝑚(𝑧	NUM
cana-4617	51	36	)	)	PUNCT
cana-4617	51	37	=	=	PRON
cana-4617	51	38	{	{	PUNCT
cana-4617	51	39	−1	−1	NOUN
cana-4617	51	40	𝑚	𝑚	NOUN
cana-4617	51	41	+	+	PROPN
cana-4617	51	42	1	1	NUM
cana-4617	51	43	(	(	PUNCT
cana-4617	51	44	1	1	NUM
cana-4617	51	45	−	−	NOUN
cana-4617	51	46	𝑧)𝑚+1	𝑧)𝑚+1	PROPN
cana-4617	51	47	,	,	PUNCT
cana-4617	51	48	𝑚	𝑚	ADP
cana-4617	51	49	≠	≠	PROPN
cana-4617	51	50	−1	−1	NOUN
cana-4617	51	51	−	−	NOUN
cana-4617	52	1	ln(1	ln(1	NOUN
cana-4617	52	2	−	−	NOUN
cana-4617	52	3	𝑧	𝑧	NOUN
cana-4617	52	4	)	)	PUNCT
cana-4617	52	5	,	,	PUNCT
cana-4617	52	6	𝑚	𝑚	X
cana-4617	52	7	=	=	PUNCT
cana-4617	52	8	−1	−1	NOUN
cana-4617	52	9	and	and	CCONJ
cana-4617	52	10	𝑔𝑚(𝑧	𝑔𝑚(𝑧	NOUN
cana-4617	52	11	)	)	PUNCT
cana-4617	53	1	=	=	SYM
cana-4617	53	2	ℎ𝑚(𝑧	ℎ𝑚(𝑧	X
cana-4617	53	3	)	)	PUNCT
cana-4617	53	4	−	−	PROPN
cana-4617	54	1	ℎ𝑚(0	ℎ𝑚(0	PROPN
cana-4617	54	2	)	)	PUNCT
cana-4617	54	3	,	,	PUNCT
cana-4617	54	4	𝑧	𝑧	PROPN
cana-4617	54	5	∈	∈	PROPN
cana-4617	54	6	[	[	X
cana-4617	54	7	0,1	0,1	NUM
cana-4617	54	8	)	)	PUNCT
cana-4617	54	9	.	.	PUNCT
cana-4617	55	1	we	we	PRON
cana-4617	55	2	also	also	ADV
cana-4617	55	3	set	set	VERB
cana-4617	55	4	𝑍(0	𝑍(0	PROPN
cana-4617	55	5	,	,	PUNCT
cana-4617	55	6	𝑛	𝑛	PROPN
cana-4617	55	7	,	,	PUNCT
cana-4617	55	8	𝑚	𝑚	PROPN
cana-4617	55	9	,	,	PUNCT
cana-4617	55	10	𝑘	𝑘	NOUN
cana-4617	55	11	)	)	PUNCT
cana-4617	55	12	=	=	SYM
cana-4617	56	1	0	0	X
cana-4617	56	2	.	.	PUNCT
cana-4617	57	1	if	if	SCONJ
cana-4617	57	2	𝑚	𝑚	PROPN
cana-4617	57	3	=	=	SYM
cana-4617	57	4	0	0	NUM
cana-4617	57	5	,	,	PUNCT
cana-4617	57	6	𝑘	𝑘	X
cana-4617	57	7	=	=	NOUN
cana-4617	57	8	1	1	NUM
cana-4617	57	9	then	then	ADV
cana-4617	57	10	𝑍(𝑟	𝑍(𝑟	X
cana-4617	57	11	,	,	PUNCT
cana-4617	57	12	𝑛	𝑛	PROPN
cana-4617	57	13	,	,	PUNCT
cana-4617	57	14	𝑚	𝑚	PROPN
cana-4617	57	15	,	,	PUNCT
cana-4617	57	16	𝑘	𝑘	NOUN
cana-4617	57	17	)	)	PUNCT
cana-4617	57	18	simplifies	simplifie	NOUN
cana-4617	57	19	to	to	ADP
cana-4617	57	20	the	the	DET
cana-4617	57	21	(	(	PUNCT
cana-4617	57	22	𝑛	𝑛	PROPN
cana-4617	57	23	−	−	PROPN
cana-4617	57	24	𝑟	𝑟	NOUN
cana-4617	58	1	+	+	CCONJ
cana-4617	58	2	1)𝑡ℎ	1)𝑡ℎ	NUM
cana-4617	58	3	order	order	NOUN
cana-4617	58	4	statistics	statistic	NOUN
cana-4617	58	5	,	,	PUNCT
cana-4617	58	6	𝑍𝑛−𝑟+1:𝑛	𝑍𝑛−𝑟+1:𝑛	PROPN
cana-4617	58	7	from	from	ADP
cana-4617	58	8	the	the	DET
cana-4617	58	9	sample	sample	NOUN
cana-4617	58	10	𝑍1	𝑍1	PROPN
cana-4617	58	11	,	,	PUNCT
cana-4617	58	12	𝑍2	𝑍2	VERB
cana-4617	58	13	,	,	PUNCT
cana-4617	58	14	…	…	PUNCT
cana-4617	58	15	,	,	PUNCT
cana-4617	58	16	𝑍𝑛.	𝑍𝑛.	PROPN
cana-4617	58	17	when	when	SCONJ
cana-4617	58	18	𝑚	𝑚	X
cana-4617	58	19	=	=	SYM
cana-4617	58	20	−1	−1	NOUN
cana-4617	58	21	then	then	ADV
cana-4617	58	22	𝑍(𝑟	𝑍(𝑟	NOUN
cana-4617	58	23	,	,	PUNCT
cana-4617	58	24	𝑛	𝑛	PROPN
cana-4617	58	25	,	,	PUNCT
cana-4617	58	26	𝑚	𝑚	PROPN
cana-4617	58	27	,	,	PUNCT
cana-4617	58	28	𝑘	𝑘	NOUN
cana-4617	58	29	)	)	PUNCT
cana-4617	58	30	simplifies	simplifie	NOUN
cana-4617	58	31	to	to	ADP
cana-4617	58	32	the	the	DET
cana-4617	58	33	kth	kth	PROPN
cana-4617	58	34	record	record	NOUN
cana-4617	58	35	values	value	NOUN
cana-4617	58	36	as	as	SCONJ
cana-4617	58	37	noted	note	VERB
cana-4617	58	38	(	(	PUNCT
cana-4617	58	39	by	by	ADP
cana-4617	58	40	pawlas	pawla	NOUN
cana-4617	58	41	.	.	PROPN
cana-4617	58	42	and	and	CCONJ
cana-4617	58	43	szynal	szynal	ADJ
cana-4617	58	44	.	.	PUNCT
cana-4617	59	1	(	(	PUNCT
cana-4617	59	2	2001	2001	NUM
cana-4617	59	3	)	)	PUNCT
cana-4617	59	4	)	)	PUNCT
cana-4617	59	5	.	.	PUNCT
cana-4617	60	1	in	in	ADP
cana-4617	60	2	this	this	DET
cana-4617	60	3	research	research	NOUN
cana-4617	60	4	,	,	PUNCT
cana-4617	60	5	we	we	PRON
cana-4617	60	6	provide	provide	VERB
cana-4617	60	7	explicit	explicit	ADJ
cana-4617	60	8	expressions	expression	NOUN
cana-4617	60	9	and	and	CCONJ
cana-4617	60	10	some	some	DET
cana-4617	60	11	recurrence	recurrence	NOUN
cana-4617	60	12	relations	relation	NOUN
cana-4617	60	13	for	for	ADP
cana-4617	60	14	single	single	ADJ
cana-4617	60	15	and	and	CCONJ
cana-4617	60	16	product	product	NOUN
cana-4617	60	17	moments	moment	NOUN
cana-4617	60	18	of	of	ADP
cana-4617	60	19	gos	go	NOUN
cana-4617	60	20	from	from	ADP
cana-4617	60	21	abrd	abrd	NOUN
cana-4617	60	22	.	.	PUNCT
cana-4617	61	1	its	its	PRON
cana-4617	61	2	many	many	ADJ
cana-4617	61	3	deductions	deduction	NOUN
cana-4617	61	4	and	and	CCONJ
cana-4617	61	5	special	special	ADJ
cana-4617	61	6	cases	case	NOUN
cana-4617	61	7	are	be	AUX
cana-4617	61	8	also	also	ADV
cana-4617	61	9	studied	study	VERB
cana-4617	61	10	.	.	PUNCT
cana-4617	62	1	a	a	DET
cana-4617	62	2	recurrence	recurrence	NOUN
cana-4617	62	3	relation	relation	NOUN
cana-4617	62	4	for	for	ADP
cana-4617	62	5	single	single	ADJ
cana-4617	62	6	moments	moment	NOUN
cana-4617	62	7	was	be	AUX
cana-4617	62	8	utilized	utilize	VERB
cana-4617	62	9	to	to	PART
cana-4617	62	10	characterize	characterize	VERB
cana-4617	62	11	abrd	abrd	NOUN
cana-4617	62	12	.	.	PUNCT
cana-4617	63	1	2	2	X
cana-4617	63	2	.	.	X
cana-4617	63	3	recurrence	recurrence	NOUN
cana-4617	63	4	relation	relation	NOUN
cana-4617	63	5	for	for	ADP
cana-4617	63	6	single	single	ADJ
cana-4617	63	7	moments	moment	NOUN
cana-4617	63	8	of	of	ADP
cana-4617	63	9	gos	go	NOUN
cana-4617	63	10	the	the	DET
cana-4617	63	11	single	single	ADJ
cana-4617	63	12	moments	moment	NOUN
cana-4617	63	13	of	of	ADP
cana-4617	63	14	gos	go	NOUN
cana-4617	63	15	for	for	ADP
cana-4617	63	16	abrd	abrd	ADJ
cana-4617	63	17	are	be	AUX
cana-4617	63	18	as	as	SCONJ
cana-4617	63	19	the	the	PRON
cana-4617	63	20	follows	follow	VERB
cana-4617	63	21	communications	communication	NOUN
cana-4617	63	22	on	on	ADP
cana-4617	63	23	applied	apply	VERB
cana-4617	63	24	nonlinear	nonlinear	ADJ
cana-4617	63	25	analysis	analysis	NOUN
cana-4617	63	26	issn	issn	NOUN
cana-4617	63	27	:	:	PUNCT
cana-4617	63	28	1074	1074	NUM
cana-4617	63	29	-	-	PUNCT
cana-4617	63	30	133x	133x	NUM
cana-4617	63	31	vol	vol	NOUN
cana-4617	63	32	32	32	NUM
cana-4617	63	33	no	no	NOUN
cana-4617	63	34	.	.	PUNCT
cana-4617	64	1	9s	9s	NUM
cana-4617	64	2	(	(	PUNCT
cana-4617	64	3	2025	2025	NUM
cana-4617	64	4	)	)	PUNCT
cana-4617	64	5	3023	3023	NUM
cana-4617	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	64	7	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	64	8	,	,	PUNCT
cana-4617	64	9	𝑛	𝑛	PROPN
cana-4617	64	10	,	,	PUNCT
cana-4617	64	11	𝑚	𝑚	PROPN
cana-4617	64	12	,	,	PUNCT
cana-4617	64	13	𝑘	𝑘	NOUN
cana-4617	64	14	)	)	PUNCT
cana-4617	64	15	]	]	PUNCT
cana-4617	65	1	=	=	PUNCT
cana-4617	65	2	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	65	3	(	(	PUNCT
cana-4617	65	4	𝑟	𝑟	NOUN
cana-4617	65	5	−	−	PROPN
cana-4617	65	6	1	1	NUM
cana-4617	65	7	)	)	PUNCT
cana-4617	65	8	!	!	PUNCT
cana-4617	66	1	∫	∫	PROPN
cana-4617	67	1	𝑍𝑗	𝑍𝑗	PROPN
cana-4617	67	2	∞	∞	PROPN
cana-4617	67	3	0	0	PUNCT
cana-4617	68	1	[	[	X
cana-4617	68	2	�	�	NOUN
cana-4617	68	3	̅	̅	NOUN
cana-4617	68	4	�	�	NOUN
cana-4617	68	5	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	68	6	𝑟−1	𝑟−1	PROPN
cana-4617	68	7	[	[	X
cana-4617	68	8	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	68	9	)	)	PUNCT
cana-4617	68	10	]	]	PUNCT
cana-4617	68	11	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	68	12	=	=	PUNCT
cana-4617	68	13	𝐶𝑟−1	𝐶𝑟−1	PROPN
cana-4617	68	14	(	(	PUNCT
cana-4617	68	15	𝑚	𝑚	PROPN
cana-4617	68	16	+	+	NOUN
cana-4617	68	17	1)𝑟−1(𝑟	1)𝑟−1(𝑟	NUM
cana-4617	68	18	−	−	NUM
cana-4617	68	19	1	1	NUM
cana-4617	68	20	)	)	PUNCT
cana-4617	68	21	!	!	PUNCT
cana-4617	69	1	∫	∫	PROPN
cana-4617	70	1	𝑍𝑗	𝑍𝑗	PROPN
cana-4617	70	2	∞	∞	PROPN
cana-4617	70	3	0	0	PUNCT
cana-4617	71	1	[	[	X
cana-4617	71	2	�	�	NOUN
cana-4617	71	3	̅	̅	NOUN
cana-4617	71	4	�	�	NOUN
cana-4617	71	5	(𝑧)]𝛾𝑟−1𝑓(𝑧	(𝑧)]𝛾𝑟−1𝑓(𝑧	NOUN
cana-4617	71	6	)	)	PUNCT
cana-4617	72	1	[	[	X
cana-4617	72	2	1	1	NUM
cana-4617	72	3	−	−	PROPN
cana-4617	72	4	(	(	PUNCT
cana-4617	72	5	�	�	NOUN
cana-4617	72	6	̅	̅	NOUN
cana-4617	72	7	�	�	NOUN
cana-4617	72	8	(𝑧	(𝑧	NOUN
cana-4617	72	9	)	)	PUNCT
cana-4617	72	10	)	)	PUNCT
cana-4617	73	1	𝑚+1	𝑚+1	NUM
cana-4617	73	2	]	]	PUNCT
cana-4617	74	1	𝑟−1	𝑟−1	PROPN
cana-4617	74	2	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	74	3	=	=	NOUN
cana-4617	74	4	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	74	5	∑	∑	PUNCT
cana-4617	74	6	(	(	PUNCT
cana-4617	74	7	𝑟−1	𝑟−1	PROPN
cana-4617	74	8	𝑤	𝑤	ADP
cana-4617	74	9	)	)	PUNCT
cana-4617	74	10	(	(	PUNCT
cana-4617	74	11	−1)𝑤𝑟−1	−1)𝑤𝑟−1	NOUN
cana-4617	74	12	𝑤=0	𝑤=0	PUNCT
cana-4617	74	13	(	(	PUNCT
cana-4617	74	14	𝑚	𝑚	PROPN
cana-4617	74	15	+	+	NOUN
cana-4617	74	16	1)𝑟−1(𝑟	1)𝑟−1(𝑟	NUM
cana-4617	74	17	−	−	NUM
cana-4617	74	18	1	1	NUM
cana-4617	74	19	)	)	PUNCT
cana-4617	74	20	!	!	PUNCT
cana-4617	75	1	∫	∫	PROPN
cana-4617	76	1	𝑍𝑗	𝑍𝑗	PROPN
cana-4617	76	2	∞	∞	PROPN
cana-4617	76	3	0	0	PUNCT
cana-4617	77	1	[	[	X
cana-4617	77	2	�	�	NOUN
cana-4617	77	3	̅	̅	NOUN
cana-4617	77	4	�	�	NOUN
cana-4617	77	5	(𝑧)]𝛾𝑟+𝑤(𝑚+1)−1𝑓(𝑧	(𝑧)]𝛾𝑟+𝑤(𝑚+1)−1𝑓(𝑧	NOUN
cana-4617	77	6	)	)	PUNCT
cana-4617	77	7	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	77	8	=	=	PUNCT
cana-4617	77	9	𝑗	𝑗	INTJ
cana-4617	77	10	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	77	11	(	(	PUNCT
cana-4617	77	12	𝑟	𝑟	NOUN
cana-4617	77	13	−	−	PROPN
cana-4617	77	14	1	1	NUM
cana-4617	77	15	)	)	PUNCT
cana-4617	77	16	!	!	PUNCT
cana-4617	78	1	(	(	PUNCT
cana-4617	78	2	𝑚	𝑚	X
cana-4617	78	3	+	+	X
cana-4617	78	4	1)𝑟−1	1)𝑟−1	NUM
cana-4617	78	5	∑	∑	PUNCT
cana-4617	78	6	(	(	PUNCT
cana-4617	78	7	𝑟−1	𝑟−1	PROPN
cana-4617	78	8	𝑤	𝑤	ADP
cana-4617	78	9	)	)	PUNCT
cana-4617	78	10	(	(	PUNCT
cana-4617	78	11	−1)𝑤	−1)𝑤	X
cana-4617	79	1	[	[	X
cana-4617	79	2	𝛾𝑟	𝛾𝑟	X
cana-4617	79	3	+	+	PUNCT
cana-4617	79	4	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	79	5	+	+	CCONJ
cana-4617	79	6	1	1	NUM
cana-4617	79	7	)	)	PUNCT
cana-4617	79	8	]	]	PUNCT
cana-4617	80	1	𝑟−1	𝑟−1	PROPN
cana-4617	80	2	𝑤=0	𝑤=0	SYM
cana-4617	80	3	∫	∫	PROPN
cana-4617	81	1	𝑍𝑗−1	𝑍𝑗−1	NUM
cana-4617	81	2	∞	∞	NOUN
cana-4617	81	3	0	0	PUNCT
cana-4617	82	1	[	[	X
cana-4617	82	2	�	�	NOUN
cana-4617	82	3	̅	̅	NOUN
cana-4617	82	4	�	�	NOUN
cana-4617	82	5	(𝑧)]𝛾𝑟+𝑤(𝑚+1	(𝑧)]𝛾𝑟+𝑤(𝑚+1	PUNCT
cana-4617	82	6	)	)	PUNCT
cana-4617	82	7	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	82	8	using	use	VERB
cana-4617	82	9	equation	equation	NOUN
cana-4617	82	10	(	(	PUNCT
cana-4617	82	11	2	2	NUM
cana-4617	82	12	)	)	PUNCT
cana-4617	82	13	,	,	PUNCT
cana-4617	82	14	we	we	PRON
cana-4617	82	15	get	get	VERB
cana-4617	82	16	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	82	17	,	,	PUNCT
cana-4617	82	18	𝑛	𝑛	PROPN
cana-4617	82	19	,	,	PUNCT
cana-4617	82	20	𝑚	𝑚	PROPN
cana-4617	82	21	,	,	PUNCT
cana-4617	82	22	𝑘	𝑘	NOUN
cana-4617	82	23	)	)	PUNCT
cana-4617	82	24	]	]	PUNCT
cana-4617	83	1	=	=	PUNCT
cana-4617	83	2	𝑗	𝑗	INTJ
cana-4617	84	1	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	84	2	(	(	PUNCT
cana-4617	84	3	𝑟	𝑟	NOUN
cana-4617	84	4	−	−	PROPN
cana-4617	84	5	1	1	NUM
cana-4617	84	6	)	)	PUNCT
cana-4617	84	7	!	!	PUNCT
cana-4617	85	1	(	(	PUNCT
cana-4617	85	2	𝑚	𝑚	X
cana-4617	85	3	+	+	X
cana-4617	85	4	1)𝑟−1	1)𝑟−1	NUM
cana-4617	85	5	∑	∑	PUNCT
cana-4617	85	6	(	(	PUNCT
cana-4617	85	7	𝑟−1	𝑟−1	PROPN
cana-4617	85	8	𝑤	𝑤	ADP
cana-4617	85	9	)	)	PUNCT
cana-4617	85	10	(	(	PUNCT
cana-4617	85	11	−1)𝑤	−1)𝑤	X
cana-4617	86	1	[	[	X
cana-4617	86	2	𝛾𝑟	𝛾𝑟	X
cana-4617	86	3	+	+	PUNCT
cana-4617	86	4	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	86	5	+	+	CCONJ
cana-4617	86	6	1	1	NUM
cana-4617	86	7	)	)	PUNCT
cana-4617	86	8	]	]	PUNCT
cana-4617	87	1	𝑟−1	𝑟−1	PROPN
cana-4617	87	2	𝑤=0	𝑤=0	SYM
cana-4617	87	3	∫	∫	PROPN
cana-4617	88	1	𝑍𝑗−1	𝑍𝑗−1	NUM
cana-4617	88	2	∞	∞	NOUN
cana-4617	88	3	0	0	PUNCT
cana-4617	89	1	[	[	X
cana-4617	89	2	(	(	PUNCT
cana-4617	89	3	1	1	NUM
cana-4617	89	4	+	+	NUM
cana-4617	89	5	𝑧2	𝑧2	PROPN
cana-4617	89	6	𝛽2	𝛽2	NOUN
cana-4617	89	7	)	)	PUNCT
cana-4617	89	8	]	]	PUNCT
cana-4617	89	9	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	PROPN
cana-4617	89	10	)	)	PUNCT
cana-4617	89	11	𝒆𝒙𝒑	𝒆𝒙𝒑	NOUN
cana-4617	89	12	(	(	PUNCT
cana-4617	89	13	−(𝛾𝑟	−(𝛾𝑟	PROPN
cana-4617	89	14	+	+	NUM
cana-4617	89	15	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	89	16	+	+	CCONJ
cana-4617	89	17	1	1	NUM
cana-4617	89	18	)	)	PUNCT
cana-4617	89	19	)	)	PUNCT
cana-4617	89	20	𝑧2	𝑧2	PROPN
cana-4617	89	21	𝛽2	𝛽2	PROPN
cana-4617	89	22	)	)	PUNCT
cana-4617	89	23	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	89	24	by	by	ADP
cana-4617	89	25	applying	apply	VERB
cana-4617	89	26	the	the	DET
cana-4617	89	27	binomial	binomial	ADJ
cana-4617	89	28	expansion	expansion	NOUN
cana-4617	89	29	,	,	PUNCT
cana-4617	89	30	we	we	PRON
cana-4617	89	31	get	get	VERB
cana-4617	89	32	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	89	33	,	,	PUNCT
cana-4617	89	34	𝑛	𝑛	PROPN
cana-4617	89	35	,	,	PUNCT
cana-4617	89	36	𝑚	𝑚	PROPN
cana-4617	89	37	,	,	PUNCT
cana-4617	89	38	𝑘	𝑘	NOUN
cana-4617	89	39	)	)	PUNCT
cana-4617	89	40	]	]	PUNCT
cana-4617	90	1	=	=	PUNCT
cana-4617	90	2	𝑗	𝑗	INTJ
cana-4617	91	1	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	91	2	(	(	PUNCT
cana-4617	91	3	𝑟	𝑟	NOUN
cana-4617	91	4	−	−	PROPN
cana-4617	91	5	1	1	NUM
cana-4617	91	6	)	)	PUNCT
cana-4617	91	7	!	!	PUNCT
cana-4617	92	1	(	(	PUNCT
cana-4617	92	2	𝑚	𝑚	X
cana-4617	92	3	+	+	PUNCT
cana-4617	92	4	1)𝑟−1	1)𝑟−1	NUM
cana-4617	92	5	∑	∑	PUNCT
cana-4617	92	6	∑	∑	PUNCT
cana-4617	92	7	(	(	PUNCT
cana-4617	92	8	𝑟−1	𝑟−1	PROPN
cana-4617	92	9	𝑤	𝑤	ADP
cana-4617	92	10	)	)	PUNCT
cana-4617	92	11	(	(	PUNCT
cana-4617	92	12	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	NUM
cana-4617	92	13	)	)	PUNCT
cana-4617	92	14	𝑣	𝑣	X
cana-4617	92	15	)	)	PUNCT
cana-4617	92	16	(	(	PUNCT
cana-4617	92	17	−1)𝑤	−1)𝑤	X
cana-4617	92	18	𝛽2𝑣[𝛾𝑟	𝛽2𝑣[𝛾𝑟	NOUN
cana-4617	92	19	+	+	CCONJ
cana-4617	92	20	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	92	21	+	+	CCONJ
cana-4617	92	22	1	1	NUM
cana-4617	92	23	)	)	PUNCT
cana-4617	92	24	]	]	PUNCT
cana-4617	93	1	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	VERB
cana-4617	93	2	)	)	PUNCT
cana-4617	93	3	𝑣=0	𝑣=0	NUM
cana-4617	93	4	𝑟−1	𝑟−1	PROPN
cana-4617	93	5	𝑤=0	𝑤=0	PUNCT
cana-4617	93	6	∫(𝑧2)𝑣+	∫(𝑧2)𝑣+	NOUN
cana-4617	93	7	𝑗−1	𝑗−1	PROPN
cana-4617	93	8	2	2	NUM
cana-4617	93	9	∞	∞	PROPN
cana-4617	93	10	0	0	NUM
cana-4617	93	11	𝒆𝒙𝒑	𝒆𝒙𝒑	PROPN
cana-4617	93	12	(	(	PUNCT
cana-4617	93	13	−(𝛾𝑟	−(𝛾𝑟	PROPN
cana-4617	93	14	+	+	NUM
cana-4617	93	15	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	93	16	+	+	CCONJ
cana-4617	93	17	1	1	NUM
cana-4617	93	18	)	)	PUNCT
cana-4617	93	19	)	)	PUNCT
cana-4617	93	20	𝑧2	𝑧2	PROPN
cana-4617	93	21	𝛽2	𝛽2	PROPN
cana-4617	93	22	)	)	PUNCT
cana-4617	93	23	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	93	24	by	by	ADP
cana-4617	93	25	substitution	substitution	NOUN
cana-4617	93	26	,	,	PUNCT
cana-4617	93	27	𝑦	𝑦	NOUN
cana-4617	93	28	=	=	SYM
cana-4617	93	29	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	ADJ
cana-4617	93	30	)	)	PUNCT
cana-4617	93	31	𝛽2	𝛽2	PROPN
cana-4617	93	32	𝑧2	𝑧2	PROPN
cana-4617	93	33	in	in	ADP
cana-4617	93	34	the	the	DET
cana-4617	93	35	integration	integration	NOUN
cana-4617	93	36	process	process	NOUN
cana-4617	93	37	,	,	PUNCT
cana-4617	93	38	we	we	PRON
cana-4617	93	39	obtain	obtain	VERB
cana-4617	93	40	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NUM
cana-4617	93	41	,	,	PUNCT
cana-4617	93	42	𝑛	𝑛	PROPN
cana-4617	93	43	,	,	PUNCT
cana-4617	93	44	𝑚	𝑚	PROPN
cana-4617	93	45	,	,	PUNCT
cana-4617	93	46	𝑘	𝑘	NOUN
cana-4617	93	47	)	)	PUNCT
cana-4617	93	48	]	]	PUNCT
cana-4617	94	1	=	=	SYM
cana-4617	94	2	𝑗𝛽𝑗	𝑗𝛽𝑗	NOUN
cana-4617	94	3	𝐶𝑟−1	𝐶𝑟−1	ADV
cana-4617	94	4	2(𝑟	2(𝑟	NUM
cana-4617	94	5	−	−	NOUN
cana-4617	94	6	1	1	NUM
cana-4617	94	7	)	)	PUNCT
cana-4617	94	8	!	!	PUNCT
cana-4617	95	1	(	(	PUNCT
cana-4617	95	2	𝑚	𝑚	X
cana-4617	95	3	+	+	PUNCT
cana-4617	95	4	1)𝑟−1	1)𝑟−1	NUM
cana-4617	95	5	∑	∑	PUNCT
cana-4617	95	6	∑	∑	PUNCT
cana-4617	95	7	(	(	PUNCT
cana-4617	95	8	𝑟−1	𝑟−1	PROPN
cana-4617	95	9	𝑤	𝑤	ADP
cana-4617	95	10	)	)	PUNCT
cana-4617	95	11	(	(	PUNCT
cana-4617	95	12	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	NUM
cana-4617	95	13	)	)	PUNCT
cana-4617	95	14	𝑣	𝑣	X
cana-4617	95	15	)	)	PUNCT
cana-4617	95	16	(	(	PUNCT
cana-4617	95	17	−1)𝑤	−1)𝑤	X
cana-4617	96	1	[	[	X
cana-4617	96	2	𝛾𝑟	𝛾𝑟	X
cana-4617	96	3	+	+	CCONJ
cana-4617	96	4	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	96	5	+	+	CCONJ
cana-4617	96	6	1)]𝑣+	1)]𝑣+	ADJ
cana-4617	96	7	𝑗	𝑗	PRON
cana-4617	96	8	2	2	NUM
cana-4617	96	9	+1	+1	NOUN
cana-4617	96	10	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	PROPN
cana-4617	96	11	)	)	PUNCT
cana-4617	96	12	𝑣=0	𝑣=0	NUM
cana-4617	96	13	𝑟−1	𝑟−1	PROPN
cana-4617	96	14	𝑤=0	𝑤=0	PUNCT
cana-4617	96	15	∫(𝑦)𝑣+	∫(𝑦)𝑣+	ADJ
cana-4617	96	16	𝑗	𝑗	X
cana-4617	96	17	2	2	NUM
cana-4617	96	18	−1	−1	NOUN
cana-4617	96	19	∞	∞	NUM
cana-4617	96	20	0	0	X
cana-4617	96	21	𝒆𝒙𝒑(−𝑦	𝒆𝒙𝒑(−𝑦	NOUN
cana-4617	96	22	)	)	PUNCT
cana-4617	96	23	𝑑𝑦	𝑑𝑦	ADP
cana-4617	96	24	therefore	therefore	ADV
cana-4617	96	25	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NUM
cana-4617	96	26	,	,	PUNCT
cana-4617	96	27	𝑛	𝑛	PROPN
cana-4617	96	28	,	,	PUNCT
cana-4617	96	29	𝑚	𝑚	PROPN
cana-4617	96	30	,	,	PUNCT
cana-4617	96	31	𝑘	𝑘	NOUN
cana-4617	96	32	)	)	PUNCT
cana-4617	96	33	]	]	PUNCT
cana-4617	97	1	=	=	SYM
cana-4617	97	2	𝑗𝛽𝑗	𝑗𝛽𝑗	NOUN
cana-4617	97	3	𝐶𝑟−1	𝐶𝑟−1	ADV
cana-4617	97	4	2(𝑟	2(𝑟	NUM
cana-4617	97	5	−	−	NOUN
cana-4617	97	6	1	1	NUM
cana-4617	97	7	)	)	PUNCT
cana-4617	97	8	!	!	PUNCT
cana-4617	98	1	(	(	PUNCT
cana-4617	98	2	𝑚	𝑚	X
cana-4617	98	3	+	+	PUNCT
cana-4617	98	4	1)𝑟−1	1)𝑟−1	NUM
cana-4617	98	5	∑	∑	PUNCT
cana-4617	98	6	∑	∑	PUNCT
cana-4617	98	7	(	(	PUNCT
cana-4617	98	8	𝑟−1	𝑟−1	PROPN
cana-4617	98	9	𝑤	𝑤	ADP
cana-4617	98	10	)	)	PUNCT
cana-4617	98	11	(	(	PUNCT
cana-4617	98	12	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	NUM
cana-4617	98	13	)	)	PUNCT
cana-4617	98	14	𝑣	𝑣	X
cana-4617	98	15	)	)	PUNCT
cana-4617	98	16	(	(	PUNCT
cana-4617	98	17	−1)𝑤	−1)𝑤	X
cana-4617	99	1	[	[	X
cana-4617	99	2	𝛾𝑟	𝛾𝑟	X
cana-4617	99	3	+	+	CCONJ
cana-4617	99	4	𝑤(𝑚	𝑤(𝑚	PROPN
cana-4617	99	5	+	+	CCONJ
cana-4617	99	6	1)]𝑣+	1)]𝑣+	ADJ
cana-4617	99	7	𝑗	𝑗	PRON
cana-4617	99	8	2	2	NUM
cana-4617	99	9	+1	+1	NOUN
cana-4617	99	10	𝛾𝑟+𝑤(𝑚+1	𝛾𝑟+𝑤(𝑚+1	PROPN
cana-4617	99	11	)	)	PUNCT
cana-4617	99	12	𝑣=0	𝑣=0	NUM
cana-4617	99	13	𝑟−1	𝑟−1	PROPN
cana-4617	99	14	𝑤=0	𝑤=0	PUNCT
cana-4617	99	15	𝛤	𝛤	PROPN
cana-4617	99	16	(	(	PUNCT
cana-4617	99	17	𝑣	𝑣	PART
cana-4617	99	18	+	+	NOUN
cana-4617	99	19	𝑗	𝑗	PROPN
cana-4617	99	20	2	2	NUM
cana-4617	99	21	)	)	PUNCT
cana-4617	99	22	(	(	PUNCT
cana-4617	99	23	10	10	NUM
cana-4617	99	24	)	)	PUNCT
cana-4617	99	25	remark	remark	VERB
cana-4617	99	26	2.1	2.1	NUM
cana-4617	99	27	setting	set	VERB
cana-4617	99	28	𝑚	𝑚	X
cana-4617	99	29	=	=	SYM
cana-4617	99	30	0	0	NUM
cana-4617	99	31	,	,	PUNCT
cana-4617	99	32	𝑘	𝑘	X
cana-4617	99	33	=	=	NOUN
cana-4617	99	34	1	1	NUM
cana-4617	99	35	in	in	ADP
cana-4617	99	36	equation	equation	NOUN
cana-4617	99	37	(	(	PUNCT
cana-4617	99	38	10	10	NUM
cana-4617	99	39	)	)	PUNCT
cana-4617	99	40	,	,	PUNCT
cana-4617	99	41	we	we	PRON
cana-4617	99	42	derive	derive	VERB
cana-4617	99	43	the	the	DET
cana-4617	99	44	single	single	ADJ
cana-4617	99	45	moments	moment	NOUN
cana-4617	99	46	of	of	ADP
cana-4617	99	47	order	order	NOUN
cana-4617	99	48	statistics	statistic	NOUN
cana-4617	99	49	for	for	ADP
cana-4617	99	50	abrd	abrd	NOUN
cana-4617	99	51	as	as	ADP
cana-4617	99	52	following	follow	VERB
cana-4617	99	53	form	form	NOUN
cana-4617	99	54	communications	communication	NOUN
cana-4617	99	55	on	on	ADP
cana-4617	99	56	applied	apply	VERB
cana-4617	99	57	nonlinear	nonlinear	ADJ
cana-4617	99	58	analysis	analysis	NOUN
cana-4617	99	59	issn	issn	NOUN
cana-4617	99	60	:	:	PUNCT
cana-4617	99	61	1074	1074	NUM
cana-4617	99	62	-	-	PUNCT
cana-4617	99	63	133x	133x	NUM
cana-4617	99	64	vol	vol	NOUN
cana-4617	99	65	32	32	NUM
cana-4617	99	66	no	no	NOUN
cana-4617	99	67	.	.	PUNCT
cana-4617	100	1	9s	9s	NUM
cana-4617	100	2	(	(	PUNCT
cana-4617	100	3	2025	2025	NUM
cana-4617	100	4	)	)	PUNCT
cana-4617	100	5	3024	3024	NUM
cana-4617	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	100	7	𝐸[𝑍𝑟:𝑛	𝐸[𝑍𝑟:𝑛	NOUN
cana-4617	100	8	𝑗	𝑗	NOUN
cana-4617	100	9	]	]	X
cana-4617	100	10	=	=	SYM
cana-4617	100	11	𝑗𝑛	𝑗𝑛	PART
cana-4617	100	12	!	!	PUNCT
cana-4617	101	1	𝛽𝑗	𝛽𝑗	NOUN
cana-4617	101	2	2(𝑟	2(𝑟	NUM
cana-4617	101	3	−	−	NOUN
cana-4617	101	4	1	1	NUM
cana-4617	101	5	)	)	PUNCT
cana-4617	101	6	!	!	PUNCT
cana-4617	102	1	(	(	PUNCT
cana-4617	102	2	𝑛	𝑛	DET
cana-4617	102	3	−	−	NOUN
cana-4617	102	4	𝑟	𝑟	NOUN
cana-4617	102	5	)	)	PUNCT
cana-4617	102	6	!	!	PUNCT
cana-4617	103	1	∑	∑	PUNCT
cana-4617	103	2	∑	∑	PUNCT
cana-4617	103	3	(	(	PUNCT
cana-4617	103	4	𝑟−1	𝑟−1	PROPN
cana-4617	103	5	𝑤	𝑤	X
cana-4617	103	6	)	)	PUNCT
cana-4617	103	7	(	(	PUNCT
cana-4617	103	8	𝑛−𝑟+𝑤+1	𝑛−𝑟+𝑤+1	NOUN
cana-4617	103	9	𝑣	𝑣	X
cana-4617	103	10	)	)	PUNCT
cana-4617	103	11	(	(	PUNCT
cana-4617	103	12	−1)𝑤	−1)𝑤	X
cana-4617	104	1	[	[	X
cana-4617	104	2	𝑛	𝑛	ADP
cana-4617	104	3	−	−	PROPN
cana-4617	104	4	𝑟	𝑟	NOUN
cana-4617	105	1	+	+	CCONJ
cana-4617	105	2	𝑤	𝑤	X
cana-4617	105	3	+	+	SYM
cana-4617	105	4	1]𝑣+	1]𝑣+	NUM
cana-4617	105	5	𝑗	𝑗	SYM
cana-4617	105	6	2	2	NUM
cana-4617	105	7	+1	+1	PROPN
cana-4617	105	8	𝑛−𝑟+𝑤+1	𝑛−𝑟+𝑤+1	NOUN
cana-4617	105	9	𝑣=0	𝑣=0	NUM
cana-4617	105	10	𝑟−1	𝑟−1	PROPN
cana-4617	105	11	𝑤=0	𝑤=0	PUNCT
cana-4617	105	12	𝛤	𝛤	PROPN
cana-4617	105	13	(	(	PUNCT
cana-4617	105	14	𝑣	𝑣	PART
cana-4617	105	15	+	+	NOUN
cana-4617	105	16	𝑗	𝑗	PROPN
cana-4617	105	17	2	2	NUM
cana-4617	105	18	)	)	PUNCT
cana-4617	105	19	then	then	ADV
cana-4617	105	20	𝐸[𝑍𝑟:𝑛	𝐸[𝑍𝑟:𝑛	NOUN
cana-4617	105	21	𝑗	𝑗	X
cana-4617	105	22	]	]	X
cana-4617	105	23	=	=	SYM
cana-4617	105	24	𝑗𝑛	𝑗𝑛	PART
cana-4617	105	25	!	!	PUNCT
cana-4617	106	1	𝛽𝑗	𝛽𝑗	NOUN
cana-4617	106	2	2(𝑛−𝑟	2(𝑛−𝑟	NUM
cana-4617	106	3	)	)	PUNCT
cana-4617	106	4	!	!	PUNCT
cana-4617	107	1	∑	∑	PUNCT
cana-4617	107	2	∑	∑	PUNCT
cana-4617	107	3	(	(	PUNCT
cana-4617	107	4	𝑛−𝑟+𝑤+1)−𝑣−	𝑛−𝑟+𝑤+1)−𝑣−	VERB
cana-4617	107	5	𝑗	𝑗	PROPN
cana-4617	107	6	2.(𝑛−𝑟+𝑤)!(−1)𝑤	2.(𝑛−𝑟+𝑤)!(−1)𝑤	PROPN
cana-4617	107	7	𝑤!(𝑟−1−𝑤)!(𝑛−𝑟+𝑤+1−𝑣)!𝑣	𝑤!(𝑟−1−𝑤)!(𝑛−𝑟+𝑤+1−𝑣)!𝑣	NOUN
cana-4617	107	8	!	!	PUNCT
cana-4617	108	1	𝑛−𝑟+𝑤+1	𝑛−𝑟+𝑤+1	NOUN
cana-4617	108	2	𝑣=0	𝑣=0	NUM
cana-4617	108	3	𝑟−1	𝑟−1	PROPN
cana-4617	108	4	𝑤=0	𝑤=0	PUNCT
cana-4617	108	5	𝛤	𝛤	PROPN
cana-4617	108	6	(	(	PUNCT
cana-4617	108	7	𝑣	𝑣	PART
cana-4617	108	8	+	+	NOUN
cana-4617	108	9	𝑗	𝑗	PROPN
cana-4617	108	10	2	2	NUM
cana-4617	108	11	)	)	PUNCT
cana-4617	108	12	(	(	PUNCT
cana-4617	108	13	11	11	X
cana-4617	108	14	)	)	PUNCT
cana-4617	108	15	using	use	VERB
cana-4617	108	16	equation	equation	NOUN
cana-4617	108	17	(	(	PUNCT
cana-4617	108	18	11	11	NUM
cana-4617	108	19	)	)	PUNCT
cana-4617	108	20	,	,	PUNCT
cana-4617	108	21	some	some	DET
cana-4617	108	22	numerical	numerical	ADJ
cana-4617	108	23	results	result	NOUN
cana-4617	108	24	for	for	ADP
cana-4617	108	25	the	the	DET
cana-4617	108	26	mean	mean	NOUN
cana-4617	108	27	and	and	CCONJ
cana-4617	108	28	variance	variance	NOUN
cana-4617	108	29	of	of	ADP
cana-4617	108	30	order	order	NOUN
cana-4617	108	31	statistics	statistic	NOUN
cana-4617	108	32	from	from	ADP
cana-4617	108	33	abrd	abrd	NOUN
cana-4617	108	34	,	,	PUNCT
cana-4617	108	35	as	as	SCONJ
cana-4617	108	36	presented	present	VERB
cana-4617	108	37	in	in	ADP
cana-4617	108	38	the	the	DET
cana-4617	108	39	following	follow	VERB
cana-4617	108	40	tables	table	NOUN
cana-4617	108	41	.	.	PUNCT
cana-4617	109	1	table	table	NOUN
cana-4617	109	2	1	1	NUM
cana-4617	109	3	:	:	PUNCT
cana-4617	109	4	mean	mean	VERB
cana-4617	109	5	of	of	ADP
cana-4617	109	6	order	order	NOUN
cana-4617	109	7	statistics	statistic	NOUN
cana-4617	109	8	for	for	ADP
cana-4617	109	9	abrd	abrd	ADJ
cana-4617	109	10	parameter	parameter	NOUN
cana-4617	109	11	n	n	CCONJ
cana-4617	109	12	β=3.5	β=3.5	ADJ
cana-4617	109	13	β=3	β=3	PUNCT
cana-4617	109	14	β=2.5	β=2.5	NOUN
cana-4617	109	15	β=2	β=2	PART
cana-4617	110	1	β=1.5	β=1.5	NOUN
cana-4617	110	2	β=1.3	β=1.3	NOUN
cana-4617	110	3	β=1	β=1	PUNCT
cana-4617	110	4	β=0.8	β=0.8	X
cana-4617	110	5	β=0.6	β=0.6	NOUN
cana-4617	110	6	β=0.4	β=0.4	NOUN
cana-4617	110	7	r	r	NOUN
cana-4617	110	8	4.653	4.653	NUM
cana-4617	110	9	3.988	3.988	NUM
cana-4617	110	10	3.323	3.323	NUM
cana-4617	110	11	2.659	2.659	NUM
cana-4617	110	12	1.994	1.994	NUM
cana-4617	110	13	1.728	1.728	NUM
cana-4617	110	14	1.329	1.329	NUM
cana-4617	110	15	1.063	1.063	NUM
cana-4617	110	16	0.798	0.798	NUM
cana-4617	110	17	0.532	0.532	NUM
cana-4617	110	18	1	1	NUM
cana-4617	110	19	1	1	NUM
cana-4617	110	20	3.701	3.701	NUM
cana-4617	110	21	3.172	3.172	NUM
cana-4617	110	22	2.644	2.644	NUM
cana-4617	110	23	2.115	2.115	NUM
cana-4617	110	24	1.586	1.586	NUM
cana-4617	110	25	1.375	1.375	NUM
cana-4617	110	26	1.057	1.057	NUM
cana-4617	110	27	0.846	0.846	NUM
cana-4617	110	28	0.634	0.634	NUM
cana-4617	110	29	0.423	0.423	NUM
cana-4617	110	30	1	1	NUM
cana-4617	110	31	2	2	NUM
cana-4617	110	32	5.604	5.604	NUM
cana-4617	110	33	4.804	4.804	NUM
cana-4617	110	34	4.003	4.003	NUM
cana-4617	110	35	3.202	3.202	NUM
cana-4617	110	36	2.402	2.402	NUM
cana-4617	110	37	2.082	2.082	NUM
cana-4617	110	38	1.601	1.601	NUM
cana-4617	110	39	1.281	1.281	NUM
cana-4617	110	40	0.961	0.961	NUM
cana-4617	110	41	0.64	0.64	NUM
cana-4617	110	42	2	2	NUM
cana-4617	110	43	3.258	3.258	NUM
cana-4617	110	44	2.793	2.793	NUM
cana-4617	110	45	2.327	2.327	NUM
cana-4617	110	46	1.862	1.862	NUM
cana-4617	110	47	1.396	1.396	NUM
cana-4617	110	48	1.21	1.21	NUM
cana-4617	110	49	0.931	0.931	NUM
cana-4617	110	50	0.745	0.745	NUM
cana-4617	110	51	0.559	0.559	NUM
cana-4617	110	52	0.372	0.372	NUM
cana-4617	110	53	1	1	NUM
cana-4617	110	54	3	3	NUM
cana-4617	110	55	4.587	4.587	NUM
cana-4617	110	56	3.932	3.932	NUM
cana-4617	110	57	3.276	3.276	NUM
cana-4617	110	58	2.621	2.621	NUM
cana-4617	110	59	1.966	1.966	NUM
cana-4617	110	60	1.704	1.704	NUM
cana-4617	110	61	1.311	1.311	NUM
cana-4617	110	62	1.048	1.048	NUM
cana-4617	110	63	0.786	0.786	NUM
cana-4617	110	64	0.524	0.524	NUM
cana-4617	110	65	2	2	NUM
cana-4617	110	66	6.113	6.113	NUM
cana-4617	110	67	5.24	5.24	NUM
cana-4617	110	68	4.366	4.366	NUM
cana-4617	110	69	3.493	3.493	NUM
cana-4617	110	70	2.62	2.62	NUM
cana-4617	110	71	2.27	2.27	NUM
cana-4617	110	72	1.747	1.747	NUM
cana-4617	110	73	1.397	1.397	NUM
cana-4617	110	74	1.048	1.048	NUM
cana-4617	110	75	0.699	0.699	NUM
cana-4617	110	76	3	3	NUM
cana-4617	110	77	2.984	2.984	NUM
cana-4617	110	78	2.558	2.558	NUM
cana-4617	110	79	2.131	2.131	NUM
cana-4617	110	80	1.705	1.705	NUM
cana-4617	110	81	1.279	1.279	NUM
cana-4617	110	82	1.108	1.108	NUM
cana-4617	110	83	0.853	0.853	NUM
cana-4617	110	84	0.682	0.682	NUM
cana-4617	110	85	0.512	0.512	NUM
cana-4617	110	86	0.341	0.341	NUM
cana-4617	110	87	1	1	NUM
cana-4617	110	88	4	4	NUM
cana-4617	110	89	4.081	4.081	NUM
cana-4617	110	90	3.498	3.498	NUM
cana-4617	110	91	2.915	2.915	NUM
cana-4617	110	92	2.332	2.332	NUM
cana-4617	110	93	1.749	1.749	NUM
cana-4617	110	94	1.516	1.516	NUM
cana-4617	110	95	1.166	1.166	NUM
cana-4617	110	96	0.933	0.933	NUM
cana-4617	110	97	0.7	0.7	NUM
cana-4617	110	98	0.466	0.466	NUM
cana-4617	110	99	2	2	NUM
cana-4617	110	100	5.093	5.093	NUM
cana-4617	110	101	4.365	4.365	NUM
cana-4617	110	102	3.638	3.638	NUM
cana-4617	110	103	2.91	2.91	NUM
cana-4617	110	104	2.183	2.183	NUM
cana-4617	110	105	1.892	1.892	NUM
cana-4617	110	106	1.455	1.455	NUM
cana-4617	110	107	1.164	1.164	NUM
cana-4617	110	108	0.873	0.873	NUM
cana-4617	110	109	0.582	0.582	NUM
cana-4617	110	110	3	3	NUM
cana-4617	110	111	6.453	6.453	NUM
cana-4617	110	112	5.531	5.531	NUM
cana-4617	110	113	4.609	4.609	NUM
cana-4617	110	114	3.687	3.687	NUM
cana-4617	110	115	2.765	2.765	NUM
cana-4617	110	116	2.397	2.397	NUM
cana-4617	110	117	1.844	1.844	NUM
cana-4617	110	118	1.475	1.475	NUM
cana-4617	110	119	1.106	1.106	NUM
cana-4617	110	120	0.737	0.737	NUM
cana-4617	110	121	4	4	NUM
cana-4617	110	122	2.791	2.791	NUM
cana-4617	110	123	2.392	2.392	NUM
cana-4617	110	124	1.994	1.994	NUM
cana-4617	110	125	1.595	1.595	NUM
cana-4617	110	126	1.196	1.196	NUM
cana-4617	110	127	1.037	1.037	NUM
cana-4617	110	128	0.797	0.797	NUM
cana-4617	110	129	0.638	0.638	NUM
cana-4617	110	130	0.478	0.478	NUM
cana-4617	110	131	0.319	0.319	NUM
cana-4617	110	132	1	1	NUM
cana-4617	110	133	5	5	NUM
cana-4617	110	134	3.757	3.757	NUM
cana-4617	110	135	3.22	3.22	NUM
cana-4617	110	136	2.683	2.683	NUM
cana-4617	110	137	2.147	2.147	NUM
cana-4617	110	138	1.61	1.61	NUM
cana-4617	110	139	1.395	1.395	NUM
cana-4617	110	140	1.073	1.073	NUM
cana-4617	110	141	0.859	0.859	NUM
cana-4617	110	142	0.644	0.644	NUM
cana-4617	110	143	0.429	0.429	NUM
cana-4617	110	144	2	2	NUM
cana-4617	110	145	4.568	4.568	NUM
cana-4617	110	146	3.915	3.915	NUM
cana-4617	110	147	3.263	3.263	NUM
cana-4617	110	148	2.61	2.61	NUM
cana-4617	110	149	1.958	1.958	NUM
cana-4617	110	150	1.697	1.697	NUM
cana-4617	110	151	1.305	1.305	NUM
cana-4617	110	152	1.044	1.044	NUM
cana-4617	110	153	0.783	0.783	NUM
cana-4617	110	154	0.522	0.522	NUM
cana-4617	110	155	3	3	NUM
cana-4617	110	156	5.443	5.443	NUM
cana-4617	110	157	4.665	4.665	NUM
cana-4617	110	158	3.888	3.888	NUM
cana-4617	110	159	3.11	3.11	NUM
cana-4617	110	160	2.333	2.333	NUM
cana-4617	110	161	2.022	2.022	NUM
cana-4617	110	162	1.555	1.555	NUM
cana-4617	110	163	1.244	1.244	NUM
cana-4617	110	164	0.933	0.933	NUM
cana-4617	110	165	0.622	0.622	NUM
cana-4617	110	166	4	4	NUM
cana-4617	110	167	6.705	6.705	NUM
cana-4617	110	168	5.747	5.747	NUM
cana-4617	110	169	4.789	4.789	NUM
cana-4617	110	170	3.832	3.832	NUM
cana-4617	110	171	2.874	2.874	NUM
cana-4617	110	172	2.491	2.491	NUM
cana-4617	110	173	1.916	1.916	NUM
cana-4617	110	174	1.533	1.533	NUM
cana-4617	110	175	1.149	1.149	NUM
cana-4617	110	176	0.766	0.766	NUM
cana-4617	110	177	5	5	NUM
cana-4617	110	178	2.644	2.644	NUM
cana-4617	110	179	2.267	2.267	NUM
cana-4617	110	180	1.889	1.889	NUM
cana-4617	110	181	1.511	1.511	NUM
cana-4617	110	182	1.133	1.133	NUM
cana-4617	110	183	0.982	0.982	NUM
cana-4617	110	184	0.756	0.756	NUM
cana-4617	110	185	0.604	0.604	NUM
cana-4617	110	186	0.453	0.453	NUM
cana-4617	110	187	0.302	0.302	NUM
cana-4617	110	188	1	1	NUM
cana-4617	110	189	6	6	NUM
cana-4617	110	190	3.523	3.523	NUM
cana-4617	110	191	3.02	3.02	NUM
cana-4617	110	192	2.517	2.517	NUM
cana-4617	110	193	2.013	2.013	NUM
cana-4617	110	194	1.51	1.51	NUM
cana-4617	110	195	1.309	1.309	NUM
cana-4617	110	196	1.007	1.007	NUM
cana-4617	110	197	0.805	0.805	NUM
cana-4617	110	198	0.604	0.604	NUM
cana-4617	110	199	0.403	0.403	NUM
cana-4617	110	200	2	2	NUM
cana-4617	110	201	4.223	4.223	NUM
cana-4617	110	202	3.62	3.62	NUM
cana-4617	110	203	3.017	3.017	NUM
cana-4617	110	204	2.413	2.413	NUM
cana-4617	110	205	1.81	1.81	NUM
cana-4617	110	206	1.569	1.569	NUM
cana-4617	110	207	1.207	1.207	NUM
cana-4617	110	208	0.965	0.965	NUM
cana-4617	110	209	0.724	0.724	NUM
cana-4617	110	210	0.483	0.483	NUM
cana-4617	110	211	3	3	NUM
cana-4617	110	212	4.912	4.912	NUM
cana-4617	110	213	4.211	4.211	NUM
cana-4617	110	214	3.509	3.509	NUM
cana-4617	110	215	2.807	2.807	NUM
cana-4617	110	216	2.105	2.105	NUM
cana-4617	110	217	1.825	1.825	NUM
cana-4617	110	218	1.404	1.404	NUM
cana-4617	110	219	1.123	1.123	NUM
cana-4617	110	220	0.842	0.842	NUM
cana-4617	110	221	0.561	0.561	NUM
cana-4617	110	222	4	4	NUM
cana-4617	110	223	5.708	5.708	NUM
cana-4617	110	224	4.893	4.893	NUM
cana-4617	110	225	4.077	4.077	NUM
cana-4617	110	226	3.262	3.262	NUM
cana-4617	110	227	2.446	2.446	NUM
cana-4617	110	228	2.12	2.12	NUM
cana-4617	110	229	1.631	1.631	NUM
cana-4617	110	230	1.305	1.305	NUM
cana-4617	110	231	0.979	0.979	NUM
cana-4617	110	232	0.652	0.652	NUM
cana-4617	110	233	5	5	NUM
cana-4617	110	234	6.905	6.905	NUM
cana-4617	110	235	5.918	5.918	NUM
cana-4617	110	236	4.932	4.932	NUM
cana-4617	110	237	3.946	3.946	NUM
cana-4617	110	238	2.959	2.959	NUM
cana-4617	110	239	2.565	2.565	NUM
cana-4617	110	240	1.973	1.973	NUM
cana-4617	110	241	1.578	1.578	NUM
cana-4617	110	242	1.184	1.184	NUM
cana-4617	110	243	0.789	0.789	NUM
cana-4617	110	244	6	6	NUM
cana-4617	110	245	note	note	NOUN
cana-4617	110	246	that	that	SCONJ
cana-4617	110	247	:	:	PUNCT
cana-4617	110	248	the	the	DET
cana-4617	110	249	results	result	NOUN
cana-4617	110	250	presented	present	VERB
cana-4617	110	251	in	in	ADP
cana-4617	110	252	table1	table1	PROPN
cana-4617	110	253	are	be	AUX
cana-4617	110	254	consistent	consistent	ADJ
cana-4617	110	255	with	with	ADP
cana-4617	110	256	the	the	DET
cana-4617	110	257	properties	property	NOUN
cana-4617	110	258	of	of	ADP
cana-4617	110	259	order	order	NOUN
cana-4617	110	260	statistics	statistic	NOUN
cana-4617	110	261	described	describe	VERB
cana-4617	110	262	by	by	ADP
cana-4617	110	263	david	david	PROPN
cana-4617	110	264	and	and	CCONJ
cana-4617	110	265	nagaraja	nagaraja	PROPN
cana-4617	110	266	(	(	PUNCT
cana-4617	110	267	2004	2004	NUM
cana-4617	110	268	)	)	PUNCT
cana-4617	110	269	,	,	PUNCT
cana-4617	110	270	specifically	specifically	ADV
cana-4617	110	271	∑	∑	ADP
cana-4617	110	272	𝜇𝑖:𝑛	𝜇𝑖:𝑛	PROPN
cana-4617	110	273	=	=	SYM
cana-4617	110	274	𝑛𝜇1:1	𝑛𝜇1:1	NOUN
cana-4617	110	275	𝑛	𝑛	PRON
cana-4617	110	276	𝑖=1	𝑖=1	PROPN
cana-4617	110	277	communications	communication	NOUN
cana-4617	110	278	on	on	ADP
cana-4617	110	279	applied	apply	VERB
cana-4617	110	280	nonlinear	nonlinear	ADJ
cana-4617	110	281	analysis	analysis	NOUN
cana-4617	110	282	issn	issn	NOUN
cana-4617	110	283	:	:	PUNCT
cana-4617	110	284	1074	1074	NUM
cana-4617	110	285	-	-	PUNCT
cana-4617	110	286	133x	133x	NUM
cana-4617	110	287	vol	vol	NOUN
cana-4617	110	288	32	32	NUM
cana-4617	110	289	no	no	NOUN
cana-4617	110	290	.	.	PUNCT
cana-4617	111	1	9s	9s	NUM
cana-4617	111	2	(	(	PUNCT
cana-4617	111	3	2025	2025	NUM
cana-4617	111	4	)	)	PUNCT
cana-4617	111	5	3025	3025	NUM
cana-4617	111	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	111	7	table	table	NOUN
cana-4617	111	8	2	2	NUM
cana-4617	111	9	:	:	PUNCT
cana-4617	111	10	variance	variance	NOUN
cana-4617	111	11	of	of	ADP
cana-4617	111	12	order	order	NOUN
cana-4617	111	13	statistics	statistic	NOUN
cana-4617	111	14	for	for	ADP
cana-4617	111	15	abrd	abrd	ADJ
cana-4617	111	16	parameter	parameter	NOUN
cana-4617	111	17	n	n	CCONJ
cana-4617	111	18	β=3.5	β=3.5	ADJ
cana-4617	111	19	β=3	β=3	PUNCT
cana-4617	111	20	β=2.5	β=2.5	NOUN
cana-4617	111	21	β=2	β=2	PART
cana-4617	112	1	β=1.5	β=1.5	NOUN
cana-4617	112	2	β=1.3	β=1.3	NOUN
cana-4617	112	3	β=1	β=1	PUNCT
cana-4617	112	4	β=0.8	β=0.8	X
cana-4617	112	5	β=0.6	β=0.6	NOUN
cana-4617	112	6	β=0.4	β=0.4	NOUN
cana-4617	112	7	r	r	NOUN
cana-4617	112	8	2.852	2.852	NUM
cana-4617	112	9	2.096	2.096	NUM
cana-4617	112	10	1.455	1.455	NUM
cana-4617	112	11	0.931	0.931	NUM
cana-4617	112	12	0.524	0.524	NUM
cana-4617	112	13	0.394	0.394	NUM
cana-4617	112	14	0.233	0.233	NUM
cana-4617	112	15	0.149	0.149	NUM
cana-4617	112	16	0.084	0.084	NUM
cana-4617	112	17	0.037	0.037	NUM
cana-4617	112	18	1	1	NUM
cana-4617	112	19	1	1	NUM
cana-4617	112	20	1.614	1.614	NUM
cana-4617	112	21	1.186	1.186	NUM
cana-4617	112	22	0.823	0.823	NUM
cana-4617	112	23	0.527	0.527	NUM
cana-4617	112	24	0.296	0.296	NUM
cana-4617	112	25	0.223	0.223	NUM
cana-4617	112	26	0.132	0.132	NUM
cana-4617	112	27	0.084	0.084	NUM
cana-4617	112	28	0.047	0.047	NUM
cana-4617	112	29	0.021	0.021	NUM
cana-4617	112	30	1	1	NUM
cana-4617	112	31	2	2	NUM
cana-4617	112	32	2.281	2.281	NUM
cana-4617	112	33	1.676	1.676	NUM
cana-4617	112	34	1.164	1.164	NUM
cana-4617	112	35	0.745	0.745	NUM
cana-4617	112	36	0.419	0.419	NUM
cana-4617	112	37	0.315	0.315	NUM
cana-4617	112	38	0.186	0.186	NUM
cana-4617	112	39	0.119	0.119	NUM
cana-4617	112	40	0.067	0.067	NUM
cana-4617	112	41	0.03	0.03	NUM
cana-4617	112	42	2	2	NUM
cana-4617	112	43	1.18	1.18	NUM
cana-4617	112	44	0.867	0.867	NUM
cana-4617	112	45	0.602	0.602	NUM
cana-4617	112	46	0.385	0.385	NUM
cana-4617	112	47	0.217	0.217	NUM
cana-4617	112	48	0.163	0.163	NUM
cana-4617	112	49	0.096	0.096	NUM
cana-4617	112	50	0.062	0.062	NUM
cana-4617	112	51	0.035	0.035	NUM
cana-4617	112	52	0.015	0.015	NUM
cana-4617	112	53	1	1	NUM
cana-4617	112	54	3	3	NUM
cana-4617	112	55	1.305	1.305	NUM
cana-4617	112	56	0.958	0.958	NUM
cana-4617	112	57	0.666	0.666	NUM
cana-4617	112	58	0.426	0.426	NUM
cana-4617	112	59	0.24	0.24	NUM
cana-4617	112	60	0.18	0.18	NUM
cana-4617	112	61	0.106	0.106	NUM
cana-4617	112	62	0.068	0.068	NUM
cana-4617	112	63	0.038	0.038	NUM
cana-4617	112	64	0.017	0.017	NUM
cana-4617	112	65	2	2	NUM
cana-4617	112	66	1.993	1.993	NUM
cana-4617	112	67	1.464	1.464	NUM
cana-4617	112	68	1.017	1.017	NUM
cana-4617	112	69	0.651	0.651	NUM
cana-4617	112	70	0.366	0.366	NUM
cana-4617	112	71	0.275	0.275	NUM
cana-4617	112	72	0.163	0.163	NUM
cana-4617	112	73	0.104	0.104	NUM
cana-4617	112	74	0.059	0.059	NUM
cana-4617	112	75	0.026	0.026	NUM
cana-4617	112	76	3	3	NUM
cana-4617	112	77	0.953	0.953	NUM
cana-4617	112	78	0.7	0.7	NUM
cana-4617	112	79	0.486	0.486	NUM
cana-4617	112	80	0.311	0.311	NUM
cana-4617	112	81	0.175	0.175	NUM
cana-4617	112	82	0.131	0.131	NUM
cana-4617	112	83	0.078	0.078	NUM
cana-4617	112	84	0.05	0.05	NUM
cana-4617	112	85	0.023	0.023	NUM
cana-4617	112	86	0.012	0.012	NUM
cana-4617	112	87	1	1	NUM
cana-4617	112	88	4	4	NUM
cana-4617	112	89	0.958	0.958	NUM
cana-4617	112	90	0.704	0.704	NUM
cana-4617	112	91	0.489	0.489	NUM
cana-4617	112	92	0.313	0.313	NUM
cana-4617	112	93	0.176	0.176	NUM
cana-4617	112	94	0.132	0.132	NUM
cana-4617	112	95	0.078	0.078	NUM
cana-4617	112	96	0.05	0.05	NUM
cana-4617	112	97	0.028	0.028	NUM
cana-4617	112	98	0.013	0.013	NUM
cana-4617	112	99	2	2	NUM
cana-4617	112	100	1.14	1.14	NUM
cana-4617	112	101	0.837	0.837	NUM
cana-4617	112	102	0.581	0.581	NUM
cana-4617	112	103	0.372	0.372	NUM
cana-4617	112	104	0.209	0.209	NUM
cana-4617	112	105	0.157	0.157	NUM
cana-4617	112	106	0.093	0.093	NUM
cana-4617	112	107	0.06	0.06	NUM
cana-4617	112	108	0.033	0.033	NUM
cana-4617	112	109	0.015	0.015	NUM
cana-4617	112	110	3	3	NUM
cana-4617	112	111	1.815	1.815	NUM
cana-4617	112	112	1.333	1.333	NUM
cana-4617	112	113	0.926	0.926	NUM
cana-4617	112	114	0.592	0.592	NUM
cana-4617	112	115	0.333	0.333	NUM
cana-4617	112	116	0.25	0.25	NUM
cana-4617	112	117	0.148	0.148	NUM
cana-4617	112	118	0.095	0.095	NUM
cana-4617	112	119	0.053	0.053	NUM
cana-4617	112	120	0.024	0.024	NUM
cana-4617	112	121	4	4	NUM
cana-4617	112	122	0.811	0.811	NUM
cana-4617	112	123	0.596	0.596	NUM
cana-4617	112	124	0.414	0.414	NUM
cana-4617	112	125	0.265	0.265	NUM
cana-4617	112	126	0.149	0.149	NUM
cana-4617	112	127	0.112	0.112	NUM
cana-4617	112	128	0.066	0.066	NUM
cana-4617	112	129	0.042	0.042	NUM
cana-4617	112	130	0.024	0.024	NUM
cana-4617	112	131	0.011	0.011	NUM
cana-4617	112	132	1	1	NUM
cana-4617	112	133	5	5	NUM
cana-4617	112	134	0.773	0.773	NUM
cana-4617	112	135	0.568	0.568	NUM
cana-4617	112	136	0.395	0.395	NUM
cana-4617	112	137	0.253	0.253	NUM
cana-4617	112	138	0.142	0.142	NUM
cana-4617	112	139	0.107	0.107	NUM
cana-4617	112	140	0.063	0.063	NUM
cana-4617	112	141	0.04	0.04	NUM
cana-4617	112	142	0.023	0.023	NUM
cana-4617	112	143	0.01	0.01	NUM
cana-4617	112	144	2	2	NUM
cana-4617	112	145	0.839	0.839	NUM
cana-4617	112	146	0.616	0.616	NUM
cana-4617	112	147	0.428	0.428	NUM
cana-4617	112	148	0.274	0.274	NUM
cana-4617	112	149	0.154	0.154	NUM
cana-4617	112	150	0.116	0.116	NUM
cana-4617	112	151	0.068	0.068	NUM
cana-4617	112	152	0.044	0.044	NUM
cana-4617	112	153	0.025	0.025	NUM
cana-4617	112	154	0.011	0.011	NUM
cana-4617	112	155	3	3	NUM
cana-4617	112	156	1.034	1.034	NUM
cana-4617	112	157	0.759	0.759	NUM
cana-4617	112	158	0.527	0.527	NUM
cana-4617	112	159	0.338	0.338	NUM
cana-4617	112	160	0.19	0.19	NUM
cana-4617	112	161	0.143	0.143	NUM
cana-4617	112	162	0.084	0.084	NUM
cana-4617	112	163	0.054	0.054	NUM
cana-4617	112	164	0.03	0.03	NUM
cana-4617	112	165	0.014	0.014	NUM
cana-4617	112	166	4	4	NUM
cana-4617	112	167	1.691	1.691	NUM
cana-4617	112	168	1.242	1.242	NUM
cana-4617	112	169	0.863	0.863	NUM
cana-4617	112	170	0.552	0.552	NUM
cana-4617	112	171	0.311	0.311	NUM
cana-4617	112	172	0.233	0.233	NUM
cana-4617	112	173	0.138	0.138	NUM
cana-4617	112	174	0.088	0.088	NUM
cana-4617	112	175	0.05	0.05	NUM
cana-4617	112	176	0.022	0.022	NUM
cana-4617	112	177	5	5	NUM
cana-4617	112	178	0.713	0.713	NUM
cana-4617	112	179	0.524	0.524	NUM
cana-4617	112	180	0.364	0.364	NUM
cana-4617	112	181	0.233	0.233	NUM
cana-4617	112	182	0.131	0.131	NUM
cana-4617	112	183	0.098	0.098	NUM
cana-4617	112	184	0.058	0.058	NUM
cana-4617	112	185	0.037	0.037	NUM
cana-4617	112	186	0.021	0.021	NUM
cana-4617	112	187	0.0093	0.0093	NUM
cana-4617	112	188	1	1	NUM
cana-4617	112	189	6	6	NUM
cana-4617	112	190	0.657	0.657	NUM
cana-4617	112	191	0.483	0.483	NUM
cana-4617	112	192	0.335	0.335	NUM
cana-4617	112	193	0.215	0.215	NUM
cana-4617	112	194	0.121	0.121	NUM
cana-4617	112	195	0.091	0.091	NUM
cana-4617	112	196	0.054	0.054	NUM
cana-4617	112	197	0.034	0.034	NUM
cana-4617	112	198	0.019	0.019	NUM
cana-4617	112	199	0.0086	0.0086	NUM
cana-4617	112	200	2	2	NUM
cana-4617	112	201	0.679	0.679	NUM
cana-4617	112	202	0.499	0.499	NUM
cana-4617	112	203	0.346	0.346	NUM
cana-4617	112	204	0.222	0.222	NUM
cana-4617	112	205	0.125	0.125	NUM
cana-4617	112	206	0.094	0.094	NUM
cana-4617	112	207	0.055	0.055	NUM
cana-4617	112	208	0.035	0.035	NUM
cana-4617	112	209	0.02	0.02	NUM
cana-4617	112	210	0.0089	0.0089	NUM
cana-4617	112	211	3	3	NUM
cana-4617	112	212	0.762	0.762	NUM
cana-4617	112	213	0.56	0.56	NUM
cana-4617	112	214	0.389	0.389	NUM
cana-4617	112	215	0.249	0.249	NUM
cana-4617	112	216	0.14	0.14	NUM
cana-4617	112	217	0.105	0.105	NUM
cana-4617	112	218	0.062	0.062	NUM
cana-4617	112	219	0.04	0.04	NUM
cana-4617	112	220	0.022	0.022	NUM
cana-4617	112	221	0.0099	0.0099	NUM
cana-4617	112	222	4	4	NUM
cana-4617	112	223	communications	communication	NOUN
cana-4617	112	224	on	on	ADP
cana-4617	112	225	applied	apply	VERB
cana-4617	112	226	nonlinear	nonlinear	ADJ
cana-4617	112	227	analysis	analysis	NOUN
cana-4617	112	228	issn	issn	NOUN
cana-4617	112	229	:	:	PUNCT
cana-4617	112	230	1074	1074	NUM
cana-4617	112	231	-	-	PUNCT
cana-4617	112	232	133x	133x	NUM
cana-4617	112	233	vol	vol	NOUN
cana-4617	112	234	32	32	NUM
cana-4617	112	235	no	no	NOUN
cana-4617	112	236	.	.	PUNCT
cana-4617	113	1	9s	9s	NUM
cana-4617	113	2	(	(	PUNCT
cana-4617	113	3	2025	2025	NUM
cana-4617	113	4	)	)	PUNCT
cana-4617	113	5	3026	3026	NUM
cana-4617	114	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	114	2	0.958	0.958	NUM
cana-4617	114	3	0.704	0.704	NUM
cana-4617	114	4	0.489	0.489	NUM
cana-4617	114	5	0.313	0.313	NUM
cana-4617	114	6	0.176	0.176	NUM
cana-4617	114	7	0.132	0.132	NUM
cana-4617	114	8	0.078	0.078	NUM
cana-4617	114	9	0.05	0.05	NUM
cana-4617	114	10	0.028	0.028	NUM
cana-4617	114	11	0.013	0.013	NUM
cana-4617	114	12	5	5	NUM
cana-4617	114	13	1.599	1.599	NUM
cana-4617	114	14	1.175	1.175	NUM
cana-4617	114	15	0.816	0.816	NUM
cana-4617	114	16	0.522	0.522	NUM
cana-4617	114	17	0.294	0.294	NUM
cana-4617	114	18	0.221	0.221	NUM
cana-4617	114	19	0.131	0.131	NUM
cana-4617	114	20	0.084	0.084	NUM
cana-4617	114	21	0.047	0.047	NUM
cana-4617	114	22	0.021	0.021	NUM
cana-4617	114	23	6	6	NUM
cana-4617	114	24	2.1	2.1	NUM
cana-4617	114	25	the	the	DET
cana-4617	114	26	rth	rth	PROPN
cana-4617	114	27	tl	tl	PROPN
cana-4617	114	28	-	-	PUNCT
cana-4617	114	29	moments	moments	PROPN
cana-4617	114	30	and	and	CCONJ
cana-4617	114	31	rth	rth	PROPN
cana-4617	114	32	l	l	PROPN
cana-4617	114	33	-	-	NOUN
cana-4617	114	34	moments	moment	NOUN
cana-4617	114	35	the	the	DET
cana-4617	114	36	rth	rth	PROPN
cana-4617	114	37	tl	tl	PROPN
cana-4617	114	38	-	-	PUNCT
cana-4617	114	39	moments	moment	NOUN
cana-4617	114	40	are	be	AUX
cana-4617	114	41	given	give	VERB
cana-4617	114	42	in	in	ADP
cana-4617	114	43	the	the	DET
cana-4617	114	44	following	follow	VERB
cana-4617	114	45	formula	formula	NOUN
cana-4617	114	46	(	(	PUNCT
cana-4617	114	47	by	by	ADP
cana-4617	114	48	elamir	elamir	X
cana-4617	114	49	.	.	PUNCT
cana-4617	114	50	and	and	CCONJ
cana-4617	114	51	seheult	seheult	VERB
cana-4617	114	52	.	.	PUNCT
cana-4617	115	1	(	(	PUNCT
cana-4617	115	2	2003	2003	NUM
cana-4617	115	3	)	)	PUNCT
cana-4617	115	4	)	)	PUNCT
cana-4617	115	5	.	.	PUNCT
cana-4617	116	1	𝐿𝑟	𝐿𝑟	PROPN
cana-4617	116	2	(	(	PUNCT
cana-4617	116	3	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	116	4	)	)	PUNCT
cana-4617	116	5	=	=	SYM
cana-4617	116	6	1	1	NUM
cana-4617	116	7	𝑟	𝑟	NOUN
cana-4617	116	8	∑(−1)𝑘	∑(−1)𝑘	VERB
cana-4617	116	9	𝑟−1	𝑟−1	PROPN
cana-4617	116	10	𝑘=0	𝑘=0	PROPN
cana-4617	116	11	(	(	PUNCT
cana-4617	116	12	𝑟	𝑟	NOUN
cana-4617	116	13	−	−	PROPN
cana-4617	116	14	1	1	NUM
cana-4617	116	15	𝑘	𝑘	NOUN
cana-4617	116	16	)	)	PUNCT
cana-4617	116	17	𝐸(𝑍𝑟+𝑠−𝑘:𝑟+𝑠+𝑡	𝐸(𝑍𝑟+𝑠−𝑘:𝑟+𝑠+𝑡	NOUN
cana-4617	116	18	)	)	PUNCT
cana-4617	116	19	,	,	PUNCT
cana-4617	116	20	(	(	PUNCT
cana-4617	116	21	12	12	NUM
cana-4617	116	22	)	)	PUNCT
cana-4617	116	23	whereas	whereas	SCONJ
cana-4617	116	24	r	r	NOUN
cana-4617	116	25	,	,	PUNCT
cana-4617	116	26	s	s	PART
cana-4617	116	27	and	and	CCONJ
cana-4617	116	28	t	t	PROPN
cana-4617	116	29	take	take	VERB
cana-4617	116	30	the	the	DET
cana-4617	116	31	values	value	NOUN
cana-4617	116	32	1,2,3	1,2,3	NUM
cana-4617	116	33	,	,	PUNCT
cana-4617	116	34	...	...	PUNCT
cana-4617	116	35	we	we	PRON
cana-4617	116	36	have	have	AUX
cana-4617	116	37	noted	note	VERB
cana-4617	116	38	that	that	SCONJ
cana-4617	116	39	the	the	DET
cana-4617	116	40	rth	rth	PROPN
cana-4617	116	41	l	l	PROPN
cana-4617	116	42	-	-	NOUN
cana-4617	116	43	moments	moment	NOUN
cana-4617	116	44	can	can	AUX
cana-4617	116	45	be	be	AUX
cana-4617	116	46	obtained	obtain	VERB
cana-4617	116	47	by	by	ADP
cana-4617	116	48	taking	take	VERB
cana-4617	116	49	s=	s=	NOUN
cana-4617	116	50	t	t	PROPN
cana-4617	116	51	=	=	SYM
cana-4617	116	52	0	0	X
cana-4617	116	53	.	.	PUNCT
cana-4617	117	1	using	use	VERB
cana-4617	117	2	(	(	PUNCT
cana-4617	117	3	12	12	NUM
cana-4617	117	4	)	)	PUNCT
cana-4617	117	5	and	and	CCONJ
cana-4617	117	6	(	(	PUNCT
cana-4617	117	7	11	11	NUM
cana-4617	117	8	)	)	PUNCT
cana-4617	117	9	with	with	ADP
cana-4617	117	10	j=1	j=1	PROPN
cana-4617	117	11	,	,	PUNCT
cana-4617	117	12	n=	n=	ADJ
cana-4617	117	13	r+s+t	r+s+t	NOUN
cana-4617	117	14	and	and	CCONJ
cana-4617	117	15	r=	r=	ADJ
cana-4617	117	16	r+s	r+s	PROPN
cana-4617	117	17	-	-	PUNCT
cana-4617	117	18	k	k	ADP
cana-4617	117	19	the	the	DET
cana-4617	117	20	rth	rth	PROPN
cana-4617	117	21	tl	tl	PROPN
cana-4617	117	22	-	-	PUNCT
cana-4617	117	23	moments	moment	NOUN
cana-4617	117	24	can	can	AUX
cana-4617	117	25	be	be	AUX
cana-4617	117	26	obtained	obtain	VERB
cana-4617	117	27	as	as	SCONJ
cana-4617	117	28	follows	follow	VERB
cana-4617	117	29	communications	communication	NOUN
cana-4617	117	30	on	on	ADP
cana-4617	117	31	applied	apply	VERB
cana-4617	117	32	nonlinear	nonlinear	ADJ
cana-4617	117	33	analysis	analysis	NOUN
cana-4617	117	34	issn	issn	NOUN
cana-4617	117	35	:	:	PUNCT
cana-4617	117	36	1074	1074	NUM
cana-4617	117	37	-	-	PUNCT
cana-4617	117	38	133x	133x	NUM
cana-4617	117	39	vol	vol	NOUN
cana-4617	117	40	32	32	NUM
cana-4617	117	41	no	no	NOUN
cana-4617	117	42	.	.	PUNCT
cana-4617	118	1	9s	9s	NUM
cana-4617	118	2	(	(	PUNCT
cana-4617	118	3	2025	2025	NUM
cana-4617	118	4	)	)	PUNCT
cana-4617	118	5	3027	3027	NUM
cana-4617	119	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	119	2	𝐿𝑟	𝐿𝑟	PROPN
cana-4617	119	3	(	(	PUNCT
cana-4617	119	4	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	119	5	)	)	PUNCT
cana-4617	119	6	=	=	SYM
cana-4617	119	7	1	1	NUM
cana-4617	119	8	𝑟	𝑟	NOUN
cana-4617	119	9	∑(−1)𝑘	∑(−1)𝑘	VERB
cana-4617	119	10	𝑟−1	𝑟−1	PROPN
cana-4617	119	11	𝑘=0	𝑘=0	PROPN
cana-4617	119	12	(	(	PUNCT
cana-4617	119	13	𝑟	𝑟	NOUN
cana-4617	119	14	−	−	PROPN
cana-4617	119	15	1	1	NUM
cana-4617	119	16	𝑘	𝑘	NOUN
cana-4617	119	17	)	)	PUNCT
cana-4617	119	18	∑	∑	ADP
cana-4617	119	19	∑	∑	PUNCT
cana-4617	119	20	𝛽.	𝛽.	NOUN
cana-4617	119	21	(	(	PUNCT
cana-4617	119	22	𝑟	𝑟	NOUN
cana-4617	119	23	+	+	CCONJ
cana-4617	119	24	𝑠	𝑠	PROPN
cana-4617	119	25	+	+	NUM
cana-4617	119	26	𝑡	𝑡	NOUN
cana-4617	119	27	)	)	PUNCT
cana-4617	119	28	!	!	PUNCT
cana-4617	120	1	(	(	PUNCT
cana-4617	120	2	𝑡	𝑡	X
cana-4617	120	3	+	+	X
cana-4617	120	4	𝑘	𝑘	X
cana-4617	120	5	+	+	NOUN
cana-4617	120	6	𝑤	𝑤	ADP
cana-4617	120	7	+	+	NOUN
cana-4617	120	8	1)−𝑣−	1)−𝑣−	NUM
cana-4617	120	9	1	1	NUM
cana-4617	120	10	2	2	NUM
cana-4617	120	11	.	.	PUNCT
cana-4617	121	1	(	(	PUNCT
cana-4617	121	2	𝑡	𝑡	X
cana-4617	121	3	+	+	X
cana-4617	121	4	𝑘	𝑘	PROPN
cana-4617	121	5	+	+	NOUN
cana-4617	121	6	𝑤	𝑤	X
cana-4617	121	7	)	)	PUNCT
cana-4617	121	8	!	!	PUNCT
cana-4617	122	1	(	(	PUNCT
cana-4617	122	2	−1)𝑤	−1)𝑤	NOUN
cana-4617	122	3	2𝑤	2𝑤	NUM
cana-4617	122	4	!	!	PUNCT
cana-4617	123	1	(	(	PUNCT
cana-4617	123	2	𝑟	𝑟	X
cana-4617	123	3	+	+	CCONJ
cana-4617	124	1	𝑠	𝑠	INTJ
cana-4617	124	2	−	−	NOUN
cana-4617	124	3	𝑘	𝑘	INTJ
cana-4617	124	4	−	−	PROPN
cana-4617	124	5	1	1	NUM
cana-4617	124	6	−	−	NOUN
cana-4617	124	7	𝑤	𝑤	ADP
cana-4617	124	8	)	)	PUNCT
cana-4617	124	9	!	!	PUNCT
cana-4617	125	1	(	(	PUNCT
cana-4617	125	2	𝑡	𝑡	X
cana-4617	125	3	+	+	X
cana-4617	125	4	𝑘	𝑘	X
cana-4617	125	5	+	+	NOUN
cana-4617	125	6	𝑤	𝑤	ADP
cana-4617	125	7	+	+	NUM
cana-4617	125	8	1	1	NUM
cana-4617	125	9	−	−	NOUN
cana-4617	125	10	𝑣	𝑣	X
cana-4617	125	11	)	)	PUNCT
cana-4617	125	12	!	!	PUNCT
cana-4617	126	1	𝑣	𝑣	X
cana-4617	126	2	!	!	PUNCT
cana-4617	127	1	(	(	PUNCT
cana-4617	127	2	𝑡	𝑡	X
cana-4617	127	3	+	+	X
cana-4617	127	4	𝑘	𝑘	NOUN
cana-4617	127	5	)	)	PUNCT
cana-4617	127	6	!	!	PUNCT
cana-4617	128	1	𝑡+𝑘+𝑤+1	𝑡+𝑘+𝑤+1	NOUN
cana-4617	128	2	𝑣=0	𝑣=0	NUM
cana-4617	128	3	𝑟+𝑠−𝑘−1	𝑟+𝑠−𝑘−1	NOUN
cana-4617	128	4	𝑤=0	𝑤=0	PUNCT
cana-4617	128	5	×	×	PROPN
cana-4617	128	6	𝛤	𝛤	PROPN
cana-4617	128	7	(	(	PUNCT
cana-4617	128	8	𝑣	𝑣	PART
cana-4617	128	9	+	+	NOUN
cana-4617	128	10	1	1	NUM
cana-4617	128	11	2	2	NUM
cana-4617	128	12	)	)	PUNCT
cana-4617	128	13	then	then	ADV
cana-4617	128	14	𝐿𝑟	𝐿𝑟	PROPN
cana-4617	128	15	(	(	PUNCT
cana-4617	128	16	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	128	17	)	)	PUNCT
cana-4617	128	18	=	=	SYM
cana-4617	128	19	1	1	NUM
cana-4617	128	20	𝑟	𝑟	NOUN
cana-4617	128	21	∑	∑	ADP
cana-4617	128	22	∑	∑	PUNCT
cana-4617	128	23	∑	∑	VERB
cana-4617	128	24	𝛽.	𝛽.	VERB
cana-4617	128	25	(	(	PUNCT
cana-4617	128	26	𝑟	𝑟	NOUN
cana-4617	128	27	+	+	CCONJ
cana-4617	128	28	𝑠	𝑠	PROPN
cana-4617	128	29	+	+	NUM
cana-4617	128	30	𝑡	𝑡	NOUN
cana-4617	128	31	)	)	PUNCT
cana-4617	128	32	!	!	PUNCT
cana-4617	129	1	(	(	PUNCT
cana-4617	129	2	𝑟	𝑟	X
cana-4617	129	3	−	−	PROPN
cana-4617	129	4	1	1	NUM
cana-4617	129	5	)	)	PUNCT
cana-4617	129	6	!	!	PUNCT
cana-4617	130	1	(	(	PUNCT
cana-4617	130	2	𝑡	𝑡	X
cana-4617	130	3	+	+	X
cana-4617	130	4	𝑘	𝑘	X
cana-4617	130	5	+	+	NOUN
cana-4617	130	6	𝑤	𝑤	ADP
cana-4617	130	7	+	+	NOUN
cana-4617	130	8	1)−𝑣−	1)−𝑣−	NUM
cana-4617	130	9	1	1	NUM
cana-4617	130	10	2	2	NUM
cana-4617	130	11	.	.	PUNCT
cana-4617	131	1	(	(	PUNCT
cana-4617	131	2	𝑡	𝑡	X
cana-4617	131	3	+	+	X
cana-4617	131	4	𝑘	𝑘	PROPN
cana-4617	131	5	+	+	NOUN
cana-4617	131	6	𝑤	𝑤	X
cana-4617	131	7	)	)	PUNCT
cana-4617	131	8	!	!	PUNCT
cana-4617	132	1	(	(	PUNCT
cana-4617	132	2	−1)𝑤+𝑘	−1)𝑤+𝑘	NOUN
cana-4617	132	3	2𝑤	2𝑤	NUM
cana-4617	132	4	!	!	PUNCT
cana-4617	133	1	𝑘	𝑘	X
cana-4617	133	2	!	!	PUNCT
cana-4617	134	1	(	(	PUNCT
cana-4617	134	2	𝑟	𝑟	X
cana-4617	134	3	−	−	ADP
cana-4617	134	4	1	1	NUM
cana-4617	134	5	−	−	PROPN
cana-4617	134	6	𝑘	𝑘	NOUN
cana-4617	134	7	)	)	PUNCT
cana-4617	134	8	!	!	PUNCT
cana-4617	135	1	(	(	PUNCT
cana-4617	135	2	𝑟	𝑟	X
cana-4617	135	3	+	+	CCONJ
cana-4617	136	1	𝑠	𝑠	INTJ
cana-4617	136	2	−	−	NOUN
cana-4617	136	3	𝑘	𝑘	INTJ
cana-4617	136	4	−	−	PROPN
cana-4617	136	5	1	1	NUM
cana-4617	136	6	−	−	NOUN
cana-4617	136	7	𝑤	𝑤	ADP
cana-4617	136	8	)	)	PUNCT
cana-4617	136	9	!	!	PUNCT
cana-4617	137	1	(	(	PUNCT
cana-4617	137	2	𝑡	𝑡	X
cana-4617	137	3	+	+	X
cana-4617	137	4	𝑘	𝑘	X
cana-4617	137	5	+	+	NOUN
cana-4617	137	6	𝑤	𝑤	ADP
cana-4617	137	7	+	+	NUM
cana-4617	137	8	1	1	NUM
cana-4617	137	9	−	−	NOUN
cana-4617	137	10	𝑣	𝑣	X
cana-4617	137	11	)	)	PUNCT
cana-4617	137	12	!	!	PUNCT
cana-4617	138	1	𝑣	𝑣	X
cana-4617	138	2	!	!	PUNCT
cana-4617	139	1	(	(	PUNCT
cana-4617	139	2	𝑡	𝑡	X
cana-4617	139	3	+	+	X
cana-4617	139	4	𝑘	𝑘	NOUN
cana-4617	139	5	)	)	PUNCT
cana-4617	139	6	!	!	PUNCT
cana-4617	140	1	(	(	PUNCT
cana-4617	140	2	13	13	NUM
cana-4617	140	3	)	)	PUNCT
cana-4617	140	4	𝑡+𝑘+𝑤+1	𝑡+𝑘+𝑤+1	NOUN
cana-4617	140	5	𝑣=0	𝑣=0	NUM
cana-4617	140	6	𝑟+𝑠−𝑘−1	𝑟+𝑠−𝑘−1	NOUN
cana-4617	140	7	𝑤=0	𝑤=0	PUNCT
cana-4617	140	8	𝑟−1	𝑟−1	PROPN
cana-4617	140	9	𝑘=0	𝑘=0	VERB
cana-4617	140	10	×	×	PROPN
cana-4617	140	11	𝛤	𝛤	PROPN
cana-4617	140	12	(	(	PUNCT
cana-4617	140	13	𝑣	𝑣	PART
cana-4617	140	14	+	+	NOUN
cana-4617	140	15	1	1	NUM
cana-4617	140	16	2	2	NUM
cana-4617	140	17	)	)	PUNCT
cana-4617	140	18	the	the	DET
cana-4617	140	19	initial	initial	ADJ
cana-4617	140	20	four	four	NUM
cana-4617	140	21	tl	tl	PROPN
cana-4617	140	22	-	-	PUNCT
cana-4617	140	23	moments	moment	NOUN
cana-4617	140	24	can	can	AUX
cana-4617	140	25	be	be	AUX
cana-4617	140	26	obtained	obtain	VERB
cana-4617	140	27	from	from	ADP
cana-4617	140	28	(	(	PUNCT
cana-4617	140	29	13	13	NUM
cana-4617	140	30	)	)	PUNCT
cana-4617	140	31	by	by	ADP
cana-4617	140	32	setting	set	VERB
cana-4617	140	33	r	r	NOUN
cana-4617	140	34	=	=	SYM
cana-4617	140	35	1,2,3	1,2,3	NUM
cana-4617	140	36	and	and	CCONJ
cana-4617	140	37	4	4	NUM
cana-4617	140	38	respectively	respectively	ADV
cana-4617	140	39	.	.	PUNCT
cana-4617	141	1	the	the	DET
cana-4617	141	2	generalized	generalize	VERB
cana-4617	141	3	tl	tl	PROPN
cana-4617	141	4	-	-	PUNCT
cana-4617	141	5	moments	moment	NOUN
cana-4617	141	6	ratios	ratio	NOUN
cana-4617	141	7	,	,	PUNCT
cana-4617	141	8	such	such	ADJ
cana-4617	141	9	as	as	ADP
cana-4617	141	10	the	the	DET
cana-4617	141	11	coefficient	coefficient	NOUN
cana-4617	141	12	of	of	ADP
cana-4617	141	13	variation	variation	NOUN
cana-4617	141	14	,	,	PUNCT
cana-4617	141	15	coefficient	coefficient	NOUN
cana-4617	141	16	of	of	ADP
cana-4617	141	17	skewness	skewness	NOUN
cana-4617	141	18	and	and	CCONJ
cana-4617	141	19	coefficient	coefficient	NOUN
cana-4617	141	20	of	of	ADP
cana-4617	141	21	kurtosis	kurtosis	NOUN
cana-4617	141	22	,	,	PUNCT
cana-4617	141	23	are	be	AUX
cana-4617	141	24	calculated	calculate	VERB
cana-4617	141	25	from	from	ADP
cana-4617	141	26	the	the	DET
cana-4617	141	27	initial	initial	ADJ
cana-4617	141	28	four	four	NUM
cana-4617	141	29	generalized	generalized	ADJ
cana-4617	141	30	tlmoments	tlmoment	NOUN
cana-4617	141	31	.	.	PUNCT
cana-4617	142	1	these	these	DET
cana-4617	142	2	ratios	ratio	NOUN
cana-4617	142	3	are	be	AUX
cana-4617	142	4	defined	define	VERB
cana-4617	142	5	as	as	ADP
cana-4617	142	6	𝜏1	𝜏1	NOUN
cana-4617	142	7	(	(	PUNCT
cana-4617	142	8	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	9	)	)	PUNCT
cana-4617	142	10	=	=	SYM
cana-4617	142	11	𝐿1	𝐿1	X
cana-4617	142	12	(	(	PUNCT
cana-4617	142	13	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	14	)	)	PUNCT
cana-4617	142	15	𝐿2	𝐿2	PROPN
cana-4617	142	16	(	(	PUNCT
cana-4617	142	17	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	18	)	)	PUNCT
cana-4617	142	19	,	,	PUNCT
cana-4617	142	20	𝜏3	𝜏3	PROPN
cana-4617	142	21	(	(	PUNCT
cana-4617	142	22	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	23	)	)	PUNCT
cana-4617	142	24	=	=	SYM
cana-4617	142	25	𝐿3	𝐿3	NOUN
cana-4617	142	26	(	(	PUNCT
cana-4617	142	27	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	28	)	)	PUNCT
cana-4617	142	29	𝐿2	𝐿2	PROPN
cana-4617	142	30	(	(	PUNCT
cana-4617	142	31	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	32	)	)	PUNCT
cana-4617	142	33	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-4617	142	34	𝜏4	𝜏4	PROPN
cana-4617	142	35	(	(	PUNCT
cana-4617	142	36	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	37	)	)	PUNCT
cana-4617	142	38	=	=	SYM
cana-4617	142	39	𝐿4	𝐿4	NOUN
cana-4617	142	40	(	(	PUNCT
cana-4617	142	41	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	42	)	)	PUNCT
cana-4617	142	43	𝐿2	𝐿2	PROPN
cana-4617	142	44	(	(	PUNCT
cana-4617	142	45	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	142	46	)	)	PUNCT
cana-4617	142	47	respectively	respectively	ADV
cana-4617	142	48	.	.	PUNCT
cana-4617	143	1	the	the	DET
cana-4617	143	2	rth	rth	PROPN
cana-4617	143	3	l	l	PROPN
cana-4617	143	4	-	-	NOUN
cana-4617	143	5	moments	moment	NOUN
cana-4617	143	6	can	can	AUX
cana-4617	143	7	be	be	AUX
cana-4617	143	8	obtained	obtain	VERB
cana-4617	143	9	by	by	ADP
cana-4617	143	10	taking	take	VERB
cana-4617	143	11	s=	s=	NOUN
cana-4617	143	12	t=	t=	NOUN
cana-4617	143	13	0	0	PUNCT
cana-4617	144	1	in	in	ADP
cana-4617	144	2	equation	equation	NOUN
cana-4617	144	3	(	(	PUNCT
cana-4617	144	4	13	13	NUM
cana-4617	144	5	)	)	PUNCT
cana-4617	144	6	as	as	ADP
cana-4617	144	7	𝐿𝑟	𝐿𝑟	PROPN
cana-4617	144	8	=	=	SYM
cana-4617	144	9	1	1	NUM
cana-4617	144	10	𝑟	𝑟	NOUN
cana-4617	144	11	∑	∑	ADP
cana-4617	144	12	∑	∑	PUNCT
cana-4617	144	13	∑	∑	VERB
cana-4617	144	14	𝛽.	𝛽.	NOUN
cana-4617	144	15	(	(	PUNCT
cana-4617	144	16	𝑟	𝑟	NOUN
cana-4617	144	17	)	)	PUNCT
cana-4617	144	18	!	!	PUNCT
cana-4617	145	1	(	(	PUNCT
cana-4617	145	2	𝑟	𝑟	X
cana-4617	145	3	−	−	PROPN
cana-4617	145	4	1	1	NUM
cana-4617	145	5	)	)	PUNCT
cana-4617	145	6	!	!	PUNCT
cana-4617	146	1	(	(	PUNCT
cana-4617	146	2	𝑘	𝑘	X
cana-4617	146	3	+	+	NOUN
cana-4617	146	4	𝑤	𝑤	X
cana-4617	146	5	+	+	NOUN
cana-4617	146	6	1)−𝑣−	1)−𝑣−	NUM
cana-4617	146	7	1	1	NUM
cana-4617	146	8	2	2	NUM
cana-4617	146	9	.	.	PUNCT
cana-4617	147	1	(	(	PUNCT
cana-4617	147	2	𝑘	𝑘	X
cana-4617	147	3	+	+	NOUN
cana-4617	147	4	𝑤	𝑤	X
cana-4617	147	5	)	)	PUNCT
cana-4617	147	6	!	!	PUNCT
cana-4617	148	1	(	(	PUNCT
cana-4617	148	2	−1)𝑤+𝑘	−1)𝑤+𝑘	NOUN
cana-4617	148	3	2𝑤	2𝑤	NUM
cana-4617	148	4	!	!	PUNCT
cana-4617	149	1	𝑘	𝑘	X
cana-4617	149	2	!	!	PUNCT
cana-4617	150	1	(	(	PUNCT
cana-4617	150	2	𝑟	𝑟	X
cana-4617	150	3	−	−	ADP
cana-4617	150	4	1	1	NUM
cana-4617	150	5	−	−	PROPN
cana-4617	150	6	𝑘	𝑘	NOUN
cana-4617	150	7	)	)	PUNCT
cana-4617	150	8	!	!	PUNCT
cana-4617	151	1	(	(	PUNCT
cana-4617	151	2	𝑟	𝑟	X
cana-4617	151	3	−	−	NOUN
cana-4617	151	4	𝑘	𝑘	PRON
cana-4617	151	5	−	−	PROPN
cana-4617	151	6	1	1	NUM
cana-4617	151	7	−	−	NOUN
cana-4617	151	8	𝑤	𝑤	ADP
cana-4617	151	9	)	)	PUNCT
cana-4617	151	10	!	!	PUNCT
cana-4617	152	1	(	(	PUNCT
cana-4617	152	2	𝑘	𝑘	X
cana-4617	152	3	+	+	NOUN
cana-4617	152	4	𝑤	𝑤	ADP
cana-4617	152	5	+	+	NUM
cana-4617	152	6	1	1	NUM
cana-4617	152	7	−	−	NOUN
cana-4617	152	8	𝑣	𝑣	X
cana-4617	152	9	)	)	PUNCT
cana-4617	152	10	!	!	PUNCT
cana-4617	153	1	𝑣	𝑣	X
cana-4617	153	2	!	!	PUNCT
cana-4617	153	3	(	(	PUNCT
cana-4617	153	4	𝑘	𝑘	NOUN
cana-4617	153	5	)	)	PUNCT
cana-4617	153	6	!	!	PUNCT
cana-4617	154	1	𝛤	𝛤	PROPN
cana-4617	154	2	(	(	PUNCT
cana-4617	154	3	𝑣	𝑣	ADP
cana-4617	154	4	𝑘+𝑤+1	𝑘+𝑤+1	PROPN
cana-4617	154	5	𝑣=0	𝑣=0	NUM
cana-4617	154	6	𝑟−𝑘−1	𝑟−𝑘−1	X
cana-4617	154	7	𝑤=0	𝑤=0	PUNCT
cana-4617	154	8	𝑟−1	𝑟−1	PROPN
cana-4617	154	9	𝑘=0	𝑘=0	VERB
cana-4617	155	1	+	+	CCONJ
cana-4617	155	2	1	1	NUM
cana-4617	155	3	2	2	NUM
cana-4617	155	4	)	)	PUNCT
cana-4617	155	5	(	(	PUNCT
cana-4617	155	6	14	14	NUM
cana-4617	155	7	)	)	PUNCT
cana-4617	155	8	the	the	DET
cana-4617	155	9	initial	initial	ADJ
cana-4617	155	10	four	four	NUM
cana-4617	155	11	l	l	NOUN
cana-4617	155	12	-	-	PUNCT
cana-4617	155	13	moments	moment	NOUN
cana-4617	155	14	can	can	AUX
cana-4617	155	15	be	be	AUX
cana-4617	155	16	obtained	obtain	VERB
cana-4617	155	17	from	from	ADP
cana-4617	155	18	equation	equation	NOUN
cana-4617	155	19	(	(	PUNCT
cana-4617	155	20	14	14	NUM
cana-4617	155	21	)	)	PUNCT
cana-4617	155	22	by	by	ADP
cana-4617	155	23	setting	set	VERB
cana-4617	155	24	r	r	NOUN
cana-4617	155	25	=	=	NOUN
cana-4617	155	26	1,2,3	1,2,3	NUM
cana-4617	155	27	and	and	CCONJ
cana-4617	155	28	4	4	NUM
cana-4617	155	29	respectively	respectively	ADV
cana-4617	155	30	.	.	PUNCT
cana-4617	156	1	using	use	VERB
cana-4617	156	2	equation	equation	NOUN
cana-4617	156	3	(	(	PUNCT
cana-4617	156	4	13	13	NUM
cana-4617	156	5	)	)	PUNCT
cana-4617	156	6	,	,	PUNCT
cana-4617	156	7	some	some	DET
cana-4617	156	8	numerical	numerical	ADJ
cana-4617	156	9	results	result	NOUN
cana-4617	156	10	for	for	ADP
cana-4617	156	11	𝐿1	𝐿1	NOUN
cana-4617	156	12	(	(	PUNCT
cana-4617	156	13	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	14	)	)	PUNCT
cana-4617	156	15	,	,	PUNCT
cana-4617	156	16	𝐿2	𝐿2	PROPN
cana-4617	156	17	(	(	PUNCT
cana-4617	156	18	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	19	)	)	PUNCT
cana-4617	156	20	,	,	PUNCT
cana-4617	156	21	𝐿3	𝐿3	PROPN
cana-4617	156	22	(	(	PUNCT
cana-4617	156	23	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	24	)	)	PUNCT
cana-4617	156	25	𝐿4	𝐿4	PROPN
cana-4617	156	26	(	(	PUNCT
cana-4617	156	27	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	28	)	)	PUNCT
cana-4617	156	29	,	,	PUNCT
cana-4617	156	30	𝐿1	𝐿1	PROPN
cana-4617	156	31	,	,	PUNCT
cana-4617	156	32	𝐿2	𝐿2	PROPN
cana-4617	156	33	,	,	PUNCT
cana-4617	156	34	𝐿3	𝐿3	PROPN
cana-4617	156	35	,	,	PUNCT
cana-4617	156	36	𝐿4	𝐿4	PROPN
cana-4617	156	37	,	,	PUNCT
cana-4617	156	38	𝜏1	𝜏1	NOUN
cana-4617	156	39	(	(	PUNCT
cana-4617	156	40	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	41	)	)	PUNCT
cana-4617	156	42	,	,	PUNCT
cana-4617	156	43	𝜏1	𝜏1	NOUN
cana-4617	156	44	(	(	PUNCT
cana-4617	156	45	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	46	)	)	PUNCT
cana-4617	156	47	,	,	PUNCT
cana-4617	156	48	𝜏3	𝜏3	PROPN
cana-4617	156	49	(	(	PUNCT
cana-4617	156	50	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	51	)	)	PUNCT
cana-4617	156	52	,	,	PUNCT
cana-4617	156	53	𝜏4	𝜏4	PROPN
cana-4617	156	54	(	(	PUNCT
cana-4617	156	55	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	156	56	)	)	PUNCT
cana-4617	156	57	,	,	PUNCT
cana-4617	156	58	𝜏1,𝜏2𝑎𝑛𝑑	𝜏1,𝜏2𝑎𝑛𝑑	NOUN
cana-4617	156	59	𝜏3	𝜏3	NOUN
cana-4617	156	60	are	be	AUX
cana-4617	156	61	obtained	obtain	VERB
cana-4617	156	62	in	in	ADP
cana-4617	156	63	table.3	table.3	PROPN
cana-4617	156	64	.	.	PUNCT
cana-4617	156	65	table	table	NOUN
cana-4617	156	66	3	3	NUM
cana-4617	156	67	(	(	PUNCT
cana-4617	156	68	0,0	0,0	NOUN
cana-4617	156	69	)	)	PUNCT
cana-4617	156	70	(	(	PUNCT
cana-4617	156	71	2,0	2,0	NUM
cana-4617	156	72	)	)	PUNCT
cana-4617	156	73	(	(	PUNCT
cana-4617	156	74	1,0	1,0	NUM
cana-4617	156	75	)	)	PUNCT
cana-4617	156	76	(	(	PUNCT
cana-4617	156	77	0,2	0,2	NUM
cana-4617	156	78	)	)	PUNCT
cana-4617	156	79	(	(	PUNCT
cana-4617	156	80	0,1	0,1	NUM
cana-4617	156	81	)	)	PUNCT
cana-4617	156	82	(	(	PUNCT
cana-4617	156	83	2,2	2,2	NUM
cana-4617	156	84	)	)	PUNCT
cana-4617	156	85	(	(	PUNCT
cana-4617	156	86	1,1	1,1	NUM
cana-4617	156	87	)	)	PUNCT
cana-4617	156	88	(	(	PUNCT
cana-4617	156	89	𝑠	𝑠	PROPN
cana-4617	156	90	,	,	PUNCT
cana-4617	156	91	𝑡	𝑡	NOUN
cana-4617	156	92	)	)	PUNCT
cana-4617	156	93	parameter	parameter	NOUN
cana-4617	156	94	’s	’s	PART
cana-4617	156	95	0.532	0.532	NUM
cana-4617	156	96	0.699	0.699	NUM
cana-4617	156	97	0.64	0.64	NUM
cana-4617	156	98	0.372	0.372	NUM
cana-4617	156	99	0.423	0.423	NUM
cana-4617	156	100	0.522	0.522	NUM
cana-4617	156	101	0.524	0.524	NUM
cana-4617	156	102	𝐿1	𝐿1	PROPN
cana-4617	157	1	(	(	PUNCT
cana-4617	157	2	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	157	3	)	)	PUNCT
cana-4617	157	4	𝛽	𝛽	NOUN
cana-4617	157	5	=	=	NOUN
cana-4617	157	6	0.4	0.4	NUM
cana-4617	157	7	0.109	0.109	NUM
cana-4617	157	8	0.078	0.078	NUM
cana-4617	157	9	0.087	0.087	NUM
cana-4617	157	10	0.063	0.063	NUM
cana-4617	157	11	0.076	0.076	NUM
cana-4617	157	12	0.039	0.039	NUM
cana-4617	157	13	0.058	0.058	NUM
cana-4617	157	14	𝐿2	𝐿2	NOUN
cana-4617	157	15	(	(	PUNCT
cana-4617	157	16	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	157	17	)	)	PUNCT
cana-4617	157	18	0.008	0.008	NUM
cana-4617	157	19	0.015	0.015	NUM
cana-4617	157	20	0.013	0.013	NUM
cana-4617	157	21	-0.006	-0.006	X
cana-4617	157	22	-0.003	-0.003	NOUN
cana-4617	157	23	0.001	0.001	NUM
cana-4617	157	24	0.002	0.002	NUM
cana-4617	157	25	𝐿3	𝐿3	NOUN
cana-4617	157	26	(	(	PUNCT
cana-4617	157	27	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	157	28	)	)	PUNCT
cana-4617	157	29	0.012	0.012	NUM
cana-4617	157	30	0.008	0.008	NUM
cana-4617	157	31	0.009	0.009	NUM
cana-4617	157	32	0.005	0.005	NUM
cana-4617	157	33	0.006	0.006	NUM
cana-4617	157	34	0.001	0.001	NUM
cana-4617	157	35	0.003	0.003	NUM
cana-4617	157	36	𝐿4	𝐿4	NOUN
cana-4617	157	37	(	(	PUNCT
cana-4617	157	38	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	157	39	)	)	PUNCT
cana-4617	157	40	4.89	4.89	NUM
cana-4617	157	41	8.99	8.99	NUM
cana-4617	157	42	7.346	7.346	NUM
cana-4617	157	43	5.94	5.94	NUM
cana-4617	157	44	5.571	5.571	NUM
cana-4617	157	45	13.263	13.263	NUM
cana-4617	157	46	9.067	9.067	NUM
cana-4617	157	47	𝜏1	𝜏1	NOUN
cana-4617	157	48	0.069	0.069	NUM
cana-4617	157	49	0.19	0.19	NUM
cana-4617	157	50	0.152	0.152	NUM
cana-4617	157	51	-0.094	-0.094	PUNCT
cana-4617	157	52	-0.043	-0.043	PUNCT
cana-4617	157	53	0.03	0.03	NUM
cana-4617	157	54	0.042	0.042	NUM
cana-4617	157	55	𝜏3	𝜏3	NOUN
cana-4617	157	56	communications	communication	NOUN
cana-4617	157	57	on	on	ADP
cana-4617	157	58	applied	apply	VERB
cana-4617	157	59	nonlinear	nonlinear	ADJ
cana-4617	157	60	analysis	analysis	NOUN
cana-4617	157	61	issn	issn	NOUN
cana-4617	157	62	:	:	PUNCT
cana-4617	157	63	1074	1074	NUM
cana-4617	157	64	-	-	PUNCT
cana-4617	157	65	133x	133x	NUM
cana-4617	157	66	vol	vol	NOUN
cana-4617	157	67	32	32	NUM
cana-4617	157	68	no	no	NOUN
cana-4617	157	69	.	.	PUNCT
cana-4617	158	1	9s	9s	NUM
cana-4617	158	2	(	(	PUNCT
cana-4617	158	3	2025	2025	NUM
cana-4617	158	4	)	)	PUNCT
cana-4617	158	5	3028	3028	NUM
cana-4617	158	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	158	7	0.114	0.114	NUM
cana-4617	158	8	0.108	0.108	NUM
cana-4617	158	9	0.106	0.106	NUM
cana-4617	158	10	0.076	0.076	NUM
cana-4617	158	11	0.082	0.082	NUM
cana-4617	158	12	0.036	0.036	NUM
cana-4617	158	13	0.059	0.059	NUM
cana-4617	158	14	𝜏4	𝜏4	NOUN
cana-4617	158	15	0.798	0.798	NUM
cana-4617	158	16	1.048	1.048	NUM
cana-4617	158	17	0.961	0.961	NUM
cana-4617	158	18	0.559	0.559	NUM
cana-4617	158	19	0.634	0.634	NUM
cana-4617	158	20	0.783	0.783	NUM
cana-4617	158	21	0.786	0.786	NUM
cana-4617	158	22	𝐿1	𝐿1	NOUN
cana-4617	158	23	(	(	PUNCT
cana-4617	158	24	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	158	25	)	)	PUNCT
cana-4617	158	26	𝛽	𝛽	NOUN
cana-4617	158	27	=	=	SYM
cana-4617	158	28	0.6	0.6	NUM
cana-4617	158	29	0.163	0.163	NUM
cana-4617	158	30	0.117	0.117	NUM
cana-4617	158	31	0.131	0.131	NUM
cana-4617	158	32	0.094	0.094	NUM
cana-4617	158	33	0.114	0.114	NUM
cana-4617	158	34	0.059	0.059	NUM
cana-4617	158	35	0.087	0.087	NUM
cana-4617	158	36	𝐿2	𝐿2	NOUN
cana-4617	158	37	(	(	PUNCT
cana-4617	158	38	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	158	39	)	)	PUNCT
cana-4617	158	40	0.011	0.011	NUM
cana-4617	158	41	0.022	0.022	NUM
cana-4617	158	42	0.02	0.02	NUM
cana-4617	158	43	-0.009	-0.009	NUM
cana-4617	158	44	-0.005	-0.005	PUNCT
cana-4617	158	45	0.002	0.002	NUM
cana-4617	158	46	0.004	0.004	NUM
cana-4617	158	47	𝐿3	𝐿3	NOUN
cana-4617	158	48	(	(	PUNCT
cana-4617	158	49	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	158	50	)	)	PUNCT
cana-4617	158	51	0.019	0.019	NUM
cana-4617	158	52	0.013	0.013	NUM
cana-4617	158	53	0.014	0.014	NUM
cana-4617	158	54	0.007	0.007	NUM
cana-4617	158	55	0.009	0.009	NUM
cana-4617	158	56	0.002	0.002	NUM
cana-4617	158	57	0.005	0.005	NUM
cana-4617	158	58	𝐿4	𝐿4	NOUN
cana-4617	158	59	(	(	PUNCT
cana-4617	158	60	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	158	61	)	)	PUNCT
cana-4617	158	62	4.89	4.89	NUM
cana-4617	158	63	8.99	8.99	NUM
cana-4617	158	64	7.346	7.346	NUM
cana-4617	158	65	5.94	5.94	NUM
cana-4617	158	66	5.571	5.571	NUM
cana-4617	158	67	13.263	13.263	NUM
cana-4617	158	68	9.067	9.067	NUM
cana-4617	158	69	𝜏1	𝜏1	NOUN
cana-4617	158	70	0.069	0.069	NUM
cana-4617	158	71	0.19	0.19	NUM
cana-4617	158	72	0.152	0.152	NUM
cana-4617	158	73	-0.094	-0.094	PUNCT
cana-4617	158	74	-0.043	-0.043	PUNCT
cana-4617	158	75	0.03	0.03	NUM
cana-4617	158	76	0.042	0.042	NUM
cana-4617	158	77	𝜏3	𝜏3	NOUN
cana-4617	158	78	0.114	0.114	NUM
cana-4617	158	79	0.108	0.108	NUM
cana-4617	158	80	0.106	0.106	NUM
cana-4617	158	81	0.076	0.076	NUM
cana-4617	158	82	0.082	0.082	NUM
cana-4617	158	83	0.036	0.036	NUM
cana-4617	158	84	0.059	0.059	NUM
cana-4617	158	85	𝜏4	𝜏4	NOUN
cana-4617	158	86	1.063	1.063	NUM
cana-4617	158	87	1.397	1.397	NUM
cana-4617	158	88	1.281	1.281	NUM
cana-4617	158	89	0.745	0.745	NUM
cana-4617	158	90	0.846	0.846	NUM
cana-4617	158	91	1.044	1.044	NUM
cana-4617	158	92	1.048	1.048	NUM
cana-4617	158	93	𝐿1	𝐿1	NOUN
cana-4617	159	1	(	(	PUNCT
cana-4617	159	2	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	159	3	)	)	PUNCT
cana-4617	159	4	𝛽	𝛽	NOUN
cana-4617	159	5	=	=	NOUN
cana-4617	159	6	0.8	0.8	NUM
cana-4617	159	7	0.217	0.217	NUM
cana-4617	159	8	0.155	0.155	NUM
cana-4617	159	9	0.174	0.174	NUM
cana-4617	159	10	0.125	0.125	NUM
cana-4617	159	11	0.152	0.152	NUM
cana-4617	159	12	0.079	0.079	NUM
cana-4617	159	13	0.116	0.116	NUM
cana-4617	159	14	𝐿2	𝐿2	PROPN
cana-4617	159	15	(	(	PUNCT
cana-4617	159	16	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	159	17	)	)	PUNCT
cana-4617	159	18	0.015	0.015	NUM
cana-4617	159	19	0.03	0.03	NUM
cana-4617	159	20	0.027	0.027	NUM
cana-4617	159	21	-0.012	-0.012	NUM
cana-4617	159	22	-0.006	-0.006	PROPN
cana-4617	159	23	0.002	0.002	NUM
cana-4617	159	24	0.005	0.005	NUM
cana-4617	159	25	𝐿3	𝐿3	NOUN
cana-4617	159	26	(	(	PUNCT
cana-4617	159	27	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	159	28	)	)	PUNCT
cana-4617	159	29	0.025	0.025	NUM
cana-4617	159	30	0.017	0.017	NUM
cana-4617	159	31	0.018	0.018	NUM
cana-4617	159	32	0.0095	0.0095	NUM
cana-4617	159	33	0.012	0.012	NUM
cana-4617	159	34	0.003	0.003	NUM
cana-4617	159	35	0.007	0.007	NUM
cana-4617	159	36	𝐿4	𝐿4	NOUN
cana-4617	159	37	(	(	PUNCT
cana-4617	159	38	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	159	39	)	)	PUNCT
cana-4617	159	40	4.89	4.89	NUM
cana-4617	159	41	8.99	8.99	NUM
cana-4617	159	42	7.346	7.346	NUM
cana-4617	159	43	5.94	5.94	NUM
cana-4617	159	44	5.571	5.571	NUM
cana-4617	159	45	13.263	13.263	NUM
cana-4617	159	46	9.067	9.067	NUM
cana-4617	159	47	𝜏1	𝜏1	NOUN
cana-4617	159	48	0.069	0.069	NUM
cana-4617	159	49	0.19	0.19	NUM
cana-4617	159	50	0.152	0.152	NUM
cana-4617	159	51	-0.094	-0.094	PUNCT
cana-4617	159	52	-0.043	-0.043	PUNCT
cana-4617	159	53	0.03	0.03	NUM
cana-4617	159	54	0.042	0.042	NUM
cana-4617	159	55	𝜏3	𝜏3	NOUN
cana-4617	159	56	0.114	0.114	NUM
cana-4617	159	57	0.108	0.108	NUM
cana-4617	159	58	0.106	0.106	NUM
cana-4617	159	59	0.076	0.076	NUM
cana-4617	159	60	0.082	0.082	NUM
cana-4617	159	61	0.036	0.036	NUM
cana-4617	159	62	0.05	0.05	NUM
cana-4617	159	63	𝜏4	𝜏4	NOUN
cana-4617	159	64	1.329	1.329	NUM
cana-4617	159	65	1.747	1.747	NUM
cana-4617	159	66	1.601	1.601	NUM
cana-4617	159	67	0.931	0.931	NUM
cana-4617	159	68	1.057	1.057	NUM
cana-4617	159	69	1.305	1.305	NUM
cana-4617	159	70	1.311	1.311	NUM
cana-4617	159	71	𝐿1	𝐿1	NOUN
cana-4617	159	72	(	(	PUNCT
cana-4617	159	73	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	159	74	)	)	PUNCT
cana-4617	159	75	𝛽	𝛽	NOUN
cana-4617	159	76	=	=	SYM
cana-4617	159	77	1	1	NUM
cana-4617	159	78	0.272	0.272	NUM
cana-4617	159	79	0.194	0.194	NUM
cana-4617	159	80	0.218	0.218	NUM
cana-4617	159	81	0.157	0.157	NUM
cana-4617	159	82	0.19	0.19	NUM
cana-4617	159	83	0.098	0.098	NUM
cana-4617	159	84	0.145	0.145	NUM
cana-4617	160	1	𝐿2	𝐿2	NOUN
cana-4617	161	1	(	(	PUNCT
cana-4617	161	2	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	3	)	)	PUNCT
cana-4617	161	4	0.019	0.019	NUM
cana-4617	161	5	0.037	0.037	NUM
cana-4617	161	6	0.033	0.033	NUM
cana-4617	161	7	-0.015	-0.015	PUNCT
cana-4617	161	8	-0.008	-0.008	NOUN
cana-4617	161	9	0.003	0.003	NUM
cana-4617	161	10	0.006	0.006	NUM
cana-4617	161	11	𝐿3	𝐿3	NOUN
cana-4617	161	12	(	(	PUNCT
cana-4617	161	13	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	14	)	)	PUNCT
cana-4617	161	15	0.031	0.031	NUM
cana-4617	161	16	0.021	0.021	NUM
cana-4617	161	17	0.023	0.023	NUM
cana-4617	161	18	0.012	0.012	NUM
cana-4617	161	19	0.016	0.016	NUM
cana-4617	161	20	0.004	0.004	NUM
cana-4617	161	21	0.008	0.008	NUM
cana-4617	161	22	𝐿4	𝐿4	NOUN
cana-4617	161	23	(	(	PUNCT
cana-4617	161	24	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	25	)	)	PUNCT
cana-4617	161	26	4.89	4.89	NUM
cana-4617	161	27	8.99	8.99	NUM
cana-4617	161	28	7.346	7.346	NUM
cana-4617	161	29	5.94	5.94	NUM
cana-4617	161	30	5.571	5.571	NUM
cana-4617	161	31	13.263	13.263	NUM
cana-4617	161	32	9.067	9.067	NUM
cana-4617	161	33	𝜏1	𝜏1	NOUN
cana-4617	161	34	0.069	0.069	NUM
cana-4617	161	35	0.19	0.19	NUM
cana-4617	161	36	0.152	0.152	NUM
cana-4617	161	37	-0.094	-0.094	PUNCT
cana-4617	161	38	-0.043	-0.043	PUNCT
cana-4617	161	39	0.03	0.03	NUM
cana-4617	161	40	0.042	0.042	NUM
cana-4617	161	41	𝜏3	𝜏3	NOUN
cana-4617	161	42	0.114	0.114	NUM
cana-4617	161	43	0.108	0.108	NUM
cana-4617	161	44	0.106	0.106	NUM
cana-4617	161	45	0.076	0.076	NUM
cana-4617	161	46	0.082	0.082	NUM
cana-4617	161	47	0.036	0.036	NUM
cana-4617	161	48	0.059	0.059	NUM
cana-4617	161	49	𝜏4	𝜏4	PROPN
cana-4617	161	50	1.728	1.728	NUM
cana-4617	161	51	2.27	2.27	NUM
cana-4617	161	52	2.082	2.082	NUM
cana-4617	161	53	1.21	1.21	NUM
cana-4617	161	54	1.375	1.375	NUM
cana-4617	161	55	1.697	1.697	NUM
cana-4617	161	56	1.704	1.704	NUM
cana-4617	161	57	𝐿1	𝐿1	NOUN
cana-4617	161	58	(	(	PUNCT
cana-4617	161	59	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	60	)	)	PUNCT
cana-4617	161	61	𝛽	𝛽	NOUN
cana-4617	161	62	=	=	NOUN
cana-4617	161	63	1.3	1.3	NUM
cana-4617	161	64	0.353	0.353	NUM
cana-4617	161	65	0.253	0.253	NUM
cana-4617	161	66	0.283	0.283	NUM
cana-4617	161	67	0.204	0.204	NUM
cana-4617	161	68	0.247	0.247	NUM
cana-4617	161	69	0.128	0.128	NUM
cana-4617	161	70	0.188	0.188	NUM
cana-4617	161	71	𝐿2	𝐿2	NOUN
cana-4617	161	72	(	(	PUNCT
cana-4617	161	73	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	74	)	)	PUNCT
cana-4617	161	75	0.024	0.024	NUM
cana-4617	161	76	0.048	0.048	NUM
cana-4617	161	77	0.043	0.043	NUM
cana-4617	161	78	-0.019	-0.019	PUNCT
cana-4617	161	79	-0.011	-0.011	NUM
cana-4617	161	80	0.004	0.004	NUM
cana-4617	161	81	0.008	0.008	NUM
cana-4617	161	82	𝐿3	𝐿3	NOUN
cana-4617	161	83	(	(	PUNCT
cana-4617	161	84	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	85	)	)	PUNCT
cana-4617	161	86	0.04	0.04	NUM
cana-4617	161	87	0.027	0.027	NUM
cana-4617	161	88	0.03	0.03	NUM
cana-4617	161	89	0.015	0.015	NUM
cana-4617	161	90	0.02	0.02	NUM
cana-4617	161	91	0.005	0.005	NUM
cana-4617	161	92	0.011	0.011	NUM
cana-4617	161	93	𝐿4	𝐿4	NOUN
cana-4617	161	94	(	(	PUNCT
cana-4617	161	95	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	96	)	)	PUNCT
cana-4617	161	97	4.89	4.89	NUM
cana-4617	161	98	8.99	8.99	NUM
cana-4617	161	99	7.346	7.346	NUM
cana-4617	161	100	5.94	5.94	NUM
cana-4617	161	101	5.571	5.571	NUM
cana-4617	161	102	13.263	13.263	NUM
cana-4617	161	103	9.067	9.067	NUM
cana-4617	161	104	𝜏1	𝜏1	NOUN
cana-4617	161	105	0.069	0.069	NUM
cana-4617	161	106	0.19	0.19	NUM
cana-4617	161	107	0.152	0.152	NUM
cana-4617	161	108	-0.094	-0.094	PUNCT
cana-4617	161	109	-0.043	-0.043	PUNCT
cana-4617	161	110	0.03	0.03	NUM
cana-4617	161	111	0.042	0.042	NUM
cana-4617	161	112	𝜏3	𝜏3	NOUN
cana-4617	161	113	0.114	0.114	NUM
cana-4617	161	114	0.108	0.108	NUM
cana-4617	161	115	0.106	0.106	NUM
cana-4617	161	116	0.076	0.076	NUM
cana-4617	161	117	0.082	0.082	NUM
cana-4617	161	118	0.036	0.036	NUM
cana-4617	161	119	0.059	0.059	NUM
cana-4617	161	120	𝜏4	𝜏4	NOUN
cana-4617	161	121	1.994	1.994	NUM
cana-4617	161	122	2.62	2.62	NUM
cana-4617	161	123	2.402	2.402	NUM
cana-4617	161	124	1.396	1.396	NUM
cana-4617	161	125	1.586	1.586	NUM
cana-4617	161	126	1.958	1.958	NUM
cana-4617	161	127	1.966	1.966	NUM
cana-4617	161	128	𝐿1	𝐿1	PROPN
cana-4617	161	129	(	(	PUNCT
cana-4617	161	130	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	131	)	)	PUNCT
cana-4617	161	132	𝛽	𝛽	NOUN
cana-4617	161	133	=	=	NOUN
cana-4617	161	134	1.5	1.5	NUM
cana-4617	161	135	0.408	0.408	NUM
cana-4617	161	136	0.291	0.291	NUM
cana-4617	161	137	0.327	0.327	NUM
cana-4617	161	138	0.235	0.235	NUM
cana-4617	161	139	0.285	0.285	NUM
cana-4617	161	140	0.148	0.148	NUM
cana-4617	161	141	0.217	0.217	NUM
cana-4617	161	142	𝐿2	𝐿2	PROPN
cana-4617	161	143	(	(	PUNCT
cana-4617	161	144	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	145	)	)	PUNCT
cana-4617	161	146	0.028	0.028	NUM
cana-4617	161	147	0.055	0.055	NUM
cana-4617	161	148	0.05	0.05	NUM
cana-4617	161	149	-0.022	-0.022	NUM
cana-4617	161	150	-0.012	-0.012	NUM
cana-4617	161	151	0.004	0.004	NUM
cana-4617	161	152	0.009	0.009	NUM
cana-4617	161	153	𝐿3	𝐿3	NOUN
cana-4617	161	154	(	(	PUNCT
cana-4617	161	155	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	156	)	)	PUNCT
cana-4617	161	157	0.046	0.046	NUM
cana-4617	161	158	0.031	0.031	NUM
cana-4617	161	159	0.035	0.035	NUM
cana-4617	161	160	0.018	0.018	NUM
cana-4617	161	161	0.023	0.023	NUM
cana-4617	161	162	0.005	0.005	NUM
cana-4617	161	163	0.013	0.013	NUM
cana-4617	161	164	𝐿4	𝐿4	NOUN
cana-4617	161	165	(	(	PUNCT
cana-4617	161	166	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	161	167	)	)	PUNCT
cana-4617	161	168	4.89	4.89	NUM
cana-4617	161	169	8.99	8.99	NUM
cana-4617	161	170	7.346	7.346	NUM
cana-4617	161	171	5.94	5.94	NUM
cana-4617	161	172	5.571	5.571	NUM
cana-4617	161	173	13.263	13.263	NUM
cana-4617	161	174	9.067	9.067	NUM
cana-4617	161	175	𝜏1	𝜏1	NOUN
cana-4617	161	176	0.069	0.069	NUM
cana-4617	161	177	0.19	0.19	NUM
cana-4617	161	178	0.152	0.152	NUM
cana-4617	161	179	-0.094	-0.094	PUNCT
cana-4617	161	180	-0.043	-0.043	PUNCT
cana-4617	161	181	0.03	0.03	NUM
cana-4617	161	182	0.042	0.042	NUM
cana-4617	161	183	𝜏3	𝜏3	NOUN
cana-4617	161	184	0.114	0.114	NUM
cana-4617	161	185	0.108	0.108	NUM
cana-4617	161	186	0.106	0.106	NUM
cana-4617	161	187	0.076	0.076	NUM
cana-4617	161	188	0.082	0.082	NUM
cana-4617	161	189	0.036	0.036	NUM
cana-4617	161	190	0.059	0.059	NUM
cana-4617	161	191	𝜏4	𝜏4	ADJ
cana-4617	161	192	communications	communication	NOUN
cana-4617	161	193	on	on	ADP
cana-4617	161	194	applied	apply	VERB
cana-4617	161	195	nonlinear	nonlinear	ADJ
cana-4617	161	196	analysis	analysis	NOUN
cana-4617	161	197	issn	issn	NOUN
cana-4617	161	198	:	:	PUNCT
cana-4617	161	199	1074	1074	NUM
cana-4617	161	200	-	-	PUNCT
cana-4617	161	201	133x	133x	NUM
cana-4617	161	202	vol	vol	NOUN
cana-4617	161	203	32	32	NUM
cana-4617	161	204	no	no	NOUN
cana-4617	161	205	.	.	PUNCT
cana-4617	162	1	9s	9s	NUM
cana-4617	162	2	(	(	PUNCT
cana-4617	162	3	2025	2025	NUM
cana-4617	162	4	)	)	PUNCT
cana-4617	162	5	3029	3029	NUM
cana-4617	162	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	162	7	2.659	2.659	NUM
cana-4617	162	8	3.493	3.493	NUM
cana-4617	162	9	3.202	3.202	NUM
cana-4617	162	10	1.862	1.862	NUM
cana-4617	162	11	2.115	2.115	NUM
cana-4617	162	12	2.61	2.61	NUM
cana-4617	162	13	2.621	2.621	NUM
cana-4617	162	14	𝐿1	𝐿1	NOUN
cana-4617	162	15	(	(	PUNCT
cana-4617	162	16	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	162	17	)	)	PUNCT
cana-4617	162	18	𝛽	𝛽	NOUN
cana-4617	162	19	=	=	SYM
cana-4617	162	20	2	2	NUM
cana-4617	162	21	0.544	0.544	NUM
cana-4617	162	22	0.389	0.389	NUM
cana-4617	162	23	0.436	0.436	NUM
cana-4617	162	24	0.313	0.313	NUM
cana-4617	162	25	0.38	0.38	NUM
cana-4617	162	26	0.197	0.197	NUM
cana-4617	162	27	0.289	0.289	NUM
cana-4617	162	28	𝐿2	𝐿2	PROPN
cana-4617	162	29	(	(	PUNCT
cana-4617	162	30	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	162	31	)	)	PUNCT
cana-4617	162	32	0.038	0.038	NUM
cana-4617	162	33	0.074	0.074	NUM
cana-4617	162	34	0.066	0.066	NUM
cana-4617	162	35	-0.029	-0.029	NOUN
cana-4617	162	36	-0.016	-0.016	ADP
cana-4617	162	37	0.006	0.006	NUM
cana-4617	162	38	0.012	0.012	NUM
cana-4617	162	39	𝐿3	𝐿3	NOUN
cana-4617	162	40	(	(	PUNCT
cana-4617	162	41	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	162	42	)	)	PUNCT
cana-4617	162	43	0.062	0.062	NUM
cana-4617	162	44	0.042	0.042	NUM
cana-4617	162	45	0.046	0.046	NUM
cana-4617	162	46	0.024	0.024	NUM
cana-4617	162	47	0.031	0.031	NUM
cana-4617	162	48	0.007	0.007	NUM
cana-4617	162	49	0.017	0.017	NUM
cana-4617	162	50	𝐿4	𝐿4	NOUN
cana-4617	162	51	(	(	PUNCT
cana-4617	162	52	𝑠,𝑡	𝑠,𝑡	NOUN
cana-4617	162	53	)	)	PUNCT
cana-4617	162	54	4.89	4.89	NUM
cana-4617	162	55	8.99	8.99	NUM
cana-4617	162	56	7.346	7.346	NUM
cana-4617	162	57	5.94	5.94	NUM
cana-4617	162	58	5.571	5.571	NUM
cana-4617	162	59	13.263	13.263	NUM
cana-4617	162	60	9.067	9.067	NUM
cana-4617	162	61	𝜏1	𝜏1	NOUN
cana-4617	162	62	0.069	0.069	NUM
cana-4617	162	63	0.19	0.19	NUM
cana-4617	162	64	0.152	0.152	NUM
cana-4617	162	65	-0.094	-0.094	PUNCT
cana-4617	162	66	-0.043	-0.043	PUNCT
cana-4617	162	67	0.03	0.03	NUM
cana-4617	162	68	0.042	0.042	NUM
cana-4617	162	69	𝜏3	𝜏3	NOUN
cana-4617	162	70	0.114	0.114	NUM
cana-4617	162	71	0.108	0.108	NUM
cana-4617	162	72	0.106	0.106	NUM
cana-4617	162	73	0.076	0.076	NUM
cana-4617	162	74	0.082	0.082	NUM
cana-4617	162	75	0.036	0.036	NUM
cana-4617	162	76	0.059	0.059	NUM
cana-4617	162	77	𝜏4	𝜏4	NOUN
cana-4617	162	78	theorem	theorem	VERB
cana-4617	162	79	2.1	2.1	NUM
cana-4617	162	80	.	.	PUNCT
cana-4617	163	1	let	let	VERB
cana-4617	163	2	z	z	PRON
cana-4617	163	3	be	be	AUX
cana-4617	163	4	a	a	DET
cana-4617	163	5	random	random	ADJ
cana-4617	163	6	variable	variable	NOUN
cana-4617	163	7	has	have	VERB
cana-4617	163	8	a	a	DET
cana-4617	163	9	probability	probability	NOUN
cana-4617	163	10	density	density	NOUN
cana-4617	163	11	function	function	NOUN
cana-4617	163	12	given	give	VERB
cana-4617	163	13	by	by	ADP
cana-4617	163	14	equation	equation	NOUN
cana-4617	163	15	(	(	PUNCT
cana-4617	163	16	1	1	NUM
cana-4617	163	17	)	)	PUNCT
cana-4617	163	18	.	.	PUNCT
cana-4617	164	1	for	for	ADP
cana-4617	164	2	an	an	DET
cana-4617	164	3	integer	integer	NOUN
cana-4617	164	4	j	j	PROPN
cana-4617	164	5	such	such	ADJ
cana-4617	164	6	that	that	SCONJ
cana-4617	164	7	j	j	PROPN
cana-4617	164	8	>	>	X
cana-4617	164	9	0	0	PROPN
cana-4617	164	10	,	,	PUNCT
cana-4617	164	11	the	the	DET
cana-4617	164	12	moments	moment	NOUN
cana-4617	164	13	of	of	ADP
cana-4617	164	14	z	z	NOUN
cana-4617	164	15	satisfy	satisfy	VERB
cana-4617	164	16	the	the	DET
cana-4617	164	17	following	follow	VERB
cana-4617	164	18	recurrence	recurrence	NOUN
cana-4617	164	19	relation	relation	PROPN
cana-4617	164	20	:	:	PUNCT
cana-4617	164	21	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	164	22	,	,	PUNCT
cana-4617	164	23	𝑛	𝑛	PROPN
cana-4617	164	24	,	,	PUNCT
cana-4617	164	25	�	�	PROPN
cana-4617	164	26	̃	̃	PROPN
cana-4617	164	27	�	�	PROPN
cana-4617	164	28	,	,	PUNCT
cana-4617	164	29	𝑘	𝑘	NOUN
cana-4617	164	30	)	)	PUNCT
cana-4617	164	31	]	]	PUNCT
cana-4617	164	32	−	−	PROPN
cana-4617	164	33	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	164	34	−	−	PROPN
cana-4617	164	35	1	1	NUM
cana-4617	164	36	,	,	PUNCT
cana-4617	164	37	𝑛	𝑛	PROPN
cana-4617	164	38	,	,	PUNCT
cana-4617	164	39	�	�	PROPN
cana-4617	164	40	̃	̃	PROPN
cana-4617	164	41	�	�	PROPN
cana-4617	164	42	,	,	PUNCT
cana-4617	164	43	𝑘	𝑘	NOUN
cana-4617	164	44	)	)	PUNCT
cana-4617	164	45	]	]	PUNCT
cana-4617	165	1	=	=	PUNCT
cana-4617	165	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	165	3	2𝛾𝑟	2𝛾𝑟	NOUN
cana-4617	165	4	{	{	PUNCT
cana-4617	165	5	𝐸[𝑍𝑗−2(𝑟	𝐸[𝑍𝑗−2(𝑟	NOUN
cana-4617	165	6	,	,	PUNCT
cana-4617	165	7	𝑛	𝑛	PROPN
cana-4617	165	8	,	,	PUNCT
cana-4617	165	9	�	�	PROPN
cana-4617	165	10	̃	̃	PROPN
cana-4617	165	11	�	�	PROPN
cana-4617	165	12	,	,	PUNCT
cana-4617	165	13	𝑘	𝑘	NOUN
cana-4617	165	14	)	)	PUNCT
cana-4617	165	15	]	]	PUNCT
cana-4617	166	1	+	+	CCONJ
cana-4617	166	2	𝛽2𝐸[𝑍𝑗−4(𝑟	𝛽2𝐸[𝑍𝑗−4(𝑟	ADJ
cana-4617	166	3	,	,	PUNCT
cana-4617	166	4	𝑛	𝑛	PROPN
cana-4617	166	5	,	,	PUNCT
cana-4617	166	6	�	�	PROPN
cana-4617	166	7	̃	̃	PROPN
cana-4617	166	8	�	�	PROPN
cana-4617	166	9	,	,	PUNCT
cana-4617	166	10	𝑘	𝑘	NOUN
cana-4617	166	11	)	)	PUNCT
cana-4617	166	12	]	]	PUNCT
cana-4617	166	13	}	}	PUNCT
cana-4617	166	14	(	(	PUNCT
cana-4617	166	15	15	15	X
cana-4617	166	16	)	)	PUNCT
cana-4617	166	17	proof	proof	NOUN
cana-4617	166	18	.	.	PUNCT
cana-4617	167	1	we	we	PRON
cana-4617	167	2	have	have	VERB
cana-4617	167	3	from	from	ADP
cana-4617	167	4	lemma	lemma	PROPN
cana-4617	167	5	2.3	2.3	NUM
cana-4617	167	6	(	(	PUNCT
cana-4617	167	7	by	by	ADP
cana-4617	167	8	athar	athar	PROPN
cana-4617	167	9	.	.	PUNCT
cana-4617	168	1	and	and	CCONJ
cana-4617	168	2	islam	islam	PROPN
cana-4617	168	3	.	.	PUNCT
cana-4617	169	1	(	(	PUNCT
cana-4617	169	2	2004	2004	NUM
cana-4617	169	3	)	)	PUNCT
cana-4617	169	4	)	)	PUNCT
cana-4617	170	1	that	that	DET
cana-4617	170	2	𝐸[𝜉{𝑍(𝑟	𝐸[𝜉{𝑍(𝑟	NOUN
cana-4617	170	3	,	,	PUNCT
cana-4617	170	4	𝑛	𝑛	PROPN
cana-4617	170	5	,	,	PUNCT
cana-4617	170	6	�	�	PROPN
cana-4617	170	7	̃	̃	PROPN
cana-4617	170	8	�	�	PROPN
cana-4617	170	9	,	,	PUNCT
cana-4617	170	10	𝑘	𝑘	NOUN
cana-4617	170	11	)	)	PUNCT
cana-4617	170	12	}	}	PUNCT
cana-4617	170	13	]	]	PUNCT
cana-4617	170	14	−	−	PUNCT
cana-4617	170	15	𝐸[𝜉{𝑍(𝑟	𝐸[𝜉{𝑍(𝑟	NOUN
cana-4617	170	16	−	−	NOUN
cana-4617	170	17	1	1	NUM
cana-4617	170	18	,	,	PUNCT
cana-4617	170	19	𝑛	𝑛	PROPN
cana-4617	170	20	,	,	PUNCT
cana-4617	170	21	�	�	PROPN
cana-4617	170	22	̃	̃	PROPN
cana-4617	170	23	�	�	PROPN
cana-4617	170	24	,	,	PUNCT
cana-4617	170	25	𝑘	𝑘	NOUN
cana-4617	170	26	)	)	PUNCT
cana-4617	170	27	}	}	PUNCT
cana-4617	170	28	]	]	PUNCT
cana-4617	171	1	=	=	SYM
cana-4617	171	2	𝐶𝑟−2	𝐶𝑟−2	PROPN
cana-4617	171	3	∫	∫	PROPN
cana-4617	171	4	𝜉	𝜉	X
cana-4617	171	5	‘	'	PUNCT
cana-4617	171	6	(	(	PUNCT
cana-4617	171	7	𝑧	𝑧	NOUN
cana-4617	171	8	)	)	PUNCT
cana-4617	171	9	𝛽	𝛽	NOUN
cana-4617	171	10	𝜃	𝜃	NOUN
cana-4617	171	11	∑	∑	PUNCT
cana-4617	171	12	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NUM
cana-4617	171	13	)	)	PUNCT
cana-4617	171	14	𝑟	𝑟	X
cana-4617	171	15	𝑖=1	𝑖=1	PUNCT
cana-4617	172	1	[	[	X
cana-4617	172	2	�	�	NOUN
cana-4617	172	3	̅	̅	NOUN
cana-4617	172	4	�	�	NOUN
cana-4617	172	5	(𝑧)]𝛾𝑖	(𝑧)]𝛾𝑖	NOUN
cana-4617	172	6	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	172	7	if	if	SCONJ
cana-4617	172	8	we	we	PRON
cana-4617	172	9	let	let	VERB
cana-4617	172	10	𝜉(𝑧	𝜉(𝑧	PRON
cana-4617	172	11	)	)	PUNCT
cana-4617	173	1	=	=	PUNCT
cana-4617	173	2	𝑧𝑗	𝑧𝑗	INTJ
cana-4617	173	3	,	,	PUNCT
cana-4617	173	4	then	then	ADV
cana-4617	173	5	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NUM
cana-4617	173	6	,	,	PUNCT
cana-4617	173	7	𝑛	𝑛	PROPN
cana-4617	173	8	,	,	PUNCT
cana-4617	173	9	�	�	PROPN
cana-4617	173	10	̃	̃	PROPN
cana-4617	173	11	�	�	PROPN
cana-4617	173	12	,	,	PUNCT
cana-4617	173	13	𝑘	𝑘	NOUN
cana-4617	173	14	)	)	PUNCT
cana-4617	173	15	]	]	PUNCT
cana-4617	174	1	−	−	PROPN
cana-4617	174	2	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	174	3	−	−	PROPN
cana-4617	174	4	1	1	NUM
cana-4617	174	5	,	,	PUNCT
cana-4617	174	6	𝑛	𝑛	PROPN
cana-4617	174	7	,	,	PUNCT
cana-4617	174	8	�	�	PROPN
cana-4617	174	9	̃	̃	PROPN
cana-4617	174	10	�	�	PROPN
cana-4617	174	11	,	,	PUNCT
cana-4617	174	12	𝑘	𝑘	NOUN
cana-4617	174	13	)	)	PUNCT
cana-4617	174	14	]	]	PUNCT
cana-4617	175	1	=	=	PUNCT
cana-4617	175	2	𝑗𝐶𝑟−2	𝑗𝐶𝑟−2	NOUN
cana-4617	175	3	∫	∫	PROPN
cana-4617	175	4	𝑧𝑗−1	𝑧𝑗−1	PROPN
cana-4617	175	5	𝛽	𝛽	PROPN
cana-4617	175	6	𝜃	𝜃	NOUN
cana-4617	175	7	∑	∑	PUNCT
cana-4617	175	8	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NUM
cana-4617	175	9	)	)	PUNCT
cana-4617	175	10	𝑟	𝑟	X
cana-4617	175	11	𝑖=1	𝑖=1	PUNCT
cana-4617	176	1	[	[	X
cana-4617	176	2	�	�	NOUN
cana-4617	176	3	̅	̅	NOUN
cana-4617	176	4	�	�	NOUN
cana-4617	176	5	(𝑧)]𝛾𝑖	(𝑧)]𝛾𝑖	NOUN
cana-4617	176	6	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	176	7	(	(	PUNCT
cana-4617	176	8	16	16	NUM
cana-4617	176	9	)	)	PUNCT
cana-4617	176	10	on	on	ADP
cana-4617	176	11	using	use	VERB
cana-4617	176	12	(	(	PUNCT
cana-4617	176	13	3	3	NUM
cana-4617	176	14	)	)	PUNCT
cana-4617	176	15	in	in	ADP
cana-4617	176	16	(	(	PUNCT
cana-4617	176	17	16	16	NUM
cana-4617	176	18	)	)	PUNCT
cana-4617	176	19	,	,	PUNCT
cana-4617	176	20	we	we	PRON
cana-4617	176	21	get	get	VERB
cana-4617	176	22	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	176	23	,	,	PUNCT
cana-4617	176	24	𝑛	𝑛	PROPN
cana-4617	176	25	,	,	PUNCT
cana-4617	176	26	�	�	PROPN
cana-4617	176	27	̃	̃	PROPN
cana-4617	176	28	�	�	PROPN
cana-4617	176	29	,	,	PUNCT
cana-4617	176	30	𝑘	𝑘	NOUN
cana-4617	176	31	)	)	PUNCT
cana-4617	176	32	]	]	PUNCT
cana-4617	177	1	−	−	PROPN
cana-4617	177	2	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	177	3	−	−	PROPN
cana-4617	177	4	1	1	NUM
cana-4617	177	5	,	,	PUNCT
cana-4617	177	6	𝑛	𝑛	PROPN
cana-4617	177	7	,	,	PUNCT
cana-4617	177	8	�	�	PROPN
cana-4617	177	9	̃	̃	PROPN
cana-4617	177	10	�	�	PROPN
cana-4617	177	11	,	,	PUNCT
cana-4617	177	12	𝑘	𝑘	NOUN
cana-4617	177	13	)	)	PUNCT
cana-4617	177	14	]	]	PUNCT
cana-4617	178	1	=	=	PUNCT
cana-4617	178	2	𝑗𝐶𝑟−1	𝑗𝐶𝑟−1	VERB
cana-4617	178	3	𝛾𝑟	𝛾𝑟	ADP
cana-4617	178	4	∫	∫	PROPN
cana-4617	178	5	𝑧𝑗−1	𝑧𝑗−1	PROPN
cana-4617	178	6	(	(	PUNCT
cana-4617	178	7	𝛽2	𝛽2	ADJ
cana-4617	178	8	2𝑧	2𝑧	NOUN
cana-4617	178	9	+	+	CCONJ
cana-4617	178	10	𝛽4	𝛽4	PROPN
cana-4617	178	11	2𝑧3	2𝑧3	NUM
cana-4617	178	12	)	)	PUNCT
cana-4617	179	1	∞	∞	NUM
cana-4617	179	2	0	0	NUM
cana-4617	179	3	∑	∑	X
cana-4617	179	4	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NUM
cana-4617	179	5	)	)	PUNCT
cana-4617	179	6	𝑟	𝑟	X
cana-4617	179	7	𝑖=1	𝑖=1	PUNCT
cana-4617	180	1	[	[	X
cana-4617	180	2	�	�	NOUN
cana-4617	180	3	̅	̅	NOUN
cana-4617	180	4	�	�	NOUN
cana-4617	180	5	(𝑧)]𝛾𝑖−1	(𝑧)]𝛾𝑖−1	X
cana-4617	180	6	𝑓(𝑧	𝑓(𝑧	PROPN
cana-4617	180	7	)	)	PUNCT
cana-4617	180	8	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	180	9	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	180	10	,	,	PUNCT
cana-4617	180	11	𝑛	𝑛	PROPN
cana-4617	180	12	,	,	PUNCT
cana-4617	180	13	�	�	PROPN
cana-4617	180	14	̃	̃	PROPN
cana-4617	180	15	�	�	PROPN
cana-4617	180	16	,	,	PUNCT
cana-4617	180	17	𝑘	𝑘	NOUN
cana-4617	180	18	)	)	PUNCT
cana-4617	180	19	]	]	PUNCT
cana-4617	180	20	−	−	PROPN
cana-4617	180	21	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	180	22	−	−	PROPN
cana-4617	180	23	1	1	NUM
cana-4617	180	24	,	,	PUNCT
cana-4617	180	25	𝑛	𝑛	PROPN
cana-4617	180	26	,	,	PUNCT
cana-4617	180	27	�	�	PROPN
cana-4617	180	28	̃	̃	PROPN
cana-4617	180	29	�	�	PROPN
cana-4617	180	30	,	,	PUNCT
cana-4617	180	31	𝑘	𝑘	NOUN
cana-4617	180	32	)	)	PUNCT
cana-4617	180	33	]	]	PUNCT
cana-4617	181	1	=	=	PUNCT
cana-4617	181	2	𝑗𝛽2𝐶𝑟−1	𝑗𝛽2𝐶𝑟−1	PROPN
cana-4617	181	3	2𝛾𝑟	2𝛾𝑟	PROPN
cana-4617	181	4	∫	∫	PROPN
cana-4617	181	5	(	(	PUNCT
cana-4617	181	6	1	1	NUM
cana-4617	181	7	𝑧	𝑧	PRON
cana-4617	181	8	+	+	NUM
cana-4617	181	9	𝛽2	𝛽2	ADJ
cana-4617	181	10	𝑧3	𝑧3	ADJ
cana-4617	181	11	)	)	PUNCT
cana-4617	181	12	𝑧𝑗−1	𝑧𝑗−1	NOUN
cana-4617	181	13	𝐶𝑟−1	𝐶𝑟−1	NUM
cana-4617	181	14	∞	∞	NOUN
cana-4617	181	15	0	0	NUM
cana-4617	181	16	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	181	17	)	)	PUNCT
cana-4617	181	18	∑	∑	ADP
cana-4617	181	19	𝑎𝑖(𝑟	𝑎𝑖(𝑟	NUM
cana-4617	181	20	)	)	PUNCT
cana-4617	181	21	𝑟	𝑟	X
cana-4617	181	22	𝑖=1	𝑖=1	PUNCT
cana-4617	182	1	[	[	X
cana-4617	182	2	�	�	NOUN
cana-4617	182	3	̅	̅	NOUN
cana-4617	182	4	�	�	NOUN
cana-4617	182	5	(𝑧)]𝛾𝑖−1	(𝑧)]𝛾𝑖−1	SYM
cana-4617	182	6	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	182	7	after	after	ADP
cana-4617	182	8	simplification	simplification	NOUN
cana-4617	182	9	,	,	PUNCT
cana-4617	182	10	the	the	DET
cana-4617	182	11	recurrence	recurrence	NOUN
cana-4617	182	12	relation	relation	NOUN
cana-4617	182	13	in	in	ADP
cana-4617	182	14	equation	equation	NOUN
cana-4617	182	15	(	(	PUNCT
cana-4617	182	16	15	15	NUM
cana-4617	182	17	)	)	PUNCT
cana-4617	182	18	is	be	AUX
cana-4617	182	19	derived	derive	VERB
cana-4617	182	20	.	.	PUNCT
cana-4617	183	1	corollary	corollary	ADJ
cana-4617	183	2	2.2	2.2	NUM
cana-4617	184	1	when	when	SCONJ
cana-4617	184	2	𝑚1	𝑚1	NOUN
cana-4617	184	3	=	=	SYM
cana-4617	184	4	𝑚2	𝑚2	PROPN
cana-4617	184	5	=	=	SYM
cana-4617	184	6	⋯	⋯	PROPN
cana-4617	184	7	=	=	SYM
cana-4617	184	8	𝑚𝑛−1	𝑚𝑛−1	PROPN
cana-4617	184	9	=	=	PUNCT
cana-4617	184	10	𝑚	𝑚	ADP
cana-4617	184	11	≠	≠	NUM
cana-4617	184	12	−1	−1	NOUN
cana-4617	184	13	the	the	DET
cana-4617	184	14	recurrence	recurrence	NOUN
cana-4617	184	15	relations	relation	NOUN
cana-4617	184	16	for	for	ADP
cana-4617	184	17	single	single	ADJ
cana-4617	184	18	moment	moment	NOUN
cana-4617	184	19	of	of	ADP
cana-4617	184	20	gos	go	NOUN
cana-4617	184	21	for	for	ADP
cana-4617	184	22	abrd	abrd	ADJ
cana-4617	184	23	are	be	AUX
cana-4617	184	24	provided	provide	VERB
cana-4617	184	25	as	as	SCONJ
cana-4617	184	26	follows	follow	VERB
cana-4617	184	27	communications	communication	NOUN
cana-4617	184	28	on	on	ADP
cana-4617	184	29	applied	apply	VERB
cana-4617	184	30	nonlinear	nonlinear	ADJ
cana-4617	184	31	analysis	analysis	NOUN
cana-4617	184	32	issn	issn	NOUN
cana-4617	184	33	:	:	PUNCT
cana-4617	184	34	1074	1074	NUM
cana-4617	184	35	-	-	PUNCT
cana-4617	184	36	133x	133x	NUM
cana-4617	184	37	vol	vol	NOUN
cana-4617	184	38	32	32	NUM
cana-4617	184	39	no	no	NOUN
cana-4617	184	40	.	.	PUNCT
cana-4617	185	1	9s	9s	NUM
cana-4617	185	2	(	(	PUNCT
cana-4617	185	3	2025	2025	NUM
cana-4617	185	4	)	)	PUNCT
cana-4617	185	5	3030	3030	NUM
cana-4617	185	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	185	7	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	185	8	,	,	PUNCT
cana-4617	185	9	𝑛	𝑛	PROPN
cana-4617	185	10	,	,	PUNCT
cana-4617	185	11	𝑚	𝑚	PROPN
cana-4617	185	12	,	,	PUNCT
cana-4617	185	13	𝑘	𝑘	NOUN
cana-4617	185	14	)	)	PUNCT
cana-4617	185	15	]	]	PUNCT
cana-4617	186	1	−	−	PROPN
cana-4617	186	2	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	186	3	−	−	PROPN
cana-4617	186	4	1	1	NUM
cana-4617	186	5	,	,	PUNCT
cana-4617	186	6	𝑛	𝑛	PROPN
cana-4617	186	7	,	,	PUNCT
cana-4617	186	8	𝑚	𝑚	PROPN
cana-4617	186	9	,	,	PUNCT
cana-4617	186	10	𝑘	𝑘	NOUN
cana-4617	186	11	)	)	PUNCT
cana-4617	186	12	]	]	PUNCT
cana-4617	187	1	=	=	PUNCT
cana-4617	187	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	187	3	2𝛾𝑟	2𝛾𝑟	NOUN
cana-4617	187	4	{	{	PUNCT
cana-4617	187	5	𝐸[𝑍𝑗−2(𝑟	𝐸[𝑍𝑗−2(𝑟	NOUN
cana-4617	187	6	,	,	PUNCT
cana-4617	187	7	𝑛	𝑛	PROPN
cana-4617	187	8	,	,	PUNCT
cana-4617	187	9	𝑚	𝑚	PROPN
cana-4617	187	10	,	,	PUNCT
cana-4617	187	11	𝑘	𝑘	NOUN
cana-4617	187	12	)	)	PUNCT
cana-4617	187	13	]	]	PUNCT
cana-4617	188	1	+	+	CCONJ
cana-4617	188	2	𝛽2𝐸[𝑍𝑗−4(𝑟	𝛽2𝐸[𝑍𝑗−4(𝑟	ADJ
cana-4617	188	3	,	,	PUNCT
cana-4617	188	4	𝑛	𝑛	PROPN
cana-4617	188	5	,	,	PUNCT
cana-4617	188	6	𝑚	𝑚	PROPN
cana-4617	188	7	,	,	PUNCT
cana-4617	188	8	𝑘	𝑘	NOUN
cana-4617	188	9	)	)	PUNCT
cana-4617	188	10	]	]	PUNCT
cana-4617	188	11	}	}	PUNCT
cana-4617	188	12	(	(	PUNCT
cana-4617	188	13	17	17	NUM
cana-4617	188	14	)	)	PUNCT
cana-4617	188	15	proof	proof	NOUN
cana-4617	188	16	.	.	PUNCT
cana-4617	189	1	this	this	PRON
cana-4617	189	2	can	can	AUX
cana-4617	189	3	easily	easily	ADV
cana-4617	189	4	be	be	AUX
cana-4617	189	5	deduced	deduce	VERB
cana-4617	189	6	from	from	ADP
cana-4617	189	7	(	(	PUNCT
cana-4617	189	8	15	15	NUM
cana-4617	189	9	)	)	PUNCT
cana-4617	189	10	given	give	VERB
cana-4617	189	11	the	the	DET
cana-4617	189	12	relation	relation	NOUN
cana-4617	189	13	(	(	PUNCT
cana-4617	189	14	6	6	NUM
cana-4617	189	15	)	)	PUNCT
cana-4617	189	16	.	.	PUNCT
cana-4617	190	1	remark	remark	VERB
cana-4617	190	2	2.3	2.3	NUM
cana-4617	190	3	by	by	ADP
cana-4617	190	4	setting	set	VERB
cana-4617	190	5	𝑚	𝑚	X
cana-4617	190	6	=	=	SYM
cana-4617	190	7	0	0	NUM
cana-4617	190	8	,	,	PUNCT
cana-4617	190	9	𝑘	𝑘	X
cana-4617	190	10	=	=	SYM
cana-4617	190	11	1	1	NUM
cana-4617	190	12	in	in	ADP
cana-4617	190	13	theorem	theorem	NOUN
cana-4617	190	14	2.1	2.1	NUM
cana-4617	190	15	.	.	PUNCT
cana-4617	191	1	,	,	PUNCT
cana-4617	191	2	we	we	PRON
cana-4617	191	3	derive	derive	VERB
cana-4617	191	4	the	the	DET
cana-4617	191	5	recurrence	recurrence	NOUN
cana-4617	191	6	relations	relation	NOUN
cana-4617	191	7	for	for	ADP
cana-4617	191	8	a	a	DET
cana-4617	191	9	single	single	ADJ
cana-4617	191	10	moment	moment	NOUN
cana-4617	191	11	of	of	ADP
cana-4617	191	12	order	order	NOUN
cana-4617	191	13	statistics	statistic	NOUN
cana-4617	191	14	from	from	ADP
cana-4617	191	15	abrd	abrd	PROPN
cana-4617	191	16	𝐸(𝑍𝑟:𝑛	𝐸(𝑍𝑟:𝑛	PROPN
cana-4617	191	17	𝑗	𝑗	PROPN
cana-4617	191	18	)	)	PUNCT
cana-4617	191	19	−	−	PROPN
cana-4617	192	1	𝐸(𝑍𝑟−1:𝑛	𝐸(𝑍𝑟−1:𝑛	INTJ
cana-4617	192	2	𝑗	𝑗	X
cana-4617	192	3	)	)	PUNCT
cana-4617	192	4	=	=	SYM
cana-4617	193	1	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	193	2	2(𝑛	2(𝑛	NUM
cana-4617	193	3	−	−	NOUN
cana-4617	194	1	𝑟	𝑟	NOUN
cana-4617	194	2	+	+	NOUN
cana-4617	194	3	1	1	X
cana-4617	194	4	)	)	PUNCT
cana-4617	195	1	[	[	X
cana-4617	195	2	𝐸(𝑍𝑟:𝑛	𝐸(𝑍𝑟:𝑛	X
cana-4617	195	3	𝑗−2	𝑗−2	PROPN
cana-4617	195	4	)	)	PUNCT
cana-4617	196	1	+	+	CCONJ
cana-4617	196	2	𝛽2𝐸(𝑍𝑟:𝑛	𝛽2𝐸(𝑍𝑟:𝑛	PROPN
cana-4617	196	3	𝑗−4	𝑗−4	PROPN
cana-4617	196	4	)	)	PUNCT
cana-4617	196	5	]	]	PUNCT
cana-4617	196	6	(	(	PUNCT
cana-4617	196	7	18	18	NUM
cana-4617	196	8	)	)	PUNCT
cana-4617	196	9	remark	remark	VERB
cana-4617	196	10	2.4	2.4	NUM
cana-4617	196	11	setting	set	VERB
cana-4617	196	12	𝑚	𝑚	X
cana-4617	196	13	=	=	SYM
cana-4617	196	14	−1	−1	NOUN
cana-4617	196	15	,	,	PUNCT
cana-4617	196	16	𝑘	𝑘	X
cana-4617	196	17	=	=	SYM
cana-4617	196	18	1	1	NUM
cana-4617	196	19	in	in	ADP
cana-4617	196	20	theorem	theorem	NOUN
cana-4617	196	21	2.1	2.1	NUM
cana-4617	196	22	.	.	PUNCT
cana-4617	196	23	,	,	PUNCT
cana-4617	196	24	we	we	PRON
cana-4617	196	25	derive	derive	VERB
cana-4617	196	26	the	the	DET
cana-4617	196	27	recurrence	recurrence	NOUN
cana-4617	196	28	relations	relation	NOUN
cana-4617	196	29	for	for	ADP
cana-4617	196	30	upper	upper	ADJ
cana-4617	196	31	record	record	NOUN
cana-4617	196	32	values	value	NOUN
cana-4617	196	33	as	as	ADP
cana-4617	196	34	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	196	35	,	,	PUNCT
cana-4617	196	36	𝑛	𝑛	NOUN
cana-4617	196	37	,	,	PUNCT
cana-4617	196	38	−1,1	−1,1	NOUN
cana-4617	196	39	)	)	PUNCT
cana-4617	196	40	]	]	PUNCT
cana-4617	197	1	−	−	PROPN
cana-4617	197	2	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	197	3	−	−	PROPN
cana-4617	197	4	1	1	NUM
cana-4617	197	5	,	,	PUNCT
cana-4617	197	6	𝑛	𝑛	ADJ
cana-4617	197	7	,	,	PUNCT
cana-4617	197	8	−1,1	−1,1	NOUN
cana-4617	197	9	)	)	PUNCT
cana-4617	197	10	]	]	PUNCT
cana-4617	198	1	=	=	PUNCT
cana-4617	198	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	198	3	2	2	NUM
cana-4617	198	4	{	{	PUNCT
cana-4617	198	5	𝐸[𝑍𝑗−2(𝑟	𝐸[𝑍𝑗−2(𝑟	NOUN
cana-4617	198	6	,	,	PUNCT
cana-4617	198	7	𝑛	𝑛	NOUN
cana-4617	198	8	,	,	PUNCT
cana-4617	198	9	−1,1	−1,1	NOUN
cana-4617	198	10	)	)	PUNCT
cana-4617	198	11	]	]	PUNCT
cana-4617	199	1	+	+	CCONJ
cana-4617	199	2	𝛽2𝐸[𝑍𝑗−4(𝑟	𝛽2𝐸[𝑍𝑗−4(𝑟	ADJ
cana-4617	199	3	,	,	PUNCT
cana-4617	199	4	𝑛	𝑛	PROPN
cana-4617	199	5	,	,	PUNCT
cana-4617	199	6	−1,1	−1,1	NOUN
cana-4617	199	7	)	)	PUNCT
cana-4617	199	8	]	]	PUNCT
cana-4617	199	9	}	}	PUNCT
cana-4617	199	10	(	(	PUNCT
cana-4617	199	11	19	19	NUM
cana-4617	199	12	)	)	PUNCT
cana-4617	199	13	3	3	NUM
cana-4617	199	14	.	.	X
cana-4617	199	15	recurrence	recurrence	NOUN
cana-4617	199	16	relation	relation	NOUN
cana-4617	199	17	for	for	ADP
cana-4617	199	18	product	product	NOUN
cana-4617	199	19	moments	moment	NOUN
cana-4617	199	20	of	of	ADP
cana-4617	199	21	gos	gos	PROPN
cana-4617	199	22	theorem	theorem	VERB
cana-4617	199	23	3.1	3.1	NUM
cana-4617	199	24	let	let	VERB
cana-4617	199	25	z	z	PRON
cana-4617	199	26	be	be	AUX
cana-4617	199	27	a	a	DET
cana-4617	199	28	random	random	ADJ
cana-4617	199	29	variable	variable	NOUN
cana-4617	199	30	has	have	VERB
cana-4617	199	31	a	a	DET
cana-4617	199	32	probability	probability	NOUN
cana-4617	199	33	density	density	NOUN
cana-4617	199	34	function	function	NOUN
cana-4617	199	35	given	give	VERB
cana-4617	199	36	by	by	ADP
cana-4617	199	37	equation	equation	NOUN
cana-4617	199	38	(	(	PUNCT
cana-4617	199	39	1	1	NUM
cana-4617	199	40	)	)	PUNCT
cana-4617	199	41	.	.	PUNCT
cana-4617	200	1	for	for	ADP
cana-4617	200	2	integer	integer	PROPN
cana-4617	200	3	i	i	PROPN
cana-4617	200	4	,	,	PUNCT
cana-4617	200	5	j	j	PROPN
cana-4617	200	6	such	such	ADJ
cana-4617	200	7	that	that	SCONJ
cana-4617	200	8	i	i	PRON
cana-4617	200	9	,	,	PUNCT
cana-4617	200	10	j	j	PROPN
cana-4617	200	11	>	>	PROPN
cana-4617	200	12	0	0	PROPN
cana-4617	200	13	,	,	PUNCT
cana-4617	200	14	the	the	DET
cana-4617	200	15	product	product	NOUN
cana-4617	200	16	moments	moment	NOUN
cana-4617	200	17	of	of	ADP
cana-4617	200	18	z	z	NOUN
cana-4617	200	19	satisfy	satisfy	VERB
cana-4617	200	20	the	the	DET
cana-4617	200	21	following	follow	VERB
cana-4617	200	22	recurrence	recurrence	NOUN
cana-4617	200	23	relation	relation	PROPN
cana-4617	200	24	:	:	PUNCT
cana-4617	200	25	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	200	26	,	,	PUNCT
cana-4617	200	27	𝑛	𝑛	PROPN
cana-4617	200	28	,	,	PUNCT
cana-4617	200	29	�	�	PROPN
cana-4617	200	30	̃	̃	PROPN
cana-4617	200	31	�	�	PROPN
cana-4617	200	32	,	,	PUNCT
cana-4617	200	33	𝑘	𝑘	NOUN
cana-4617	200	34	)	)	PUNCT
cana-4617	200	35	.	.	PUNCT
cana-4617	201	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	PROPN
cana-4617	201	2	,	,	PUNCT
cana-4617	201	3	𝑛	𝑛	PROPN
cana-4617	201	4	,	,	PUNCT
cana-4617	201	5	�	�	PROPN
cana-4617	201	6	̃	̃	PROPN
cana-4617	201	7	�	�	PROPN
cana-4617	201	8	,	,	PUNCT
cana-4617	201	9	𝑘	𝑘	NOUN
cana-4617	201	10	)	)	PUNCT
cana-4617	201	11	]	]	PUNCT
cana-4617	201	12	−	−	PROPN
cana-4617	201	13	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	201	14	,	,	PUNCT
cana-4617	201	15	𝑛	𝑛	PROPN
cana-4617	201	16	,	,	PUNCT
cana-4617	201	17	�	�	PROPN
cana-4617	201	18	̃	̃	PROPN
cana-4617	201	19	�	�	PROPN
cana-4617	201	20	,	,	PUNCT
cana-4617	201	21	𝑘	𝑘	NOUN
cana-4617	201	22	)	)	PUNCT
cana-4617	201	23	.	.	PUNCT
cana-4617	202	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	INTJ
cana-4617	202	2	−	−	ADP
cana-4617	202	3	1	1	NUM
cana-4617	202	4	,	,	PUNCT
cana-4617	202	5	𝑛	𝑛	PROPN
cana-4617	202	6	,	,	PUNCT
cana-4617	202	7	�	�	PROPN
cana-4617	202	8	̃	̃	PROPN
cana-4617	202	9	�	�	PROPN
cana-4617	202	10	,	,	PUNCT
cana-4617	202	11	𝑘	𝑘	NOUN
cana-4617	202	12	)	)	PUNCT
cana-4617	202	13	]	]	PUNCT
cana-4617	203	1	=	=	PUNCT
cana-4617	203	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	203	3	2𝛾𝑠	2𝛾𝑠	NOUN
cana-4617	203	4	{	{	PUNCT
cana-4617	203	5	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	203	6	,	,	PUNCT
cana-4617	203	7	𝑛	𝑛	PROPN
cana-4617	203	8	,	,	PUNCT
cana-4617	203	9	�	�	PROPN
cana-4617	203	10	̃	̃	PROPN
cana-4617	203	11	�	�	PROPN
cana-4617	203	12	,	,	PUNCT
cana-4617	203	13	𝑘	𝑘	NOUN
cana-4617	203	14	)	)	PUNCT
cana-4617	203	15	.	.	PUNCT
cana-4617	204	1	𝑍𝑗−2(𝑠	𝑍𝑗−2(𝑠	PROPN
cana-4617	204	2	,	,	PUNCT
cana-4617	204	3	𝑛	𝑛	PROPN
cana-4617	204	4	,	,	PUNCT
cana-4617	204	5	�	�	PROPN
cana-4617	204	6	̃	̃	PROPN
cana-4617	204	7	�	�	PROPN
cana-4617	204	8	,	,	PUNCT
cana-4617	204	9	𝑘	𝑘	NOUN
cana-4617	204	10	)	)	PUNCT
cana-4617	204	11	]	]	PUNCT
cana-4617	205	1	+	+	CCONJ
cana-4617	205	2	𝛽2𝐸[𝑍𝑖(𝑟	𝛽2𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	205	3	,	,	PUNCT
cana-4617	205	4	𝑛	𝑛	PROPN
cana-4617	205	5	,	,	PUNCT
cana-4617	205	6	�	�	PROPN
cana-4617	205	7	̃	̃	PROPN
cana-4617	205	8	�	�	PROPN
cana-4617	205	9	,	,	PUNCT
cana-4617	205	10	𝑘	𝑘	NOUN
cana-4617	205	11	)	)	PUNCT
cana-4617	205	12	.	.	PUNCT
cana-4617	206	1	𝑍𝑗−4(𝑠	𝑍𝑗−4(𝑠	PROPN
cana-4617	206	2	,	,	PUNCT
cana-4617	206	3	𝑛	𝑛	PROPN
cana-4617	206	4	,	,	PUNCT
cana-4617	206	5	�	�	PROPN
cana-4617	206	6	̃	̃	PROPN
cana-4617	206	7	�	�	PROPN
cana-4617	206	8	,	,	PUNCT
cana-4617	206	9	𝑘	𝑘	NOUN
cana-4617	206	10	)	)	PUNCT
cana-4617	206	11	]	]	PUNCT
cana-4617	206	12	}	}	PUNCT
cana-4617	206	13	(	(	PUNCT
cana-4617	206	14	20	20	X
cana-4617	206	15	)	)	PUNCT
cana-4617	206	16	proof	proof	NOUN
cana-4617	206	17	.	.	PUNCT
cana-4617	207	1	we	we	PRON
cana-4617	207	2	have	have	VERB
cana-4617	207	3	from	from	ADP
cana-4617	207	4	lemma	lemma	PROPN
cana-4617	207	5	3.2	3.2	NUM
cana-4617	207	6	(	(	PUNCT
cana-4617	207	7	by	by	ADP
cana-4617	207	8	athar	athar	PROPN
cana-4617	207	9	.	.	PUNCT
cana-4617	208	1	and	and	CCONJ
cana-4617	208	2	islam	islam	PROPN
cana-4617	208	3	.	.	PUNCT
cana-4617	209	1	(	(	PUNCT
cana-4617	209	2	2004	2004	NUM
cana-4617	209	3	)	)	PUNCT
cana-4617	209	4	)	)	PUNCT
cana-4617	210	1	that	that	SCONJ
cana-4617	210	2	𝐸[𝜉{𝑍	𝐸[𝜉{𝑍	PROPN
cana-4617	210	3	(	(	PUNCT
cana-4617	210	4	𝑟	𝑟	NOUN
cana-4617	210	5	,	,	PUNCT
cana-4617	210	6	𝑛	𝑛	PROPN
cana-4617	210	7	,	,	PUNCT
cana-4617	210	8	�	�	PROPN
cana-4617	210	9	̃	̃	PROPN
cana-4617	210	10	�	�	PROPN
cana-4617	210	11	,	,	PUNCT
cana-4617	210	12	𝑘	𝑘	NOUN
cana-4617	210	13	)	)	PUNCT
cana-4617	210	14	.	.	PUNCT
cana-4617	211	1	𝑍(𝑠	𝑍(𝑠	NUM
cana-4617	211	2	,	,	PUNCT
cana-4617	211	3	𝑛	𝑛	PROPN
cana-4617	211	4	,	,	PUNCT
cana-4617	211	5	�	�	PROPN
cana-4617	211	6	̃	̃	PROPN
cana-4617	211	7	�	�	PROPN
cana-4617	211	8	,	,	PUNCT
cana-4617	211	9	𝑘	𝑘	NOUN
cana-4617	211	10	)	)	PUNCT
cana-4617	211	11	}	}	PUNCT
cana-4617	211	12	]	]	PUNCT
cana-4617	211	13	−	−	PROPN
cana-4617	211	14	𝐸[𝜉{𝑍(𝑟	𝐸[𝜉{𝑍(𝑟	PROPN
cana-4617	211	15	,	,	PUNCT
cana-4617	211	16	𝑛	𝑛	PROPN
cana-4617	211	17	,	,	PUNCT
cana-4617	211	18	�	�	PROPN
cana-4617	211	19	̃	̃	PROPN
cana-4617	211	20	�	�	PROPN
cana-4617	211	21	,	,	PUNCT
cana-4617	211	22	𝑘	𝑘	NOUN
cana-4617	211	23	)	)	PUNCT
cana-4617	211	24	.	.	PUNCT
cana-4617	212	1	𝑍(𝑠	𝑍(𝑠	PUNCT
cana-4617	212	2	−	−	PROPN
cana-4617	212	3	1	1	NUM
cana-4617	212	4	,	,	PUNCT
cana-4617	212	5	𝑛	𝑛	PROPN
cana-4617	212	6	,	,	PUNCT
cana-4617	212	7	�	�	PROPN
cana-4617	212	8	̃	̃	PROPN
cana-4617	212	9	�	�	PROPN
cana-4617	212	10	,	,	PUNCT
cana-4617	212	11	𝑘	𝑘	NOUN
cana-4617	212	12	)	)	PUNCT
cana-4617	212	13	}	}	PUNCT
cana-4617	212	14	]	]	PUNCT
cana-4617	212	15	=	=	SYM
cana-4617	212	16	𝐶𝑠−2	𝐶𝑠−2	PROPN
cana-4617	212	17	∫	∫	PROPN
cana-4617	212	18	∫	∫	PROPN
cana-4617	212	19	𝜕	𝜕	PROPN
cana-4617	212	20	𝜕𝑡	𝜕𝑡	PROPN
cana-4617	212	21	𝜉(𝑧	𝜉(𝑧	PROPN
cana-4617	212	22	,	,	PUNCT
cana-4617	212	23	𝑡	𝑡	PROPN
cana-4617	212	24	)	)	PUNCT
cana-4617	212	25	∑	∑	ADV
cana-4617	212	26	𝑎𝑙	𝑎𝑙	NOUN
cana-4617	212	27	(	(	PUNCT
cana-4617	212	28	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	212	29	)	)	PUNCT
cana-4617	212	30	[	[	PUNCT
cana-4617	212	31	�	�	NOUN
cana-4617	212	32	̅	̅	NOUN
cana-4617	212	33	�	�	SYM
cana-4617	212	34	(𝑡	(𝑡	SYM
cana-4617	212	35	)	)	PUNCT
cana-4617	212	36	�	�	PROPN
cana-4617	212	37	̅	̅	NOUN
cana-4617	212	38	�	�	NOUN
cana-4617	212	39	(𝑧	(𝑧	NOUN
cana-4617	212	40	)	)	PUNCT
cana-4617	212	41	]	]	PUNCT
cana-4617	213	1	𝛾𝑙	𝛾𝑙	ADP
cana-4617	213	2	∑	∑	PROPN
cana-4617	213	3	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	213	4	�	�	PROPN
cana-4617	213	5	̅	̅	NOUN
cana-4617	213	6	�	�	NOUN
cana-4617	213	7	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	213	8	𝑟	𝑟	NOUN
cana-4617	213	9	𝑙=1	𝑙=1	SYM
cana-4617	213	10	𝑠	𝑠	PROPN
cana-4617	213	11	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	213	12	𝛽	𝛽	PROPN
cana-4617	213	13	𝑧	𝑧	ADP
cana-4617	213	14	𝛽	𝛽	PROPN
cana-4617	213	15	𝜃	𝜃	DET
cana-4617	213	16	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	213	17	)	)	PUNCT
cana-4617	213	18	�	�	PROPN
cana-4617	213	19	̅	̅	NOUN
cana-4617	213	20	�	�	NOUN
cana-4617	213	21	(𝑧	(𝑧	NOUN
cana-4617	213	22	)	)	PUNCT
cana-4617	213	23	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	213	24	if	if	SCONJ
cana-4617	213	25	we	we	PRON
cana-4617	213	26	let	let	VERB
cana-4617	213	27	𝜉(𝑧	𝜉(𝑧	PROPN
cana-4617	213	28	,	,	PUNCT
cana-4617	213	29	𝑡	𝑡	NOUN
cana-4617	213	30	)	)	PUNCT
cana-4617	213	31	=	=	SYM
cana-4617	213	32	𝑧𝑖𝑡𝑗	𝑧𝑖𝑡𝑗	NOUN
cana-4617	213	33	,	,	PUNCT
cana-4617	213	34	then	then	ADV
cana-4617	213	35	communications	communication	NOUN
cana-4617	213	36	on	on	ADP
cana-4617	213	37	applied	apply	VERB
cana-4617	213	38	nonlinear	nonlinear	ADJ
cana-4617	213	39	analysis	analysis	NOUN
cana-4617	213	40	issn	issn	NOUN
cana-4617	213	41	:	:	PUNCT
cana-4617	213	42	1074	1074	NUM
cana-4617	213	43	-	-	PUNCT
cana-4617	213	44	133x	133x	NUM
cana-4617	213	45	vol	vol	NOUN
cana-4617	213	46	32	32	NUM
cana-4617	213	47	no	no	NOUN
cana-4617	213	48	.	.	PUNCT
cana-4617	214	1	9s	9s	NUM
cana-4617	214	2	(	(	PUNCT
cana-4617	214	3	2025	2025	NUM
cana-4617	214	4	)	)	PUNCT
cana-4617	214	5	3031	3031	NUM
cana-4617	214	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	214	7	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	214	8	,	,	PUNCT
cana-4617	214	9	𝑛	𝑛	PROPN
cana-4617	214	10	,	,	PUNCT
cana-4617	214	11	�	�	PROPN
cana-4617	214	12	̃	̃	PROPN
cana-4617	214	13	�	�	PROPN
cana-4617	214	14	,	,	PUNCT
cana-4617	214	15	𝑘	𝑘	NOUN
cana-4617	214	16	)	)	PUNCT
cana-4617	214	17	.	.	PUNCT
cana-4617	215	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	PROPN
cana-4617	215	2	,	,	PUNCT
cana-4617	215	3	𝑛	𝑛	PROPN
cana-4617	215	4	,	,	PUNCT
cana-4617	215	5	�	�	PROPN
cana-4617	215	6	̃	̃	PROPN
cana-4617	215	7	�	�	PROPN
cana-4617	215	8	,	,	PUNCT
cana-4617	215	9	𝑘	𝑘	NOUN
cana-4617	215	10	)	)	PUNCT
cana-4617	215	11	]	]	PUNCT
cana-4617	215	12	−	−	PROPN
cana-4617	215	13	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	215	14	,	,	PUNCT
cana-4617	215	15	𝑛	𝑛	PROPN
cana-4617	215	16	,	,	PUNCT
cana-4617	215	17	�	�	PROPN
cana-4617	215	18	̃	̃	PROPN
cana-4617	215	19	�	�	PROPN
cana-4617	215	20	,	,	PUNCT
cana-4617	215	21	𝑘	𝑘	NOUN
cana-4617	215	22	)	)	PUNCT
cana-4617	215	23	.	.	PUNCT
cana-4617	216	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	INTJ
cana-4617	216	2	−	−	ADP
cana-4617	216	3	1	1	NUM
cana-4617	216	4	,	,	PUNCT
cana-4617	216	5	𝑛	𝑛	PROPN
cana-4617	216	6	,	,	PUNCT
cana-4617	216	7	�	�	PROPN
cana-4617	216	8	̃	̃	PROPN
cana-4617	216	9	�	�	PROPN
cana-4617	216	10	,	,	PUNCT
cana-4617	216	11	𝑘	𝑘	NOUN
cana-4617	216	12	)	)	PUNCT
cana-4617	216	13	]	]	PUNCT
cana-4617	217	1	=	=	SYM
cana-4617	217	2	𝑗𝐶𝑠−1	𝑗𝐶𝑠−1	PROPN
cana-4617	217	3	𝛾𝑠	𝛾𝑠	ADJ
cana-4617	217	4	∫	∫	PROPN
cana-4617	217	5	∫	∫	PROPN
cana-4617	217	6	𝑧𝑖𝑡𝑗−1	𝑧𝑖𝑡𝑗−1	X
cana-4617	217	7	∑	∑	PUNCT
cana-4617	217	8	𝑎𝑙	𝑎𝑙	X
cana-4617	217	9	(	(	PUNCT
cana-4617	217	10	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	217	11	)	)	PUNCT
cana-4617	217	12	[	[	PUNCT
cana-4617	217	13	�	�	NOUN
cana-4617	217	14	̅	̅	NOUN
cana-4617	217	15	�	�	SYM
cana-4617	217	16	(𝑡	(𝑡	SYM
cana-4617	217	17	)	)	PUNCT
cana-4617	217	18	�	�	PROPN
cana-4617	217	19	̅	̅	NOUN
cana-4617	217	20	�	�	NOUN
cana-4617	217	21	(𝑧	(𝑧	NOUN
cana-4617	217	22	)	)	PUNCT
cana-4617	217	23	]	]	PUNCT
cana-4617	217	24	𝛾𝑙	𝛾𝑙	ADP
cana-4617	217	25	∑	∑	PROPN
cana-4617	217	26	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	217	27	�	�	PROPN
cana-4617	217	28	̅	̅	NOUN
cana-4617	217	29	�	�	NOUN
cana-4617	217	30	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	217	31	𝑟	𝑟	NOUN
cana-4617	217	32	𝑙=1	𝑙=1	SYM
cana-4617	217	33	𝑠	𝑠	INTJ
cana-4617	217	34	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	217	35	∞	∞	NUM
cana-4617	217	36	𝑧	𝑧	VERB
cana-4617	217	37	∞	∞	PROPN
cana-4617	217	38	0	0	NUM
cana-4617	217	39	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	217	40	)	)	PUNCT
cana-4617	217	41	�	�	PROPN
cana-4617	217	42	̅	̅	NOUN
cana-4617	217	43	�	�	NOUN
cana-4617	217	44	(𝑧	(𝑧	NOUN
cana-4617	217	45	)	)	PUNCT
cana-4617	217	46	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	217	47	in	in	ADP
cana-4617	217	48	view	view	NOUN
cana-4617	217	49	of	of	ADP
cana-4617	217	50	equation	equation	NOUN
cana-4617	217	51	(	(	PUNCT
cana-4617	217	52	3	3	NUM
cana-4617	217	53	)	)	PUNCT
cana-4617	217	54	,	,	PUNCT
cana-4617	217	55	note	note	VERB
cana-4617	217	56	that	that	SCONJ
cana-4617	217	57	�	�	PROPN
cana-4617	217	58	̅	̅	NOUN
cana-4617	217	59	�	�	NOUN
cana-4617	217	60	(𝑡	(𝑡	NOUN
cana-4617	217	61	)	)	PUNCT
cana-4617	217	62	𝑓(𝑡	𝑓(𝑡	PROPN
cana-4617	217	63	)	)	PUNCT
cana-4617	218	1	=	=	PUNCT
cana-4617	218	2	(	(	PUNCT
cana-4617	218	3	𝛽2	𝛽2	PROPN
cana-4617	218	4	2𝑡	2𝑡	NOUN
cana-4617	218	5	+	+	CCONJ
cana-4617	218	6	𝛽4	𝛽4	PROPN
cana-4617	218	7	2𝑡3	2𝑡3	NUM
cana-4617	218	8	)	)	PUNCT
cana-4617	218	9	=	=	SYM
cana-4617	218	10	𝛽2	𝛽2	PROPN
cana-4617	218	11	2	2	NUM
cana-4617	218	12	𝑡−1	𝑡−1	PROPN
cana-4617	218	13	(	(	PUNCT
cana-4617	218	14	1	1	NUM
cana-4617	218	15	+	+	NUM
cana-4617	218	16	𝛽2	𝛽2	PROPN
cana-4617	218	17	𝑡2	𝑡2	PROPN
cana-4617	218	18	)	)	PUNCT
cana-4617	218	19	therefore	therefore	ADV
cana-4617	218	20	,	,	PUNCT
cana-4617	218	21	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	ADV
cana-4617	218	22	,	,	PUNCT
cana-4617	218	23	𝑛	𝑛	PROPN
cana-4617	218	24	,	,	PUNCT
cana-4617	218	25	�	�	PROPN
cana-4617	218	26	̃	̃	PROPN
cana-4617	218	27	�	�	PROPN
cana-4617	218	28	,	,	PUNCT
cana-4617	218	29	𝑘	𝑘	NOUN
cana-4617	218	30	)	)	PUNCT
cana-4617	218	31	.	.	PUNCT
cana-4617	219	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	PROPN
cana-4617	219	2	,	,	PUNCT
cana-4617	219	3	𝑛	𝑛	PROPN
cana-4617	219	4	,	,	PUNCT
cana-4617	219	5	�	�	PROPN
cana-4617	219	6	̃	̃	PROPN
cana-4617	219	7	�	�	PROPN
cana-4617	219	8	,	,	PUNCT
cana-4617	219	9	𝑘	𝑘	NOUN
cana-4617	219	10	)	)	PUNCT
cana-4617	219	11	]	]	PUNCT
cana-4617	219	12	−	−	PROPN
cana-4617	219	13	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	219	14	,	,	PUNCT
cana-4617	219	15	𝑛	𝑛	PROPN
cana-4617	219	16	,	,	PUNCT
cana-4617	219	17	�	�	PROPN
cana-4617	219	18	̃	̃	PROPN
cana-4617	219	19	�	�	PROPN
cana-4617	219	20	,	,	PUNCT
cana-4617	219	21	𝑘	𝑘	NOUN
cana-4617	219	22	)	)	PUNCT
cana-4617	219	23	.	.	PUNCT
cana-4617	220	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	INTJ
cana-4617	220	2	−	−	ADP
cana-4617	220	3	1	1	NUM
cana-4617	220	4	,	,	PUNCT
cana-4617	220	5	𝑛	𝑛	PROPN
cana-4617	220	6	,	,	PUNCT
cana-4617	220	7	�	�	PROPN
cana-4617	220	8	̃	̃	PROPN
cana-4617	220	9	�	�	PROPN
cana-4617	220	10	,	,	PUNCT
cana-4617	220	11	𝑘	𝑘	NOUN
cana-4617	220	12	)	)	PUNCT
cana-4617	220	13	]	]	PUNCT
cana-4617	221	1	=	=	SYM
cana-4617	221	2	𝑗𝐶𝑠−1	𝑗𝐶𝑠−1	PROPN
cana-4617	221	3	𝛾𝑠	𝛾𝑠	ADJ
cana-4617	221	4	∫	∫	PROPN
cana-4617	221	5	∫	∫	PROPN
cana-4617	221	6	𝑧𝑖𝑡𝑗−1	𝑧𝑖𝑡𝑗−1	X
cana-4617	221	7	∑	∑	PUNCT
cana-4617	221	8	𝑎𝑙	𝑎𝑙	X
cana-4617	221	9	(	(	PUNCT
cana-4617	221	10	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	221	11	)	)	PUNCT
cana-4617	221	12	[	[	PUNCT
cana-4617	221	13	�	�	NOUN
cana-4617	221	14	̅	̅	NOUN
cana-4617	221	15	�	�	SYM
cana-4617	221	16	(𝑡	(𝑡	SYM
cana-4617	221	17	)	)	PUNCT
cana-4617	221	18	�	�	PROPN
cana-4617	221	19	̅	̅	NOUN
cana-4617	221	20	�	�	NOUN
cana-4617	221	21	(𝑧	(𝑧	NOUN
cana-4617	221	22	)	)	PUNCT
cana-4617	221	23	]	]	PUNCT
cana-4617	221	24	𝛾𝑙	𝛾𝑙	ADP
cana-4617	221	25	∑	∑	PROPN
cana-4617	221	26	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	221	27	�	�	PROPN
cana-4617	221	28	̅	̅	NOUN
cana-4617	221	29	�	�	NOUN
cana-4617	221	30	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	221	31	𝑟	𝑟	NOUN
cana-4617	221	32	𝑙=1	𝑙=1	SYM
cana-4617	221	33	𝑠	𝑠	INTJ
cana-4617	221	34	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	221	35	∞	∞	NUM
cana-4617	221	36	𝑧	𝑧	VERB
cana-4617	221	37	∞	∞	PROPN
cana-4617	221	38	0	0	NUM
cana-4617	221	39	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	221	40	)	)	PUNCT
cana-4617	221	41	�	�	PROPN
cana-4617	221	42	̅	̅	NOUN
cana-4617	221	43	�	�	NOUN
cana-4617	221	44	(𝑧	(𝑧	NOUN
cana-4617	221	45	)	)	PUNCT
cana-4617	221	46	(	(	PUNCT
cana-4617	221	47	�	�	NOUN
cana-4617	221	48	̅	̅	NOUN
cana-4617	221	49	�	�	NOUN
cana-4617	221	50	(𝑡	(𝑡	NOUN
cana-4617	221	51	)	)	PUNCT
cana-4617	221	52	𝑓(𝑡	𝑓(𝑡	PROPN
cana-4617	221	53	)	)	PUNCT
cana-4617	221	54	.	.	PUNCT
cana-4617	222	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4617	222	2	)	)	PUNCT
cana-4617	222	3	�	�	PROPN
cana-4617	222	4	̅	̅	NOUN
cana-4617	222	5	�	�	NOUN
cana-4617	222	6	(𝑡	(𝑡	NOUN
cana-4617	222	7	)	)	PUNCT
cana-4617	222	8	)	)	PUNCT
cana-4617	222	9	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	222	10	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	222	11	,	,	PUNCT
cana-4617	222	12	𝑛	𝑛	PROPN
cana-4617	222	13	,	,	PUNCT
cana-4617	222	14	�	�	PROPN
cana-4617	222	15	̃	̃	PROPN
cana-4617	222	16	�	�	PROPN
cana-4617	222	17	,	,	PUNCT
cana-4617	222	18	𝑘	𝑘	NOUN
cana-4617	222	19	)	)	PUNCT
cana-4617	222	20	.	.	PUNCT
cana-4617	223	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	PROPN
cana-4617	223	2	,	,	PUNCT
cana-4617	223	3	𝑛	𝑛	PROPN
cana-4617	223	4	,	,	PUNCT
cana-4617	223	5	�	�	PROPN
cana-4617	223	6	̃	̃	PROPN
cana-4617	223	7	�	�	PROPN
cana-4617	223	8	,	,	PUNCT
cana-4617	223	9	𝑘	𝑘	NOUN
cana-4617	223	10	)	)	PUNCT
cana-4617	223	11	]	]	PUNCT
cana-4617	223	12	−	−	PROPN
cana-4617	223	13	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	223	14	,	,	PUNCT
cana-4617	223	15	𝑛	𝑛	PROPN
cana-4617	223	16	,	,	PUNCT
cana-4617	223	17	�	�	PROPN
cana-4617	223	18	̃	̃	PROPN
cana-4617	223	19	�	�	PROPN
cana-4617	223	20	,	,	PUNCT
cana-4617	223	21	𝑘	𝑘	NOUN
cana-4617	223	22	)	)	PUNCT
cana-4617	223	23	.	.	PUNCT
cana-4617	224	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	INTJ
cana-4617	224	2	−	−	ADP
cana-4617	224	3	1	1	NUM
cana-4617	224	4	,	,	PUNCT
cana-4617	224	5	𝑛	𝑛	PROPN
cana-4617	224	6	,	,	PUNCT
cana-4617	224	7	�	�	PROPN
cana-4617	224	8	̃	̃	PROPN
cana-4617	224	9	�	�	PROPN
cana-4617	224	10	,	,	PUNCT
cana-4617	224	11	𝑘	𝑘	NOUN
cana-4617	224	12	)	)	PUNCT
cana-4617	224	13	]	]	PUNCT
cana-4617	225	1	=	=	SYM
cana-4617	225	2	𝑗𝐶𝑠−1	𝑗𝐶𝑠−1	PROPN
cana-4617	225	3	𝛾𝑠	𝛾𝑠	ADJ
cana-4617	225	4	∫	∫	PROPN
cana-4617	225	5	∫	∫	PROPN
cana-4617	225	6	𝑧𝑖𝑡𝑗−1	𝑧𝑖𝑡𝑗−1	NUM
cana-4617	225	7	𝛽2	𝛽2	PROPN
cana-4617	225	8	2	2	NUM
cana-4617	225	9	𝑡−1	𝑡−1	PROPN
cana-4617	225	10	(	(	PUNCT
cana-4617	225	11	1	1	NUM
cana-4617	225	12	∞	∞	NUM
cana-4617	225	13	𝑧	𝑧	PRON
cana-4617	225	14	∞	∞	NUM
cana-4617	225	15	0	0	NUM
cana-4617	226	1	+	+	CCONJ
cana-4617	226	2	𝛽2	𝛽2	PROPN
cana-4617	226	3	𝑡2	𝑡2	PROPN
cana-4617	226	4	)	)	PUNCT
cana-4617	226	5	∑	∑	PUNCT
cana-4617	226	6	𝑎𝑙	𝑎𝑙	X
cana-4617	226	7	(	(	PUNCT
cana-4617	226	8	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	226	9	)	)	PUNCT
cana-4617	226	10	[	[	PUNCT
cana-4617	226	11	�	�	NOUN
cana-4617	226	12	̅	̅	NOUN
cana-4617	226	13	�	�	SYM
cana-4617	226	14	(𝑡	(𝑡	SYM
cana-4617	226	15	)	)	PUNCT
cana-4617	226	16	�	�	PROPN
cana-4617	226	17	̅	̅	NOUN
cana-4617	226	18	�	�	NOUN
cana-4617	226	19	(𝑧	(𝑧	NOUN
cana-4617	226	20	)	)	PUNCT
cana-4617	226	21	]	]	PUNCT
cana-4617	226	22	𝛾𝑙	𝛾𝑙	ADP
cana-4617	226	23	∑	∑	PROPN
cana-4617	226	24	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	226	25	�	�	PROPN
cana-4617	226	26	̅	̅	NOUN
cana-4617	226	27	�	�	NOUN
cana-4617	226	28	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	226	29	𝑟	𝑟	NOUN
cana-4617	226	30	𝑙=1	𝑙=1	SYM
cana-4617	226	31	𝑠	𝑠	PROPN
cana-4617	226	32	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	226	33	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	226	34	)	)	PUNCT
cana-4617	226	35	�	�	PROPN
cana-4617	226	36	̅	̅	NOUN
cana-4617	226	37	�	�	NOUN
cana-4617	226	38	(𝑧	(𝑧	NOUN
cana-4617	226	39	)	)	PUNCT
cana-4617	226	40	.	.	PUNCT
cana-4617	227	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4617	227	2	)	)	PUNCT
cana-4617	227	3	�	�	PROPN
cana-4617	227	4	̅	̅	NOUN
cana-4617	227	5	�	�	NOUN
cana-4617	227	6	(𝑡	(𝑡	SYM
cana-4617	227	7	)	)	PUNCT
cana-4617	227	8	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	227	9	=	=	SYM
cana-4617	228	1	𝑗𝛽2𝐶𝑠−1	𝑗𝛽2𝐶𝑠−1	PROPN
cana-4617	228	2	2𝛾𝑠	2𝛾𝑠	ADJ
cana-4617	228	3	∫	∫	PROPN
cana-4617	228	4	∫	∫	PROPN
cana-4617	229	1	𝑧𝑖𝑡𝑗−2	𝑧𝑖𝑡𝑗−2	X
cana-4617	229	2	∑	∑	NOUN
cana-4617	229	3	𝑎𝑙	𝑎𝑙	NOUN
cana-4617	229	4	(	(	PUNCT
cana-4617	229	5	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	229	6	)	)	PUNCT
cana-4617	229	7	[	[	PUNCT
cana-4617	229	8	�	�	NOUN
cana-4617	229	9	̅	̅	NOUN
cana-4617	229	10	�	�	SYM
cana-4617	229	11	(𝑡	(𝑡	SYM
cana-4617	229	12	)	)	PUNCT
cana-4617	229	13	�	�	PROPN
cana-4617	229	14	̅	̅	NOUN
cana-4617	229	15	�	�	NOUN
cana-4617	229	16	(𝑧	(𝑧	NOUN
cana-4617	229	17	)	)	PUNCT
cana-4617	229	18	]	]	PUNCT
cana-4617	230	1	𝛾𝑙	𝛾𝑙	ADP
cana-4617	230	2	∑	∑	PROPN
cana-4617	230	3	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	230	4	�	�	PROPN
cana-4617	230	5	̅	̅	NOUN
cana-4617	230	6	�	�	NOUN
cana-4617	230	7	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	230	8	𝑟	𝑟	NOUN
cana-4617	230	9	𝑙=1	𝑙=1	SYM
cana-4617	230	10	𝑠	𝑠	INTJ
cana-4617	230	11	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	230	12	∞	∞	NUM
cana-4617	230	13	𝑧	𝑧	VERB
cana-4617	230	14	∞	∞	PROPN
cana-4617	230	15	0	0	NUM
cana-4617	230	16	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	230	17	)	)	PUNCT
cana-4617	230	18	�	�	PROPN
cana-4617	230	19	̅	̅	NOUN
cana-4617	230	20	�	�	NOUN
cana-4617	230	21	(𝑧	(𝑧	NOUN
cana-4617	230	22	)	)	PUNCT
cana-4617	230	23	.	.	PUNCT
cana-4617	231	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4617	231	2	)	)	PUNCT
cana-4617	231	3	�	�	PROPN
cana-4617	231	4	̅	̅	NOUN
cana-4617	231	5	�	�	NOUN
cana-4617	231	6	(𝑡	(𝑡	SYM
cana-4617	231	7	)	)	PUNCT
cana-4617	231	8	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	231	9	+	+	CCONJ
cana-4617	231	10	𝑗𝛽2𝐶𝑠−1	𝑗𝛽2𝐶𝑠−1	PROPN
cana-4617	231	11	2𝛾𝑠	2𝛾𝑠	ADJ
cana-4617	231	12	∫	∫	PROPN
cana-4617	231	13	∫	∫	PROPN
cana-4617	231	14	𝑧𝑖𝑡𝑗−4𝛽2	𝑧𝑖𝑡𝑗−4𝛽2	PROPN
cana-4617	231	15	∑	∑	PUNCT
cana-4617	231	16	𝑎𝑙	𝑎𝑙	PROPN
cana-4617	231	17	(	(	PUNCT
cana-4617	231	18	𝑟)(𝑠	𝑟)(𝑠	NOUN
cana-4617	231	19	)	)	PUNCT
cana-4617	231	20	[	[	PUNCT
cana-4617	231	21	�	�	NOUN
cana-4617	231	22	̅	̅	NOUN
cana-4617	231	23	�	�	SYM
cana-4617	231	24	(𝑡	(𝑡	SYM
cana-4617	231	25	)	)	PUNCT
cana-4617	231	26	�	�	PROPN
cana-4617	231	27	̅	̅	NOUN
cana-4617	231	28	�	�	NOUN
cana-4617	231	29	(𝑧	(𝑧	NOUN
cana-4617	231	30	)	)	PUNCT
cana-4617	231	31	]	]	PUNCT
cana-4617	232	1	𝛾𝑙	𝛾𝑙	ADP
cana-4617	232	2	∑	∑	PROPN
cana-4617	232	3	𝑎𝑙(𝑟)[	𝑎𝑙(𝑟)[	PROPN
cana-4617	232	4	�	�	PROPN
cana-4617	232	5	̅	̅	NOUN
cana-4617	232	6	�	�	NOUN
cana-4617	232	7	(𝑧)]𝛾𝑙	(𝑧)]𝛾𝑙	PUNCT
cana-4617	232	8	𝑟	𝑟	NOUN
cana-4617	232	9	𝑙=1	𝑙=1	SYM
cana-4617	232	10	𝑠	𝑠	INTJ
cana-4617	232	11	𝑙=𝑟+1	𝑙=𝑟+1	NOUN
cana-4617	232	12	∞	∞	NUM
cana-4617	232	13	𝑧	𝑧	VERB
cana-4617	232	14	∞	∞	PROPN
cana-4617	232	15	0	0	NUM
cana-4617	232	16	𝑓(𝑧	𝑓(𝑧	NUM
cana-4617	232	17	)	)	PUNCT
cana-4617	232	18	�	�	PROPN
cana-4617	232	19	̅	̅	NOUN
cana-4617	232	20	�	�	NOUN
cana-4617	232	21	(𝑧	(𝑧	NOUN
cana-4617	232	22	)	)	PUNCT
cana-4617	232	23	.	.	PUNCT
cana-4617	233	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-4617	233	2	)	)	PUNCT
cana-4617	233	3	�	�	PROPN
cana-4617	233	4	̅	̅	NOUN
cana-4617	233	5	�	�	NOUN
cana-4617	233	6	(𝑡	(𝑡	SYM
cana-4617	233	7	)	)	PUNCT
cana-4617	233	8	𝑑𝑡𝑑𝑧	𝑑𝑡𝑑𝑧	NOUN
cana-4617	233	9	after	after	ADP
cana-4617	233	10	simplification	simplification	NOUN
cana-4617	233	11	,	,	PUNCT
cana-4617	233	12	the	the	DET
cana-4617	233	13	recurrence	recurrence	NOUN
cana-4617	233	14	relation	relation	NOUN
cana-4617	233	15	in	in	ADP
cana-4617	233	16	equation	equation	NOUN
cana-4617	233	17	(	(	PUNCT
cana-4617	233	18	20	20	NUM
cana-4617	233	19	)	)	PUNCT
cana-4617	233	20	is	be	AUX
cana-4617	233	21	derived	derive	VERB
cana-4617	233	22	.	.	PUNCT
cana-4617	234	1	corollary	corollary	ADJ
cana-4617	234	2	3.2	3.2	NUM
cana-4617	234	3	for	for	ADP
cana-4617	234	4	𝑚1	𝑚1	NOUN
cana-4617	234	5	=	=	SYM
cana-4617	234	6	𝑚2	𝑚2	PROPN
cana-4617	234	7	=	=	SYM
cana-4617	235	1	⋯	⋯	PROPN
cana-4617	235	2	=	=	SYM
cana-4617	235	3	𝑚𝑛−1	𝑚𝑛−1	PROPN
cana-4617	235	4	=	=	PUNCT
cana-4617	235	5	𝑚	𝑚	ADP
cana-4617	235	6	≠	≠	NUM
cana-4617	235	7	−1	−1	NOUN
cana-4617	235	8	the	the	DET
cana-4617	235	9	recurrence	recurrence	NOUN
cana-4617	235	10	relations	relation	NOUN
cana-4617	235	11	for	for	ADP
cana-4617	235	12	product	product	NOUN
cana-4617	235	13	moments	moment	NOUN
cana-4617	235	14	of	of	ADP
cana-4617	235	15	the	the	DET
cana-4617	235	16	generalized	generalize	VERB
cana-4617	235	17	order	order	NOUN
cana-4617	235	18	statistics	statistic	NOUN
cana-4617	235	19	(	(	PUNCT
cana-4617	235	20	gos	gos	PROPN
cana-4617	235	21	)	)	PUNCT
cana-4617	235	22	for	for	ADP
cana-4617	235	23	abrd	abrd	NOUN
cana-4617	235	24	are	be	AUX
cana-4617	235	25	derived	derive	VERB
cana-4617	235	26	from	from	ADP
cana-4617	235	27	equation	equation	NOUN
cana-4617	235	28	(	(	PUNCT
cana-4617	235	29	20	20	NUM
cana-4617	235	30	)	)	PUNCT
cana-4617	235	31	in	in	ADP
cana-4617	235	32	relation	relation	NOUN
cana-4617	235	33	to	to	ADP
cana-4617	235	34	equation	equation	NOUN
cana-4617	235	35	(	(	PUNCT
cana-4617	235	36	7	7	X
cana-4617	235	37	)	)	PUNCT
cana-4617	235	38	is	be	AUX
cana-4617	235	39	given	give	VERB
cana-4617	235	40	as	as	ADP
cana-4617	235	41	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	235	42	,	,	PUNCT
cana-4617	235	43	𝑛	𝑛	PROPN
cana-4617	235	44	,	,	PUNCT
cana-4617	235	45	𝑚	𝑚	PROPN
cana-4617	235	46	,	,	PUNCT
cana-4617	235	47	𝑘	𝑘	NOUN
cana-4617	235	48	)	)	PUNCT
cana-4617	235	49	.	.	PUNCT
cana-4617	236	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	PROPN
cana-4617	236	2	,	,	PUNCT
cana-4617	236	3	𝑛	𝑛	PROPN
cana-4617	236	4	,	,	PUNCT
cana-4617	236	5	𝑚	𝑚	PROPN
cana-4617	236	6	,	,	PUNCT
cana-4617	236	7	𝑘	𝑘	NOUN
cana-4617	236	8	)	)	PUNCT
cana-4617	236	9	]	]	PUNCT
cana-4617	236	10	−	−	PROPN
cana-4617	236	11	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	NOUN
cana-4617	236	12	,	,	PUNCT
cana-4617	236	13	𝑛	𝑛	PROPN
cana-4617	236	14	,	,	PUNCT
cana-4617	236	15	𝑚	𝑚	PROPN
cana-4617	236	16	,	,	PUNCT
cana-4617	236	17	𝑘	𝑘	NOUN
cana-4617	236	18	)	)	PUNCT
cana-4617	236	19	.	.	PUNCT
cana-4617	237	1	𝑍𝑗(𝑠	𝑍𝑗(𝑠	INTJ
cana-4617	237	2	−	−	ADP
cana-4617	237	3	1	1	NUM
cana-4617	237	4	,	,	PUNCT
cana-4617	237	5	𝑛	𝑛	PROPN
cana-4617	237	6	,	,	PUNCT
cana-4617	237	7	𝑚	𝑚	PROPN
cana-4617	237	8	,	,	PUNCT
cana-4617	237	9	𝑘	𝑘	NOUN
cana-4617	237	10	)	)	PUNCT
cana-4617	237	11	]	]	PUNCT
cana-4617	238	1	=	=	PUNCT
cana-4617	238	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	238	3	2𝛾𝑠	2𝛾𝑠	NOUN
cana-4617	238	4	{	{	PUNCT
cana-4617	238	5	𝐸[𝑍𝑖(𝑟	𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	238	6	,	,	PUNCT
cana-4617	238	7	𝑛	𝑛	PROPN
cana-4617	238	8	,	,	PUNCT
cana-4617	238	9	𝑚	𝑚	PROPN
cana-4617	238	10	,	,	PUNCT
cana-4617	238	11	𝑘	𝑘	NOUN
cana-4617	238	12	)	)	PUNCT
cana-4617	238	13	.	.	PUNCT
cana-4617	239	1	𝑍𝑗−2(𝑠	𝑍𝑗−2(𝑠	PROPN
cana-4617	239	2	,	,	PUNCT
cana-4617	239	3	𝑛	𝑛	PROPN
cana-4617	239	4	,	,	PUNCT
cana-4617	239	5	𝑚	𝑚	PROPN
cana-4617	239	6	,	,	PUNCT
cana-4617	239	7	𝑘	𝑘	NOUN
cana-4617	239	8	)	)	PUNCT
cana-4617	239	9	]	]	PUNCT
cana-4617	240	1	+	+	CCONJ
cana-4617	240	2	𝛽2𝐸[𝑍𝑖(𝑟	𝛽2𝐸[𝑍𝑖(𝑟	PROPN
cana-4617	240	3	,	,	PUNCT
cana-4617	240	4	𝑛	𝑛	PROPN
cana-4617	240	5	,	,	PUNCT
cana-4617	240	6	𝑚	𝑚	PROPN
cana-4617	240	7	,	,	PUNCT
cana-4617	240	8	𝑘	𝑘	NOUN
cana-4617	240	9	)	)	PUNCT
cana-4617	240	10	.	.	PUNCT
cana-4617	241	1	𝑍𝑗−4(𝑠	𝑍𝑗−4(𝑠	PROPN
cana-4617	241	2	,	,	PUNCT
cana-4617	241	3	𝑛	𝑛	PROPN
cana-4617	241	4	,	,	PUNCT
cana-4617	241	5	𝑚	𝑚	PROPN
cana-4617	241	6	,	,	PUNCT
cana-4617	241	7	𝑘	𝑘	NOUN
cana-4617	241	8	)	)	PUNCT
cana-4617	241	9	]	]	PUNCT
cana-4617	241	10	}	}	PUNCT
cana-4617	241	11	(	(	PUNCT
cana-4617	241	12	21	21	NUM
cana-4617	241	13	)	)	PUNCT
cana-4617	241	14	proof	proof	NOUN
cana-4617	241	15	.	.	PUNCT
cana-4617	242	1	this	this	PRON
cana-4617	242	2	follows	follow	VERB
cana-4617	242	3	directly	directly	ADV
cana-4617	242	4	from	from	ADP
cana-4617	242	5	equation	equation	NOUN
cana-4617	242	6	(	(	PUNCT
cana-4617	242	7	20	20	NUM
cana-4617	242	8	)	)	PUNCT
cana-4617	242	9	,	,	PUNCT
cana-4617	242	10	considering	consider	VERB
cana-4617	242	11	the	the	DET
cana-4617	242	12	relation	relation	NOUN
cana-4617	242	13	given	give	VERB
cana-4617	242	14	in	in	ADP
cana-4617	242	15	equation	equation	NOUN
cana-4617	242	16	(	(	PUNCT
cana-4617	242	17	7	7	NUM
cana-4617	242	18	)	)	PUNCT
cana-4617	242	19	.	.	PUNCT
cana-4617	243	1	remark	remark	VERB
cana-4617	243	2	3.3	3.3	NUM
cana-4617	243	3	by	by	ADP
cana-4617	243	4	setting	set	VERB
cana-4617	243	5	𝑚	𝑚	X
cana-4617	243	6	=	=	SYM
cana-4617	243	7	0	0	NUM
cana-4617	243	8	,	,	PUNCT
cana-4617	243	9	𝑘	𝑘	X
cana-4617	243	10	=	=	NOUN
cana-4617	243	11	1	1	NUM
cana-4617	243	12	in	in	ADP
cana-4617	243	13	equation	equation	NOUN
cana-4617	243	14	(	(	PUNCT
cana-4617	243	15	21	21	NUM
cana-4617	243	16	)	)	PUNCT
cana-4617	243	17	,	,	PUNCT
cana-4617	243	18	we	we	PRON
cana-4617	243	19	derive	derive	VERB
cana-4617	243	20	the	the	DET
cana-4617	243	21	recurrence	recurrence	NOUN
cana-4617	243	22	relations	relation	NOUN
cana-4617	243	23	for	for	ADP
cana-4617	243	24	product	product	NOUN
cana-4617	243	25	moments	moment	NOUN
cana-4617	243	26	of	of	ADP
cana-4617	243	27	order	order	NOUN
cana-4617	243	28	statistics.as	statistics.as	NUM
cana-4617	243	29	communications	communication	NOUN
cana-4617	243	30	on	on	ADP
cana-4617	243	31	applied	apply	VERB
cana-4617	243	32	nonlinear	nonlinear	ADJ
cana-4617	243	33	analysis	analysis	NOUN
cana-4617	243	34	issn	issn	NOUN
cana-4617	243	35	:	:	PUNCT
cana-4617	243	36	1074	1074	NUM
cana-4617	243	37	-	-	PUNCT
cana-4617	243	38	133x	133x	NUM
cana-4617	243	39	vol	vol	NOUN
cana-4617	243	40	32	32	NUM
cana-4617	243	41	no	no	NOUN
cana-4617	243	42	.	.	PUNCT
cana-4617	244	1	9s	9s	NUM
cana-4617	244	2	(	(	PUNCT
cana-4617	244	3	2025	2025	NUM
cana-4617	244	4	)	)	PUNCT
cana-4617	244	5	3032	3032	NUM
cana-4617	244	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	245	1	𝐸(𝑍𝑟,𝑠:𝑛	𝐸(𝑍𝑟,𝑠:𝑛	VERB
cana-4617	245	2	𝑖,𝑗	𝑖,𝑗	PRON
cana-4617	245	3	)	)	PUNCT
cana-4617	245	4	−	−	ADP
cana-4617	245	5	𝐸(𝑍𝑟,𝑠−1:𝑛	𝐸(𝑍𝑟,𝑠−1:𝑛	INTJ
cana-4617	245	6	𝑖,𝑗	𝑖,𝑗	NOUN
cana-4617	245	7	)	)	PUNCT
cana-4617	246	1	=	=	PUNCT
cana-4617	246	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	246	3	2(𝑛	2(𝑛	NUM
cana-4617	247	1	−	−	NOUN
cana-4617	247	2	𝑠	𝑠	INTJ
cana-4617	247	3	+	+	NOUN
cana-4617	247	4	1	1	NUM
cana-4617	247	5	)	)	PUNCT
cana-4617	248	1	[	[	X
cana-4617	248	2	𝐸(𝑍𝑟,𝑠∶𝑛	𝐸(𝑍𝑟,𝑠∶𝑛	NOUN
cana-4617	248	3	𝑖,𝑗−2	𝑖,𝑗−2	NUM
cana-4617	248	4	)	)	PUNCT
cana-4617	249	1	+	+	CCONJ
cana-4617	249	2	𝛽2𝐸(𝑍𝑟,𝑠∶𝑛	𝛽2𝐸(𝑍𝑟,𝑠∶𝑛	ADP
cana-4617	249	3	𝑖,𝑗−4	𝑖,𝑗−4	PROPN
cana-4617	249	4	)	)	PUNCT
cana-4617	249	5	]	]	PUNCT
cana-4617	249	6	(	(	PUNCT
cana-4617	249	7	22	22	NUM
cana-4617	249	8	)	)	PUNCT
cana-4617	249	9	remark	remark	NOUN
cana-4617	249	10	3.4	3.4	NUM
cana-4617	249	11	setting	set	VERB
cana-4617	249	12	𝑚	𝑚	X
cana-4617	249	13	=	=	PUNCT
cana-4617	249	14	−1	−1	NOUN
cana-4617	249	15	in	in	ADP
cana-4617	249	16	equation	equation	NOUN
cana-4617	249	17	(	(	PUNCT
cana-4617	249	18	21	21	NUM
cana-4617	249	19	)	)	PUNCT
cana-4617	249	20	,	,	PUNCT
cana-4617	249	21	gives	give	VERB
cana-4617	249	22	us	we	PRON
cana-4617	249	23	the	the	DET
cana-4617	249	24	recurrence	recurrence	NOUN
cana-4617	249	25	relations	relation	NOUN
cana-4617	249	26	for	for	ADP
cana-4617	249	27	product	product	NOUN
cana-4617	249	28	moments	moment	NOUN
cana-4617	249	29	of	of	ADP
cana-4617	249	30	kth	kth	PROPN
cana-4617	249	31	record	record	NOUN
cana-4617	249	32	values	value	NOUN
cana-4617	249	33	as	as	ADP
cana-4617	249	34	𝐸	𝐸	PROPN
cana-4617	249	35	[	[	X
cana-4617	249	36	(	(	PUNCT
cana-4617	249	37	𝑍𝑟	𝑍𝑟	PROPN
cana-4617	249	38	(	(	PUNCT
cana-4617	249	39	𝑘	𝑘	NOUN
cana-4617	249	40	)	)	PUNCT
cana-4617	249	41	)	)	PUNCT
cana-4617	250	1	𝑖	𝑖	X
cana-4617	250	2	(	(	PUNCT
cana-4617	250	3	𝑍𝑠	𝑍𝑠	PROPN
cana-4617	250	4	(	(	PUNCT
cana-4617	250	5	𝑘	𝑘	NOUN
cana-4617	250	6	)	)	PUNCT
cana-4617	250	7	)	)	PUNCT
cana-4617	251	1	𝑗	𝑗	X
cana-4617	251	2	]	]	X
cana-4617	251	3	−	−	PROPN
cana-4617	251	4	𝐸	𝐸	PROPN
cana-4617	251	5	[	[	X
cana-4617	251	6	(	(	PUNCT
cana-4617	251	7	𝑍𝑟	𝑍𝑟	PROPN
cana-4617	251	8	(	(	PUNCT
cana-4617	251	9	𝑘	𝑘	NOUN
cana-4617	251	10	)	)	PUNCT
cana-4617	251	11	)	)	PUNCT
cana-4617	252	1	𝑖	𝑖	X
cana-4617	253	1	(	(	PUNCT
cana-4617	253	2	𝑍𝑠−1	𝑍𝑠−1	PROPN
cana-4617	253	3	(	(	PUNCT
cana-4617	253	4	𝑘	𝑘	NOUN
cana-4617	253	5	)	)	PUNCT
cana-4617	253	6	)	)	PUNCT
cana-4617	253	7	𝑗	𝑗	X
cana-4617	253	8	]	]	X
cana-4617	254	1	=	=	PUNCT
cana-4617	255	1	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	256	1	2𝑘	2𝑘	NUM
cana-4617	256	2	{	{	PUNCT
cana-4617	256	3	𝐸	𝐸	PROPN
cana-4617	256	4	[	[	X
cana-4617	256	5	(	(	PUNCT
cana-4617	256	6	𝑍𝑟	𝑍𝑟	PROPN
cana-4617	256	7	(	(	PUNCT
cana-4617	256	8	𝑘	𝑘	NOUN
cana-4617	256	9	)	)	PUNCT
cana-4617	256	10	)	)	PUNCT
cana-4617	257	1	𝑖	𝑖	X
cana-4617	257	2	(	(	PUNCT
cana-4617	257	3	𝑍𝑠	𝑍𝑠	PROPN
cana-4617	257	4	(	(	PUNCT
cana-4617	257	5	𝑘	𝑘	NOUN
cana-4617	257	6	)	)	PUNCT
cana-4617	257	7	)	)	PUNCT
cana-4617	258	1	𝑗−2	𝑗−2	PRON
cana-4617	258	2	]	]	PUNCT
cana-4617	259	1	+	+	CCONJ
cana-4617	259	2	𝛽2𝐸	𝛽2𝐸	X
cana-4617	259	3	[	[	X
cana-4617	259	4	(	(	PUNCT
cana-4617	259	5	𝑍𝑟	𝑍𝑟	PROPN
cana-4617	259	6	(	(	PUNCT
cana-4617	259	7	𝑘	𝑘	NOUN
cana-4617	259	8	)	)	PUNCT
cana-4617	259	9	)	)	PUNCT
cana-4617	260	1	𝑖	𝑖	X
cana-4617	260	2	(	(	PUNCT
cana-4617	260	3	𝑍𝑠	𝑍𝑠	PROPN
cana-4617	260	4	(	(	PUNCT
cana-4617	260	5	𝑘	𝑘	NOUN
cana-4617	260	6	)	)	PUNCT
cana-4617	260	7	)	)	PUNCT
cana-4617	261	1	𝑗−4	𝑗−4	PROPN
cana-4617	261	2	]	]	PUNCT
cana-4617	261	3	}	}	PUNCT
cana-4617	261	4	(	(	PUNCT
cana-4617	261	5	23	23	NUM
cana-4617	261	6	)	)	SYM
cana-4617	261	7	4	4	NUM
cana-4617	261	8	.	.	PUNCT
cana-4617	261	9	characterization	characterization	NOUN
cana-4617	261	10	theorem	theorem	VERB
cana-4617	261	11	4.1	4.1	NUM
cana-4617	261	12	let	let	VERB
cana-4617	261	13	z	z	PRON
cana-4617	261	14	be	be	AUX
cana-4617	261	15	a	a	DET
cana-4617	261	16	non	non	ADJ
cana-4617	261	17	-	-	ADJ
cana-4617	261	18	negative	negative	ADJ
cana-4617	261	19	random	random	ADJ
cana-4617	261	20	variable	variable	NOUN
cana-4617	261	21	with	with	ADP
cana-4617	261	22	a	a	DET
cana-4617	261	23	continuous	continuous	ADJ
cana-4617	261	24	distribution	distribution	NOUN
cana-4617	261	25	function	function	NOUN
cana-4617	262	1	f	f	PROPN
cana-4617	262	2	(	(	PUNCT
cana-4617	262	3	z	z	NOUN
cana-4617	262	4	)	)	PUNCT
cana-4617	262	5	such	such	ADJ
cana-4617	262	6	that	that	SCONJ
cana-4617	262	7	f	f	PROPN
cana-4617	262	8	(	(	PUNCT
cana-4617	262	9	0	0	NUM
cana-4617	262	10	)	)	PUNCT
cana-4617	262	11	=	=	SYM
cana-4617	262	12	0	0	NUM
cana-4617	262	13	and	and	CCONJ
cana-4617	262	14	0	0	NUM
cana-4617	262	15	<	<	X
cana-4617	262	16	f	f	X
cana-4617	262	17	(	(	PUNCT
cana-4617	262	18	z	z	NOUN
cana-4617	262	19	)	)	PUNCT
cana-4617	262	20	<	<	X
cana-4617	262	21	1	1	NUM
cana-4617	262	22	for	for	ADP
cana-4617	262	23	all	all	DET
cana-4617	262	24	z	z	NOUN
cana-4617	262	25	>	>	X
cana-4617	262	26	0	0	NUM
cana-4617	262	27	,	,	PUNCT
cana-4617	262	28	then	then	ADV
cana-4617	262	29	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NUM
cana-4617	262	30	,	,	PUNCT
cana-4617	262	31	𝑛	𝑛	PROPN
cana-4617	262	32	,	,	PUNCT
cana-4617	262	33	𝑚	𝑚	PROPN
cana-4617	262	34	,	,	PUNCT
cana-4617	262	35	𝑘	𝑘	NOUN
cana-4617	262	36	)	)	PUNCT
cana-4617	262	37	]	]	PUNCT
cana-4617	263	1	−	−	PROPN
cana-4617	263	2	𝐸[𝑍𝑗(𝑟	𝐸[𝑍𝑗(𝑟	NOUN
cana-4617	263	3	−	−	PROPN
cana-4617	263	4	1	1	NUM
cana-4617	263	5	,	,	PUNCT
cana-4617	263	6	𝑛	𝑛	PROPN
cana-4617	263	7	,	,	PUNCT
cana-4617	263	8	𝑚	𝑚	PROPN
cana-4617	263	9	,	,	PUNCT
cana-4617	263	10	𝑘	𝑘	NOUN
cana-4617	263	11	)	)	PUNCT
cana-4617	263	12	]	]	PUNCT
cana-4617	264	1	=	=	PUNCT
cana-4617	264	2	𝑗𝛽2	𝑗𝛽2	PROPN
cana-4617	264	3	2𝛾𝑟	2𝛾𝑟	NOUN
cana-4617	264	4	{	{	PUNCT
cana-4617	264	5	𝐸[𝑍𝑗−2(𝑟	𝐸[𝑍𝑗−2(𝑟	NOUN
cana-4617	264	6	,	,	PUNCT
cana-4617	264	7	𝑛	𝑛	PROPN
cana-4617	264	8	,	,	PUNCT
cana-4617	264	9	𝑚	𝑚	PROPN
cana-4617	264	10	,	,	PUNCT
cana-4617	264	11	𝑘	𝑘	NOUN
cana-4617	264	12	)	)	PUNCT
cana-4617	264	13	]	]	PUNCT
cana-4617	265	1	+	+	CCONJ
cana-4617	265	2	𝛽2𝐸[𝑍𝑗−4(𝑟	𝛽2𝐸[𝑍𝑗−4(𝑟	ADJ
cana-4617	265	3	,	,	PUNCT
cana-4617	265	4	𝑛	𝑛	PROPN
cana-4617	265	5	,	,	PUNCT
cana-4617	265	6	𝑚	𝑚	PROPN
cana-4617	265	7	,	,	PUNCT
cana-4617	265	8	𝑘	𝑘	NOUN
cana-4617	265	9	)	)	PUNCT
cana-4617	265	10	]	]	PUNCT
cana-4617	265	11	}	}	PUNCT
cana-4617	265	12	if	if	SCONJ
cana-4617	265	13	and	and	CCONJ
cana-4617	265	14	only	only	ADV
cana-4617	265	15	if	if	SCONJ
cana-4617	265	16	�	�	NOUN
cana-4617	265	17	̅	̅	VERB
cana-4617	265	18	�	�	NOUN
cana-4617	265	19	(𝑧	(𝑧	NOUN
cana-4617	265	20	)	)	PUNCT
cana-4617	265	21	=	=	PUNCT
cana-4617	265	22	(	(	PUNCT
cana-4617	265	23	1	1	NUM
cana-4617	265	24	+	+	NUM
cana-4617	265	25	𝑧2	𝑧2	PROPN
cana-4617	265	26	𝛽2	𝛽2	PROPN
cana-4617	265	27	)	)	PUNCT
cana-4617	265	28	𝒆𝒙𝒑	𝒆𝒙𝒑	NOUN
cana-4617	265	29	(	(	PUNCT
cana-4617	265	30	−	−	PROPN
cana-4617	265	31	𝑧2	𝑧2	PROPN
cana-4617	265	32	𝛽2	𝛽2	PROPN
cana-4617	265	33	)	)	PUNCT
cana-4617	265	34	(	(	PUNCT
cana-4617	265	35	24	24	NUM
cana-4617	265	36	)	)	PUNCT
cana-4617	265	37	proof	proof	NOUN
cana-4617	265	38	:	:	PUNCT
cana-4617	265	39	the	the	DET
cana-4617	265	40	necessity	necessity	NOUN
cana-4617	265	41	part	part	NOUN
cana-4617	265	42	follows	follow	VERB
cana-4617	265	43	directly	directly	ADV
cana-4617	265	44	from	from	ADP
cana-4617	265	45	equation	equation	NOUN
cana-4617	265	46	(	(	PUNCT
cana-4617	265	47	17	17	NUM
cana-4617	265	48	)	)	PUNCT
cana-4617	265	49	.	.	PUNCT
cana-4617	266	1	conversely	conversely	ADV
cana-4617	266	2	,	,	PUNCT
cana-4617	266	3	if	if	SCONJ
cana-4617	266	4	the	the	DET
cana-4617	266	5	recurrence	recurrence	NOUN
cana-4617	266	6	relation	relation	NOUN
cana-4617	266	7	given	give	VERB
cana-4617	266	8	in	in	ADP
cana-4617	266	9	equation	equation	NOUN
cana-4617	266	10	(	(	PUNCT
cana-4617	266	11	24	24	NUM
cana-4617	266	12	)	)	PUNCT
cana-4617	266	13	is	be	AUX
cana-4617	266	14	satisfied	satisfied	ADJ
cana-4617	266	15	,	,	PUNCT
cana-4617	266	16	then	then	ADV
cana-4617	266	17	by	by	ADP
cana-4617	266	18	using	use	VERB
cana-4617	266	19	equation	equation	NOUN
cana-4617	266	20	(	(	PUNCT
cana-4617	266	21	8)	8)	NUM
cana-4617	266	22	,	,	PUNCT
cana-4617	266	23	we	we	PRON
cana-4617	266	24	establish	establish	VERB
cana-4617	266	25	that	that	SCONJ
cana-4617	266	26	𝐶𝑟−1	𝐶𝑟−1	PROPN
cana-4617	266	27	(	(	PUNCT
cana-4617	266	28	𝑟	𝑟	NOUN
cana-4617	266	29	−	−	PROPN
cana-4617	266	30	1	1	NUM
cana-4617	266	31	)	)	PUNCT
cana-4617	266	32	!	!	PUNCT
cana-4617	267	1	∫	∫	PROPN
cana-4617	268	1	𝑍𝑗	𝑍𝑗	PROPN
cana-4617	268	2	[	[	NOUN
cana-4617	268	3	�	�	NOUN
cana-4617	268	4	̅	̅	NOUN
cana-4617	268	5	�	�	NOUN
cana-4617	268	6	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	268	7	𝑟−1	𝑟−1	PROPN
cana-4617	268	8	[	[	X
cana-4617	268	9	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	268	10	)	)	PUNCT
cana-4617	268	11	]	]	PUNCT
cana-4617	268	12	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	268	13	∞	∞	PROPN
cana-4617	268	14	0	0	NUM
cana-4617	269	1	−	−	PROPN
cana-4617	269	2	𝐶𝑟−2	𝐶𝑟−2	PROPN
cana-4617	269	3	(	(	PUNCT
cana-4617	269	4	𝑟	𝑟	NOUN
cana-4617	269	5	−	−	PROPN
cana-4617	269	6	2	2	NUM
cana-4617	269	7	)	)	PUNCT
cana-4617	269	8	!	!	PUNCT
cana-4617	270	1	∫	∫	PROPN
cana-4617	271	1	𝑍𝑗	𝑍𝑗	PROPN
cana-4617	271	2	[	[	NOUN
cana-4617	271	3	�	�	NOUN
cana-4617	271	4	̅	̅	NOUN
cana-4617	271	5	�	�	PROPN
cana-4617	271	6	(𝑧)]𝛾𝑟−1−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1−1𝑓(𝑧)𝑔𝑚	PROPN
cana-4617	271	7	𝑟−2	𝑟−2	PROPN
cana-4617	271	8	[	[	X
cana-4617	271	9	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	271	10	)	)	PUNCT
cana-4617	271	11	]	]	PUNCT
cana-4617	271	12	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	271	13	∞	∞	NOUN
cana-4617	271	14	0	0	NUM
cana-4617	271	15	=	=	PUNCT
cana-4617	272	1	𝑗	𝑗	PROPN
cana-4617	272	2	𝛽2𝐶𝑟−1	𝛽2𝐶𝑟−1	PROPN
cana-4617	272	3	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	272	4	−	−	NOUN
cana-4617	272	5	1	1	NUM
cana-4617	272	6	)	)	PUNCT
cana-4617	272	7	!	!	PUNCT
cana-4617	273	1	∫	∫	PROPN
cana-4617	273	2	𝑍𝑗−2	𝑍𝑗−2	PROPN
cana-4617	274	1	[	[	PUNCT
cana-4617	274	2	�	�	NOUN
cana-4617	274	3	̅	̅	NOUN
cana-4617	274	4	�	�	NOUN
cana-4617	274	5	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	274	6	𝑟−1	𝑟−1	PROPN
cana-4617	274	7	[	[	X
cana-4617	274	8	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	274	9	)	)	PUNCT
cana-4617	274	10	]	]	PUNCT
cana-4617	274	11	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	274	12	∞	∞	NOUN
cana-4617	274	13	0	0	NUM
cana-4617	275	1	+	+	CCONJ
cana-4617	275	2	𝑗	𝑗	PRON
cana-4617	275	3	𝛽4𝐶𝑟−1	𝛽4𝐶𝑟−1	PROPN
cana-4617	275	4	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	275	5	−	−	NOUN
cana-4617	275	6	1	1	NUM
cana-4617	275	7	)	)	PUNCT
cana-4617	275	8	!	!	PUNCT
cana-4617	276	1	∫	∫	PROPN
cana-4617	277	1	𝑍𝑗−4	𝑍𝑗−4	PROPN
cana-4617	277	2	[	[	X
cana-4617	277	3	�	�	NOUN
cana-4617	277	4	̅	̅	NOUN
cana-4617	277	5	�	�	NOUN
cana-4617	277	6	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	277	7	𝑟−1	𝑟−1	PROPN
cana-4617	277	8	[	[	X
cana-4617	277	9	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	277	10	)	)	PUNCT
cana-4617	277	11	]	]	PUNCT
cana-4617	277	12	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	277	13	∞	∞	PROPN
cana-4617	277	14	0	0	NUM
cana-4617	277	15	integrating	integrate	VERB
cana-4617	277	16	the	the	DET
cana-4617	277	17	first	first	ADJ
cana-4617	277	18	term	term	NOUN
cana-4617	277	19	in	in	ADP
cana-4617	277	20	left	left	ADJ
cana-4617	277	21	-	-	PUNCT
cana-4617	277	22	hand	hand	NOUN
cana-4617	277	23	side	side	NOUN
cana-4617	277	24	by	by	ADP
cana-4617	277	25	parts	part	NOUN
cana-4617	277	26	,	,	PUNCT
cana-4617	277	27	we	we	PRON
cana-4617	277	28	get	get	VERB
cana-4617	277	29	communications	communication	NOUN
cana-4617	277	30	on	on	ADP
cana-4617	277	31	applied	apply	VERB
cana-4617	277	32	nonlinear	nonlinear	ADJ
cana-4617	277	33	analysis	analysis	NOUN
cana-4617	277	34	issn	issn	NOUN
cana-4617	277	35	:	:	PUNCT
cana-4617	277	36	1074	1074	NUM
cana-4617	277	37	-	-	PUNCT
cana-4617	277	38	133x	133x	NUM
cana-4617	277	39	vol	vol	NOUN
cana-4617	277	40	32	32	NUM
cana-4617	277	41	no	no	NOUN
cana-4617	277	42	.	.	PUNCT
cana-4617	278	1	9s	9s	NUM
cana-4617	278	2	(	(	PUNCT
cana-4617	278	3	2025	2025	NUM
cana-4617	278	4	)	)	PUNCT
cana-4617	278	5	3033	3033	NUM
cana-4617	279	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	279	2	𝑗𝐶𝑟−1	𝑗𝐶𝑟−1	VERB
cana-4617	279	3	𝛾𝑟(𝑟	𝛾𝑟(𝑟	PUNCT
cana-4617	279	4	−	−	PROPN
cana-4617	279	5	1	1	NUM
cana-4617	279	6	)	)	PUNCT
cana-4617	279	7	!	!	PUNCT
cana-4617	280	1	∫	∫	PROPN
cana-4617	281	1	𝑍𝑗−1	𝑍𝑗−1	PROPN
cana-4617	281	2	[	[	X
cana-4617	281	3	�	�	NOUN
cana-4617	281	4	̅	̅	NOUN
cana-4617	281	5	�	�	NOUN
cana-4617	281	6	(𝑧)]𝛾𝑟	(𝑧)]𝛾𝑟	NOUN
cana-4617	281	7	𝑔𝑚	𝑔𝑚	VERB
cana-4617	281	8	𝑟−1	𝑟−1	PROPN
cana-4617	281	9	[	[	X
cana-4617	281	10	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	281	11	)	)	PUNCT
cana-4617	281	12	]	]	PUNCT
cana-4617	281	13	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	281	14	∞	∞	PROPN
cana-4617	281	15	0	0	NUM
cana-4617	282	1	−	−	NOUN
cana-4617	282	2	𝑗	𝑗	INTJ
cana-4617	282	3	𝛽2𝐶𝑟−1	𝛽2𝐶𝑟−1	PROPN
cana-4617	282	4	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	282	5	−	−	NOUN
cana-4617	282	6	1	1	NUM
cana-4617	282	7	)	)	PUNCT
cana-4617	282	8	!	!	PUNCT
cana-4617	283	1	∫	∫	PROPN
cana-4617	283	2	𝑍𝑗−2	𝑍𝑗−2	PROPN
cana-4617	284	1	[	[	PUNCT
cana-4617	284	2	�	�	NOUN
cana-4617	284	3	̅	̅	NOUN
cana-4617	284	4	�	�	NOUN
cana-4617	284	5	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	284	6	𝑟−1	𝑟−1	PROPN
cana-4617	284	7	[	[	X
cana-4617	284	8	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	284	9	)	)	PUNCT
cana-4617	284	10	]	]	PUNCT
cana-4617	284	11	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	284	12	∞	∞	PROPN
cana-4617	284	13	0	0	NUM
cana-4617	285	1	−	−	NOUN
cana-4617	286	1	𝑗	𝑗	INTJ
cana-4617	286	2	𝛽4𝐶𝑟−1	𝛽4𝐶𝑟−1	PROPN
cana-4617	286	3	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	286	4	−	−	NOUN
cana-4617	286	5	1	1	NUM
cana-4617	286	6	)	)	PUNCT
cana-4617	286	7	!	!	PUNCT
cana-4617	287	1	∫	∫	PROPN
cana-4617	288	1	𝑍𝑗−4	𝑍𝑗−4	PROPN
cana-4617	288	2	[	[	X
cana-4617	288	3	�	�	NOUN
cana-4617	288	4	̅	̅	NOUN
cana-4617	288	5	�	�	NOUN
cana-4617	288	6	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	288	7	𝑟−1	𝑟−1	PROPN
cana-4617	288	8	[	[	X
cana-4617	288	9	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	288	10	)	)	PUNCT
cana-4617	288	11	]	]	PUNCT
cana-4617	288	12	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	288	13	=	=	NOUN
cana-4617	288	14	0	0	NUM
cana-4617	288	15	∞	∞	NUM
cana-4617	288	16	0	0	NUM
cana-4617	289	1	then	then	ADV
cana-4617	289	2	𝑗𝐶𝑟−1	𝑗𝐶𝑟−1	VERB
cana-4617	289	3	𝛾𝑟(𝑟	𝛾𝑟(𝑟	PUNCT
cana-4617	289	4	−	−	PROPN
cana-4617	289	5	1	1	NUM
cana-4617	289	6	)	)	PUNCT
cana-4617	289	7	!	!	PUNCT
cana-4617	290	1	∫	∫	PROPN
cana-4617	291	1	𝑍𝑗−1	𝑍𝑗−1	PROPN
cana-4617	291	2	[	[	X
cana-4617	291	3	�	�	NOUN
cana-4617	291	4	̅	̅	NOUN
cana-4617	291	5	�	�	PROPN
cana-4617	291	6	(𝑧)]𝛾𝑟−1	(𝑧)]𝛾𝑟−1	PUNCT
cana-4617	291	7	�	�	NOUN
cana-4617	291	8	̅	̅	NOUN
cana-4617	291	9	�	�	NOUN
cana-4617	291	10	(𝑧	(𝑧	NOUN
cana-4617	291	11	)	)	PUNCT
cana-4617	291	12	𝑔𝑚	𝑔𝑚	NOUN
cana-4617	291	13	𝑟−1	𝑟−1	PROPN
cana-4617	292	1	[	[	X
cana-4617	292	2	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	292	3	)	)	PUNCT
cana-4617	292	4	]	]	PUNCT
cana-4617	293	1	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	293	2	∞	∞	PROPN
cana-4617	293	3	0	0	NUM
cana-4617	294	1	−	−	NOUN
cana-4617	294	2	𝑗	𝑗	INTJ
cana-4617	294	3	𝛽2𝐶𝑟−1	𝛽2𝐶𝑟−1	PROPN
cana-4617	294	4	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	294	5	−	−	NOUN
cana-4617	294	6	1	1	NUM
cana-4617	294	7	)	)	PUNCT
cana-4617	294	8	!	!	PUNCT
cana-4617	295	1	∫	∫	PROPN
cana-4617	295	2	𝑍𝑗−2	𝑍𝑗−2	PROPN
cana-4617	296	1	[	[	PUNCT
cana-4617	296	2	�	�	NOUN
cana-4617	296	3	̅	̅	NOUN
cana-4617	296	4	�	�	NOUN
cana-4617	296	5	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	296	6	𝑟−1	𝑟−1	PROPN
cana-4617	296	7	[	[	X
cana-4617	296	8	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	296	9	)	)	PUNCT
cana-4617	296	10	]	]	PUNCT
cana-4617	296	11	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	296	12	∞	∞	PROPN
cana-4617	296	13	0	0	NUM
cana-4617	297	1	−	−	NOUN
cana-4617	298	1	𝑗	𝑗	INTJ
cana-4617	298	2	𝛽2𝐶𝑟−1	𝛽2𝐶𝑟−1	PROPN
cana-4617	298	3	2𝛾𝑟(𝑟	2𝛾𝑟(𝑟	NUM
cana-4617	298	4	−	−	NOUN
cana-4617	298	5	1	1	NUM
cana-4617	298	6	)	)	PUNCT
cana-4617	298	7	!	!	PUNCT
cana-4617	299	1	∫	∫	PROPN
cana-4617	299	2	𝛽2	𝛽2	PROPN
cana-4617	299	3	𝑍−2𝑍𝑗−2	𝑍−2𝑍𝑗−2	NUM
cana-4617	299	4	[	[	PUNCT
cana-4617	299	5	�	�	NOUN
cana-4617	299	6	̅	̅	NOUN
cana-4617	299	7	�	�	NOUN
cana-4617	299	8	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	299	9	𝑟−1	𝑟−1	PROPN
cana-4617	300	1	[	[	X
cana-4617	300	2	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	300	3	)	)	PUNCT
cana-4617	300	4	]	]	PUNCT
cana-4617	301	1	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	301	2	=	=	SYM
cana-4617	301	3	0	0	NUM
cana-4617	301	4	∞	∞	NUM
cana-4617	301	5	0	0	NUM
cana-4617	302	1	this	this	PRON
cana-4617	302	2	implies	imply	VERB
cana-4617	302	3	that	that	SCONJ
cana-4617	302	4	𝑗𝐶𝑟−1	𝑗𝐶𝑟−1	VERB
cana-4617	302	5	𝛾𝑟(𝑟	𝛾𝑟(𝑟	PUNCT
cana-4617	302	6	−	−	PROPN
cana-4617	302	7	1	1	NUM
cana-4617	302	8	)	)	PUNCT
cana-4617	302	9	!	!	PUNCT
cana-4617	303	1	∫	∫	PROPN
cana-4617	304	1	𝑍𝑗−1	𝑍𝑗−1	PROPN
cana-4617	304	2	[	[	X
cana-4617	304	3	�	�	NOUN
cana-4617	304	4	̅	̅	NOUN
cana-4617	304	5	�	�	PROPN
cana-4617	304	6	(𝑧)]𝛾𝑟−1	(𝑧)]𝛾𝑟−1	PUNCT
cana-4617	304	7	�	�	NOUN
cana-4617	304	8	̅	̅	NOUN
cana-4617	304	9	�	�	NOUN
cana-4617	304	10	(𝑧	(𝑧	NOUN
cana-4617	304	11	)	)	PUNCT
cana-4617	304	12	𝑔𝑚	𝑔𝑚	NOUN
cana-4617	304	13	𝑟−1	𝑟−1	PROPN
cana-4617	305	1	[	[	X
cana-4617	305	2	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	305	3	)	)	PUNCT
cana-4617	305	4	]	]	PUNCT
cana-4617	306	1	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	306	2	∞	∞	PROPN
cana-4617	306	3	0	0	NUM
cana-4617	307	1	−	−	NOUN
cana-4617	308	1	𝑗	𝑗	INTJ
cana-4617	308	2	𝐶𝑟−1	𝐶𝑟−1	INTJ
cana-4617	308	3	𝛾𝑟(𝑟	𝛾𝑟(𝑟	PUNCT
cana-4617	308	4	−	−	PROPN
cana-4617	309	1	1	1	NUM
cana-4617	309	2	)	)	PUNCT
cana-4617	309	3	!	!	PUNCT
cana-4617	310	1	∫	∫	PROPN
cana-4617	310	2	𝛽2	𝛽2	PROPN
cana-4617	310	3	2	2	NUM
cana-4617	310	4	[	[	X
cana-4617	310	5	𝑧−1	𝑧−1	PROPN
cana-4617	310	6	+	+	CCONJ
cana-4617	310	7	𝛽2	𝛽2	PROPN
cana-4617	310	8	𝑍−3]𝑍𝑗−1	𝑍−3]𝑍𝑗−1	PROPN
cana-4617	310	9	[	[	X
cana-4617	310	10	�	�	NOUN
cana-4617	310	11	̅	̅	NOUN
cana-4617	310	12	�	�	NOUN
cana-4617	310	13	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	(𝑧)]𝛾𝑟−1𝑓(𝑧)𝑔𝑚	PUNCT
cana-4617	310	14	𝑟−1	𝑟−1	PROPN
cana-4617	310	15	[	[	X
cana-4617	310	16	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	310	17	)	)	PUNCT
cana-4617	310	18	]	]	PUNCT
cana-4617	310	19	𝑑𝑧	𝑑𝑧	PROPN
cana-4617	311	1	=	=	SYM
cana-4617	311	2	0	0	NUM
cana-4617	311	3	∞	∞	NOUN
cana-4617	311	4	0	0	PUNCT
cana-4617	312	1	therefore	therefore	ADV
cana-4617	312	2	,	,	PUNCT
cana-4617	312	3	𝑗𝐶𝑟−1	𝑗𝐶𝑟−1	ADJ
cana-4617	312	4	𝛾𝑟(𝑟	𝛾𝑟(𝑟	PUNCT
cana-4617	312	5	−	−	PROPN
cana-4617	312	6	1	1	NUM
cana-4617	312	7	)	)	PUNCT
cana-4617	312	8	!	!	PUNCT
cana-4617	313	1	∫	∫	PROPN
cana-4617	314	1	𝑍𝑗−1	𝑍𝑗−1	PROPN
cana-4617	314	2	[	[	X
cana-4617	314	3	�	�	NOUN
cana-4617	314	4	̅	̅	NOUN
cana-4617	314	5	�	�	PROPN
cana-4617	314	6	(𝑧)]𝛾𝑟−1	(𝑧)]𝛾𝑟−1	PUNCT
cana-4617	314	7	𝑔𝑚	𝑔𝑚	PROPN
cana-4617	314	8	𝑟−1	𝑟−1	PROPN
cana-4617	314	9	[	[	X
cana-4617	314	10	𝐹(𝑧	𝐹(𝑧	NUM
cana-4617	314	11	)	)	PUNCT
cana-4617	314	12	]	]	PUNCT
cana-4617	314	13	{	{	PUNCT
cana-4617	314	14	�	�	NOUN
cana-4617	314	15	̅	̅	NOUN
cana-4617	314	16	�	�	NOUN
cana-4617	314	17	(𝑧	(𝑧	NOUN
cana-4617	314	18	)	)	PUNCT
cana-4617	314	19	−	−	PROPN
cana-4617	314	20	𝛽2	𝛽2	PROPN
cana-4617	314	21	2	2	NUM
cana-4617	314	22	[	[	X
cana-4617	314	23	𝑧−1	𝑧−1	PROPN
cana-4617	314	24	+	+	PROPN
cana-4617	314	25	𝛽2	𝛽2	NOUN
cana-4617	314	26	𝑍−3]𝑓(𝑧	𝑍−3]𝑓(𝑧	NUM
cana-4617	314	27	)	)	PUNCT
cana-4617	314	28	}	}	PUNCT
cana-4617	314	29	𝑑𝑧	𝑑𝑧	NOUN
cana-4617	314	30	∞	∞	NOUN
cana-4617	314	31	0	0	NUM
cana-4617	315	1	=	=	SYM
cana-4617	315	2	0	0	NUM
cana-4617	315	3	(	(	PUNCT
cana-4617	315	4	25	25	NUM
cana-4617	315	5	)	)	PUNCT
cana-4617	315	6	now	now	ADV
cana-4617	315	7	applying	apply	VERB
cana-4617	315	8	a	a	DET
cana-4617	315	9	generalization	generalization	NOUN
cana-4617	315	10	of	of	ADP
cana-4617	315	11	the	the	DET
cana-4617	315	12	muntz	muntz	PROPN
cana-4617	315	13	-	-	PUNCT
cana-4617	315	14	szasz	szasz	NOUN
cana-4617	315	15	theorem	theorem	NOUN
cana-4617	315	16	(	(	PUNCT
cana-4617	315	17	by	by	ADP
cana-4617	315	18	hwang	hwang	PROPN
cana-4617	315	19	.	.	PUNCT
cana-4617	315	20	and	and	CCONJ
cana-4617	315	21	lin	lin	PROPN
cana-4617	315	22	.	.	PUNCT
cana-4617	316	1	(	(	PUNCT
cana-4617	316	2	1984	1984	NUM
cana-4617	316	3	)	)	PUNCT
cana-4617	316	4	)	)	PUNCT
cana-4617	317	1	to	to	ADP
cana-4617	317	2	equation	equation	NOUN
cana-4617	317	3	(	(	PUNCT
cana-4617	317	4	25	25	NUM
cana-4617	317	5	)	)	PUNCT
cana-4617	317	6	,	,	PUNCT
cana-4617	317	7	we	we	PRON
cana-4617	317	8	get	get	VERB
cana-4617	317	9	�	�	NOUN
cana-4617	317	10	̅	̅	NOUN
cana-4617	317	11	�	�	NOUN
cana-4617	317	12	(𝑧	(𝑧	NOUN
cana-4617	317	13	)	)	PUNCT
cana-4617	317	14	−	−	PROPN
cana-4617	317	15	𝛽2	𝛽2	PROPN
cana-4617	317	16	2	2	NUM
cana-4617	317	17	[	[	X
cana-4617	317	18	𝑧−1	𝑧−1	PROPN
cana-4617	317	19	+	+	PROPN
cana-4617	317	20	𝛽2	𝛽2	NOUN
cana-4617	317	21	𝑍−3]𝑓(𝑧	𝑍−3]𝑓(𝑧	NUM
cana-4617	317	22	)	)	PUNCT
cana-4617	318	1	=	=	SYM
cana-4617	318	2	0	0	NUM
cana-4617	318	3	�	�	NOUN
cana-4617	318	4	̅	̅	NOUN
cana-4617	318	5	�	�	NOUN
cana-4617	318	6	(𝑧	(𝑧	NOUN
cana-4617	318	7	)	)	PUNCT
cana-4617	318	8	𝑓(𝑧	𝑓(𝑧	PROPN
cana-4617	318	9	)	)	PUNCT
cana-4617	318	10	=	=	SYM
cana-4617	318	11	𝛽2	𝛽2	NOUN
cana-4617	318	12	2	2	NUM
cana-4617	318	13	[	[	X
cana-4617	318	14	𝛽2	𝛽2	PROPN
cana-4617	318	15	𝑍−3	𝑍−3	PROPN
cana-4617	318	16	+	+	CCONJ
cana-4617	318	17	𝑧−1	𝑧−1	X
cana-4617	318	18	]	]	X
cana-4617	318	19	hence	hence	ADV
cana-4617	318	20	,	,	PUNCT
cana-4617	318	21	𝑓(𝑧	𝑓(𝑧	PROPN
cana-4617	318	22	)	)	PUNCT
cana-4617	318	23	�	�	PROPN
cana-4617	318	24	̅	̅	NOUN
cana-4617	318	25	�	�	NOUN
cana-4617	318	26	(𝑧	(𝑧	NOUN
cana-4617	318	27	)	)	PUNCT
cana-4617	318	28	=	=	PUNCT
cana-4617	319	1	[	[	PUNCT
cana-4617	319	2	2𝑧3	2𝑧3	NUM
cana-4617	319	3	𝛽2(𝛽2	𝛽2(𝛽2	NUM
cana-4617	319	4	+	+	CCONJ
cana-4617	319	5	𝑧2	𝑧2	NOUN
cana-4617	319	6	)	)	PUNCT
cana-4617	319	7	]	]	PUNCT
cana-4617	320	1	integrating	integrate	VERB
cana-4617	320	2	both	both	DET
cana-4617	320	3	sides	side	NOUN
cana-4617	320	4	from	from	ADP
cana-4617	320	5	0	0	NUM
cana-4617	320	6	to	to	ADP
cana-4617	320	7	t	t	PROPN
cana-4617	320	8	,	,	PUNCT
cana-4617	320	9	we	we	PRON
cana-4617	320	10	get	get	VERB
cana-4617	320	11	communications	communication	NOUN
cana-4617	320	12	on	on	ADP
cana-4617	320	13	applied	apply	VERB
cana-4617	320	14	nonlinear	nonlinear	ADJ
cana-4617	320	15	analysis	analysis	NOUN
cana-4617	320	16	issn	issn	NOUN
cana-4617	320	17	:	:	PUNCT
cana-4617	320	18	1074	1074	NUM
cana-4617	320	19	-	-	PUNCT
cana-4617	320	20	133x	133x	NUM
cana-4617	320	21	vol	vol	NOUN
cana-4617	320	22	32	32	NUM
cana-4617	320	23	no	no	NOUN
cana-4617	320	24	.	.	PUNCT
cana-4617	321	1	9s	9s	NUM
cana-4617	321	2	(	(	PUNCT
cana-4617	321	3	2025	2025	NUM
cana-4617	321	4	)	)	PUNCT
cana-4617	321	5	3034	3034	NUM
cana-4617	322	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	322	2	�	�	NOUN
cana-4617	322	3	̅	̅	NOUN
cana-4617	322	4	�	�	NOUN
cana-4617	322	5	(𝑡	(𝑡	NOUN
cana-4617	322	6	)	)	PUNCT
cana-4617	322	7	=	=	PUNCT
cana-4617	322	8	(	(	PUNCT
cana-4617	322	9	1	1	NUM
cana-4617	322	10	+	+	CCONJ
cana-4617	322	11	𝑡2	𝑡2	ADJ
cana-4617	322	12	𝛽2	𝛽2	PROPN
cana-4617	322	13	)	)	PUNCT
cana-4617	322	14	𝒆𝒙𝒑	𝒆𝒙𝒑	NOUN
cana-4617	322	15	(	(	PUNCT
cana-4617	322	16	−	−	PROPN
cana-4617	322	17	𝑡2	𝑡2	PROPN
cana-4617	322	18	𝛽2	𝛽2	PROPN
cana-4617	322	19	)	)	PUNCT
cana-4617	322	20	(	(	PUNCT
cana-4617	322	21	26	26	NUM
cana-4617	322	22	)	)	PUNCT
cana-4617	322	23	5	5	NUM
cana-4617	322	24	.	.	PUNCT
cana-4617	322	25	conclusion	conclusion	NOUN
cana-4617	322	26	in	in	ADP
cana-4617	322	27	this	this	DET
cana-4617	322	28	research	research	NOUN
cana-4617	322	29	,	,	PUNCT
cana-4617	322	30	we	we	PRON
cana-4617	322	31	employed	employ	VERB
cana-4617	322	32	the	the	DET
cana-4617	322	33	area	area	NOUN
cana-4617	322	34	-biased	-biase	VERB
cana-4617	322	35	rayleigh	rayleigh	ADJ
cana-4617	322	36	distribution	distribution	NOUN
cana-4617	322	37	to	to	PART
cana-4617	322	38	derive	derive	VERB
cana-4617	322	39	recurrence	recurrence	NOUN
cana-4617	322	40	relations	relation	NOUN
cana-4617	322	41	for	for	ADP
cana-4617	322	42	both	both	CCONJ
cana-4617	322	43	single	single	ADJ
cana-4617	322	44	and	and	CCONJ
cana-4617	322	45	product	product	NOUN
cana-4617	322	46	moments	moment	NOUN
cana-4617	322	47	of	of	ADP
cana-4617	322	48	generalized	generalized	ADJ
cana-4617	322	49	order	order	NOUN
cana-4617	322	50	statistics	statistic	NOUN
cana-4617	322	51	(	(	PUNCT
cana-4617	322	52	gos	gos	PROPN
cana-4617	322	53	)	)	PUNCT
cana-4617	322	54	.	.	PUNCT
cana-4617	323	1	additionally	additionally	ADV
cana-4617	323	2	,	,	PUNCT
cana-4617	323	3	we	we	PRON
cana-4617	323	4	explored	explore	VERB
cana-4617	323	5	specific	specific	ADJ
cana-4617	323	6	cases	case	NOUN
cana-4617	323	7	related	relate	VERB
cana-4617	323	8	to	to	PART
cana-4617	323	9	order	order	VERB
cana-4617	323	10	statistics	statistic	NOUN
cana-4617	323	11	and	and	CCONJ
cana-4617	323	12	record	record	NOUN
cana-4617	323	13	values	value	NOUN
cana-4617	323	14	.	.	PUNCT
cana-4617	324	1	the	the	DET
cana-4617	324	2	recurrence	recurrence	NOUN
cana-4617	324	3	relation	relation	NOUN
cana-4617	324	4	for	for	ADP
cana-4617	324	5	single	single	ADJ
cana-4617	324	6	moments	moment	NOUN
cana-4617	324	7	contributes	contribute	VERB
cana-4617	324	8	to	to	ADP
cana-4617	324	9	characterizing	characterize	VERB
cana-4617	324	10	the	the	DET
cana-4617	324	11	properties	property	NOUN
cana-4617	324	12	of	of	ADP
cana-4617	324	13	the	the	DET
cana-4617	324	14	area	area	NOUN
cana-4617	324	15	-biased	-biase	VERB
cana-4617	324	16	rayleigh	rayleigh	ADJ
cana-4617	324	17	distribution	distribution	NOUN
cana-4617	324	18	.	.	PUNCT
cana-4617	325	1	references	reference	NOUN
cana-4617	325	2	[	[	X
cana-4617	325	3	1	1	NUM
cana-4617	325	4	]	]	PUNCT
cana-4617	325	5	abdul	abdul	PROPN
cana-4617	325	6	-	-	PUNCT
cana-4617	325	7	moniem	moniem	PROPN
cana-4617	325	8	,	,	PUNCT
cana-4617	325	9	i.	i.	PROPN
cana-4617	325	10	b.	b.	PROPN
cana-4617	325	11	(	(	PUNCT
cana-4617	325	12	2014	2014	NUM
cana-4617	325	13	)	)	PUNCT
cana-4617	325	14	.	.	PUNCT
cana-4617	326	1	recurrence	recurrence	NOUN
cana-4617	326	2	relations	relation	NOUN
cana-4617	326	3	for	for	ADP
cana-4617	326	4	moments	moment	NOUN
cana-4617	326	5	of	of	ADP
cana-4617	326	6	generalized	generalized	ADJ
cana-4617	326	7	order	order	NOUN
cana-4617	326	8	statistics	statistic	NOUN
cana-4617	326	9	from	from	ADP
cana-4617	326	10	marshall	marshall	PROPN
cana-4617	326	11	–	–	PUNCT
cana-4617	326	12	olkin	olkin	NOUN
cana-4617	326	13	extended	extend	VERB
cana-4617	326	14	kumaraswamy	kumaraswamy	NOUN
cana-4617	326	15	distribution	distribution	NOUN
cana-4617	326	16	and	and	CCONJ
cana-4617	326	17	its	its	PRON
cana-4617	326	18	characterization	characterization	NOUN
cana-4617	326	19	.	.	PUNCT
cana-4617	327	1	american	american	ADJ
cana-4617	327	2	journal	journal	PROPN
cana-4617	327	3	of	of	ADP
cana-4617	327	4	applied	apply	VERB
cana-4617	327	5	mathematics	mathematic	NOUN
cana-4617	327	6	and	and	CCONJ
cana-4617	327	7	statistics	statistic	NOUN
cana-4617	327	8	,	,	PUNCT
cana-4617	327	9	2(5	2(5	NUM
cana-4617	327	10	)	)	PUNCT
cana-4617	327	11	,	,	PUNCT
cana-4617	327	12	324329	324329	NUM
cana-4617	327	13	.	.	PUNCT
cana-4617	328	1	[	[	X
cana-4617	328	2	2	2	NUM
cana-4617	328	3	]	]	PUNCT
cana-4617	328	4	abdul	abdul	PROPN
cana-4617	328	5	-	-	PUNCT
cana-4617	328	6	moniem	moniem	PROPN
cana-4617	328	7	,	,	PUNCT
cana-4617	328	8	i.	i.	PROPN
cana-4617	328	9	b.	b.	PROPN
cana-4617	328	10	(	(	PUNCT
cana-4617	328	11	2019	2019	NUM
cana-4617	328	12	)	)	PUNCT
cana-4617	328	13	.	.	PUNCT
cana-4617	329	1	recurrence	recurrence	NOUN
cana-4617	329	2	relations	relation	NOUN
cana-4617	329	3	for	for	ADP
cana-4617	329	4	moments	moment	NOUN
cana-4617	329	5	of	of	ADP
cana-4617	329	6	generalized	generalized	ADJ
cana-4617	329	7	order	order	NOUN
cana-4617	329	8	statistics	statistic	NOUN
cana-4617	329	9	from	from	ADP
cana-4617	329	10	marshall	marshall	PROPN
cana-4617	329	11	–	–	PUNCT
cana-4617	329	12	olkin	olkin	NOUN
cana-4617	329	13	extended	extend	VERB
cana-4617	329	14	family	family	NOUN
cana-4617	329	15	of	of	ADP
cana-4617	329	16	life	life	NOUN
cana-4617	329	17	distributions	distribution	NOUN
cana-4617	329	18	and	and	CCONJ
cana-4617	329	19	its	its	PRON
cana-4617	329	20	characterization	characterization	NOUN
cana-4617	329	21	.	.	PUNCT
cana-4617	330	1	sohag	sohag	NOUN
cana-4617	330	2	journal	journal	PROPN
cana-4617	330	3	of	of	ADP
cana-4617	330	4	mathematics	mathematic	NOUN
cana-4617	330	5	,	,	PUNCT
cana-4617	330	6	6(3	6(3	NUM
cana-4617	330	7	)	)	PUNCT
cana-4617	330	8	,	,	PUNCT
cana-4617	330	9	45	45	NUM
cana-4617	330	10	-	-	SYM
cana-4617	330	11	50	50	NUM
cana-4617	330	12	.	.	PUNCT
cana-4617	331	1	[	[	X
cana-4617	331	2	3	3	NUM
cana-4617	331	3	]	]	X
cana-4617	331	4	abdul	abdul	PROPN
cana-4617	331	5	-	-	PUNCT
cana-4617	331	6	moniem	moniem	PROPN
cana-4617	331	7	,	,	PUNCT
cana-4617	331	8	i.	i.	PROPN
cana-4617	331	9	b.	b.	PROPN
cana-4617	331	10	(	(	PUNCT
cana-4617	331	11	2022	2022	NUM
cana-4617	331	12	)	)	PUNCT
cana-4617	331	13	.	.	PUNCT
cana-4617	332	1	recurrence	recurrence	NOUN
cana-4617	332	2	relations	relation	NOUN
cana-4617	332	3	for	for	ADP
cana-4617	332	4	moments	moment	NOUN
cana-4617	332	5	of	of	ADP
cana-4617	332	6	generalized	generalized	ADJ
cana-4617	332	7	order	order	NOUN
cana-4617	332	8	statistics	statistic	NOUN
cana-4617	332	9	from	from	ADP
cana-4617	332	10	length	length	NOUN
cana-4617	332	11	-	-	PUNCT
cana-4617	332	12	biased	bias	VERB
cana-4617	332	13	weighted	weight	VERB
cana-4617	332	14	maxwell	maxwell	PROPN
cana-4617	332	15	distribution	distribution	NOUN
cana-4617	332	16	and	and	CCONJ
cana-4617	332	17	its	its	PRON
cana-4617	332	18	characterization	characterization	NOUN
cana-4617	332	19	.	.	PUNCT
cana-4617	333	1	acta	acta	PROPN
cana-4617	333	2	scientific	scientific	ADJ
cana-4617	333	3	computer	computer	NOUN
cana-4617	333	4	sciences	science	NOUN
cana-4617	333	5	,	,	PUNCT
cana-4617	333	6	4(4	4(4	NUM
cana-4617	333	7	)	)	PUNCT
cana-4617	333	8	,	,	PUNCT
cana-4617	333	9	94	94	NUM
cana-4617	333	10	-	-	SYM
cana-4617	333	11	100	100	NUM
cana-4617	333	12	.	.	PUNCT
cana-4617	334	1	[	[	X
cana-4617	334	2	4	4	NUM
cana-4617	334	3	]	]	X
cana-4617	334	4	ahmad	ahmad	PROPN
cana-4617	334	5	,	,	PUNCT
cana-4617	334	6	a.	a.	NOUN
cana-4617	334	7	a.	a.	NOUN
cana-4617	334	8	(	(	PUNCT
cana-4617	334	9	2007	2007	NUM
cana-4617	334	10	)	)	PUNCT
cana-4617	334	11	.	.	PUNCT
cana-4617	335	1	recurrence	recurrence	NOUN
cana-4617	335	2	relations	relation	NOUN
cana-4617	335	3	for	for	ADP
cana-4617	335	4	single	single	ADJ
cana-4617	335	5	and	and	CCONJ
cana-4617	335	6	product	product	NOUN
cana-4617	335	7	moments	moment	NOUN
cana-4617	335	8	of	of	ADP
cana-4617	335	9	generalized	generalized	ADJ
cana-4617	335	10	order	order	NOUN
cana-4617	335	11	statistics	statistic	NOUN
cana-4617	335	12	from	from	ADP
cana-4617	335	13	doubly	doubly	ADV
cana-4617	335	14	truncated	truncate	VERB
cana-4617	335	15	burr	burr	NOUN
cana-4617	335	16	type	type	NOUN
cana-4617	335	17	xii	xii	NOUN
cana-4617	335	18	distribution	distribution	NOUN
cana-4617	335	19	.	.	PUNCT
cana-4617	336	1	journal	journal	NOUN
cana-4617	336	2	of	of	ADP
cana-4617	336	3	the	the	DET
cana-4617	336	4	egyptian	egyptian	PROPN
cana-4617	336	5	mathematical	mathematical	PROPN
cana-4617	336	6	society	society	NOUN
cana-4617	336	7	,	,	PUNCT
cana-4617	336	8	15(1	15(1	NUM
cana-4617	336	9	)	)	PUNCT
cana-4617	336	10	,	,	PUNCT
cana-4617	336	11	117	117	NUM
cana-4617	336	12	-	-	SYM
cana-4617	336	13	128	128	NUM
cana-4617	336	14	.	.	PUNCT
cana-4617	337	1	[	[	X
cana-4617	337	2	5	5	NUM
cana-4617	337	3	]	]	X
cana-4617	337	4	ahmad	ahmad	PROPN
cana-4617	337	5	,	,	PUNCT
cana-4617	337	6	a.	a.	NOUN
cana-4617	337	7	a.	a.	PROPN
cana-4617	337	8	,	,	PUNCT
cana-4617	337	9	&	&	CCONJ
cana-4617	337	10	fawzy	fawzy	PROPN
cana-4617	337	11	,	,	PUNCT
cana-4617	337	12	a.	a.	NOUN
cana-4617	337	13	m.	m.	NOUN
cana-4617	337	14	(	(	PUNCT
cana-4617	337	15	2003	2003	NUM
cana-4617	337	16	)	)	PUNCT
cana-4617	337	17	.	.	PUNCT
cana-4617	338	1	recurrence	recurrence	NOUN
cana-4617	338	2	relations	relation	NOUN
cana-4617	338	3	for	for	ADP
cana-4617	338	4	single	single	ADJ
cana-4617	338	5	moments	moment	NOUN
cana-4617	338	6	of	of	ADP
cana-4617	338	7	generalized	generalized	ADJ
cana-4617	338	8	order	order	NOUN
cana-4617	338	9	statistics	statistic	NOUN
cana-4617	338	10	from	from	ADP
cana-4617	338	11	doubly	doubly	ADV
cana-4617	338	12	truncated	truncate	VERB
cana-4617	338	13	distribution	distribution	NOUN
cana-4617	338	14	.	.	PUNCT
cana-4617	339	1	journal	journal	NOUN
cana-4617	339	2	of	of	ADP
cana-4617	339	3	statistical	statistical	ADJ
cana-4617	339	4	planning	planning	NOUN
cana-4617	339	5	and	and	CCONJ
cana-4617	339	6	inference	inference	NOUN
cana-4617	339	7	,	,	PUNCT
cana-4617	339	8	117(2	117(2	NUM
cana-4617	339	9	)	)	PUNCT
cana-4617	339	10	,	,	PUNCT
cana-4617	339	11	241	241	PROPN
cana-4617	339	12	-	-	SYM
cana-4617	339	13	249	249	NUM
cana-4617	339	14	.	.	PUNCT
cana-4617	340	1	[	[	X
cana-4617	340	2	6	6	NUM
cana-4617	340	3	]	]	PUNCT
cana-4617	340	4	ahsanullah	ahsanullah	NOUN
cana-4617	340	5	,	,	PUNCT
cana-4617	340	6	m.	m.	NOUN
cana-4617	340	7	(	(	PUNCT
cana-4617	340	8	2000	2000	NUM
cana-4617	340	9	)	)	PUNCT
cana-4617	340	10	.	.	PUNCT
cana-4617	341	1	generalized	generalize	VERB
cana-4617	341	2	order	order	NOUN
cana-4617	341	3	statistics	statistic	NOUN
cana-4617	341	4	from	from	ADP
cana-4617	341	5	an	an	DET
cana-4617	341	6	exponential	exponential	ADJ
cana-4617	341	7	distribution	distribution	NOUN
cana-4617	341	8	.	.	PUNCT
cana-4617	342	1	journal	journal	NOUN
cana-4617	342	2	of	of	ADP
cana-4617	342	3	statistical	statistical	ADJ
cana-4617	342	4	planning	planning	NOUN
cana-4617	342	5	and	and	CCONJ
cana-4617	342	6	inference	inference	NOUN
cana-4617	342	7	,	,	PUNCT
cana-4617	342	8	85(1	85(1	NOUN
cana-4617	342	9	-	-	SYM
cana-4617	342	10	2	2	NUM
cana-4617	342	11	)	)	PUNCT
cana-4617	342	12	,	,	PUNCT
cana-4617	342	13	85	85	NUM
cana-4617	342	14	-	-	SYM
cana-4617	342	15	91	91	NUM
cana-4617	342	16	.	.	PUNCT
cana-4617	343	1	[	[	X
cana-4617	343	2	7	7	NUM
cana-4617	343	3	]	]	X
cana-4617	343	4	akhter	akhter	NOUN
cana-4617	343	5	,	,	PUNCT
cana-4617	343	6	z.	z.	PROPN
cana-4617	343	7	,	,	PUNCT
cana-4617	343	8	saran	saran	PROPN
cana-4617	343	9	,	,	PUNCT
cana-4617	343	10	j.	j.	PROPN
cana-4617	343	11	,	,	PUNCT
cana-4617	343	12	verma	verma	PROPN
cana-4617	343	13	,	,	PUNCT
cana-4617	343	14	k.	k.	PROPN
cana-4617	343	15	,	,	PUNCT
cana-4617	343	16	&	&	CCONJ
cana-4617	343	17	pushkarna	pushkarna	PROPN
cana-4617	343	18	,	,	PUNCT
cana-4617	343	19	n.	n.	NOUN
cana-4617	343	20	(	(	PUNCT
cana-4617	343	21	2020	2020	NUM
cana-4617	343	22	)	)	PUNCT
cana-4617	343	23	.	.	PUNCT
cana-4617	344	1	moments	moment	NOUN
cana-4617	344	2	of	of	ADP
cana-4617	344	3	order	order	NOUN
cana-4617	344	4	statistics	statistic	NOUN
cana-4617	344	5	from	from	ADP
cana-4617	344	6	length	length	NOUN
cana-4617	344	7	-	-	PUNCT
cana-4617	344	8	biased	bias	VERB
cana-4617	344	9	exponential	exponential	ADJ
cana-4617	344	10	distribution	distribution	NOUN
cana-4617	344	11	and	and	CCONJ
cana-4617	344	12	associated	associated	ADJ
cana-4617	344	13	inference	inference	NOUN
cana-4617	344	14	.	.	PUNCT
cana-4617	345	1	annals	annal	NOUN
cana-4617	345	2	of	of	ADP
cana-4617	345	3	data	data	NOUN
cana-4617	345	4	science	science	NOUN
cana-4617	345	5	,	,	PUNCT
cana-4617	345	6	1	1	NUM
cana-4617	345	7	-	-	SYM
cana-4617	345	8	26	26	NUM
cana-4617	345	9	.	.	PUNCT
cana-4617	346	1	[	[	X
cana-4617	346	2	8	8	NUM
cana-4617	346	3	]	]	X
cana-4617	346	4	al	al	PROPN
cana-4617	346	5	-	-	PUNCT
cana-4617	346	6	hussaini	hussaini	PROPN
cana-4617	346	7	,	,	PUNCT
cana-4617	346	8	e.	e.	PROPN
cana-4617	346	9	k.	k.	PROPN
cana-4617	346	10	,	,	PUNCT
cana-4617	346	11	ahmad	ahmad	PROPN
cana-4617	346	12	,	,	PUNCT
cana-4617	346	13	a.	a.	NOUN
cana-4617	346	14	a.	a.	PROPN
cana-4617	346	15	,	,	PUNCT
cana-4617	346	16	&	&	CCONJ
cana-4617	346	17	al	al	PROPN
cana-4617	346	18	-	-	PUNCT
cana-4617	346	19	kashif	kashif	PROPN
cana-4617	346	20	,	,	PUNCT
cana-4617	346	21	m.	m.	NOUN
cana-4617	346	22	a.	a.	NOUN
cana-4617	346	23	(	(	PUNCT
cana-4617	346	24	2005	2005	NUM
cana-4617	346	25	)	)	PUNCT
cana-4617	346	26	.	.	PUNCT
cana-4617	347	1	recurrence	recurrence	NOUN
cana-4617	347	2	relations	relation	NOUN
cana-4617	347	3	for	for	ADP
cana-4617	347	4	a	a	DET
cana-4617	347	5	moment	moment	NOUN
cana-4617	347	6	and	and	CCONJ
cana-4617	347	7	conditional	conditional	ADJ
cana-4617	347	8	moment	moment	NOUN
cana-4617	347	9	generating	generating	NOUN
cana-4617	347	10	functions	function	NOUN
cana-4617	347	11	of	of	ADP
cana-4617	347	12	generalized	generalized	ADJ
cana-4617	347	13	order	order	NOUN
cana-4617	347	14	statistics	statistic	NOUN
cana-4617	347	15	.	.	PUNCT
cana-4617	348	1	metrika	metrika	NOUN
cana-4617	348	2	,	,	PUNCT
cana-4617	348	3	61(2	61(2	NUM
cana-4617	348	4	)	)	PUNCT
cana-4617	348	5	,	,	PUNCT
cana-4617	348	6	199	199	NUM
cana-4617	348	7	-	-	SYM
cana-4617	348	8	220	220	NUM
cana-4617	348	9	.	.	PUNCT
cana-4617	349	1	[	[	X
cana-4617	349	2	9	9	NUM
cana-4617	349	3	]	]	PUNCT
cana-4617	349	4	athar	athar	PROPN
cana-4617	349	5	,	,	PUNCT
cana-4617	349	6	h.	h.	PROPN
cana-4617	349	7	,	,	PUNCT
cana-4617	349	8	&	&	CCONJ
cana-4617	349	9	islam	islam	PROPN
cana-4617	349	10	,	,	PUNCT
cana-4617	349	11	h.	h.	PROPN
cana-4617	349	12	(	(	PUNCT
cana-4617	349	13	2004	2004	NUM
cana-4617	349	14	)	)	PUNCT
cana-4617	349	15	.	.	PUNCT
cana-4617	350	1	recurrence	recurrence	NOUN
cana-4617	350	2	relations	relation	NOUN
cana-4617	350	3	for	for	ADP
cana-4617	350	4	single	single	ADJ
cana-4617	350	5	and	and	CCONJ
cana-4617	350	6	product	product	NOUN
cana-4617	350	7	moments	moment	NOUN
cana-4617	350	8	of	of	ADP
cana-4617	350	9	generalized	generalized	ADJ
cana-4617	350	10	order	order	NOUN
cana-4617	350	11	statistics	statistic	NOUN
cana-4617	350	12	from	from	ADP
cana-4617	350	13	a	a	DET
cana-4617	350	14	general	general	ADJ
cana-4617	350	15	class	class	NOUN
cana-4617	350	16	of	of	ADP
cana-4617	350	17	distribution	distribution	NOUN
cana-4617	350	18	.	.	PUNCT
cana-4617	351	1	metron	metron	PROPN
cana-4617	351	2	,	,	PUNCT
cana-4617	351	3	lxii	lxii	X
cana-4617	351	4	(	(	PUNCT
cana-4617	351	5	3	3	NUM
cana-4617	351	6	)	)	PUNCT
cana-4617	351	7	,	,	PUNCT
cana-4617	351	8	327337	327337	NUM
cana-4617	351	9	.	.	PUNCT
cana-4617	352	1	communications	communication	NOUN
cana-4617	352	2	on	on	ADP
cana-4617	352	3	applied	apply	VERB
cana-4617	352	4	nonlinear	nonlinear	ADJ
cana-4617	352	5	analysis	analysis	NOUN
cana-4617	352	6	issn	issn	NOUN
cana-4617	352	7	:	:	PUNCT
cana-4617	352	8	1074	1074	NUM
cana-4617	352	9	-	-	PUNCT
cana-4617	352	10	133x	133x	NUM
cana-4617	352	11	vol	vol	NOUN
cana-4617	352	12	32	32	NUM
cana-4617	352	13	no	no	NOUN
cana-4617	352	14	.	.	PUNCT
cana-4617	353	1	9s	9s	NUM
cana-4617	353	2	(	(	PUNCT
cana-4617	353	3	2025	2025	NUM
cana-4617	353	4	)	)	PUNCT
cana-4617	353	5	3035	3035	NUM
cana-4617	353	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4617	354	1	[	[	X
cana-4617	354	2	10	10	NUM
cana-4617	354	3	]	]	X
cana-4617	354	4	bashir	bashir	PROPN
cana-4617	354	5	,	,	PUNCT
cana-4617	354	6	s.	s.	PROPN
cana-4617	354	7	,	,	PUNCT
cana-4617	354	8	&	&	CCONJ
cana-4617	354	9	rasul	rasul	PROPN
cana-4617	354	10	,	,	PUNCT
cana-4617	354	11	m.	m.	NOUN
cana-4617	354	12	(	(	PUNCT
cana-4617	354	13	2018	2018	NUM
cana-4617	354	14	)	)	PUNCT
cana-4617	354	15	.	.	PUNCT
cana-4617	355	1	a	a	DET
cana-4617	355	2	new	new	ADJ
cana-4617	355	3	weighted	weight	VERB
cana-4617	355	4	rayleigh	rayleigh	NOUN
cana-4617	355	5	distribution	distribution	NOUN
cana-4617	355	6	:	:	PUNCT
cana-4617	355	7	properties	property	NOUN
cana-4617	355	8	and	and	CCONJ
cana-4617	355	9	applications	application	NOUN
cana-4617	355	10	on	on	ADP
cana-4617	355	11	lifetime	lifetime	NOUN
cana-4617	355	12	time	time	NOUN
cana-4617	355	13	data	data	PROPN
cana-4617	355	14	.	.	PUNCT
cana-4617	356	1	open	open	ADJ
cana-4617	356	2	journal	journal	PROPN
cana-4617	356	3	of	of	ADP
cana-4617	356	4	statistics	statistic	NOUN
cana-4617	356	5	,	,	PUNCT
cana-4617	356	6	8(03	8(03	NUM
cana-4617	356	7	)	)	PUNCT
cana-4617	356	8	,	,	PUNCT
cana-4617	356	9	640	640	NUM
cana-4617	356	10	.	.	PUNCT
cana-4617	357	1	[	[	X
cana-4617	357	2	11	11	NUM
cana-4617	357	3	]	]	X
cana-4617	357	4	cramer	cramer	PROPN
cana-4617	357	5	,	,	PUNCT
cana-4617	357	6	e.	e.	PROPN
cana-4617	357	7	,	,	PUNCT
cana-4617	357	8	&	&	CCONJ
cana-4617	357	9	kamps	kamps	PROPN
cana-4617	357	10	,	,	PUNCT
cana-4617	357	11	u.	u.	PROPN
cana-4617	357	12	(	(	PUNCT
cana-4617	357	13	2000	2000	NUM
cana-4617	357	14	)	)	PUNCT
cana-4617	357	15	.	.	PUNCT
cana-4617	358	1	relations	relation	NOUN
cana-4617	358	2	for	for	ADP
cana-4617	358	3	expectations	expectation	NOUN
cana-4617	358	4	of	of	ADP
cana-4617	358	5	functions	function	NOUN
cana-4617	358	6	of	of	ADP
cana-4617	358	7	generalized	generalized	ADJ
cana-4617	358	8	order	order	NOUN
cana-4617	358	9	statistics	statistic	NOUN
cana-4617	358	10	.	.	PUNCT
cana-4617	359	1	journal	journal	NOUN
cana-4617	359	2	of	of	ADP
cana-4617	359	3	statistical	statistical	ADJ
cana-4617	359	4	planning	planning	NOUN
cana-4617	359	5	and	and	CCONJ
cana-4617	359	6	inference	inference	NOUN
cana-4617	359	7	,	,	PUNCT
cana-4617	359	8	89(1	89(1	NOUN
cana-4617	359	9	-	-	SYM
cana-4617	359	10	2	2	NUM
cana-4617	359	11	)	)	PUNCT
cana-4617	359	12	,	,	PUNCT
cana-4617	359	13	79	79	NUM
cana-4617	359	14	-	-	SYM
cana-4617	359	15	89	89	NUM
cana-4617	359	16	.	.	PUNCT
cana-4617	360	1	[	[	X
cana-4617	360	2	12	12	NUM
cana-4617	360	3	]	]	X
cana-4617	360	4	david	david	PROPN
cana-4617	360	5	,	,	PUNCT
cana-4617	360	6	h.	h.	PROPN
cana-4617	360	7	a.	a.	PROPN
cana-4617	360	8	,	,	PUNCT
cana-4617	360	9	&	&	CCONJ
cana-4617	360	10	nagaraja	nagaraja	PROPN
cana-4617	360	11	,	,	PUNCT
cana-4617	360	12	h.	h.	PROPN
cana-4617	360	13	n.	n.	PROPN
cana-4617	360	14	(	(	PUNCT
cana-4617	360	15	2004	2004	NUM
cana-4617	360	16	)	)	PUNCT
cana-4617	360	17	.	.	PUNCT
cana-4617	361	1	order	order	NOUN
cana-4617	361	2	statistics	statistic	NOUN
cana-4617	361	3	.	.	PUNCT
cana-4617	362	1	john	john	PROPN
cana-4617	362	2	wiley	wiley	PROPN
cana-4617	362	3	&	&	CCONJ
cana-4617	362	4	sons	son	NOUN
cana-4617	362	5	.	.	PUNCT
cana-4617	363	1	[	[	X
cana-4617	363	2	13	13	NUM
cana-4617	363	3	]	]	PUNCT
cana-4617	363	4	elamir	elamir	X
cana-4617	363	5	,	,	PUNCT
cana-4617	363	6	e.	e.	PROPN
cana-4617	363	7	a.	a.	PROPN
cana-4617	363	8	,	,	PUNCT
cana-4617	363	9	&	&	CCONJ
cana-4617	363	10	seheult	seheult	PROPN
cana-4617	363	11	,	,	PUNCT
cana-4617	363	12	a.	a.	PROPN
cana-4617	363	13	h.	h.	PROPN
cana-4617	363	14	(	(	PUNCT
cana-4617	363	15	2003	2003	NUM
cana-4617	363	16	)	)	PUNCT
cana-4617	363	17	.	.	PUNCT
cana-4617	363	18	trimmed	trim	VERB
cana-4617	363	19	l	l	NOUN
cana-4617	363	20	-	-	NOUN
cana-4617	363	21	moments	moment	NOUN
cana-4617	363	22	.	.	PUNCT
cana-4617	364	1	computational	computational	ADJ
cana-4617	364	2	statistics	statistic	NOUN
cana-4617	364	3	and	and	CCONJ
cana-4617	364	4	data	datum	NOUN
cana-4617	364	5	analysis	analysis	NOUN
cana-4617	364	6	,	,	PUNCT
cana-4617	364	7	43(3	43(3	NUM
cana-4617	364	8	)	)	PUNCT
cana-4617	364	9	,	,	PUNCT
cana-4617	364	10	299	299	NUM
cana-4617	364	11	-	-	SYM
cana-4617	364	12	314	314	NUM
cana-4617	364	13	.	.	PUNCT
cana-4617	365	1	[	[	X
cana-4617	365	2	14	14	NUM
cana-4617	365	3	]	]	X
cana-4617	365	4	hwang	hwang	PROPN
cana-4617	365	5	,	,	PUNCT
cana-4617	365	6	j.	j.	PROPN
cana-4617	365	7	s.	s.	PROPN
cana-4617	365	8	,	,	PUNCT
cana-4617	365	9	&	&	CCONJ
cana-4617	365	10	lin	lin	PROPN
cana-4617	365	11	,	,	PUNCT
cana-4617	365	12	g.	g.	PROPN
cana-4617	365	13	d.	d.	PROPN
cana-4617	365	14	(	(	PUNCT
cana-4617	365	15	1984	1984	NUM
cana-4617	365	16	)	)	PUNCT
cana-4617	365	17	.	.	PUNCT
cana-4617	366	1	on	on	ADP
cana-4617	366	2	a	a	DET
cana-4617	366	3	generalized	generalized	ADJ
cana-4617	366	4	moment	moment	NOUN
cana-4617	366	5	problem	problem	PROPN
cana-4617	366	6	ii	ii	PROPN
cana-4617	366	7	.	.	PUNCT
cana-4617	367	1	proceedings	proceeding	NOUN
cana-4617	367	2	of	of	ADP
cana-4617	367	3	the	the	DET
cana-4617	367	4	american	american	PROPN
cana-4617	367	5	mathematical	mathematical	PROPN
cana-4617	367	6	society	society	NOUN
cana-4617	367	7	,	,	PUNCT
cana-4617	367	8	91	91	NUM
cana-4617	367	9	,	,	PUNCT
cana-4617	367	10	577	577	NUM
cana-4617	367	11	-	-	SYM
cana-4617	367	12	580	580	NUM
cana-4617	367	13	.	.	PUNCT
cana-4617	368	1	[	[	X
cana-4617	368	2	15	15	NUM
cana-4617	368	3	]	]	X
cana-4617	368	4	kamps	kamps	PROPN
cana-4617	368	5	,	,	PUNCT
cana-4617	368	6	u.	u.	PROPN
cana-4617	368	7	(	(	PUNCT
cana-4617	368	8	1995	1995	NUM
cana-4617	368	9	)	)	PUNCT
cana-4617	368	10	.	.	PUNCT
cana-4617	369	1	a	a	DET
cana-4617	369	2	concept	concept	NOUN
cana-4617	369	3	of	of	ADP
cana-4617	369	4	generalized	generalized	ADJ
cana-4617	369	5	order	order	NOUN
cana-4617	369	6	statistics	statistic	NOUN
cana-4617	369	7	.	.	PUNCT
cana-4617	370	1	stuttgart	stuttgart	PROPN
cana-4617	370	2	:	:	PUNCT
cana-4617	370	3	b.	b.	PROPN
cana-4617	370	4	g.	g.	PROPN
cana-4617	370	5	teubner	teubner	NOUN
cana-4617	370	6	.	.	PUNCT
cana-4617	371	1	[	[	X
cana-4617	371	2	16	16	NUM
cana-4617	371	3	]	]	X
cana-4617	371	4	kamps	kamps	PROPN
cana-4617	371	5	,	,	PUNCT
cana-4617	371	6	u.	u.	PROPN
cana-4617	371	7	,	,	PUNCT
cana-4617	371	8	&	&	CCONJ
cana-4617	371	9	gather	gather	PROPN
cana-4617	371	10	,	,	PUNCT
cana-4617	371	11	u.	u.	PROPN
cana-4617	371	12	(	(	PUNCT
cana-4617	371	13	1997	1997	NUM
cana-4617	371	14	)	)	PUNCT
cana-4617	371	15	.	.	PUNCT
cana-4617	372	1	characteristic	characteristic	ADJ
cana-4617	372	2	property	property	NOUN
cana-4617	372	3	of	of	ADP
cana-4617	372	4	generalized	generalized	ADJ
cana-4617	372	5	order	order	NOUN
cana-4617	372	6	statistics	statistic	NOUN
cana-4617	372	7	for	for	ADP
cana-4617	372	8	exponential	exponential	ADJ
cana-4617	372	9	distribution	distribution	NOUN
cana-4617	372	10	.	.	PUNCT
cana-4617	373	1	applied	apply	VERB
cana-4617	373	2	mathematics	mathematics	PROPN
cana-4617	373	3	(	(	PUNCT
cana-4617	373	4	warsaw	warsaw	PROPN
cana-4617	373	5	)	)	PUNCT
cana-4617	373	6	,	,	PUNCT
cana-4617	373	7	24	24	NUM
cana-4617	373	8	,	,	PUNCT
cana-4617	373	9	383	383	NUM
cana-4617	373	10	-	-	SYM
cana-4617	373	11	391	391	NUM
cana-4617	373	12	.	.	PUNCT
cana-4617	374	1	[	[	X
cana-4617	374	2	17	17	NUM
cana-4617	374	3	]	]	X
cana-4617	374	4	keseling	keseling	NOUN
cana-4617	374	5	,	,	PUNCT
cana-4617	374	6	c.	c.	PROPN
cana-4617	374	7	(	(	PUNCT
cana-4617	374	8	1999	1999	NUM
cana-4617	374	9	)	)	PUNCT
cana-4617	374	10	.	.	PUNCT
cana-4617	375	1	conditional	conditional	ADJ
cana-4617	375	2	distributions	distribution	NOUN
cana-4617	375	3	of	of	ADP
cana-4617	375	4	generalized	generalized	ADJ
cana-4617	375	5	order	order	NOUN
cana-4617	375	6	statistics	statistic	NOUN
cana-4617	375	7	and	and	CCONJ
cana-4617	375	8	some	some	DET
cana-4617	375	9	characterizations	characterization	NOUN
cana-4617	375	10	.	.	PUNCT
cana-4617	376	1	metrika	metrika	NOUN
cana-4617	376	2	,	,	PUNCT
cana-4617	376	3	49(1	49(1	NOUN
cana-4617	376	4	)	)	PUNCT
cana-4617	376	5	,	,	PUNCT
cana-4617	376	6	27	27	NUM
cana-4617	376	7	-	-	SYM
cana-4617	376	8	40	40	NUM
cana-4617	376	9	.	.	PUNCT
cana-4617	377	1	[	[	X
cana-4617	377	2	18	18	NUM
cana-4617	377	3	]	]	X
cana-4617	377	4	khan	khan	PROPN
cana-4617	377	5	,	,	PUNCT
cana-4617	377	6	r.	r.	PROPN
cana-4617	377	7	u.	u.	PROPN
cana-4617	377	8	,	,	PUNCT
cana-4617	377	9	anwar	anwar	PROPN
cana-4617	377	10	,	,	PUNCT
cana-4617	377	11	z.	z.	PROPN
cana-4617	377	12	,	,	PUNCT
cana-4617	377	13	&	&	CCONJ
cana-4617	377	14	athar	athar	PROPN
cana-4617	377	15	,	,	PUNCT
cana-4617	377	16	h.	h.	PROPN
cana-4617	377	17	(	(	PUNCT
cana-4617	377	18	2007	2007	NUM
cana-4617	377	19	)	)	PUNCT
cana-4617	377	20	.	.	PUNCT
cana-4617	378	1	recurrence	recurrence	NOUN
cana-4617	378	2	relations	relation	NOUN
cana-4617	378	3	for	for	ADP
cana-4617	378	4	single	single	ADJ
cana-4617	378	5	and	and	CCONJ
cana-4617	378	6	product	product	NOUN
cana-4617	378	7	moments	moment	NOUN
cana-4617	378	8	of	of	ADP
cana-4617	378	9	generalized	generalized	ADJ
cana-4617	378	10	order	order	NOUN
cana-4617	378	11	statistics	statistic	NOUN
cana-4617	378	12	from	from	ADP
cana-4617	378	13	doubly	doubly	ADV
cana-4617	378	14	truncated	truncate	VERB
cana-4617	378	15	weibull	weibull	NOUN
cana-4617	378	16	distribution	distribution	NOUN
cana-4617	378	17	.	.	PUNCT
cana-4617	379	1	aligarh	aligarh	PROPN
cana-4617	379	2	journal	journal	PROPN
cana-4617	379	3	of	of	ADP
cana-4617	379	4	statistics	statistic	NOUN
cana-4617	379	5	,	,	PUNCT
cana-4617	379	6	27	27	NUM
cana-4617	379	7	,	,	PUNCT
cana-4617	379	8	69	69	NUM
cana-4617	379	9	-	-	SYM
cana-4617	379	10	79	79	NUM
cana-4617	379	11	.	.	PUNCT
cana-4617	380	1	[	[	X
cana-4617	380	2	19	19	NUM
cana-4617	380	3	]	]	X
cana-4617	380	4	kumar	kumar	PROPN
cana-4617	380	5	,	,	PUNCT
cana-4617	380	6	d.	d.	PROPN
cana-4617	380	7	(	(	PUNCT
cana-4617	380	8	2011	2011	NUM
cana-4617	380	9	)	)	PUNCT
cana-4617	380	10	.	.	PUNCT
cana-4617	381	1	generalized	generalize	VERB
cana-4617	381	2	order	order	NOUN
cana-4617	381	3	statistics	statistic	NOUN
cana-4617	381	4	from	from	ADP
cana-4617	381	5	kumaraswamy	kumaraswamy	ADJ
cana-4617	381	6	distribution	distribution	NOUN
cana-4617	381	7	and	and	CCONJ
cana-4617	381	8	its	its	PRON
cana-4617	381	9	characterization	characterization	NOUN
cana-4617	381	10	.	.	PUNCT
cana-4617	382	1	tamsui	tamsui	PROPN
cana-4617	382	2	oxford	oxford	PROPN
cana-4617	382	3	journal	journal	PROPN
cana-4617	382	4	of	of	ADP
cana-4617	382	5	information	information	NOUN
cana-4617	382	6	and	and	CCONJ
cana-4617	382	7	mathematical	mathematical	ADJ
cana-4617	382	8	sciences	science	NOUN
cana-4617	382	9	,	,	PUNCT
cana-4617	382	10	27(4	27(4	PROPN
cana-4617	382	11	)	)	PUNCT
cana-4617	382	12	,	,	PUNCT
cana-4617	382	13	463	463	NUM
cana-4617	382	14	-	-	SYM
cana-4617	382	15	476	476	NUM
cana-4617	382	16	.	.	PUNCT
cana-4617	383	1	[	[	X
cana-4617	383	2	20	20	NUM
cana-4617	383	3	]	]	X
cana-4617	383	4	mahmoud	mahmoud	PROPN
cana-4617	383	5	,	,	PUNCT
cana-4617	383	6	m.	m.	NOUN
cana-4617	383	7	a.	a.	PROPN
cana-4617	383	8	w.	w.	PROPN
cana-4617	383	9	,	,	PUNCT
cana-4617	383	10	&	&	CCONJ
cana-4617	383	11	ghazal	ghazal	PROPN
cana-4617	383	12	,	,	PUNCT
cana-4617	383	13	m.	m.	NOUN
cana-4617	383	14	g.	g.	PROPN
cana-4617	383	15	m.	m.	PROPN
cana-4617	383	16	(	(	PUNCT
cana-4617	383	17	2012	2012	NUM
cana-4617	383	18	)	)	PUNCT
cana-4617	383	19	.	.	PUNCT
cana-4617	384	1	characterization	characterization	NOUN
cana-4617	384	2	of	of	ADP
cana-4617	384	3	exponentiated	exponentiated	ADJ
cana-4617	384	4	family	family	NOUN
cana-4617	384	5	of	of	ADP
cana-4617	384	6	distributions	distribution	NOUN
cana-4617	384	7	based	base	VERB
cana-4617	384	8	on	on	ADP
cana-4617	384	9	recurrence	recurrence	NOUN
cana-4617	384	10	relations	relation	NOUN
cana-4617	384	11	for	for	ADP
cana-4617	384	12	generalized	generalized	ADJ
cana-4617	384	13	order	order	NOUN
cana-4617	384	14	statistics	statistic	NOUN
cana-4617	384	15	.	.	PUNCT
cana-4617	385	1	journal	journal	PROPN
cana-4617	385	2	of	of	ADP
cana-4617	385	3	mathematics	mathematic	NOUN
cana-4617	385	4	and	and	CCONJ
cana-4617	385	5	computer	computer	NOUN
cana-4617	385	6	science	science	NOUN
cana-4617	385	7	,	,	PUNCT
cana-4617	385	8	2(6	2(6	NUM
cana-4617	385	9	)	)	PUNCT
cana-4617	385	10	,	,	PUNCT
cana-4617	385	11	1894	1894	NUM
cana-4617	385	12	-	-	SYM
cana-4617	385	13	1908	1908	NUM
cana-4617	385	14	.	.	PUNCT
cana-4617	386	1	[	[	X
cana-4617	386	2	21	21	NUM
cana-4617	386	3	]	]	X
cana-4617	386	4	mohsin	mohsin	PROPN
cana-4617	386	5	,	,	PUNCT
cana-4617	386	6	m.	m.	NOUN
cana-4617	386	7	,	,	PUNCT
cana-4617	386	8	shahbaz	shahbaz	PROPN
cana-4617	386	9	,	,	PUNCT
cana-4617	386	10	m.	m.	NOUN
cana-4617	386	11	q.	q.	PROPN
cana-4617	386	12	,	,	PUNCT
cana-4617	386	13	&	&	CCONJ
cana-4617	386	14	kibria	kibria	PROPN
cana-4617	386	15	,	,	PUNCT
cana-4617	386	16	g.	g.	PROPN
cana-4617	386	17	(	(	PUNCT
cana-4617	386	18	2010	2010	NUM
cana-4617	386	19	)	)	PUNCT
cana-4617	386	20	.	.	PUNCT
cana-4617	387	1	recurrence	recurrence	NOUN
cana-4617	387	2	relation	relation	NOUN
cana-4617	387	3	for	for	ADP
cana-4617	387	4	single	single	ADJ
cana-4617	387	5	moments	moment	NOUN
cana-4617	387	6	of	of	ADP
cana-4617	387	7	generalized	generalized	ADJ
cana-4617	387	8	order	order	NOUN
cana-4617	387	9	statistics	statistic	NOUN
cana-4617	387	10	from	from	ADP
cana-4617	387	11	rayleigh	rayleigh	PROPN
cana-4617	387	12	distribution	distribution	NOUN
cana-4617	387	13	.	.	PUNCT
cana-4617	388	1	journal	journal	PROPN
cana-4617	388	2	of	of	ADP
cana-4617	388	3	statistics	statistic	NOUN
cana-4617	388	4	,	,	PUNCT
cana-4617	388	5	4(3	4(3	NUM
cana-4617	388	6	)	)	PUNCT
cana-4617	388	7	,	,	PUNCT
cana-4617	388	8	273279	273279	NUM
cana-4617	388	9	.	.	PUNCT
cana-4617	389	1	[	[	X
cana-4617	389	2	22	22	NUM
cana-4617	389	3	]	]	PUNCT
cana-4617	389	4	pawlas	pawla	NOUN
cana-4617	389	5	,	,	PUNCT
cana-4617	389	6	p.	p.	NOUN
cana-4617	389	7	,	,	PUNCT
cana-4617	389	8	&	&	CCONJ
cana-4617	389	9	szynal	szynal	ADJ
cana-4617	389	10	,	,	PUNCT
cana-4617	389	11	d.	d.	PROPN
cana-4617	389	12	(	(	PUNCT
cana-4617	389	13	2001	2001	NUM
cana-4617	389	14	)	)	PUNCT
cana-4617	389	15	.	.	PUNCT
cana-4617	390	1	recurrence	recurrence	NOUN
cana-4617	390	2	relations	relation	NOUN
cana-4617	390	3	for	for	ADP
cana-4617	390	4	single	single	ADJ
cana-4617	390	5	and	and	CCONJ
cana-4617	390	6	product	product	NOUN
cana-4617	390	7	moments	moment	NOUN
cana-4617	390	8	of	of	ADP
cana-4617	390	9	generalized	generalized	ADJ
cana-4617	390	10	order	order	NOUN
cana-4617	390	11	statistics	statistic	NOUN
cana-4617	390	12	from	from	ADP
cana-4617	390	13	pareto	pareto	ADJ
cana-4617	390	14	,	,	PUNCT
cana-4617	390	15	generalized	generalize	VERB
cana-4617	390	16	pareto	pareto	NOUN
cana-4617	390	17	and	and	CCONJ
cana-4617	390	18	burr	burr	NOUN
cana-4617	390	19	distributions	distribution	NOUN
cana-4617	390	20	.	.	PUNCT
cana-4617	391	1	communications	communication	NOUN
cana-4617	391	2	in	in	ADP
cana-4617	391	3	statistics	statistic	NOUN
cana-4617	391	4	theory	theory	NOUN
cana-4617	391	5	and	and	CCONJ
cana-4617	391	6	methods	method	NOUN
cana-4617	391	7	,	,	PUNCT
cana-4617	391	8	30(4	30(4	NUM
cana-4617	391	9	)	)	PUNCT
cana-4617	391	10	,	,	PUNCT
cana-4617	391	11	739	739	NUM
cana-4617	391	12	-	-	SYM
cana-4617	391	13	746	746	NUM
cana-4617	391	14	.	.	PUNCT