id	sid	tid	token	lemma	pos
ajst-6461	1	1	academic	academic	ADJ
ajst-6461	1	2	journal	journal	NOUN
ajst-6461	1	3	of	of	ADP
ajst-6461	1	4	science	science	NOUN
ajst-6461	1	5	and	and	CCONJ
ajst-6461	1	6	technology	technology	NOUN
ajst-6461	1	7	issn	issn	NOUN
ajst-6461	1	8	:	:	PUNCT
ajst-6461	1	9	2771	2771	NUM
ajst-6461	1	10	-	-	SYM
ajst-6461	1	11	3032	3032	NUM
ajst-6461	1	12	|	|	NOUN
ajst-6461	1	13	vol	vol	NOUN
ajst-6461	1	14	.	.	PROPN
ajst-6461	2	1	5	5	NUM
ajst-6461	2	2	,	,	PUNCT
ajst-6461	2	3	no	no	INTJ
ajst-6461	2	4	.	.	NOUN
ajst-6461	2	5	2	2	NUM
ajst-6461	2	6	,	,	PUNCT
ajst-6461	2	7	2023	2023	NUM
ajst-6461	2	8	121	121	NUM
ajst-6461	2	9	generalized	generalize	VERB
ajst-6461	2	10	dirichlet	dirichlet	NOUN
ajst-6461	2	11	distribution	distribution	NOUN
ajst-6461	2	12	based	base	VERB
ajst-6461	2	13	on	on	ADP
ajst-6461	2	14	confluent	confluent	ADJ
ajst-6461	2	15	hypergeometric	hypergeometric	ADJ
ajst-6461	2	16	series	series	NOUN
ajst-6461	2	17	ruixin	ruixin	PROPN
ajst-6461	2	18	zhao	zhao	PROPN
ajst-6461	2	19	,	,	PUNCT
ajst-6461	2	20	hongmei	hongmei	PROPN
ajst-6461	2	21	liu	liu	PROPN
ajst-6461	2	22	,	,	PUNCT
ajst-6461	2	23	yu	yu	PROPN
ajst-6461	2	24	tang	tang	PROPN
ajst-6461	2	25	school	school	PROPN
ajst-6461	2	26	of	of	ADP
ajst-6461	2	27	science	science	NOUN
ajst-6461	2	28	,	,	PUNCT
ajst-6461	2	29	dalian	dalian	PROPN
ajst-6461	2	30	minzu	minzu	PROPN
ajst-6461	2	31	university	university	PROPN
ajst-6461	2	32	,	,	PUNCT
ajst-6461	2	33	liaoning	liaoning	NOUN
ajst-6461	2	34	116600	116600	NUM
ajst-6461	2	35	,	,	PUNCT
ajst-6461	2	36	p.r.china	p.r.china	ADJ
ajst-6461	2	37	abstract	abstract	NOUN
ajst-6461	2	38	:	:	PUNCT
ajst-6461	2	39	dirichlet	dirichlet	ADJ
ajst-6461	2	40	distribution	distribution	NOUN
ajst-6461	2	41	is	be	AUX
ajst-6461	2	42	a	a	DET
ajst-6461	2	43	kind	kind	NOUN
ajst-6461	2	44	of	of	ADP
ajst-6461	2	45	high	high	ADJ
ajst-6461	2	46	-	-	PUNCT
ajst-6461	2	47	dimensional	dimensional	ADJ
ajst-6461	2	48	continuous	continuous	ADJ
ajst-6461	2	49	probability	probability	NOUN
ajst-6461	2	50	distribution	distribution	NOUN
ajst-6461	2	51	,	,	PUNCT
ajst-6461	2	52	which	which	PRON
ajst-6461	2	53	has	have	VERB
ajst-6461	2	54	important	important	ADJ
ajst-6461	2	55	applications	application	NOUN
ajst-6461	2	56	in	in	ADP
ajst-6461	2	57	the	the	DET
ajst-6461	2	58	fields	field	NOUN
ajst-6461	2	59	of	of	ADP
ajst-6461	2	60	statistics	statistic	NOUN
ajst-6461	2	61	,	,	PUNCT
ajst-6461	2	62	machine	machine	NOUN
ajst-6461	2	63	learning	learning	NOUN
ajst-6461	2	64	and	and	CCONJ
ajst-6461	2	65	bioinformatics	bioinformatic	NOUN
ajst-6461	2	66	.	.	PUNCT
ajst-6461	3	1	in	in	ADP
ajst-6461	3	2	this	this	DET
ajst-6461	3	3	paper	paper	NOUN
ajst-6461	3	4	,	,	PUNCT
ajst-6461	3	5	based	base	VERB
ajst-6461	3	6	on	on	ADP
ajst-6461	3	7	gamma	gamma	NOUN
ajst-6461	3	8	distribution	distribution	NOUN
ajst-6461	3	9	we	we	PRON
ajst-6461	3	10	study	study	VERB
ajst-6461	3	11	two	two	NUM
ajst-6461	3	12	two	two	NUM
ajst-6461	3	13	-	-	PUNCT
ajst-6461	3	14	dimensional	dimensional	ADJ
ajst-6461	3	15	random	random	ADJ
ajst-6461	3	16	variables	variable	NOUN
ajst-6461	3	17	.	.	PUNCT
ajst-6461	4	1	then	then	ADV
ajst-6461	4	2	we	we	PRON
ajst-6461	4	3	derive	derive	VERB
ajst-6461	4	4	the	the	DET
ajst-6461	4	5	properties	property	NOUN
ajst-6461	4	6	of	of	ADP
ajst-6461	4	7	these	these	DET
ajst-6461	4	8	two	two	NUM
ajst-6461	4	9	two	two	NUM
ajst-6461	4	10	-	-	PUNCT
ajst-6461	4	11	dimensional	dimensional	ADJ
ajst-6461	4	12	random	random	ADJ
ajst-6461	4	13	variables	variable	NOUN
ajst-6461	4	14	by	by	ADP
ajst-6461	4	15	using	use	VERB
ajst-6461	4	16	the	the	DET
ajst-6461	4	17	properties	property	NOUN
ajst-6461	4	18	of	of	ADP
ajst-6461	4	19	non	non	ADJ
ajst-6461	4	20	-	-	ADJ
ajst-6461	4	21	central	central	ADJ
ajst-6461	4	22	gamma	gamma	NOUN
ajst-6461	4	23	distribution	distribution	NOUN
ajst-6461	4	24	and	and	CCONJ
ajst-6461	4	25	confluent	confluent	ADJ
ajst-6461	4	26	hypergeometric	hypergeometric	ADJ
ajst-6461	4	27	series	series	NOUN
ajst-6461	4	28	.	.	PUNCT
ajst-6461	5	1	from	from	ADP
ajst-6461	5	2	these	these	DET
ajst-6461	5	3	properties	property	NOUN
ajst-6461	5	4	,	,	PUNCT
ajst-6461	5	5	we	we	PRON
ajst-6461	5	6	find	find	VERB
ajst-6461	5	7	the	the	DET
ajst-6461	5	8	two	two	NUM
ajst-6461	5	9	random	random	ADJ
ajst-6461	5	10	variables	variable	NOUN
ajst-6461	5	11	follow	follow	VERB
ajst-6461	5	12	generalized	generalized	ADJ
ajst-6461	5	13	dirichlet	dirichlet	NOUN
ajst-6461	5	14	distributions	distribution	NOUN
ajst-6461	5	15	.	.	PUNCT
ajst-6461	6	1	applying	apply	VERB
ajst-6461	6	2	hypergeometric	hypergeometric	ADJ
ajst-6461	6	3	series	series	NOUN
ajst-6461	6	4	to	to	ADP
ajst-6461	6	5	dirichlet	dirichlet	NOUN
ajst-6461	6	6	distribution	distribution	NOUN
ajst-6461	6	7	broadens	broaden	VERB
ajst-6461	6	8	the	the	DET
ajst-6461	6	9	research	research	NOUN
ajst-6461	6	10	of	of	ADP
ajst-6461	6	11	dirichlet	dirichlet	ADJ
ajst-6461	6	12	distribution	distribution	NOUN
ajst-6461	6	13	.	.	PUNCT
ajst-6461	7	1	keywords	keyword	NOUN
ajst-6461	7	2	:	:	PUNCT
ajst-6461	7	3	dirichlet	dirichlet	ADJ
ajst-6461	7	4	distribution	distribution	NOUN
ajst-6461	7	5	,	,	PUNCT
ajst-6461	7	6	confluent	confluent	ADJ
ajst-6461	7	7	hypergeometric	hypergeometric	ADJ
ajst-6461	7	8	function	function	NOUN
ajst-6461	7	9	,	,	PUNCT
ajst-6461	7	10	gamma	gamma	NOUN
ajst-6461	7	11	distribution	distribution	NOUN
ajst-6461	7	12	,	,	PUNCT
ajst-6461	7	13	non	non	ADJ
ajst-6461	7	14	-	-	ADJ
ajst-6461	7	15	central	central	ADJ
ajst-6461	7	16	gamma	gamma	NOUN
ajst-6461	7	17	distribution	distribution	NOUN
ajst-6461	7	18	.	.	PUNCT
ajst-6461	8	1	1	1	X
ajst-6461	8	2	.	.	X
ajst-6461	8	3	introduction	introduction	NOUN
ajst-6461	8	4	dirichlet	dirichlet	NOUN
ajst-6461	8	5	distribution	distribution	NOUN
ajst-6461	8	6	is	be	AUX
ajst-6461	8	7	a	a	DET
ajst-6461	8	8	kind	kind	NOUN
ajst-6461	8	9	of	of	ADP
ajst-6461	8	10	high	high	ADJ
ajst-6461	8	11	-	-	PUNCT
ajst-6461	8	12	dimensional	dimensional	ADJ
ajst-6461	8	13	continuous	continuous	ADJ
ajst-6461	8	14	probability	probability	NOUN
ajst-6461	8	15	distribution	distribution	NOUN
ajst-6461	8	16	with	with	ADP
ajst-6461	8	17	positive	positive	ADJ
ajst-6461	8	18	simplex	simplex	NOUN
ajst-6461	8	19	as	as	ADP
ajst-6461	8	20	the	the	DET
ajst-6461	8	21	support	support	NOUN
ajst-6461	8	22	set	set	VERB
ajst-6461	8	23	in	in	ADP
ajst-6461	8	24	the	the	DET
ajst-6461	8	25	real	real	ADJ
ajst-6461	8	26	fields	field	NOUN
ajst-6461	8	27	,	,	PUNCT
ajst-6461	8	28	and	and	CCONJ
ajst-6461	8	29	is	be	AUX
ajst-6461	8	30	a	a	DET
ajst-6461	8	31	generalization	generalization	NOUN
ajst-6461	8	32	of	of	ADP
ajst-6461	8	33	the	the	DET
ajst-6461	8	34	beta	beta	ADJ
ajst-6461	8	35	distribution	distribution	NOUN
ajst-6461	8	36	in	in	ADP
ajst-6461	8	37	the	the	DET
ajst-6461	8	38	high	high	ADV
ajst-6461	8	39	-	-	PUNCT
ajst-6461	8	40	dimensional	dimensional	ADJ
ajst-6461	8	41	case	case	NOUN
ajst-6461	8	42	[	[	X
ajst-6461	8	43	1	1	NUM
ajst-6461	8	44	]	]	PUNCT
ajst-6461	8	45	.	.	PUNCT
ajst-6461	9	1	in	in	ADP
ajst-6461	9	2	bayesian	bayesian	NOUN
ajst-6461	9	3	analysis	analysis	NOUN
ajst-6461	9	4	,	,	PUNCT
ajst-6461	9	5	the	the	DET
ajst-6461	9	6	dirichlet	dirichlet	NOUN
ajst-6461	9	7	distribution	distribution	NOUN
ajst-6461	9	8	as	as	ADP
ajst-6461	9	9	a	a	DET
ajst-6461	9	10	conjugate	conjugate	NOUN
ajst-6461	9	11	prior	prior	ADV
ajst-6461	9	12	for	for	ADP
ajst-6461	9	13	multinomial	multinomial	ADJ
ajst-6461	9	14	distributions	distribution	NOUN
ajst-6461	9	15	is	be	AUX
ajst-6461	9	16	used	use	VERB
ajst-6461	9	17	for	for	ADP
ajst-6461	9	18	parameter	parameter	NOUN
ajst-6461	9	19	estimation	estimation	NOUN
ajst-6461	9	20	of	of	ADP
ajst-6461	9	21	multinomial	multinomial	ADJ
ajst-6461	9	22	,	,	PUNCT
ajst-6461	9	23	binomial	binomial	ADJ
ajst-6461	9	24	and	and	CCONJ
ajst-6461	9	25	type	type	NOUN
ajst-6461	9	26	distributions	distribution	NOUN
ajst-6461	9	27	[	[	X
ajst-6461	9	28	1	1	NUM
ajst-6461	9	29	]	]	PUNCT
ajst-6461	9	30	.	.	PUNCT
ajst-6461	10	1	in	in	ADP
ajst-6461	10	2	the	the	DET
ajst-6461	10	3	field	field	NOUN
ajst-6461	10	4	of	of	ADP
ajst-6461	10	5	machine	machine	NOUN
ajst-6461	10	6	learning	learning	NOUN
ajst-6461	10	7	,	,	PUNCT
ajst-6461	10	8	dirichlet	dirichlet	PROPN
ajst-6461	10	9	and	and	CCONJ
ajst-6461	10	10	generalized	generalize	VERB
ajst-6461	10	11	dirichlet	dirichlet	NOUN
ajst-6461	10	12	distributions	distribution	NOUN
ajst-6461	10	13	are	be	AUX
ajst-6461	10	14	mostly	mostly	ADV
ajst-6461	10	15	applied	apply	VERB
ajst-6461	10	16	to	to	PART
ajst-6461	10	17	build	build	VERB
ajst-6461	10	18	mixture	mixture	NOUN
ajst-6461	10	19	models	model	NOUN
ajst-6461	10	20	to	to	PART
ajst-6461	10	21	deal	deal	VERB
ajst-6461	10	22	with	with	ADP
ajst-6461	10	23	unsupervised	unsupervised	ADJ
ajst-6461	10	24	learning	learning	NOUN
ajst-6461	10	25	problems	problem	NOUN
ajst-6461	10	26	such	such	ADJ
ajst-6461	10	27	as	as	ADP
ajst-6461	10	28	highdimensional	highdimensional	ADJ
ajst-6461	10	29	clustering	clustering	NOUN
ajst-6461	10	30	and	and	CCONJ
ajst-6461	10	31	feature	feature	VERB
ajst-6461	10	32	empowerment	empowerment	NOUN
ajst-6461	11	1	[	[	X
ajst-6461	11	2	2	2	NUM
ajst-6461	11	3	]	]	PUNCT
ajst-6461	11	4	.	.	PUNCT
ajst-6461	12	1	in	in	ADP
ajst-6461	12	2	natural	natural	ADJ
ajst-6461	12	3	language	language	NOUN
ajst-6461	12	4	processing	processing	NOUN
ajst-6461	12	5	and	and	CCONJ
ajst-6461	12	6	bioinformatics	bioinformatics	NOUN
ajst-6461	12	7	research	research	NOUN
ajst-6461	12	8	,	,	PUNCT
ajst-6461	12	9	the	the	DET
ajst-6461	12	10	implicit	implicit	ADJ
ajst-6461	12	11	dirichlet	dirichlet	NOUN
ajst-6461	12	12	distribution	distribution	NOUN
ajst-6461	12	13	is	be	AUX
ajst-6461	12	14	used	use	VERB
ajst-6461	12	15	to	to	PART
ajst-6461	12	16	identify	identify	VERB
ajst-6461	12	17	potential	potential	ADJ
ajst-6461	12	18	subject	subject	ADJ
ajst-6461	12	19	word	word	NOUN
ajst-6461	12	20	information	information	NOUN
ajst-6461	12	21	in	in	ADP
ajst-6461	12	22	a	a	DET
ajst-6461	12	23	document	document	NOUN
ajst-6461	12	24	set	set	NOUN
ajst-6461	13	1	[	[	X
ajst-6461	13	2	3][4	3][4	NUM
ajst-6461	13	3	]	]	X
ajst-6461	13	4	.	.	PUNCT
ajst-6461	14	1	in	in	ADP
ajst-6461	14	2	this	this	DET
ajst-6461	14	3	article	article	NOUN
ajst-6461	14	4	,	,	PUNCT
ajst-6461	14	5	we	we	PRON
ajst-6461	14	6	study	study	VERB
ajst-6461	14	7	the	the	DET
ajst-6461	14	8	joint	joint	ADJ
ajst-6461	14	9	probability	probability	NOUN
ajst-6461	14	10	density	density	NOUN
ajst-6461	14	11	,	,	PUNCT
ajst-6461	14	12	marginal	marginal	ADJ
ajst-6461	14	13	density	density	NOUN
ajst-6461	14	14	,	,	PUNCT
ajst-6461	14	15	and	and	CCONJ
ajst-6461	14	16	the	the	DET
ajst-6461	14	17	distribution	distribution	NOUN
ajst-6461	14	18	of	of	ADP
ajst-6461	14	19	sum	sum	NOUN
ajst-6461	14	20	,	,	PUNCT
ajst-6461	14	21	product	product	NOUN
ajst-6461	14	22	and	and	CCONJ
ajst-6461	14	23	quotient	quotient	VERB
ajst-6461	14	24	for	for	ADP
ajst-6461	14	25	two	two	NUM
ajst-6461	14	26	two	two	NUM
ajst-6461	14	27	-	-	PUNCT
ajst-6461	14	28	dimensional	dimensional	ADJ
ajst-6461	14	29	random	random	ADJ
ajst-6461	14	30	variables	variable	NOUN
ajst-6461	14	31	by	by	ADP
ajst-6461	14	32	using	use	VERB
ajst-6461	14	33	the	the	DET
ajst-6461	14	34	properties	property	NOUN
ajst-6461	14	35	of	of	ADP
ajst-6461	14	36	generalized	generalized	ADJ
ajst-6461	14	37	dirichlet	dirichlet	NOUN
ajst-6461	14	38	distribution	distribution	NOUN
ajst-6461	14	39	,	,	PUNCT
ajst-6461	14	40	noncentral	noncentral	ADJ
ajst-6461	14	41	gamma	gamma	NOUN
ajst-6461	14	42	distribution	distribution	NOUN
ajst-6461	14	43	and	and	CCONJ
ajst-6461	14	44	confluent	confluent	ADJ
ajst-6461	14	45	hypergeometric	hypergeometric	ADJ
ajst-6461	14	46	function	function	NOUN
ajst-6461	14	47	.	.	PUNCT
ajst-6461	15	1	so	so	ADV
ajst-6461	15	2	we	we	PRON
ajst-6461	15	3	firstly	firstly	ADV
ajst-6461	15	4	introduce	introduce	VERB
ajst-6461	15	5	the	the	DET
ajst-6461	15	6	generalized	generalized	ADJ
ajst-6461	15	7	dirichlet	dirichlet	NOUN
ajst-6461	15	8	type	type	NOUN
ajst-6461	15	9	1	1	NUM
ajst-6461	15	10	distribution	distribution	NOUN
ajst-6461	15	11	and	and	CCONJ
ajst-6461	15	12	generalized	generalized	ADJ
ajst-6461	15	13	dirichlet	dirichlet	NOUN
ajst-6461	15	14	type	type	NOUN
ajst-6461	15	15	2	2	NUM
ajst-6461	15	16	distribution	distribution	NOUN
ajst-6461	15	17	.	.	PUNCT
ajst-6461	16	1	let	let	VERB
ajst-6461	16	2	)	)	PUNCT
ajst-6461	16	3	,	,	PUNCT
ajst-6461	16	4	(	(	PUNCT
ajst-6461	16	5	21	21	NUM
ajst-6461	16	6	zz	zz	VERB
ajst-6461	16	7	be	be	AUX
ajst-6461	16	8	a	a	DET
ajst-6461	16	9	two	two	NUM
ajst-6461	16	10	-	-	PUNCT
ajst-6461	16	11	dimensional	dimensional	ADJ
ajst-6461	16	12	random	random	ADJ
ajst-6461	16	13	variable	variable	NOUN
ajst-6461	16	14	,	,	PUNCT
ajst-6461	16	15	if	if	SCONJ
ajst-6461	16	16	its	its	PRON
ajst-6461	16	17	p.d.f	p.d.f	ADJ
ajst-6461	16	18	is	be	AUX
ajst-6461	16	19	1,0,0	1,0,0	NUM
ajst-6461	16	20	,	,	PUNCT
ajst-6461	16	21	)	)	PUNCT
ajst-6461	16	22	,	,	PUNCT
ajst-6461	16	23	,	,	PUNCT
ajst-6461	16	24	(	(	PUNCT
ajst-6461	16	25	)	)	PUNCT
ajst-6461	16	26	1	1	NUM
ajst-6461	16	27	(	(	PUNCT
ajst-6461	16	28	)	)	PUNCT
ajst-6461	16	29	,	,	PUNCT
ajst-6461	16	30	,	,	PUNCT
ajst-6461	16	31	;	;	PUNCT
ajst-6461	16	32	,	,	PUNCT
ajst-6461	16	33	(	(	PUNCT
ajst-6461	16	34	1	1	NUM
ajst-6461	16	35	2121	2121	NUM
ajst-6461	16	36	321	321	NUM
ajst-6461	16	37	1	1	NUM
ajst-6461	16	38	21	21	NUM
ajst-6461	16	39	1	1	NUM
ajst-6461	16	40	2	2	NUM
ajst-6461	16	41	1	1	NUM
ajst-6461	16	42	1	1	NUM
ajst-6461	16	43	32121	32121	NUM
ajst-6461	16	44	321	321	NUM
ajst-6461	16	45			NUM
ajst-6461	16	46			NOUN
ajst-6461	16	47			PROPN
ajst-6461	16	48			NOUN
ajst-6461	16	49	zzzz	zzzz	PROPN
ajst-6461	16	50	aaab	aaab	PROPN
ajst-6461	16	51	zzzz	zzzz	PROPN
ajst-6461	16	52	aaazzd	aaazzd	PROPN
ajst-6461	16	53	aaa	aaa	NOUN
ajst-6461	16	54	,	,	PUNCT
ajst-6461	16	55	where	where	SCONJ
ajst-6461	16	56	)	)	PUNCT
ajst-6461	16	57	(	(	PUNCT
ajst-6461	16	58	)	)	PUNCT
ajst-6461	16	59	(	(	PUNCT
ajst-6461	16	60	)	)	PUNCT
ajst-6461	16	61	(	(	PUNCT
ajst-6461	16	62	)	)	PUNCT
ajst-6461	16	63	(	(	PUNCT
ajst-6461	16	64	)	)	PUNCT
ajst-6461	16	65	,	,	PUNCT
ajst-6461	16	66	,	,	PUNCT
ajst-6461	16	67	(	(	PUNCT
ajst-6461	16	68	321	321	NUM
ajst-6461	16	69	321	321	NUM
ajst-6461	16	70	321	321	NUM
ajst-6461	16	71	aaa	aaa	NOUN
ajst-6461	16	72	aaa	aaa	NOUN
ajst-6461	16	73	aaab	aaab	PROPN
ajst-6461	16	74			PROPN
ajst-6461	16	75			NOUN
ajst-6461	16	76			NOUN
ajst-6461	16	77	,	,	PUNCT
ajst-6461	16	78	then	then	ADV
ajst-6461	16	79	)	)	PUNCT
ajst-6461	16	80	,	,	PUNCT
ajst-6461	16	81	(	(	PUNCT
ajst-6461	16	82	21	21	NUM
ajst-6461	16	83	zz	zz	PROPN
ajst-6461	16	84	follows	follow	VERB
ajst-6461	16	85	the	the	DET
ajst-6461	16	86	dirichlet	dirichlet	PROPN
ajst-6461	16	87	type	type	NOUN
ajst-6461	16	88	1	1	NUM
ajst-6461	16	89	distribution	distribution	NOUN
ajst-6461	16	90	.	.	PUNCT
ajst-6461	17	1	let	let	VERB
ajst-6461	17	2	)	)	PUNCT
ajst-6461	17	3	,	,	PUNCT
ajst-6461	17	4	(	(	PUNCT
ajst-6461	17	5	21	21	NUM
ajst-6461	17	6	tt	tt	PROPN
ajst-6461	17	7	be	be	AUX
ajst-6461	17	8	a	a	DET
ajst-6461	17	9	two	two	NUM
ajst-6461	17	10	-	-	PUNCT
ajst-6461	17	11	dimensional	dimensional	ADJ
ajst-6461	17	12	random	random	ADJ
ajst-6461	17	13	variable	variable	NOUN
ajst-6461	17	14	,	,	PUNCT
ajst-6461	17	15	if	if	SCONJ
ajst-6461	17	16	its	its	PRON
ajst-6461	17	17	p.d.f	p.d.f	ADJ
ajst-6461	17	18	is	be	AUX
ajst-6461	17	19	0,0	0,0	NOUN
ajst-6461	17	20	,	,	PUNCT
ajst-6461	17	21	)	)	PUNCT
ajst-6461	17	22	,	,	PUNCT
ajst-6461	17	23	,	,	PUNCT
ajst-6461	17	24	(	(	PUNCT
ajst-6461	17	25	)	)	PUNCT
ajst-6461	17	26	1	1	NUM
ajst-6461	17	27	(	(	PUNCT
ajst-6461	17	28	)	)	PUNCT
ajst-6461	17	29	,	,	PUNCT
ajst-6461	17	30	,	,	PUNCT
ajst-6461	17	31	;	;	PUNCT
ajst-6461	17	32	,	,	PUNCT
ajst-6461	17	33	(	(	PUNCT
ajst-6461	17	34	2	2	NUM
ajst-6461	17	35	21	21	NUM
ajst-6461	17	36	321	321	NUM
ajst-6461	17	37	)	)	PUNCT
ajst-6461	17	38	(	(	PUNCT
ajst-6461	17	39	21	21	NUM
ajst-6461	17	40	1	1	NUM
ajst-6461	17	41	2	2	NUM
ajst-6461	17	42	1	1	NUM
ajst-6461	17	43	1	1	NUM
ajst-6461	17	44	32121	32121	NUM
ajst-6461	17	45	32121	32121	NUM
ajst-6461	17	46			X
ajst-6461	18	1			ADJ
ajst-6461	18	2			PROPN
ajst-6461	18	3			NOUN
ajst-6461	18	4	tt	tt	PROPN
ajst-6461	18	5	aaab	aaab	PROPN
ajst-6461	18	6	tttt	tttt	PROPN
ajst-6461	18	7	aaattd	aaattd	NOUN
ajst-6461	18	8	aaaaa	aaaaa	NOUN
ajst-6461	18	9	,	,	PUNCT
ajst-6461	18	10	then	then	ADV
ajst-6461	18	11	)	)	PUNCT
ajst-6461	18	12	,	,	PUNCT
ajst-6461	18	13	(	(	PUNCT
ajst-6461	18	14	21	21	NUM
ajst-6461	18	15	tt	tt	PROPN
ajst-6461	18	16	follows	follow	VERB
ajst-6461	18	17	the	the	DET
ajst-6461	18	18	dirichlet	dirichlet	PROPN
ajst-6461	18	19	type	type	NOUN
ajst-6461	18	20	2	2	NUM
ajst-6461	18	21	distribution	distribution	NOUN
ajst-6461	18	22	.	.	PUNCT
ajst-6461	19	1	random	random	ADJ
ajst-6461	19	2	variable	variable	ADJ
ajst-6461	19	3	u	u	NOUN
ajst-6461	19	4	has	have	VERB
ajst-6461	19	5	a	a	DET
ajst-6461	19	6	non	non	ADJ
ajst-6461	19	7	-	-	ADJ
ajst-6461	19	8	central	central	ADJ
ajst-6461	19	9	gamma	gamma	NOUN
ajst-6461	19	10	distribution	distribution	NOUN
ajst-6461	19	11	with	with	ADP
ajst-6461	19	12	shape	shape	NOUN
ajst-6461	19	13	parameter	parameter	NOUN
ajst-6461	19	14	)	)	PUNCT
ajst-6461	19	15	0(k	0(k	NUM
ajst-6461	19	16	and	and	CCONJ
ajst-6461	19	17	non	non	ADJ
ajst-6461	19	18	-	-	ADJ
ajst-6461	19	19	central	central	ADJ
ajst-6461	19	20	parameter	parameter	NOUN
ajst-6461	19	21			PROPN
ajst-6461	19	22	0	0	PUNCT
ajst-6461	19	23	,	,	PUNCT
ajst-6461	19	24	denoted	denote	VERB
ajst-6461	19	25	by	by	ADP
ajst-6461	19	26	)	)	PUNCT
ajst-6461	19	27	;	;	PUNCT
ajst-6461	19	28	(	(	PUNCT
ajst-6461	19	29	~	~	PUNCT
ajst-6461	19	30	kncgu	kncgu	X
ajst-6461	19	31	,	,	PUNCT
ajst-6461	19	32	the	the	DET
ajst-6461	19	33	probability	probability	NOUN
ajst-6461	19	34	density	density	NOUN
ajst-6461	19	35	is	be	AUX
ajst-6461	19	36	given	give	VERB
ajst-6461	19	37	by	by	ADP
ajst-6461	19	38	[	[	X
ajst-6461	19	39	5	5	NUM
ajst-6461	19	40	]	]	PUNCT
ajst-6461	19	41	,	,	PUNCT
ajst-6461	19	42	0),;()exp	0),;()exp	PROPN
ajst-6461	19	43	(	(	PUNCT
ajst-6461	19	44	)	)	PUNCT
ajst-6461	19	45	}	}	PUNCT
ajst-6461	19	46	(	(	PUNCT
ajst-6461	19	47	{	{	X
ajst-6461	19	48	)	)	PUNCT
ajst-6461	19	49	;	;	PUNCT
ajst-6461	19	50	;	;	PUNCT
ajst-6461	19	51	(	(	PUNCT
ajst-6461	19	52	10	10	NUM
ajst-6461	19	53	11	11	NUM
ajst-6461	19	54			NUM
ajst-6461	19	55			NUM
ajst-6461	19	56	uufuukuf	uufuukuf	NOUN
ajst-6461	19	57	k	k	PROPN
ajst-6461	19	58	ncg	ncg	PROPN
ajst-6461	19	59			NOUN
ajst-6461	19	60	where	where	SCONJ
ajst-6461	19	61			X
ajst-6461	19	62			VERB
ajst-6461	19	63			PRON
ajst-6461	19	64			NOUN
ajst-6461	19	65	0	0	NUM
ajst-6461	19	66	10	10	NUM
ajst-6461	19	67	!	!	PUNCT
ajst-6461	19	68	)	)	PUNCT
ajst-6461	20	1	(	(	PUNCT
ajst-6461	20	2	1	1	NUM
ajst-6461	20	3	)	)	PUNCT
ajst-6461	20	4	;	;	PUNCT
ajst-6461	20	5	(	(	PUNCT
ajst-6461	20	6	j	j	PROPN
ajst-6461	20	7	j	j	PROPN
ajst-6461	20	8	j	j	PROPN
ajst-6461	20	9	j	j	PROPN
ajst-6461	20	10	n	n	CCONJ
ajst-6461	20	11	m	m	PROPN
ajst-6461	20	12	nmf	nmf	NOUN
ajst-6461	20	13	.	.	PUNCT
ajst-6461	21	1	when	when	SCONJ
ajst-6461	21	2	0	0	PROPN
ajst-6461	21	3	,	,	PUNCT
ajst-6461	21	4	the	the	DET
ajst-6461	21	5	noncentral	noncentral	ADJ
ajst-6461	21	6	gamma	gamma	NOUN
ajst-6461	21	7	distribution	distribution	NOUN
ajst-6461	21	8	reduces	reduce	VERB
ajst-6461	21	9	to	to	ADP
ajst-6461	21	10	the	the	DET
ajst-6461	21	11	standard	standard	ADJ
ajst-6461	21	12	gamma	gamma	NOUN
ajst-6461	21	13	distribution	distribution	NOUN
ajst-6461	21	14	,	,	PUNCT
ajst-6461	21	15	denoted	denote	VERB
ajst-6461	21	16	by	by	ADP
ajst-6461	21	17	)	)	PUNCT
ajst-6461	21	18	(	(	PUNCT
ajst-6461	21	19	~	~	PUNCT
ajst-6461	21	20	gu	gu	X
ajst-6461	21	21	.	.	PUNCT
ajst-6461	22	1	then	then	ADV
ajst-6461	22	2	we	we	PRON
ajst-6461	22	3	introduce	introduce	VERB
ajst-6461	22	4	hypergeometric	hypergeometric	ADJ
ajst-6461	22	5	series	series	NOUN
ajst-6461	22	6	.	.	PUNCT
ajst-6461	23	1	the	the	DET
ajst-6461	23	2	definition	definition	NOUN
ajst-6461	23	3	of	of	ADP
ajst-6461	23	4	generalized	generalized	ADJ
ajst-6461	23	5	hypergeometric	hypergeometric	ADJ
ajst-6461	23	6	function	function	NOUN
ajst-6461	23	7	is	be	AUX
ajst-6461	23	8	given	give	VERB
ajst-6461	23	9	by	by	ADP
ajst-6461	23	10	[	[	X
ajst-6461	23	11	6	6	NUM
ajst-6461	23	12	]	]	PUNCT
ajst-6461	23	13			X
ajst-6461	23	14			VERB
ajst-6461	23	15			PRON
ajst-6461	23	16			NOUN
ajst-6461	23	17	0	0	NUM
ajst-6461	23	18	1	1	NUM
ajst-6461	23	19	1	1	NUM
ajst-6461	23	20	11	11	NUM
ajst-6461	23	21	!	!	PUNCT
ajst-6461	23	22	)	)	PUNCT
ajst-6461	23	23	(	(	PUNCT
ajst-6461	23	24	)	)	PUNCT
ajst-6461	23	25	(	(	PUNCT
ajst-6461	23	26	)	)	PUNCT
ajst-6461	23	27	(	(	PUNCT
ajst-6461	23	28	)	)	PUNCT
ajst-6461	23	29	(	(	PUNCT
ajst-6461	23	30	)	)	PUNCT
ajst-6461	23	31	;	;	PUNCT
ajst-6461	23	32	;	;	PUNCT
ajst-6461	23	33	(	(	PUNCT
ajst-6461	23	34	k	k	PROPN
ajst-6461	23	35	kqq	kqq	PROPN
ajst-6461	23	36	k	k	PROPN
ajst-6461	23	37	kpk	kpk	PROPN
ajst-6461	23	38	qpqp	qpqp	PROPN
ajst-6461	23	39	kbb	kbb	PROPN
ajst-6461	23	40	zaa	zaa	PROPN
ajst-6461	23	41	zbbaaf	zbbaaf	X
ajst-6461	23	42	…	…	PUNCT
ajst-6461	23	43	…	…	PUNCT
ajst-6461	23	44	…	…	PUNCT
ajst-6461	23	45	…	…	PUNCT
ajst-6461	23	46	(	(	PUNCT
ajst-6461	23	47	1.1	1.1	NUM
ajst-6461	23	48	)	)	PUNCT
ajst-6461	23	49	where	where	SCONJ
ajst-6461	23	50	pochhammer	pochhammer	NOUN
ajst-6461	23	51	symbol	symbol	NOUN
ajst-6461	23	52	，	，	PROPN
ajst-6461	23	53	�	�	PROPN
ajst-6461	23	54	3,2,1),1()1	3,2,1),1()1	NUM
ajst-6461	23	55	(	(	PUNCT
ajst-6461	23	56	)	)	PUNCT
ajst-6461	23	57	(	(	PUNCT
ajst-6461	23	58			ADJ
ajst-6461	23	59	nnaaaa	nnaaaa	NOUN
ajst-6461	23	60	n	n	PRON
ajst-6461	23	61	1	1	NUM
ajst-6461	23	62	)	)	PUNCT
ajst-6461	23	63	(	(	PUNCT
ajst-6461	23	64	0	0	NUM
ajst-6461	23	65	a	a	NOUN
ajst-6461	23	66	,	,	PUNCT
ajst-6461	23	67	the	the	DET
ajst-6461	23	68	convergence	convergence	NOUN
ajst-6461	23	69	condition	condition	NOUN
ajst-6461	23	70	of	of	ADP
ajst-6461	23	71	this	this	DET
ajst-6461	23	72	series	series	NOUN
ajst-6461	23	73	is	be	AUX
ajst-6461	23	74	shown	show	VERB
ajst-6461	23	75	in	in	ADP
ajst-6461	23	76	[	[	X
ajst-6461	23	77	7	7	NUM
ajst-6461	23	78	]	]	PUNCT
ajst-6461	23	79	.	.	PUNCT
ajst-6461	24	1	the	the	DET
ajst-6461	24	2	confluent	confluent	ADJ
ajst-6461	24	3	hypergeometric	hypergeometric	ADJ
ajst-6461	24	4	function	function	NOUN
ajst-6461	24	5	is	be	AUX
ajst-6461	24	6	a	a	DET
ajst-6461	24	7	special	special	ADJ
ajst-6461	24	8	case	case	NOUN
ajst-6461	24	9	of	of	ADP
ajst-6461	24	10	the	the	DET
ajst-6461	24	11	generalized	generalized	ADJ
ajst-6461	24	12	hypergeometric	hypergeometric	ADJ
ajst-6461	24	13	function	function	NOUN
ajst-6461	24	14	,	,	PUNCT
ajst-6461	24	15	which	which	PRON
ajst-6461	24	16	is	be	AUX
ajst-6461	24	17	expressed	express	VERB
ajst-6461	24	18	as	as	SCONJ
ajst-6461	24	19	follows	follow	VERB
ajst-6461	24	20	[	[	X
ajst-6461	24	21	6	6	NUM
ajst-6461	24	22	]	]	PUNCT
ajst-6461	24	23	:	:	PUNCT
ajst-6461	24	24			X
ajst-6461	24	25			VERB
ajst-6461	24	26			PRON
ajst-6461	24	27			NOUN
ajst-6461	24	28	0	0	NUM
ajst-6461	24	29	11	11	NUM
ajst-6461	24	30	!	!	PUNCT
ajst-6461	24	31	)	)	PUNCT
ajst-6461	25	1	(	(	PUNCT
ajst-6461	25	2	)	)	PUNCT
ajst-6461	25	3	(	(	PUNCT
ajst-6461	25	4	)	)	PUNCT
ajst-6461	25	5	;	;	PUNCT
ajst-6461	25	6	;	;	PUNCT
ajst-6461	25	7	(	(	PUNCT
ajst-6461	25	8	k	k	X
ajst-6461	25	9	k	k	PROPN
ajst-6461	26	1	k	k	PROPN
ajst-6461	26	2	k	k	PROPN
ajst-6461	26	3	kb	kb	PROPN
ajst-6461	26	4	xa	xa	PROPN
ajst-6461	26	5	xbaf	xbaf	PROPN
ajst-6461	26	6	.	.	PUNCT
ajst-6461	27	1	its	its	PRON
ajst-6461	27	2	integral	integral	ADJ
ajst-6461	27	3	form	form	NOUN
ajst-6461	27	4	is	be	AUX
ajst-6461	27	5			PUNCT
ajst-6461	27	6			NUM
ajst-6461	27	7			PROPN
ajst-6461	27	8			PRON
ajst-6461	28	1			VERB
ajst-6461	28	2			NOUN
ajst-6461	28	3	1	1	NUM
ajst-6461	28	4	0	0	NUM
ajst-6461	28	5	11	11	NUM
ajst-6461	28	6	11	11	NUM
ajst-6461	28	7	)	)	PUNCT
ajst-6461	28	8	exp()1	exp()1	PROPN
ajst-6461	28	9	(	(	PUNCT
ajst-6461	28	10	)	)	PUNCT
ajst-6461	28	11	(	(	PUNCT
ajst-6461	28	12	)	)	PUNCT
ajst-6461	28	13	(	(	PUNCT
ajst-6461	28	14	)	)	PUNCT
ajst-6461	28	15	(	(	PUNCT
ajst-6461	28	16	)	)	PUNCT
ajst-6461	28	17	;	;	PUNCT
ajst-6461	28	18	;	;	PUNCT
ajst-6461	28	19	(	(	PUNCT
ajst-6461	28	20	dtxttt	dtxttt	PROPN
ajst-6461	28	21	aba	aba	PROPN
ajst-6461	28	22	b	b	X
ajst-6461	28	23	xbaf	xbaf	PROPN
ajst-6461	28	24	aba	aba	PROPN
ajst-6461	28	25	.	.	PUNCT
ajst-6461	29	1	let	let	VERB
ajst-6461	29	2	independent	independent	ADJ
ajst-6461	29	3	random	random	ADJ
ajst-6461	29	4	variable	variable	NOUN
ajst-6461	29	5	3,2,1	3,2,1	NUM
ajst-6461	29	6	,	,	PUNCT
ajst-6461	29	7	ix	ix	NUM
ajst-6461	30	1	i	i	PRON
ajst-6461	30	2	follow	follow	VERB
ajst-6461	30	3	gamma	gamma	NOUN
ajst-6461	30	4	distributions	distribution	NOUN
ajst-6461	30	5	with	with	ADP
ajst-6461	30	6	shape	shape	NOUN
ajst-6461	30	7	parameter	parameter	NOUN
ajst-6461	30	8	3,2,1	3,2,1	NUM
ajst-6461	30	9	,	,	PUNCT
ajst-6461	30	10	ivi	ivi	NOUN
ajst-6461	30	11	,	,	PUNCT
ajst-6461	30	12	)	)	PUNCT
ajst-6461	30	13	)	)	PUNCT
ajst-6461	30	14	(	(	PUNCT
ajst-6461	30	15	,	,	PUNCT
ajst-6461	30	16	)	)	PUNCT
ajst-6461	30	17	(	(	PUNCT
ajst-6461	30	18	(	(	PUNCT
ajst-6461	30	19	)	)	PUNCT
ajst-6461	30	20	,	,	PUNCT
ajst-6461	30	21	(	(	PUNCT
ajst-6461	30	22	3212321121	3212321121	NUM
ajst-6461	30	23	xxxxxxxxzz	xxxxxxxxzz	NOUN
ajst-6461	30	24			NOUN
ajst-6461	30	25	and	and	CCONJ
ajst-6461	30	26	)	)	PUNCT
ajst-6461	30	27	,	,	PUNCT
ajst-6461	30	28	(	(	PUNCT
ajst-6461	30	29	)	)	PUNCT
ajst-6461	30	30	,	,	PUNCT
ajst-6461	30	31	(	(	PUNCT
ajst-6461	30	32	323121	323121	NUM
ajst-6461	30	33	xxxxyy	xxxxyy	VERB
ajst-6461	30	34			NUM
ajst-6461	30	35	,	,	PUNCT
ajst-6461	30	36	then	then	ADV
ajst-6461	30	37	)	)	PUNCT
ajst-6461	30	38	,	,	PUNCT
ajst-6461	30	39	(	(	PUNCT
ajst-6461	30	40	21	21	NUM
ajst-6461	30	41	zz	zz	PROPN
ajst-6461	30	42	and	and	CCONJ
ajst-6461	30	43	)	)	PUNCT
ajst-6461	30	44	,	,	PUNCT
ajst-6461	30	45	(	(	PUNCT
ajst-6461	30	46	21	21	NUM
ajst-6461	30	47	yy	yy	NOUN
ajst-6461	30	48	follow	follow	VERB
ajst-6461	30	49	dirichlet	dirichlet	PROPN
ajst-6461	30	50	type	type	NOUN
ajst-6461	30	51	1	1	NUM
ajst-6461	30	52	distribution	distribution	NOUN
ajst-6461	30	53	and	and	CCONJ
ajst-6461	30	54	dirichlet	dirichlet	NOUN
ajst-6461	30	55	type	type	NOUN
ajst-6461	30	56	2	2	NUM
ajst-6461	30	57	distribution	distribution	NOUN
ajst-6461	30	58	respectively	respectively	ADV
ajst-6461	30	59	.	.	PUNCT
ajst-6461	31	1	orozco	orozco	PROPN
ajst-6461	31	2	-	-	PUNCT
ajst-6461	31	3	castañeda	castañeda	NOUN
ajst-6461	31	4	,	,	PUNCT
ajst-6461	31	5	nagar	nagar	NOUN
ajst-6461	31	6	and	and	CCONJ
ajst-6461	31	7	gupta	gupta	NOUN
ajst-6461	31	8	[	[	X
ajst-6461	31	9	6	6	NUM
ajst-6461	31	10	]	]	PUNCT
ajst-6461	31	11	generalized	generalize	VERB
ajst-6461	31	12	the	the	DET
ajst-6461	31	13	above	above	ADJ
ajst-6461	31	14	distribution	distribution	NOUN
ajst-6461	31	15	by	by	ADP
ajst-6461	31	16	hypergeometric	hypergeometric	ADJ
ajst-6461	31	17	series	series	NOUN
ajst-6461	31	18	.	.	PUNCT
ajst-6461	32	1	let	let	VERB
ajst-6461	32	2	the	the	DET
ajst-6461	32	3	random	random	ADJ
ajst-6461	32	4	variables	variable	NOUN
ajst-6461	32	5	wvu	wvu	PROPN
ajst-6461	32	6	,	,	PUNCT
ajst-6461	32	7	,	,	PUNCT
ajst-6461	32	8	be	be	AUX
ajst-6461	32	9	independent	independent	ADJ
ajst-6461	32	10	,	,	PUNCT
ajst-6461	32	11	u	u	NOUN
ajst-6461	32	12	and	and	CCONJ
ajst-6461	32	13	v	v	ADP
ajst-6461	32	14	follow	follow	NOUN
ajst-6461	32	15	gamma	gamma	NOUN
ajst-6461	32	16	distributions	distribution	NOUN
ajst-6461	32	17	with	with	ADP
ajst-6461	32	18	shape	shape	NOUN
ajst-6461	32	19	parameter	parameter	NOUN
ajst-6461	32	20	a	a	PRON
ajst-6461	32	21	and	and	CCONJ
ajst-6461	32	22	b	b	NOUN
ajst-6461	32	23	,	,	PUNCT
ajst-6461	32	24	w	w	PROPN
ajst-6461	32	25	follows	follow	VERB
ajst-6461	32	26	the	the	DET
ajst-6461	32	27	non	non	ADJ
ajst-6461	32	28	-	-	ADJ
ajst-6461	32	29	central	central	ADJ
ajst-6461	32	30	gamma	gamma	NOUN
ajst-6461	32	31	distribution	distribution	NOUN
ajst-6461	32	32	with	with	ADP
ajst-6461	32	33	shape	shape	NOUN
ajst-6461	32	34	parameter	parameter	NOUN
ajst-6461	32	35	c	c	PROPN
ajst-6461	32	36	and	and	CCONJ
ajst-6461	32	37	non	non	ADJ
ajst-6461	32	38	-	-	ADJ
ajst-6461	32	39	central	central	ADJ
ajst-6461	32	40	parameter	parameter	NOUN
ajst-6461	32	41			NUM
ajst-6461	32	42	,	,	PUNCT
ajst-6461	32	43	)	)	PUNCT
ajst-6461	32	44	(	(	PUNCT
ajst-6461	32	45	wuup	wuup	NOUN
ajst-6461	32	46			ADJ
ajst-6461	32	47	,	,	PUNCT
ajst-6461	32	48	)	)	PUNCT
ajst-6461	32	49	(	(	PUNCT
ajst-6461	32	50	wvvq	wvvq	PROPN
ajst-6461	32	51			PROPN
ajst-6461	32	52	,	,	PUNCT
ajst-6461	32	53	gupta	gupta	PROPN
ajst-6461	32	54	,	,	PUNCT
ajst-6461	32	55	orozco	orozco	PROPN
ajst-6461	32	56	-	-	PUNCT
ajst-6461	32	57	castañeda	castañeda	PROPN
ajst-6461	32	58	and	and	CCONJ
ajst-6461	32	59	nagar	nagar	NOUN
ajst-6461	33	1	[	[	X
ajst-6461	33	2	5	5	NUM
ajst-6461	33	3	]	]	PUNCT
ajst-6461	33	4	studied	study	VERB
ajst-6461	33	5	the	the	DET
ajst-6461	33	6	joint	joint	ADJ
ajst-6461	33	7	probability	probability	NOUN
ajst-6461	33	8	density	density	NOUN
ajst-6461	33	9	of	of	ADP
ajst-6461	33	10	p	p	NOUN
ajst-6461	33	11	and	and	CCONJ
ajst-6461	33	12	q	q	NOUN
ajst-6461	33	13	as	as	ADV
ajst-6461	33	14	well	well	ADV
ajst-6461	33	15	as	as	ADP
ajst-6461	33	16	other	other	ADJ
ajst-6461	33	17	statistical	statistical	ADJ
ajst-6461	33	18	properties	property	NOUN
ajst-6461	33	19	.	.	PUNCT
ajst-6461	34	1	based	base	VERB
ajst-6461	34	2	on	on	ADP
ajst-6461	34	3	the	the	DET
ajst-6461	34	4	previous	previous	ADJ
ajst-6461	34	5	work	work	NOUN
ajst-6461	34	6	,	,	PUNCT
ajst-6461	34	7	in	in	ADP
ajst-6461	34	8	this	this	DET
ajst-6461	34	9	paper	paper	NOUN
ajst-6461	34	10	we	we	PRON
ajst-6461	34	11	define	define	VERB
ajst-6461	34	12	122	122	NUM
ajst-6461	34	13	)	)	PUNCT
ajst-6461	34	14	)	)	PUNCT
ajst-6461	34	15	(	(	PUNCT
ajst-6461	34	16	,	,	PUNCT
ajst-6461	34	17	)	)	PUNCT
ajst-6461	34	18	(	(	PUNCT
ajst-6461	34	19	(	(	PUNCT
ajst-6461	34	20	)	)	PUNCT
ajst-6461	34	21	,	,	PUNCT
ajst-6461	34	22	(	(	PUNCT
ajst-6461	34	23	wvuvwvuuyx	wvuvwvuuyx	PROPN
ajst-6461	34	24			NOUN
ajst-6461	34	25	and	and	CCONJ
ajst-6461	34	26	)	)	PUNCT
ajst-6461	34	27	,	,	PUNCT
ajst-6461	34	28	(	(	PUNCT
ajst-6461	34	29	)	)	PUNCT
ajst-6461	34	30	,	,	PUNCT
ajst-6461	34	31	(	(	PUNCT
ajst-6461	34	32	11	11	NUM
ajst-6461	34	33	wvwuyx	wvwuyx	NOUN
ajst-6461	34	34			PROPN
ajst-6461	34	35	,	,	PUNCT
ajst-6461	34	36	then	then	ADV
ajst-6461	34	37	study	study	VERB
ajst-6461	34	38	their	their	PRON
ajst-6461	34	39	joint	joint	ADJ
ajst-6461	34	40	probability	probability	NOUN
ajst-6461	34	41	density	density	NOUN
ajst-6461	34	42	,	,	PUNCT
ajst-6461	34	43	marginal	marginal	ADJ
ajst-6461	34	44	probability	probability	NOUN
ajst-6461	34	45	density	density	NOUN
ajst-6461	34	46	,	,	PUNCT
ajst-6461	34	47	and	and	CCONJ
ajst-6461	34	48	statistical	statistical	ADJ
ajst-6461	34	49	properties	property	NOUN
ajst-6461	34	50	of	of	ADP
ajst-6461	34	51	sum	sum	NOUN
ajst-6461	34	52	,	,	PUNCT
ajst-6461	34	53	product	product	NOUN
ajst-6461	34	54	,	,	PUNCT
ajst-6461	34	55	quotient	quotient	NOUN
ajst-6461	34	56	.	.	PUNCT
ajst-6461	35	1	from	from	ADP
ajst-6461	35	2	these	these	DET
ajst-6461	35	3	properties	property	NOUN
ajst-6461	35	4	,	,	PUNCT
ajst-6461	35	5	authors	author	NOUN
ajst-6461	35	6	find	find	VERB
ajst-6461	35	7	that	that	SCONJ
ajst-6461	35	8	they	they	PRON
ajst-6461	35	9	follow	follow	VERB
ajst-6461	35	10	generalized	generalized	ADJ
ajst-6461	35	11	dirichlet	dirichlet	NOUN
ajst-6461	35	12	type	type	NOUN
ajst-6461	35	13	1	1	NUM
ajst-6461	35	14	distribution	distribution	NOUN
ajst-6461	35	15	and	and	CCONJ
ajst-6461	35	16	generalized	generalized	ADJ
ajst-6461	35	17	dirichlet	dirichlet	NOUN
ajst-6461	35	18	type	type	NOUN
ajst-6461	35	19	2	2	NUM
ajst-6461	35	20	distribution	distribution	NOUN
ajst-6461	35	21	respectively	respectively	ADV
ajst-6461	35	22	.	.	PUNCT
ajst-6461	36	1	2	2	X
ajst-6461	36	2	.	.	NUM
ajst-6461	36	3	generalized	generalize	VERB
ajst-6461	36	4	dirichlet	dirichlet	PROPN
ajst-6461	36	5	type	type	NOUN
ajst-6461	36	6	1	1	NUM
ajst-6461	36	7	distribution	distribution	NOUN
ajst-6461	36	8	theorem	theorem	VERB
ajst-6461	36	9	2.1	2.1	NUM
ajst-6461	36	10	:	:	PUNCT
ajst-6461	36	11	let	let	VERB
ajst-6461	36	12	vu	vu	NOUN
ajst-6461	36	13	,	,	PUNCT
ajst-6461	36	14	and	and	CCONJ
ajst-6461	36	15	w	w	NOUN
ajst-6461	36	16	be	be	AUX
ajst-6461	36	17	independent	independent	ADJ
ajst-6461	36	18	random	random	ADJ
ajst-6461	36	19	variables	variable	NOUN
ajst-6461	36	20	,	,	PUNCT
ajst-6461	36	21	)	)	PUNCT
ajst-6461	36	22	(	(	PUNCT
ajst-6461	36	23	~),(~	~),(~	NUM
ajst-6461	36	24	bgvagu	bgvagu	NOUN
ajst-6461	36	25	and	and	CCONJ
ajst-6461	36	26	)	)	PUNCT
ajst-6461	36	27	,	,	PUNCT
ajst-6461	36	28	c(~	c(~	NOUN
ajst-6461	36	29	ncgw	ncgw	NOUN
ajst-6461	36	30	,	,	PUNCT
ajst-6461	36	31	define	define	VERB
ajst-6461	36	32	)	)	PUNCT
ajst-6461	36	33	(	(	PUNCT
ajst-6461	36	34	wvuux	wvuux	PROPN
ajst-6461	36	35			PROPN
ajst-6461	36	36	,	,	PUNCT
ajst-6461	36	37	)	)	PUNCT
ajst-6461	36	38	(	(	PUNCT
ajst-6461	36	39	wvuvy	wvuvy	PROPN
ajst-6461	36	40			PUNCT
ajst-6461	36	41	,	,	PUNCT
ajst-6461	36	42	then	then	ADV
ajst-6461	36	43	the	the	DET
ajst-6461	36	44	joint	joint	ADJ
ajst-6461	36	45	density	density	NOUN
ajst-6461	36	46	of	of	ADP
ajst-6461	36	47	x	x	PUNCT
ajst-6461	36	48	and	and	CCONJ
ajst-6461	36	49	y	y	PROPN
ajst-6461	36	50	is	be	AUX
ajst-6461	36	51	give	give	VERB
ajst-6461	36	52	by	by	ADP
ajst-6461	36	53			NOUN
ajst-6461	36	54			PROPN
ajst-6461	36	55	1,0,0	1,0,0	NUM
ajst-6461	36	56	,	,	PUNCT
ajst-6461	36	57	)	)	PUNCT
ajst-6461	36	58	1	1	NUM
ajst-6461	36	59	(;	(;	X
ajst-6461	36	60	;	;	PUNCT
ajst-6461	36	61	)	)	PUNCT
ajst-6461	36	62	,	,	PUNCT
ajst-6461	36	63	,	,	PUNCT
ajst-6461	36	64	(	(	PUNCT
ajst-6461	36	65	)	)	PUNCT
ajst-6461	36	66	1	1	NUM
ajst-6461	36	67	(	(	PUNCT
ajst-6461	36	68	11	11	NUM
ajst-6461	36	69	111	111	NUM
ajst-6461	36	70			X
ajst-6461	36	71			PROPN
ajst-6461	36	72			PROPN
ajst-6461	36	73	yxyxyxccbaf	yxyxyxccbaf	PROPN
ajst-6461	36	74	cbab	cbab	PROPN
ajst-6461	36	75	eyxyx	eyxyx	PROPN
ajst-6461	36	76	cba	cba	PROPN
ajst-6461	36	77			PROPN
ajst-6461	36	78			NUM
ajst-6461	36	79	(	(	PUNCT
ajst-6461	36	80	2.1	2.1	NUM
ajst-6461	36	81	)	)	PUNCT
ajst-6461	36	82	the	the	DET
ajst-6461	36	83	p.d.f	p.d.f	NOUN
ajst-6461	36	84	of	of	ADP
ajst-6461	36	85	wvus	wvus	PROPN
ajst-6461	36	86			PROPN
ajst-6461	36	87	is	be	AUX
ajst-6461	36	88	given	give	VERB
ajst-6461	36	89	by	by	ADP
ajst-6461	36	90	)	)	PUNCT
ajst-6461	36	91	;	;	PUNCT
ajst-6461	36	92	(	(	PUNCT
ajst-6461	36	93	)	)	PUNCT
ajst-6461	36	94	(	(	PUNCT
ajst-6461	36	95	10	10	NUM
ajst-6461	36	96	1	1	NUM
ajst-6461	36	97	scbaf	scbaf	PROPN
ajst-6461	36	98	cba	cba	PROPN
ajst-6461	36	99	se	se	PROPN
ajst-6461	36	100	cbas	cbas	PROPN
ajst-6461	36	101			NUM
ajst-6461	36	102			PROPN
ajst-6461	36	103			PROPN
ajst-6461	36	104			PROPN
ajst-6461	36	105			NOUN
ajst-6461	36	106	.	.	PUNCT
ajst-6461	37	1	proof	proof	NOUN
ajst-6461	37	2	:	:	PUNCT
ajst-6461	37	3	since	since	SCONJ
ajst-6461	37	4	vu	vu	NOUN
ajst-6461	37	5	,	,	PUNCT
ajst-6461	37	6	and	and	CCONJ
ajst-6461	37	7	w	w	NOUN
ajst-6461	37	8	are	be	AUX
ajst-6461	37	9	independent	independent	ADJ
ajst-6461	37	10	random	random	ADJ
ajst-6461	37	11	variables	variable	NOUN
ajst-6461	37	12	,	,	PUNCT
ajst-6461	37	13	the	the	DET
ajst-6461	37	14	joint	joint	ADJ
ajst-6461	37	15	density	density	NOUN
ajst-6461	37	16	is	be	AUX
ajst-6461	37	17	given	give	VERB
ajst-6461	37	18	by	by	ADP
ajst-6461	37	19	.0,0,0	.0,0,0	NOUN
ajst-6461	37	20	,	,	PUNCT
ajst-6461	37	21	)	)	PUNCT
ajst-6461	37	22	;	;	PUNCT
ajst-6461	37	23	(	(	PUNCT
ajst-6461	37	24	)	)	PUNCT
ajst-6461	37	25	(	(	PUNCT
ajst-6461	37	26	)	)	PUNCT
ajst-6461	37	27	(	(	PUNCT
ajst-6461	37	28	)	)	PUNCT
ajst-6461	37	29	(	(	PUNCT
ajst-6461	37	30	10	10	NUM
ajst-6461	37	31	111	111	NUM
ajst-6461	37	32			NOUN
ajst-6461	37	33			NOUN
ajst-6461	37	34			NOUN
ajst-6461	37	35	wvuwcf	wvuwcf	VERB
ajst-6461	37	36	cba	cba	PROPN
ajst-6461	37	37	wvue	wvue	PROPN
ajst-6461	37	38	cbawvu	cbawvu	PROPN
ajst-6461	37	39			PROPN
ajst-6461	37	40			NUM
ajst-6461	37	41	(	(	PUNCT
ajst-6461	37	42	2.2	2.2	NUM
ajst-6461	37	43	)	)	PUNCT
ajst-6461	37	44	making	make	VERB
ajst-6461	37	45	the	the	DET
ajst-6461	37	46	transformation	transformation	NOUN
ajst-6461	37	47	)	)	PUNCT
ajst-6461	37	48	(	(	PUNCT
ajst-6461	37	49	)	)	PUNCT
ajst-6461	37	50	,	,	PUNCT
ajst-6461	37	51	(	(	PUNCT
ajst-6461	37	52	wvuvywvuux	wvuvywvuux	PROPN
ajst-6461	37	53			NOUN
ajst-6461	37	54	and	and	CCONJ
ajst-6461	37	55	wvus	wvu	NOUN
ajst-6461	37	56			PUNCT
ajst-6461	37	57	with	with	ADP
ajst-6461	37	58	the	the	DET
ajst-6461	37	59	jacobian	jacobian	ADJ
ajst-6461	37	60	2	2	NUM
ajst-6461	37	61	)	)	PUNCT
ajst-6461	37	62	,	,	PUNCT
ajst-6461	37	63	,	,	PUNCT
ajst-6461	37	64	,	,	PUNCT
ajst-6461	37	65	,	,	PUNCT
ajst-6461	37	66	(	(	PUNCT
ajst-6461	37	67	ssyxwvuj	ssyxwvuj	NOUN
ajst-6461	37	68			VERB
ajst-6461	37	69	,	,	PUNCT
ajst-6461	37	70	then	then	ADV
ajst-6461	37	71	we	we	PRON
ajst-6461	37	72	obtain	obtain	VERB
ajst-6461	37	73	the	the	DET
ajst-6461	37	74	joint	joint	ADJ
ajst-6461	37	75	p.d.f	p.d.f	NOUN
ajst-6461	37	76	of	of	ADP
ajst-6461	37	77	x	x	SYM
ajst-6461	37	78	,	,	PUNCT
ajst-6461	37	79	y	y	PROPN
ajst-6461	37	80	and	and	CCONJ
ajst-6461	37	81	s	s	PRON
ajst-6461	37	82	as	as	ADP
ajst-6461	37	83	:	:	PUNCT
ajst-6461	37	84			PROPN
ajst-6461	37	85			PROPN
ajst-6461	37	86	,	,	PUNCT
ajst-6461	37	87	)	)	PUNCT
ajst-6461	37	88	1	1	NUM
ajst-6461	37	89	(;	(;	X
ajst-6461	37	90	)	)	PUNCT
ajst-6461	37	91	(	(	PUNCT
ajst-6461	37	92	)	)	PUNCT
ajst-6461	37	93	(	(	PUNCT
ajst-6461	37	94	)	)	PUNCT
ajst-6461	37	95	(	(	PUNCT
ajst-6461	37	96	)	)	PUNCT
ajst-6461	37	97	1	1	NUM
ajst-6461	37	98	(	(	PUNCT
ajst-6461	37	99	10	10	NUM
ajst-6461	37	100	1	1	NUM
ajst-6461	37	101	111	111	NUM
ajst-6461	37	102	yxscfse	yxscfse	NOUN
ajst-6461	37	103	cba	cba	PROPN
ajst-6461	37	104	eyxyx	eyxyx	PROPN
ajst-6461	37	105	cbas	cbas	PROPN
ajst-6461	37	106	cba	cba	NOUN
ajst-6461	37	107			PUNCT
ajst-6461	37	108			NOUN
ajst-6461	37	109			PUNCT
ajst-6461	37	110			PROPN
ajst-6461	37	111			PROPN
ajst-6461	37	112			NUM
ajst-6461	37	113			NUM
ajst-6461	37	114	(	(	PUNCT
ajst-6461	37	115	2.3	2.3	NUM
ajst-6461	37	116	)	)	PUNCT
ajst-6461	37	117	where	where	SCONJ
ajst-6461	37	118	1,0,0	1,0,0	NUM
ajst-6461	37	119			NOUN
ajst-6461	37	120	yxyx	yxyx	NOUN
ajst-6461	37	121	and	and	CCONJ
ajst-6461	37	122	0s	0s	NUM
ajst-6461	37	123	,	,	PUNCT
ajst-6461	37	124	integrating	integrate	VERB
ajst-6461	37	125	s	s	PRON
ajst-6461	37	126	,	,	PUNCT
ajst-6461	37	127	then	then	ADV
ajst-6461	37	128	the	the	DET
ajst-6461	37	129	joint	joint	ADJ
ajst-6461	37	130	p.d.f	p.d.f	NOUN
ajst-6461	37	131	of	of	ADP
ajst-6461	37	132	)	)	PUNCT
ajst-6461	37	133	,	,	PUNCT
ajst-6461	37	134	(	(	PUNCT
ajst-6461	37	135	yx	yx	PROPN
ajst-6461	37	136	is	be	AUX
ajst-6461	37	137	given	give	VERB
ajst-6461	37	138	by	by	ADP
ajst-6461	37	139			NOUN
ajst-6461	37	140			PROPN
ajst-6461	37	141	)	)	PUNCT
ajst-6461	37	142	1(s	1(s	NUM
ajst-6461	37	143	;	;	PUNCT
ajst-6461	37	144	)	)	PUNCT
ajst-6461	37	145	(	(	PUNCT
ajst-6461	37	146	)	)	PUNCT
ajst-6461	37	147	(	(	PUNCT
ajst-6461	37	148	)	)	PUNCT
ajst-6461	37	149	(	(	PUNCT
ajst-6461	37	150	)	)	PUNCT
ajst-6461	37	151	1	1	NUM
ajst-6461	37	152	(	(	PUNCT
ajst-6461	37	153	100	100	NUM
ajst-6461	37	154	1	1	NUM
ajst-6461	37	155	111	111	NUM
ajst-6461	37	156	dsyxcfse	dsyxcfse	PROPN
ajst-6461	37	157	cba	cba	PROPN
ajst-6461	37	158	eyxyx	eyxyx	PROPN
ajst-6461	37	159	cbas	cbas	PROPN
ajst-6461	37	160	cba	cba	NOUN
ajst-6461	37	161			PUNCT
ajst-6461	37	162			NOUN
ajst-6461	37	163			NOUN
ajst-6461	37	164			NOUN
ajst-6461	38	1			PROPN
ajst-6461	38	2			VERB
ajst-6461	38	3			PROPN
ajst-6461	38	4			NUM
ajst-6461	38	5			NUM
ajst-6461	38	6	.	.	PUNCT
ajst-6461	38	7	!	!	PUNCT
ajst-6461	38	8	)	)	PUNCT
ajst-6461	39	1	(	(	PUNCT
ajst-6461	39	2	)	)	PUNCT
ajst-6461	39	3	(	(	PUNCT
ajst-6461	39	4	)	)	PUNCT
ajst-6461	39	5	1	1	NUM
ajst-6461	39	6	(	(	PUNCT
ajst-6461	39	7	)	)	PUNCT
ajst-6461	39	8	(	(	PUNCT
ajst-6461	39	9	)	)	PUNCT
ajst-6461	39	10	(	(	PUNCT
ajst-6461	39	11	)	)	PUNCT
ajst-6461	39	12	(	(	PUNCT
ajst-6461	39	13	)	)	PUNCT
ajst-6461	39	14	1	1	NUM
ajst-6461	39	15	(	(	PUNCT
ajst-6461	39	16	!	!	PUNCT
ajst-6461	39	17	)	)	PUNCT
ajst-6461	40	1	(	(	PUNCT
ajst-6461	40	2	)	)	PUNCT
ajst-6461	40	3	1	1	NUM
ajst-6461	40	4	(	(	PUNCT
ajst-6461	40	5	)	)	PUNCT
ajst-6461	40	6	(	(	PUNCT
ajst-6461	40	7	)	)	PUNCT
ajst-6461	40	8	(	(	PUNCT
ajst-6461	40	9	)	)	PUNCT
ajst-6461	40	10	(	(	PUNCT
ajst-6461	40	11	)	)	PUNCT
ajst-6461	40	12	1	1	NUM
ajst-6461	40	13	(	(	PUNCT
ajst-6461	40	14	0	0	NUM
ajst-6461	40	15	111	111	NUM
ajst-6461	40	16	0	0	NUM
ajst-6461	40	17	1	1	NUM
ajst-6461	40	18	0	0	NUM
ajst-6461	40	19	111	111	NUM
ajst-6461	40	20			X
ajst-6461	40	21			X
ajst-6461	41	1			VERB
ajst-6461	41	2			PRON
ajst-6461	41	3			NOUN
ajst-6461	41	4			PROPN
ajst-6461	41	5			PROPN
ajst-6461	41	6			VERB
ajst-6461	41	7			PRON
ajst-6461	41	8			NOUN
ajst-6461	41	9			NOUN
ajst-6461	41	10			NOUN
ajst-6461	41	11			NOUN
ajst-6461	41	12			NUM
ajst-6461	41	13			NOUN
ajst-6461	41	14			NOUN
ajst-6461	41	15			NOUN
ajst-6461	41	16			NUM
ajst-6461	41	17	j	j	PROPN
ajst-6461	42	1	j	j	PROPN
ajst-6461	42	2	jjcba	jjcba	PROPN
ajst-6461	42	3	jcbas	jcbas	PROPN
ajst-6461	42	4	j	j	PROPN
ajst-6461	42	5	j	j	PROPN
ajst-6461	42	6	jjcba	jjcba	PROPN
ajst-6461	42	7	jc	jc	PROPN
ajst-6461	42	8	jcbayx	jcbayx	PROPN
ajst-6461	42	9	cba	cba	PROPN
ajst-6461	42	10	eyxyx	eyxyx	PROPN
ajst-6461	42	11	dsse	dsse	PROPN
ajst-6461	42	12	jc	jc	PROPN
ajst-6461	42	13	yx	yx	PROPN
ajst-6461	42	14	cba	cba	PROPN
ajst-6461	42	15	eyxyx	eyxyx	PROPN
ajst-6461	42	16			NUM
ajst-6461	42	17			NUM
ajst-6461	42	18			NUM
ajst-6461	42	19			NUM
ajst-6461	42	20	from	from	ADP
ajst-6461	42	21	)	)	PUNCT
ajst-6461	42	22	(	(	PUNCT
ajst-6461	42	23	)	)	PUNCT
ajst-6461	42	24	(	(	PUNCT
ajst-6461	42	25	)	)	PUNCT
ajst-6461	42	26	(	(	PUNCT
ajst-6461	42	27	aaka	aaka	ADV
ajst-6461	42	28	k	k	VERB
ajst-6461	42	29	,	,	PUNCT
ajst-6461	42	30	(	(	PUNCT
ajst-6461	42	31	2.1	2.1	NUM
ajst-6461	42	32	)	)	PUNCT
ajst-6461	42	33	is	be	AUX
ajst-6461	42	34	proved	prove	VERB
ajst-6461	42	35	.	.	PUNCT
ajst-6461	43	1	further	far	ADV
ajst-6461	43	2	,	,	PUNCT
ajst-6461	43	3	integrating	integrate	VERB
ajst-6461	43	4	x	x	PUNCT
ajst-6461	43	5	and	and	CCONJ
ajst-6461	43	6	y	y	PROPN
ajst-6461	43	7	in	in	ADP
ajst-6461	43	8	(	(	PUNCT
ajst-6461	43	9	2.3	2.3	NUM
ajst-6461	43	10	)	)	PUNCT
ajst-6461	43	11	,	,	PUNCT
ajst-6461	43	12	we	we	PRON
ajst-6461	43	13	can	can	AUX
ajst-6461	43	14	get	get	VERB
ajst-6461	43	15	the	the	DET
ajst-6461	43	16	marginal	marginal	ADJ
ajst-6461	43	17	density	density	NOUN
ajst-6461	43	18	of	of	ADP
ajst-6461	43	19	s	s	NOUN
ajst-6461	43	20	:	:	PUNCT
ajst-6461	43	21	.	.	PUNCT
ajst-6461	43	22	)	)	PUNCT
ajst-6461	44	1	1	1	NUM
ajst-6461	44	2	1()1	1()1	NUM
ajst-6461	44	3	(	(	PUNCT
ajst-6461	44	4	)	)	PUNCT
ajst-6461	44	5	(	(	PUNCT
ajst-6461	44	6	)	)	PUNCT
ajst-6461	44	7	(	(	PUNCT
ajst-6461	44	8	)	)	PUNCT
ajst-6461	44	9	(	(	PUNCT
ajst-6461	44	10	)	)	PUNCT
ajst-6461	44	11	(	(	PUNCT
ajst-6461	44	12	)	)	PUNCT
ajst-6461	44	13	(	(	PUNCT
ajst-6461	44	14	)	)	PUNCT
ajst-6461	44	15	(	(	PUNCT
ajst-6461	44	16	)	)	PUNCT
ajst-6461	44	17	1	1	NUM
ajst-6461	44	18	(	(	PUNCT
ajst-6461	44	19	)	)	PUNCT
ajst-6461	44	20	(	(	PUNCT
ajst-6461	44	21	)	)	PUNCT
ajst-6461	44	22	(	(	PUNCT
ajst-6461	44	23	)	)	PUNCT
ajst-6461	44	24	(	(	PUNCT
ajst-6461	44	25	)	)	PUNCT
ajst-6461	44	26	1	1	NUM
ajst-6461	44	27	(	(	PUNCT
ajst-6461	44	28	1	1	NUM
ajst-6461	44	29	0	0	NUM
ajst-6461	44	30	1	1	NUM
ajst-6461	44	31	0	0	NUM
ajst-6461	44	32	1	1	NUM
ajst-6461	44	33	111	111	NUM
ajst-6461	44	34	0	0	NUM
ajst-6461	44	35	1	1	NUM
ajst-6461	44	36	0	0	NUM
ajst-6461	44	37	11	11	NUM
ajst-6461	44	38	0	0	NUM
ajst-6461	44	39	1	1	NUM
ajst-6461	44	40	0	0	NUM
ajst-6461	44	41	111	111	NUM
ajst-6461	44	42	dxdy	dxdy	NOUN
ajst-6461	44	43	x	x	PROPN
ajst-6461	44	44	y	y	PROPN
ajst-6461	44	45	yxx	yxx	PROPN
ajst-6461	45	1	c	c	PROPN
ajst-6461	45	2	s	s	PROPN
ajst-6461	45	3	cba	cba	PROPN
ajst-6461	45	4	se	se	PROPN
ajst-6461	45	5	dxdy	dxdy	PROPN
ajst-6461	45	6	c	c	PROPN
ajst-6461	45	7	yxs	yxs	PROPN
ajst-6461	45	8	se	se	PROPN
ajst-6461	45	9	cba	cba	PROPN
ajst-6461	45	10	yxyx	yxyx	PROPN
ajst-6461	46	1	x	x	PROPN
ajst-6461	46	2	jc	jc	PROPN
ajst-6461	46	3	bjca	bjca	PROPN
ajst-6461	46	4	j	j	PROPN
ajst-6461	47	1	j	j	PROPN
ajst-6461	47	2	jcbas	jcbas	PROPN
ajst-6461	47	3	j	j	PROPN
ajst-6461	47	4	j	j	PROPN
ajst-6461	47	5	jjj	jjj	PROPN
ajst-6461	47	6	cbasx	cbasx	PROPN
ajst-6461	47	7	cba	cba	PROPN
ajst-6461	47	8			PUNCT
ajst-6461	47	9			X
ajst-6461	47	10			X
ajst-6461	47	11			PUNCT
ajst-6461	47	12			PROPN
ajst-6461	47	13			PROPN
ajst-6461	47	14			NOUN
ajst-6461	47	15			VERB
ajst-6461	47	16			PRON
ajst-6461	47	17			ADJ
ajst-6461	47	18			VERB
ajst-6461	47	19			NUM
ajst-6461	47	20			NOUN
ajst-6461	47	21			NOUN
ajst-6461	47	22			PROPN
ajst-6461	47	23			NOUN
ajst-6461	47	24			PRON
ajst-6461	47	25			PROPN
ajst-6461	47	26			PROPN
ajst-6461	47	27			NOUN
ajst-6461	47	28			NOUN
ajst-6461	47	29			PUNCT
ajst-6461	47	30			NOUN
ajst-6461	47	31			ADJ
ajst-6461	47	32			NOUN
ajst-6461	47	33			NOUN
ajst-6461	47	34			NOUN
ajst-6461	47	35			NUM
ajst-6461	47	36			NUM
ajst-6461	47	37			NUM
ajst-6461	47	38			NUM
ajst-6461	47	39	setting	setting	NOUN
ajst-6461	47	40	)	)	PUNCT
ajst-6461	47	41	1	1	NUM
ajst-6461	47	42	(	(	PUNCT
ajst-6461	47	43	xyu	xyu	PROPN
ajst-6461	47	44			PROPN
ajst-6461	47	45	,	,	PUNCT
ajst-6461	47	46	from	from	ADP
ajst-6461	47	47	the	the	DET
ajst-6461	47	48	definition	definition	NOUN
ajst-6461	47	49	of	of	ADP
ajst-6461	47	50	the	the	DET
ajst-6461	47	51	beta	beta	NOUN
ajst-6461	47	52	function	function	NOUN
ajst-6461	47	53	,	,	PUNCT
ajst-6461	47	54	the	the	DET
ajst-6461	47	55	above	above	ADJ
ajst-6461	47	56	formula	formula	NOUN
ajst-6461	47	57	can	can	AUX
ajst-6461	47	58	be	be	AUX
ajst-6461	47	59	calculated	calculate	VERB
ajst-6461	47	60	as	as	ADP
ajst-6461	47	61	:	:	PUNCT
ajst-6461	47	62	.	.	PUNCT
ajst-6461	47	63	)	)	PUNCT
ajst-6461	47	64	(	(	PUNCT
ajst-6461	47	65	)	)	PUNCT
ajst-6461	47	66	(	(	PUNCT
ajst-6461	47	67	)	)	PUNCT
ajst-6461	47	68	(	(	PUNCT
ajst-6461	47	69	)	)	PUNCT
ajst-6461	47	70	(	(	PUNCT
ajst-6461	47	71	)	)	PUNCT
ajst-6461	47	72	(	(	PUNCT
ajst-6461	47	73	)	)	PUNCT
ajst-6461	47	74	(	(	PUNCT
ajst-6461	47	75	)	)	PUNCT
ajst-6461	47	76	(	(	PUNCT
ajst-6461	47	77	)	)	PUNCT
ajst-6461	47	78	(	(	PUNCT
ajst-6461	47	79	)	)	PUNCT
ajst-6461	47	80	(	(	PUNCT
ajst-6461	47	81	)	)	PUNCT
ajst-6461	47	82	(	(	PUNCT
ajst-6461	47	83	)	)	PUNCT
ajst-6461	47	84	(	(	PUNCT
ajst-6461	47	85	)	)	PUNCT
ajst-6461	47	86	(	(	PUNCT
ajst-6461	47	87	)	)	PUNCT
ajst-6461	47	88	(	(	PUNCT
ajst-6461	47	89	)	)	PUNCT
ajst-6461	47	90	(	(	PUNCT
ajst-6461	47	91	)	)	PUNCT
ajst-6461	47	92	1	1	NUM
ajst-6461	47	93	(	(	PUNCT
ajst-6461	47	94	)	)	PUNCT
ajst-6461	47	95	(	(	PUNCT
ajst-6461	47	96	)	)	PUNCT
ajst-6461	47	97	(	(	PUNCT
ajst-6461	47	98	)	)	PUNCT
ajst-6461	47	99	(	(	PUNCT
ajst-6461	47	100	)	)	PUNCT
ajst-6461	47	101	(	(	PUNCT
ajst-6461	47	102	)	)	PUNCT
ajst-6461	47	103	(	(	PUNCT
ajst-6461	47	104	0	0	NUM
ajst-6461	47	105	1	1	NUM
ajst-6461	47	106	1	1	NUM
ajst-6461	47	107	0	0	NUM
ajst-6461	47	108	11	11	NUM
ajst-6461	47	109	0	0	NUM
ajst-6461	47	110	1	1	NUM
ajst-6461	47	111			X
ajst-6461	47	112			X
ajst-6461	48	1			VERB
ajst-6461	48	2			PRON
ajst-6461	48	3			ADJ
ajst-6461	48	4			NOUN
ajst-6461	48	5			VERB
ajst-6461	48	6			PRON
ajst-6461	48	7			ADJ
ajst-6461	48	8			NOUN
ajst-6461	49	1			NUM
ajst-6461	49	2			NOUN
ajst-6461	49	3			PROPN
ajst-6461	49	4			PROPN
ajst-6461	49	5			ADJ
ajst-6461	49	6			NOUN
ajst-6461	49	7			NOUN
ajst-6461	49	8			PROPN
ajst-6461	49	9	j	j	PROPN
ajst-6461	49	10	j	j	PROPN
ajst-6461	49	11	jcbas	jcbas	PROPN
ajst-6461	50	1	jbca	jbca	PROPN
ajst-6461	50	2	j	j	PROPN
ajst-6461	50	3	j	j	PROPN
ajst-6461	50	4	jcbas	jcbas	PROPN
ajst-6461	50	5	jcbajcbc	jcbajcbc	PROPN
ajst-6461	50	6	jbcajcbs	jbcajcbs	PROPN
ajst-6461	50	7	cba	cba	PROPN
ajst-6461	50	8	se	se	PROPN
ajst-6461	50	9	dx	dx	PROPN
ajst-6461	50	10	jcb	jcb	PROPN
ajst-6461	50	11	jcb	jcb	PROPN
ajst-6461	51	1	xx	xx	NUM
ajst-6461	51	2	c	c	PROPN
ajst-6461	51	3	s	s	PROPN
ajst-6461	51	4	cba	cba	PROPN
ajst-6461	51	5	se	se	PROPN
ajst-6461	52	1			PROPN
ajst-6461	52	2			NUM
ajst-6461	52	3			NUM
ajst-6461	52	4			NUM
ajst-6461	52	5	from	from	ADP
ajst-6461	52	6	)	)	PUNCT
ajst-6461	52	7	(	(	PUNCT
ajst-6461	52	8	)	)	PUNCT
ajst-6461	52	9	(	(	PUNCT
ajst-6461	52	10	)	)	PUNCT
ajst-6461	52	11	(	(	PUNCT
ajst-6461	52	12	aaka	aaka	ADV
ajst-6461	52	13	k	k	X
ajst-6461	52	14	,	,	PUNCT
ajst-6461	52	15	the	the	DET
ajst-6461	52	16	p.d.f	p.d.f	NOUN
ajst-6461	52	17	of	of	ADP
ajst-6461	52	18	s	s	PROPN
ajst-6461	52	19	is	be	AUX
ajst-6461	52	20	proved	prove	VERB
ajst-6461	52	21	.	.	PUNCT
ajst-6461	53	1	from	from	ADP
ajst-6461	53	2	theorem	theorem	ADJ
ajst-6461	53	3	2.1	2.1	NUM
ajst-6461	53	4	,	,	PUNCT
ajst-6461	53	5	we	we	PRON
ajst-6461	53	6	find	find	VERB
ajst-6461	53	7	that	that	PRON
ajst-6461	53	8	)	)	PUNCT
ajst-6461	53	9	,	,	PUNCT
ajst-6461	53	10	(	(	PUNCT
ajst-6461	53	11	yx	yx	PROPN
ajst-6461	53	12	follows	follow	VERB
ajst-6461	53	13	the	the	DET
ajst-6461	53	14	generalized	generalized	ADJ
ajst-6461	53	15	dirichlet	dirichlet	NOUN
ajst-6461	53	16	type	type	NOUN
ajst-6461	53	17	1	1	NUM
ajst-6461	53	18	distribution	distribution	NOUN
ajst-6461	53	19	,	,	PUNCT
ajst-6461	53	20	wvus	wvus	PROPN
ajst-6461	53	21			PROPN
ajst-6461	53	22	follows	follow	VERB
ajst-6461	53	23	the	the	DET
ajst-6461	53	24	non	non	ADJ
ajst-6461	53	25	-	-	ADJ
ajst-6461	53	26	central	central	ADJ
ajst-6461	53	27	gamma	gamma	NOUN
ajst-6461	53	28	distribution	distribution	NOUN
ajst-6461	53	29	,	,	PUNCT
ajst-6461	53	30	denoted	denote	VERB
ajst-6461	53	31	by	by	ADP
ajst-6461	53	32	)	)	PUNCT
ajst-6461	53	33	;	;	PUNCT
ajst-6461	53	34	(	(	PUNCT
ajst-6461	53	35	~	~	PUNCT
ajst-6461	53	36	cbancgs	cbancgs	PROPN
ajst-6461	53	37			PROPN
ajst-6461	53	38	.	.	PUNCT
ajst-6461	54	1	theorem	theorem	VERB
ajst-6461	54	2	2.2	2.2	NUM
ajst-6461	54	3	:	:	PUNCT
ajst-6461	54	4	if	if	SCONJ
ajst-6461	54	5	the	the	DET
ajst-6461	54	6	p.d.f	p.d.f	NOUN
ajst-6461	54	7	of	of	ADP
ajst-6461	54	8	)	)	PUNCT
ajst-6461	54	9	,	,	PUNCT
ajst-6461	54	10	(	(	PUNCT
ajst-6461	54	11	yx	yx	PROPN
ajst-6461	54	12	is	be	AUX
ajst-6461	54	13	given	give	VERB
ajst-6461	54	14	by	by	ADP
ajst-6461	54	15	theorem	theorem	ADJ
ajst-6461	54	16	2.1	2.1	NUM
ajst-6461	54	17	,	,	PUNCT
ajst-6461	54	18	then	then	ADV
ajst-6461	54	19	the	the	DET
ajst-6461	54	20	marginal	marginal	ADJ
ajst-6461	54	21	density	density	NOUN
ajst-6461	54	22	of	of	ADP
ajst-6461	54	23	x	x	PUNCT
ajst-6461	54	24	is	be	AUX
ajst-6461	54	25			NOUN
ajst-6461	54	26	)1	)1	NOUN
ajst-6461	54	27	(;	(;	NOUN
ajst-6461	54	28	;	;	PUNCT
ajst-6461	54	29	)	)	PUNCT
ajst-6461	54	30	,	,	PUNCT
ajst-6461	54	31	(	(	PUNCT
ajst-6461	54	32	)	)	PUNCT
ajst-6461	54	33	1	1	NUM
ajst-6461	54	34	(	(	PUNCT
ajst-6461	54	35	11	11	NUM
ajst-6461	54	36	11	11	NUM
ajst-6461	54	37	xcbcbaf	xcbcbaf	X
ajst-6461	54	38	cbab	cbab	PROPN
ajst-6461	54	39	xxe	xxe	PROPN
ajst-6461	54	40	cba	cba	PROPN
ajst-6461	54	41			NOUN
ajst-6461	54	42			VERB
ajst-6461	54	43			VERB
ajst-6461	54	44			NOUN
ajst-6461	54	45			PROPN
ajst-6461	54	46			NUM
ajst-6461	54	47	.	.	PUNCT
ajst-6461	55	1	proof	proof	NOUN
ajst-6461	55	2	:	:	PUNCT
ajst-6461	55	3	integrating	integrate	VERB
ajst-6461	55	4	y	y	PRON
ajst-6461	55	5	in	in	ADP
ajst-6461	55	6	(	(	PUNCT
ajst-6461	55	7	2.1	2.1	NUM
ajst-6461	55	8	)	)	PUNCT
ajst-6461	55	9	,	,	PUNCT
ajst-6461	55	10	one	one	PRON
ajst-6461	55	11	obtains	obtain	VERB
ajst-6461	55	12			NOUN
ajst-6461	55	13	dyyxccbafyxyx	dyyxccbafyxyx	SYM
ajst-6461	55	14	cbab	cbab	PROPN
ajst-6461	55	15	e	e	X
ajst-6461	55	16	x	x	PROPN
ajst-6461	55	17	cba	cba	PROPN
ajst-6461	55	18	)	)	PUNCT
ajst-6461	55	19	1(;;)1	1(;;)1	PROPN
ajst-6461	55	20	(	(	PUNCT
ajst-6461	55	21	)	)	PUNCT
ajst-6461	55	22	,	,	PUNCT
ajst-6461	55	23	,	,	PUNCT
ajst-6461	55	24	(	(	PUNCT
ajst-6461	55	25	11	11	NUM
ajst-6461	55	26	1	1	NUM
ajst-6461	55	27	0	0	NUM
ajst-6461	55	28	111	111	NUM
ajst-6461	55	29			PRON
ajst-6461	55	30			NOUN
ajst-6461	55	31			VERB
ajst-6461	55	32			PROPN
ajst-6461	55	33			PROPN
ajst-6461	55	34			NUM
ajst-6461	55	35	.	.	PUNCT
ajst-6461	56	1	inserting	insert	VERB
ajst-6461	56	2	the	the	DET
ajst-6461	56	3	series	series	NOUN
ajst-6461	56	4	form	form	NOUN
ajst-6461	56	5	of	of	ADP
ajst-6461	56	6	11f	11f	NUM
ajst-6461	56	7	into	into	ADP
ajst-6461	56	8	this	this	DET
ajst-6461	56	9	formula	formula	NOUN
ajst-6461	56	10	,	,	PUNCT
ajst-6461	56	11	the	the	DET
ajst-6461	56	12	marginal	marginal	ADJ
ajst-6461	56	13	density	density	NOUN
ajst-6461	56	14	of	of	ADP
ajst-6461	56	15	x	x	NOUN
ajst-6461	56	16	is	be	AUX
ajst-6461	56	17	.	.	PUNCT
ajst-6461	57	1	1	1	NUM
ajst-6461	57	2	1)1	1)1	NUM
ajst-6461	57	3	(	(	PUNCT
ajst-6461	57	4	!	!	PUNCT
ajst-6461	57	5	)	)	PUNCT
ajst-6461	57	6	(	(	PUNCT
ajst-6461	57	7	)	)	PUNCT
ajst-6461	57	8	(	(	PUNCT
ajst-6461	57	9	)	)	PUNCT
ajst-6461	57	10	,	,	PUNCT
ajst-6461	57	11	,	,	PUNCT
ajst-6461	57	12	(	(	PUNCT
ajst-6461	57	13	)	)	PUNCT
ajst-6461	57	14	1	1	NUM
ajst-6461	57	15	(	(	PUNCT
ajst-6461	57	16	!	!	PUNCT
ajst-6461	57	17	)	)	PUNCT
ajst-6461	57	18	(	(	PUNCT
ajst-6461	57	19	)	)	PUNCT
ajst-6461	57	20	(	(	PUNCT
ajst-6461	57	21	)	)	PUNCT
ajst-6461	57	22	,	,	PUNCT
ajst-6461	57	23	,	,	PUNCT
ajst-6461	57	24	(	(	PUNCT
ajst-6461	57	25	1	1	NUM
ajst-6461	57	26	0	0	NUM
ajst-6461	57	27	1	1	NUM
ajst-6461	57	28	11	11	NUM
ajst-6461	57	29	0	0	NUM
ajst-6461	57	30	1	1	NUM
ajst-6461	57	31	1	1	NUM
ajst-6461	57	32	0	0	NUM
ajst-6461	57	33	11	11	NUM
ajst-6461	57	34	0	0	NUM
ajst-6461	57	35	1	1	NUM
ajst-6461	57	36			X
ajst-6461	57	37			X
ajst-6461	57	38			PROPN
ajst-6461	57	39			PROPN
ajst-6461	57	40			PROPN
ajst-6461	57	41			VERB
ajst-6461	57	42			PRON
ajst-6461	57	43			NOUN
ajst-6461	57	44			NOUN
ajst-6461	57	45			NOUN
ajst-6461	57	46			VERB
ajst-6461	57	47			PRON
ajst-6461	57	48			INTJ
ajst-6461	57	49			PROPN
ajst-6461	57	50			NOUN
ajst-6461	57	51			PRON
ajst-6461	57	52			PROPN
ajst-6461	57	53			PROPN
ajst-6461	57	54			NOUN
ajst-6461	57	55			PROPN
ajst-6461	57	56			PUNCT
ajst-6461	57	57			ADJ
ajst-6461	57	58			ADJ
ajst-6461	57	59			NOUN
ajst-6461	57	60			PROPN
ajst-6461	57	61	x	x	SYM
ajst-6461	57	62	jc	jc	PROPN
ajst-6461	57	63	bjc	bjc	PROPN
ajst-6461	57	64	j	j	PROPN
ajst-6461	58	1	j	j	PROPN
ajst-6461	58	2	j	j	PROPN
ajst-6461	58	3	j	j	PROPN
ajst-6461	58	4	a	a	X
ajst-6461	58	5	x	x	X
ajst-6461	58	6	jcb	jcb	PROPN
ajst-6461	58	7	j	j	PROPN
ajst-6461	59	1	j	j	PROPN
ajst-6461	59	2	j	j	PROPN
ajst-6461	59	3	j	j	PROPN
ajst-6461	59	4	a	a	DET
ajst-6461	59	5	dy	dy	NOUN
ajst-6461	59	6	x	x	PROPN
ajst-6461	59	7	y	y	PROPN
ajst-6461	59	8	yx	yx	PROPN
ajst-6461	59	9	jc	jc	PROPN
ajst-6461	59	10	cba	cba	PROPN
ajst-6461	59	11	cbab	cbab	PROPN
ajst-6461	59	12	xe	xe	PROPN
ajst-6461	59	13	dyyxy	dyyxy	PROPN
ajst-6461	59	14	jc	jc	PROPN
ajst-6461	59	15	cba	cba	PROPN
ajst-6461	59	16	cbab	cbab	PROPN
ajst-6461	59	17	xe	xe	PROPN
ajst-6461	60	1			NUM
ajst-6461	60	2			NUM
ajst-6461	60	3			NUM
ajst-6461	60	4			NUM
ajst-6461	60	5	setting	setting	NOUN
ajst-6461	60	6	)	)	PUNCT
ajst-6461	60	7	1	1	NUM
ajst-6461	60	8	(	(	PUNCT
ajst-6461	60	9	xyt	xyt	PROPN
ajst-6461	60	10			PROPN
ajst-6461	60	11	,	,	PUNCT
ajst-6461	60	12	then	then	ADV
ajst-6461	60	13	the	the	DET
ajst-6461	60	14	marginal	marginal	ADJ
ajst-6461	60	15	density	density	NOUN
ajst-6461	60	16	of	of	ADP
ajst-6461	60	17	x	x	NOUN
ajst-6461	60	18	is	be	AUX
ajst-6461	60	19	)	)	PUNCT
ajst-6461	60	20	(	(	PUNCT
ajst-6461	60	21	)	)	PUNCT
ajst-6461	60	22	(	(	PUNCT
ajst-6461	60	23	)	)	PUNCT
ajst-6461	60	24	(	(	PUNCT
ajst-6461	60	25	)	)	PUNCT
ajst-6461	60	26	1	1	NUM
ajst-6461	60	27	(	(	PUNCT
ajst-6461	60	28	!	!	PUNCT
ajst-6461	60	29	)	)	PUNCT
ajst-6461	60	30	(	(	PUNCT
ajst-6461	60	31	)	)	PUNCT
ajst-6461	60	32	(	(	PUNCT
ajst-6461	60	33	)	)	PUNCT
ajst-6461	60	34	,	,	PUNCT
ajst-6461	60	35	,	,	PUNCT
ajst-6461	60	36	(	(	PUNCT
ajst-6461	60	37	1	1	NUM
ajst-6461	60	38	0	0	NUM
ajst-6461	60	39	1	1	NUM
ajst-6461	60	40	jcb	jcb	NOUN
ajst-6461	60	41	jcb	jcb	PROPN
ajst-6461	60	42	x	x	PROPN
ajst-6461	60	43	jc	jc	PROPN
ajst-6461	60	44	cba	cba	PROPN
ajst-6461	60	45	cbab	cbab	PROPN
ajst-6461	60	46	xe	xe	PROPN
ajst-6461	60	47	bjc	bjc	PROPN
ajst-6461	61	1	j	j	PROPN
ajst-6461	62	1	j	j	PROPN
ajst-6461	62	2	j	j	PROPN
ajst-6461	62	3	j	j	PROPN
ajst-6461	62	4	a	a	DET
ajst-6461	62	5			PROPN
ajst-6461	62	6			PROPN
ajst-6461	62	7			NOUN
ajst-6461	62	8			PROPN
ajst-6461	62	9			ADJ
ajst-6461	62	10			NOUN
ajst-6461	62	11			NUM
ajst-6461	62	12			NOUN
ajst-6461	62	13			X
ajst-6461	62	14			ADJ
ajst-6461	62	15			NOUN
ajst-6461	62	16	)1	)1	NOUN
ajst-6461	62	17	(;	(;	PRON
ajst-6461	62	18	;	;	PUNCT
ajst-6461	62	19	)	)	PUNCT
ajst-6461	62	20	,	,	PUNCT
ajst-6461	62	21	(	(	PUNCT
ajst-6461	62	22	)	)	PUNCT
ajst-6461	62	23	1	1	NUM
ajst-6461	62	24	(	(	PUNCT
ajst-6461	62	25	11	11	NUM
ajst-6461	62	26	11	11	NUM
ajst-6461	62	27	xcbcbaf	xcbcbaf	X
ajst-6461	62	28	cbab	cbab	PROPN
ajst-6461	62	29	xxe	xxe	PROPN
ajst-6461	62	30	cba	cba	PROPN
ajst-6461	62	31			NOUN
ajst-6461	62	32			VERB
ajst-6461	62	33			PROPN
ajst-6461	62	34			PROPN
ajst-6461	62	35			ADV
ajst-6461	62	36			PROPN
ajst-6461	62	37			NUM
ajst-6461	62	38	.	.	PUNCT
ajst-6461	63	1	from	from	ADP
ajst-6461	63	2	theorem	theorem	ADJ
ajst-6461	63	3	2.2	2.2	NUM
ajst-6461	63	4	,	,	PUNCT
ajst-6461	63	5	we	we	PRON
ajst-6461	63	6	find	find	VERB
ajst-6461	63	7	that	that	SCONJ
ajst-6461	63	8	x	x	PRON
ajst-6461	63	9	follows	follow	VERB
ajst-6461	63	10	the	the	DET
ajst-6461	63	11	generalized	generalize	VERB
ajst-6461	63	12	beta	beta	ADJ
ajst-6461	63	13	type	type	NOUN
ajst-6461	63	14	1	1	NUM
ajst-6461	63	15	distribution	distribution	NOUN
ajst-6461	63	16	.	.	PUNCT
ajst-6461	64	1	theorem	theorem	VERB
ajst-6461	64	2	2.3	2.3	NUM
ajst-6461	64	3	:	:	PUNCT
ajst-6461	64	4	if	if	SCONJ
ajst-6461	64	5	the	the	DET
ajst-6461	64	6	p.d.f	p.d.f	NOUN
ajst-6461	64	7	of	of	ADP
ajst-6461	64	8	)	)	PUNCT
ajst-6461	64	9	,	,	PUNCT
ajst-6461	64	10	(	(	PUNCT
ajst-6461	64	11	yx	yx	PROPN
ajst-6461	64	12	is	be	AUX
ajst-6461	64	13	given	give	VERB
ajst-6461	64	14	by	by	ADP
ajst-6461	64	15	theorem	theorem	ADJ
ajst-6461	64	16	2.1	2.1	NUM
ajst-6461	64	17	,	,	PUNCT
ajst-6461	64	18	then	then	ADV
ajst-6461	64	19	the	the	DET
ajst-6461	64	20	density	density	NOUN
ajst-6461	64	21	of	of	ADP
ajst-6461	64	22	yxz	yxz	PROPN
ajst-6461	64	23			PROPN
ajst-6461	64	24	is	be	AUX
ajst-6461	64	25			NOUN
ajst-6461	64	26			PUNCT
ajst-6461	64	27	10,)1	10,)1	NUM
ajst-6461	64	28	(;	(;	PRON
ajst-6461	64	29	;	;	PUNCT
ajst-6461	64	30	)	)	PUNCT
ajst-6461	64	31	,	,	PUNCT
ajst-6461	64	32	(	(	PUNCT
ajst-6461	64	33	)	)	PUNCT
ajst-6461	64	34	1	1	NUM
ajst-6461	64	35	(	(	PUNCT
ajst-6461	64	36	11	11	NUM
ajst-6461	64	37	11	11	NUM
ajst-6461	64	38			NOUN
ajst-6461	64	39			VERB
ajst-6461	64	40			NOUN
ajst-6461	64	41			DET
ajst-6461	64	42	zzccbaf	zzccbaf	PROPN
ajst-6461	64	43	bacb	bacb	PROPN
ajst-6461	64	44	ezz	ezz	PROPN
ajst-6461	64	45	cba	cba	PROPN
ajst-6461	65	1			PROPN
ajst-6461	65	2			NUM
ajst-6461	65	3	.	.	PUNCT
ajst-6461	66	1	proof	proof	NOUN
ajst-6461	66	2	:	:	PUNCT
ajst-6461	66	3	the	the	DET
ajst-6461	66	4	p.d.f	p.d.f	ADJ
ajst-6461	66	5	(	(	PUNCT
ajst-6461	66	6	2.1	2.1	NUM
ajst-6461	66	7	)	)	PUNCT
ajst-6461	66	8	of	of	ADP
ajst-6461	66	9	)	)	PUNCT
ajst-6461	66	10	,	,	PUNCT
ajst-6461	66	11	yx	yx	NOUN
ajst-6461	66	12	（	（	PUNCT
ajst-6461	66	13	is	be	AUX
ajst-6461	66	14	known	know	VERB
ajst-6461	66	15	.	.	PUNCT
ajst-6461	67	1	by	by	ADP
ajst-6461	67	2	using	use	VERB
ajst-6461	67	3	the	the	DET
ajst-6461	67	4	convolution	convolution	NOUN
ajst-6461	67	5	formula	formula	NOUN
ajst-6461	67	6	,	,	PUNCT
ajst-6461	67	7	the	the	DET
ajst-6461	67	8	probability	probability	NOUN
ajst-6461	67	9	density	density	NOUN
ajst-6461	67	10	of	of	ADP
ajst-6461	67	11	yxz	yxz	PROPN
ajst-6461	67	12			PROPN
ajst-6461	67	13	is	be	AUX
ajst-6461	67	14	dxzccbafezxzx	dxzccbafezxzx	PROPN
ajst-6461	67	15	cbab	cbab	PROPN
ajst-6461	67	16	z	z	PROPN
ajst-6461	67	17	cba	cba	PROPN
ajst-6461	67	18	)	)	PUNCT
ajst-6461	67	19	)	)	PUNCT
ajst-6461	68	1	1(;;()1	1(;;()1	NUM
ajst-6461	68	2	(	(	PUNCT
ajst-6461	68	3	)	)	PUNCT
ajst-6461	68	4	(	(	PUNCT
ajst-6461	68	5	)	)	PUNCT
ajst-6461	68	6	,	,	PUNCT
ajst-6461	68	7	,	,	PUNCT
ajst-6461	68	8	(	(	PUNCT
ajst-6461	68	9	1	1	NUM
ajst-6461	68	10	110	110	NUM
ajst-6461	68	11	111	111	NUM
ajst-6461	68	12			VERB
ajst-6461	68	13			PROPN
ajst-6461	68	14			PROPN
ajst-6461	68	15	.1	.1	NUM
ajst-6461	68	16	!	!	PUNCT
ajst-6461	68	17	)	)	PUNCT
ajst-6461	69	1	(	(	PUNCT
ajst-6461	69	2	)	)	PUNCT
ajst-6461	69	3	1	1	NUM
ajst-6461	69	4	(	(	PUNCT
ajst-6461	69	5	)	)	PUNCT
ajst-6461	69	6	(	(	PUNCT
ajst-6461	69	7	)	)	PUNCT
ajst-6461	69	8	,	,	PUNCT
ajst-6461	69	9	,	,	PUNCT
ajst-6461	69	10	(	(	PUNCT
ajst-6461	69	11	)	)	PUNCT
ajst-6461	69	12	1	1	NUM
ajst-6461	69	13	(	(	PUNCT
ajst-6461	69	14	)	)	PUNCT
ajst-6461	69	15	(	(	PUNCT
ajst-6461	69	16	!	!	PUNCT
ajst-6461	69	17	)	)	PUNCT
ajst-6461	70	1	(	(	PUNCT
ajst-6461	70	2	)	)	PUNCT
ajst-6461	70	3	1	1	NUM
ajst-6461	70	4	(	(	PUNCT
ajst-6461	70	5	)	)	PUNCT
ajst-6461	70	6	(	(	PUNCT
ajst-6461	70	7	)	)	PUNCT
ajst-6461	70	8	,	,	PUNCT
ajst-6461	70	9	,	,	PUNCT
ajst-6461	70	10	(	(	PUNCT
ajst-6461	70	11	)	)	PUNCT
ajst-6461	70	12	1	1	NUM
ajst-6461	70	13	(	(	PUNCT
ajst-6461	70	14	0	0	NUM
ajst-6461	70	15	1	1	NUM
ajst-6461	70	16	11	11	NUM
ajst-6461	70	17	0	0	NUM
ajst-6461	70	18	1	1	NUM
ajst-6461	70	19	0	0	NUM
ajst-6461	70	20	11	11	NUM
ajst-6461	70	21	0	0	NUM
ajst-6461	70	22	1	1	NUM
ajst-6461	70	23	dx	dx	PROPN
ajst-6461	70	24	z	z	PROPN
ajst-6461	70	25	x	x	PROPN
ajst-6461	70	26	xz	xz	PROPN
ajst-6461	70	27	jc	jc	PROPN
ajst-6461	70	28	zcba	zcba	PROPN
ajst-6461	70	29	cbab	cbab	PROPN
ajst-6461	70	30	ez	ez	PROPN
ajst-6461	70	31	dxxzx	dxxzx	PROPN
ajst-6461	70	32	jc	jc	PROPN
ajst-6461	70	33	zcba	zcba	PROPN
ajst-6461	70	34	cbab	cbab	PROPN
ajst-6461	70	35	ez	ez	PROPN
ajst-6461	70	36	z	z	PROPN
ajst-6461	70	37	b	b	PROPN
ajst-6461	71	1	ab	ab	PROPN
ajst-6461	71	2	j	j	PROPN
ajst-6461	71	3	j	j	PROPN
ajst-6461	71	4	jj	jj	PROPN
ajst-6461	71	5	j	j	PROPN
ajst-6461	71	6	c	c	PROPN
ajst-6461	71	7	z	z	PROPN
ajst-6461	71	8	ba	ba	PROPN
ajst-6461	72	1	j	j	PROPN
ajst-6461	72	2	j	j	PROPN
ajst-6461	72	3	jj	jj	PROPN
ajst-6461	72	4	j	j	PROPN
ajst-6461	72	5	c	c	PROPN
ajst-6461	72	6			X
ajst-6461	72	7			X
ajst-6461	72	8			NOUN
ajst-6461	72	9			NUM
ajst-6461	72	10			VERB
ajst-6461	72	11			PRON
ajst-6461	72	12			PUNCT
ajst-6461	72	13			NOUN
ajst-6461	72	14			VERB
ajst-6461	72	15			PRON
ajst-6461	72	16			NUM
ajst-6461	72	17			PROPN
ajst-6461	72	18			NOUN
ajst-6461	72	19			PRON
ajst-6461	72	20			PROPN
ajst-6461	72	21			PROPN
ajst-6461	72	22			NOUN
ajst-6461	72	23			PROPN
ajst-6461	72	24			PROPN
ajst-6461	72	25			PROPN
ajst-6461	72	26			PROPN
ajst-6461	72	27			VERB
ajst-6461	72	28			NOUN
ajst-6461	72	29			NUM
ajst-6461	72	30			NUM
ajst-6461	72	31			NUM
ajst-6461	72	32			NUM
ajst-6461	72	33	similar	similar	ADJ
ajst-6461	72	34	to	to	ADP
ajst-6461	72	35	the	the	DET
ajst-6461	72	36	proof	proof	NOUN
ajst-6461	72	37	of	of	ADP
ajst-6461	72	38	the	the	DET
ajst-6461	72	39	previous	previous	ADJ
ajst-6461	72	40	theorem	theorem	NOUN
ajst-6461	72	41	,	,	PUNCT
ajst-6461	72	42	(	(	PUNCT
ajst-6461	72	43	2.3	2.3	NUM
ajst-6461	72	44	)	)	PUNCT
ajst-6461	72	45	is	be	AUX
ajst-6461	72	46	proved	prove	VERB
ajst-6461	72	47	.	.	PUNCT
ajst-6461	73	1	theorem	theorem	VERB
ajst-6461	73	2	2.4	2.4	NUM
ajst-6461	73	3	:	:	PUNCT
ajst-6461	73	4	if	if	SCONJ
ajst-6461	73	5	the	the	DET
ajst-6461	73	6	p.d.f	p.d.f	NOUN
ajst-6461	73	7	of	of	ADP
ajst-6461	73	8	)	)	PUNCT
ajst-6461	73	9	,	,	PUNCT
ajst-6461	73	10	(	(	PUNCT
ajst-6461	73	11	yx	yx	PROPN
ajst-6461	73	12	is	be	AUX
ajst-6461	73	13	given	give	VERB
ajst-6461	73	14	by	by	ADP
ajst-6461	73	15	theorem	theorem	ADJ
ajst-6461	73	16	2.1	2.1	NUM
ajst-6461	73	17	,	,	PUNCT
ajst-6461	73	18	then	then	ADV
ajst-6461	73	19	the	the	DET
ajst-6461	73	20	density	density	NOUN
ajst-6461	73	21	of	of	ADP
ajst-6461	73	22	xyz	xyz	PROPN
ajst-6461	73	23			PROPN
ajst-6461	73	24	is	be	AUX
ajst-6461	73	25			ADV
ajst-6461	73	26			VERB
ajst-6461	73	27			PRON
ajst-6461	73	28			NOUN
ajst-6461	73	29			NUM
ajst-6461	73	30			PROPN
ajst-6461	73	31			PROPN
ajst-6461	73	32			PRON
ajst-6461	73	33			PROPN
ajst-6461	73	34			NOUN
ajst-6461	73	35	0	0	NUM
ajst-6461	73	36	0	0	NUM
ajst-6461	73	37	12	12	NUM
ajst-6461	73	38	111	111	NUM
ajst-6461	73	39	)	)	PUNCT
ajst-6461	73	40	1	1	NUM
ajst-6461	73	41	(	(	PUNCT
ajst-6461	73	42	!	!	PUNCT
ajst-6461	73	43	)	)	PUNCT
ajst-6461	74	1	(	(	PUNCT
ajst-6461	74	2	)	)	PUNCT
ajst-6461	74	3	1()1()1	1()1()1	NUM
ajst-6461	74	4	(	(	PUNCT
ajst-6461	74	5	)	)	PUNCT
ajst-6461	74	6	(	(	PUNCT
ajst-6461	74	7	)	)	PUNCT
ajst-6461	74	8	,	,	PUNCT
ajst-6461	74	9	,	,	PUNCT
ajst-6461	74	10	(	(	PUNCT
ajst-6461	74	11	j	j	PROPN
ajst-6461	74	12	k	k	PROPN
ajst-6461	74	13	jkj	jkj	PROPN
ajst-6461	74	14	jkk	jkk	PROPN
ajst-6461	74	15	kjcjcj	kjcjcj	PROPN
ajst-6461	74	16	j	j	PROPN
ajst-6461	74	17	b	b	PROPN
ajst-6461	74	18	cbajc	cbajc	PROPN
ajst-6461	74	19	cbajczcba	cbajczcba	PROPN
ajst-6461	74	20	cbab	cbab	PROPN
ajst-6461	74	21	ez	ez	PROPN
ajst-6461	74	22			PROPN
ajst-6461	74	23	.	.	PUNCT
ajst-6461	75	1	proof	proof	NOUN
ajst-6461	75	2	:	:	PUNCT
ajst-6461	75	3	according	accord	VERB
ajst-6461	75	4	to	to	ADP
ajst-6461	75	5	the	the	DET
ajst-6461	75	6	probability	probability	NOUN
ajst-6461	75	7	density	density	NOUN
ajst-6461	75	8	formula	formula	NOUN
ajst-6461	75	9	of	of	ADP
ajst-6461	75	10	twodimensional	twodimensional	ADJ
ajst-6461	75	11	random	random	ADJ
ajst-6461	75	12	variable	variable	ADJ
ajst-6461	75	13	product	product	NOUN
ajst-6461	75	14	:	:	PUNCT
ajst-6461	75	15	123	123	NUM
ajst-6461	75	16	dx	dx	PROPN
ajst-6461	75	17	x	x	X
ajst-6461	75	18	z	z	NOUN
ajst-6461	75	19	xf	xf	PROPN
ajst-6461	75	20	x	x	PROPN
ajst-6461	75	21	zfxy	zfxy	PROPN
ajst-6461	75	22			NUM
ajst-6461	75	23			PROPN
ajst-6461	75	24			PRON
ajst-6461	75	25			PROPN
ajst-6461	75	26			PROPN
ajst-6461	75	27			PROPN
ajst-6461	76	1			PUNCT
ajst-6461	77	1			PROPN
ajst-6461	77	2			PROPN
ajst-6461	77	3	,	,	PUNCT
ajst-6461	77	4	1	1	NUM
ajst-6461	77	5	)	)	PUNCT
ajst-6461	77	6	(	(	PUNCT
ajst-6461	77	7	,	,	PUNCT
ajst-6461	77	8	similar	similar	ADJ
ajst-6461	77	9	to	to	ADP
ajst-6461	77	10	the	the	DET
ajst-6461	77	11	proof	proof	NOUN
ajst-6461	77	12	of	of	ADP
ajst-6461	77	13	the	the	DET
ajst-6461	77	14	previous	previous	ADJ
ajst-6461	77	15	theorem	theorem	NOUN
ajst-6461	77	16	,	,	PUNCT
ajst-6461	77	17	(	(	PUNCT
ajst-6461	77	18	2.4	2.4	NUM
ajst-6461	77	19	)	)	PUNCT
ajst-6461	77	20	is	be	AUX
ajst-6461	77	21	proved	prove	VERB
ajst-6461	77	22	.	.	PUNCT
ajst-6461	78	1	theorem	theorem	VERB
ajst-6461	78	2	2.5	2.5	NUM
ajst-6461	78	3	:	:	PUNCT
ajst-6461	78	4	if	if	SCONJ
ajst-6461	78	5	the	the	DET
ajst-6461	78	6	p.d.f	p.d.f	NOUN
ajst-6461	78	7	of	of	ADP
ajst-6461	78	8	)	)	PUNCT
ajst-6461	78	9	,	,	PUNCT
ajst-6461	78	10	(	(	PUNCT
ajst-6461	78	11	yx	yx	PROPN
ajst-6461	78	12	is	be	AUX
ajst-6461	78	13	given	give	VERB
ajst-6461	78	14	by	by	ADP
ajst-6461	78	15	theorem	theorem	ADJ
ajst-6461	78	16	2.1	2.1	NUM
ajst-6461	78	17	,	,	PUNCT
ajst-6461	78	18	then	then	ADV
ajst-6461	78	19	the	the	DET
ajst-6461	78	20	density	density	NOUN
ajst-6461	78	21	of	of	ADP
ajst-6461	78	22	xyz	xyz	PROPN
ajst-6461	78	23			PROPN
ajst-6461	78	24	is	be	AUX
ajst-6461	78	25			ADV
ajst-6461	78	26			VERB
ajst-6461	78	27			PRON
ajst-6461	79	1			VERB
ajst-6461	79	2			PRON
ajst-6461	79	3			NOUN
ajst-6461	79	4			ADJ
ajst-6461	79	5			PROPN
ajst-6461	79	6	0	0	NUM
ajst-6461	79	7	0	0	NUM
ajst-6461	79	8	1	1	NUM
ajst-6461	79	9	)	)	PUNCT
ajst-6461	79	10	(	(	PUNCT
ajst-6461	79	11	!	!	PUNCT
ajst-6461	79	12	!	!	PUNCT
ajst-6461	79	13	)	)	PUNCT
ajst-6461	80	1	(	(	PUNCT
ajst-6461	80	2	)	)	PUNCT
ajst-6461	80	3	1()1	1()1	NUM
ajst-6461	80	4	(	(	PUNCT
ajst-6461	80	5	)	)	PUNCT
ajst-6461	80	6	(	(	PUNCT
ajst-6461	80	7	)	)	PUNCT
ajst-6461	80	8	,	,	PUNCT
ajst-6461	80	9	,	,	PUNCT
ajst-6461	80	10	(	(	PUNCT
ajst-6461	80	11	j	j	PROPN
ajst-6461	80	12	k	k	PROPN
ajst-6461	81	1	j	j	PROPN
ajst-6461	82	1	k	k	PROPN
ajst-6461	83	1	k	k	PROPN
ajst-6461	84	1	j	j	PROPN
ajst-6461	85	1	j	j	PROPN
ajst-6461	85	2	b	b	PROPN
ajst-6461	85	3	kbakjc	kbakjc	PROPN
ajst-6461	85	4	zjccba	zjccba	PROPN
ajst-6461	85	5	cbab	cbab	PROPN
ajst-6461	85	6	ez	ez	PROPN
ajst-6461	85	7			PROPN
ajst-6461	85	8	.	.	PUNCT
ajst-6461	86	1	proof	proof	NOUN
ajst-6461	86	2	:	:	PUNCT
ajst-6461	86	3	according	accord	VERB
ajst-6461	86	4	to	to	ADP
ajst-6461	86	5	probability	probability	NOUN
ajst-6461	86	6	density	density	NOUN
ajst-6461	86	7	formula	formula	NOUN
ajst-6461	86	8	of	of	ADP
ajst-6461	86	9	twodimensional	twodimensional	ADJ
ajst-6461	86	10	random	random	ADJ
ajst-6461	86	11	variable	variable	ADJ
ajst-6461	86	12	quotient	quotient	NOUN
ajst-6461	86	13	：	：	PUNCT
ajst-6461	86	14	dxxzxfxzf	dxxzxfxzf	PROPN
ajst-6461	86	15	x	x	SYM
ajst-6461	86	16	y	y	PROPN
ajst-6461	86	17	)	)	PUNCT
ajst-6461	86	18	,	,	PUNCT
ajst-6461	86	19	(	(	PUNCT
ajst-6461	86	20	)	)	PUNCT
ajst-6461	86	21	(	(	PUNCT
ajst-6461	86	22			X
ajst-6461	86	23			X
ajst-6461	86	24			NOUN
ajst-6461	86	25			NUM
ajst-6461	86	26	,	,	PUNCT
ajst-6461	86	27	similar	similar	ADJ
ajst-6461	86	28	to	to	ADP
ajst-6461	86	29	the	the	DET
ajst-6461	86	30	proof	proof	NOUN
ajst-6461	86	31	of	of	ADP
ajst-6461	86	32	the	the	DET
ajst-6461	86	33	previous	previous	ADJ
ajst-6461	86	34	theorem	theorem	NOUN
ajst-6461	86	35	,	,	PUNCT
ajst-6461	86	36	(	(	PUNCT
ajst-6461	86	37	2.5	2.5	NUM
ajst-6461	86	38	)	)	PUNCT
ajst-6461	86	39	is	be	AUX
ajst-6461	86	40	proved	prove	VERB
ajst-6461	86	41	.	.	PUNCT
ajst-6461	87	1	3	3	X
ajst-6461	87	2	.	.	X
ajst-6461	87	3	generalized	generalize	VERB
ajst-6461	87	4	dirichlet	dirichlet	PROPN
ajst-6461	87	5	type	type	NOUN
ajst-6461	87	6	2	2	NUM
ajst-6461	87	7	distribution	distribution	NOUN
ajst-6461	87	8	theorem	theorem	VERB
ajst-6461	87	9	3.1	3.1	NUM
ajst-6461	87	10	:	:	PUNCT
ajst-6461	87	11	let	let	VERB
ajst-6461	87	12	vu	vu	NOUN
ajst-6461	87	13	,	,	PUNCT
ajst-6461	87	14	and	and	CCONJ
ajst-6461	87	15	w	w	NOUN
ajst-6461	87	16	be	be	AUX
ajst-6461	87	17	independent	independent	ADJ
ajst-6461	87	18	random	random	ADJ
ajst-6461	87	19	variables	variable	NOUN
ajst-6461	87	20	,	,	PUNCT
ajst-6461	87	21	)	)	PUNCT
ajst-6461	87	22	(	(	PUNCT
ajst-6461	87	23	~),(~	~),(~	NUM
ajst-6461	87	24	bgvagu	bgvagu	NOUN
ajst-6461	87	25	and	and	CCONJ
ajst-6461	87	26	)	)	PUNCT
ajst-6461	87	27	,	,	PUNCT
ajst-6461	87	28	c(~	c(~	NOUN
ajst-6461	87	29	ncgw	ncgw	NOUN
ajst-6461	87	30	,	,	PUNCT
ajst-6461	87	31	define	define	VERB
ajst-6461	87	32	wvywux	wvywux	ADJ
ajst-6461	87	33			SYM
ajst-6461	87	34	11	11	NUM
ajst-6461	87	35	,	,	PUNCT
ajst-6461	87	36	,	,	PUNCT
ajst-6461	87	37	then	then	ADV
ajst-6461	87	38	the	the	DET
ajst-6461	87	39	p.d.f	p.d.f	NOUN
ajst-6461	87	40	of	of	ADP
ajst-6461	87	41	)	)	PUNCT
ajst-6461	87	42	,	,	PUNCT
ajst-6461	87	43	(	(	PUNCT
ajst-6461	87	44	11	11	NUM
ajst-6461	87	45	yx	yx	NOUN
ajst-6461	87	46	is	be	AUX
ajst-6461	87	47	0,0	0,0	NOUN
ajst-6461	87	48	,	,	PUNCT
ajst-6461	87	49	1	1	NUM
ajst-6461	87	50	;	;	PUNCT
ajst-6461	87	51	;	;	PUNCT
ajst-6461	87	52	)	)	PUNCT
ajst-6461	87	53	1	1	X
ajst-6461	87	54	)	)	PUNCT
ajst-6461	87	55	(	(	PUNCT
ajst-6461	87	56	,	,	PUNCT
ajst-6461	87	57	,	,	PUNCT
ajst-6461	87	58	(	(	PUNCT
ajst-6461	87	59	11	11	NUM
ajst-6461	87	60	11	11	NUM
ajst-6461	87	61	11	11	NUM
ajst-6461	87	62	11	11	NUM
ajst-6461	87	63	1	1	NUM
ajst-6461	87	64	1	1	NUM
ajst-6461	87	65	1	1	NUM
ajst-6461	87	66	1	1	NUM
ajst-6461	87	67			NOUN
ajst-6461	87	68			NOUN
ajst-6461	87	69			PROPN
ajst-6461	87	70			PROPN
ajst-6461	87	71			PROPN
ajst-6461	87	72			NOUN
ajst-6461	87	73			PROPN
ajst-6461	87	74			PROPN
ajst-6461	87	75			PROPN
ajst-6461	87	76			PROPN
ajst-6461	87	77			NOUN
ajst-6461	87	78	yx	yx	PROPN
ajst-6461	87	79	yx	yx	PROPN
ajst-6461	87	80	ccbaf	ccbaf	PROPN
ajst-6461	87	81	yxcbab	yxcbab	PROPN
ajst-6461	87	82	yxe	yxe	VERB
ajst-6461	87	83	cba	cba	PROPN
ajst-6461	87	84	ba	ba	PROPN
ajst-6461	87	85			X
ajst-6461	87	86	(	(	PUNCT
ajst-6461	87	87	3.1	3.1	NUM
ajst-6461	87	88	)	)	PUNCT
ajst-6461	87	89	proof	proof	NOUN
ajst-6461	87	90	:	:	PUNCT
ajst-6461	87	91	making	make	VERB
ajst-6461	87	92	the	the	DET
ajst-6461	87	93	transformation	transformation	NOUN
ajst-6461	87	94	wwwvywux	wwwvywux	NOUN
ajst-6461	87	95			VERB
ajst-6461	87	96	,	,	PUNCT
ajst-6461	87	97	,	,	PUNCT
ajst-6461	87	98	11	11	NUM
ajst-6461	87	99	with	with	ADP
ajst-6461	87	100	the	the	DET
ajst-6461	87	101	jacobian	jacobian	ADJ
ajst-6461	87	102	2	2	NUM
ajst-6461	87	103	11	11	NUM
ajst-6461	87	104	)	)	PUNCT
ajst-6461	87	105	,	,	PUNCT
ajst-6461	87	106	,	,	PUNCT
ajst-6461	87	107	,	,	PUNCT
ajst-6461	87	108	,	,	PUNCT
ajst-6461	87	109	(	(	PUNCT
ajst-6461	87	110	wwyxwvuj	wwyxwvuj	NOUN
ajst-6461	87	111			PROPN
ajst-6461	87	112	in	in	ADP
ajst-6461	87	113	(	(	PUNCT
ajst-6461	87	114	2.2	2.2	NUM
ajst-6461	87	115	)	)	PUNCT
ajst-6461	87	116	,	,	PUNCT
ajst-6461	87	117	then	then	ADV
ajst-6461	87	118	the	the	DET
ajst-6461	87	119	joint	joint	ADJ
ajst-6461	87	120	p.d.f	p.d.f	NOUN
ajst-6461	87	121	of	of	ADP
ajst-6461	87	122	11,yx	11,yx	NUM
ajst-6461	87	123	and	and	CCONJ
ajst-6461	87	124	w	w	PROPN
ajst-6461	87	125	is	be	AUX
ajst-6461	87	126	0,0	0,0	NOUN
ajst-6461	87	127	)	)	PUNCT
ajst-6461	87	128	;	;	PUNCT
ajst-6461	87	129	(	(	PUNCT
ajst-6461	87	130	)	)	PUNCT
ajst-6461	87	131	(	(	PUNCT
ajst-6461	87	132	)	)	PUNCT
ajst-6461	87	133	(	(	PUNCT
ajst-6461	87	134	)	)	PUNCT
ajst-6461	87	135	(	(	PUNCT
ajst-6461	87	136	1110	1110	NUM
ajst-6461	87	137	11	11	NUM
ajst-6461	87	138	1	1	NUM
ajst-6461	87	139	1	1	NUM
ajst-6461	87	140	1	1	NUM
ajst-6461	87	141	)	)	PUNCT
ajst-6461	87	142	1	1	NUM
ajst-6461	87	143	(	(	PUNCT
ajst-6461	87	144	11	11	NUM
ajst-6461	87	145			ADP
ajst-6461	87	146			PRON
ajst-6461	87	147			AUX
ajst-6461	87	148	yxwcf	yxwcf	NOUN
ajst-6461	87	149	cba	cba	PROPN
ajst-6461	87	150	wyxe	wyxe	NOUN
ajst-6461	87	151	cbabawyx	cbabawyx	NOUN
ajst-6461	88	1	，	，	SCONJ
ajst-6461	88	2			PROPN
ajst-6461	88	3			NUM
ajst-6461	88	4	.	.	PUNCT
ajst-6461	89	1	integrating	integrate	VERB
ajst-6461	89	2	w	w	NOUN
ajst-6461	89	3	in	in	ADP
ajst-6461	89	4	the	the	DET
ajst-6461	89	5	above	above	ADJ
ajst-6461	89	6	formula	formula	NOUN
ajst-6461	89	7	,	,	PUNCT
ajst-6461	89	8	we	we	PRON
ajst-6461	89	9	get	get	VERB
ajst-6461	89	10	the	the	DET
ajst-6461	89	11	p.d.f	p.d.f	NOUN
ajst-6461	89	12	of	of	ADP
ajst-6461	89	13	)	)	PUNCT
ajst-6461	89	14	,	,	PUNCT
ajst-6461	89	15	(	(	PUNCT
ajst-6461	89	16	11	11	NUM
ajst-6461	89	17	yx	yx	NOUN
ajst-6461	89	18	:	:	PUNCT
ajst-6461	89	19			X
ajst-6461	89	20			X
ajst-6461	89	21			X
ajst-6461	90	1			PROPN
ajst-6461	90	2			NOUN
ajst-6461	90	3			VERB
ajst-6461	90	4			PRON
ajst-6461	90	5			NOUN
ajst-6461	90	6			PROPN
ajst-6461	90	7			VERB
ajst-6461	90	8			PRON
ajst-6461	90	9			NOUN
ajst-6461	90	10			NUM
ajst-6461	90	11			NOUN
ajst-6461	90	12			ADJ
ajst-6461	90	13			NOUN
ajst-6461	90	14	0	0	NUM
ajst-6461	90	15	1)1	1)1	NUM
ajst-6461	90	16	(	(	PUNCT
ajst-6461	90	17	0	0	NUM
ajst-6461	90	18	1	1	NUM
ajst-6461	90	19	1	1	NUM
ajst-6461	90	20	1	1	NUM
ajst-6461	90	21	1	1	NUM
ajst-6461	90	22	0	0	NUM
ajst-6461	90	23	0	0	NUM
ajst-6461	90	24	1)1	1)1	NUM
ajst-6461	90	25	(	(	PUNCT
ajst-6461	90	26	1	1	NUM
ajst-6461	90	27	1	1	NUM
ajst-6461	90	28	1	1	NUM
ajst-6461	90	29	1	1	NUM
ajst-6461	90	30	11	11	NUM
ajst-6461	90	31	11	11	NUM
ajst-6461	90	32	!	!	PUNCT
ajst-6461	90	33	)	)	PUNCT
ajst-6461	90	34	(	(	PUNCT
ajst-6461	90	35	)	)	PUNCT
ajst-6461	90	36	(	(	PUNCT
ajst-6461	90	37	)	)	PUNCT
ajst-6461	90	38	(	(	PUNCT
ajst-6461	90	39	)	)	PUNCT
ajst-6461	90	40	(	(	PUNCT
ajst-6461	90	41	!	!	PUNCT
ajst-6461	90	42	)	)	PUNCT
ajst-6461	90	43	(	(	PUNCT
ajst-6461	90	44	)	)	PUNCT
ajst-6461	90	45	(	(	PUNCT
ajst-6461	90	46	)	)	PUNCT
ajst-6461	90	47	(	(	PUNCT
ajst-6461	90	48	)	)	PUNCT
ajst-6461	90	49	(	(	PUNCT
ajst-6461	90	50	)	)	PUNCT
ajst-6461	90	51	(	(	PUNCT
ajst-6461	90	52	dwwe	dwwe	ADJ
ajst-6461	90	53	kccba	kccba	PROPN
ajst-6461	90	54	yxe	yxe	PROPN
ajst-6461	90	55	dw	dw	PROPN
ajst-6461	90	56	kc	kc	PROPN
ajst-6461	90	57	w	w	PROPN
ajst-6461	90	58	we	we	PRON
ajst-6461	90	59	cba	cba	PROPN
ajst-6461	90	60	yxe	yxe	VERB
ajst-6461	90	61	kcbawyx	kcbawyx	PROPN
ajst-6461	91	1	k	k	PROPN
ajst-6461	91	2	k	k	PROPN
ajst-6461	91	3	kba	kba	PROPN
ajst-6461	91	4	k	k	PROPN
ajst-6461	91	5	k	k	PROPN
ajst-6461	91	6	k	k	PROPN
ajst-6461	91	7	cbawyx	cbawyx	PROPN
ajst-6461	91	8	ba	ba	PROPN
ajst-6461	92	1			NUM
ajst-6461	92	2			NUM
ajst-6461	92	3			NUM
ajst-6461	92	4			NUM
ajst-6461	92	5	.	.	PUNCT
ajst-6461	92	6	!	!	PUNCT
ajst-6461	92	7	)	)	PUNCT
ajst-6461	93	1	(	(	PUNCT
ajst-6461	93	2	)	)	PUNCT
ajst-6461	93	3	(	(	PUNCT
ajst-6461	93	4	)	)	PUNCT
ajst-6461	93	5	1	1	NUM
ajst-6461	93	6	(	(	PUNCT
ajst-6461	93	7	)	)	PUNCT
ajst-6461	93	8	1	1	NUM
ajst-6461	93	9	)	)	PUNCT
ajst-6461	93	10	(	(	PUNCT
ajst-6461	93	11	(	(	PUNCT
ajst-6461	93	12	)	)	PUNCT
ajst-6461	93	13	(	(	PUNCT
ajst-6461	93	14	)	)	PUNCT
ajst-6461	93	15	(	(	PUNCT
ajst-6461	93	16	0	0	NUM
ajst-6461	93	17	11	11	NUM
ajst-6461	93	18	11	11	NUM
ajst-6461	93	19	1	1	NUM
ajst-6461	93	20	1	1	NUM
ajst-6461	93	21	1	1	NUM
ajst-6461	93	22	1	1	NUM
ajst-6461	93	23			X
ajst-6461	93	24			VERB
ajst-6461	93	25			PRON
ajst-6461	93	26			PROPN
ajst-6461	93	27			PROPN
ajst-6461	93	28			NOUN
ajst-6461	93	29			NOUN
ajst-6461	93	30			VERB
ajst-6461	93	31			PROPN
ajst-6461	93	32	k	k	NOUN
ajst-6461	93	33	k	k	PROPN
ajst-6461	93	34	kk	kk	PROPN
ajst-6461	93	35	cba	cba	PROPN
ajst-6461	93	36	ba	ba	PROPN
ajst-6461	93	37	kc	kc	PROPN
ajst-6461	93	38	kcbayx	kcbayx	PROPN
ajst-6461	93	39	yxcba	yxcba	PROPN
ajst-6461	93	40	yxe	yxe	VERB
ajst-6461	93	41			PROPN
ajst-6461	93	42	after	after	ADP
ajst-6461	93	43	simplification	simplification	NOUN
ajst-6461	93	44	,	,	PUNCT
ajst-6461	93	45	(	(	PUNCT
ajst-6461	93	46	3.1	3.1	NUM
ajst-6461	93	47	)	)	PUNCT
ajst-6461	93	48	is	be	AUX
ajst-6461	93	49	proved	prove	VERB
ajst-6461	93	50	.	.	PUNCT
ajst-6461	94	1	from	from	ADP
ajst-6461	94	2	theorem	theorem	ADJ
ajst-6461	94	3	3.1	3.1	NUM
ajst-6461	94	4	,	,	PUNCT
ajst-6461	94	5	we	we	PRON
ajst-6461	94	6	find	find	VERB
ajst-6461	94	7	that	that	PRON
ajst-6461	94	8	)	)	PUNCT
ajst-6461	94	9	,	,	PUNCT
ajst-6461	94	10	(	(	PUNCT
ajst-6461	94	11	11	11	NUM
ajst-6461	94	12	yx	yx	NOUN
ajst-6461	94	13	follows	follow	VERB
ajst-6461	94	14	the	the	DET
ajst-6461	94	15	generalized	generalized	ADJ
ajst-6461	94	16	dirichlet	dirichlet	NOUN
ajst-6461	94	17	type	type	NOUN
ajst-6461	94	18	2	2	NUM
ajst-6461	94	19	distribution	distribution	NOUN
ajst-6461	94	20	.	.	PUNCT
ajst-6461	95	1	theorem	theorem	ADJ
ajst-6461	95	2	3.2	3.2	NUM
ajst-6461	95	3	:	:	PUNCT
ajst-6461	95	4	if	if	SCONJ
ajst-6461	95	5	the	the	DET
ajst-6461	95	6	p.d.f	p.d.f	NOUN
ajst-6461	95	7	of	of	ADP
ajst-6461	95	8	）	）	PROPN
ajst-6461	95	9	（	（	PROPN
ajst-6461	95	10	11,yx	11,yx	NUM
ajst-6461	95	11	is	be	AUX
ajst-6461	95	12	given	give	VERB
ajst-6461	95	13	by	by	ADP
ajst-6461	95	14	theorem	theorem	ADJ
ajst-6461	95	15	3.1	3.1	NUM
ajst-6461	95	16	,	,	PUNCT
ajst-6461	95	17	then	then	ADV
ajst-6461	95	18	the	the	DET
ajst-6461	95	19	marginal	marginal	ADJ
ajst-6461	95	20	density	density	NOUN
ajst-6461	95	21	of	of	ADP
ajst-6461	95	22	1x	1x	NUM
ajst-6461	95	23	is	be	AUX
ajst-6461	95	24			NOUN
ajst-6461	95	25			NOUN
ajst-6461	95	26			PROPN
ajst-6461	95	27			PROPN
ajst-6461	95	28			PROPN
ajst-6461	95	29			NOUN
ajst-6461	95	30			ADV
ajst-6461	95	31			PROPN
ajst-6461	95	32			PUNCT
ajst-6461	95	33			PUNCT
ajst-6461	95	34			PUNCT
ajst-6461	95	35	1	1	NUM
ajst-6461	95	36	11	11	NUM
ajst-6461	95	37	1	1	NUM
ajst-6461	95	38	1	1	NUM
ajst-6461	95	39	1	1	NUM
ajst-6461	95	40	1	1	NUM
ajst-6461	95	41	;	;	PUNCT
ajst-6461	95	42	;	;	PUNCT
ajst-6461	95	43	)	)	PUNCT
ajst-6461	95	44	1	1	X
ajst-6461	95	45	)	)	PUNCT
ajst-6461	95	46	(	(	PUNCT
ajst-6461	95	47	,	,	PUNCT
ajst-6461	95	48	(	(	PUNCT
ajst-6461	95	49	x	x	SYM
ajst-6461	95	50	ccaf	ccaf	NOUN
ajst-6461	95	51	xcab	xcab	PROPN
ajst-6461	95	52	xe	xe	PROPN
ajst-6461	95	53	ca	can	AUX
ajst-6461	95	54	a	a	DET
ajst-6461	95	55			PROPN
ajst-6461	95	56	.	.	PUNCT
ajst-6461	96	1	proof	proof	NOUN
ajst-6461	96	2	:	:	PUNCT
ajst-6461	96	3	integrating	integrate	VERB
ajst-6461	96	4	1y	1y	PRON
ajst-6461	96	5	in	in	ADP
ajst-6461	96	6	(	(	PUNCT
ajst-6461	96	7	3.1	3.1	NUM
ajst-6461	96	8	)	)	PUNCT
ajst-6461	96	9	,	,	PUNCT
ajst-6461	96	10	(	(	PUNCT
ajst-6461	96	11	3.2	3.2	NUM
ajst-6461	96	12	)	)	PUNCT
ajst-6461	96	13	is	be	AUX
ajst-6461	96	14	proved	prove	VERB
ajst-6461	96	15	.	.	PUNCT
ajst-6461	97	1	from	from	ADP
ajst-6461	97	2	theorem	theorem	ADJ
ajst-6461	97	3	3.2	3.2	NUM
ajst-6461	97	4	,	,	PUNCT
ajst-6461	97	5	we	we	PRON
ajst-6461	97	6	find	find	VERB
ajst-6461	97	7	that	that	SCONJ
ajst-6461	97	8	1x	1x	PROPN
ajst-6461	97	9	follows	follow	VERB
ajst-6461	97	10	the	the	DET
ajst-6461	97	11	generalized	generalize	VERB
ajst-6461	97	12	beta	beta	ADJ
ajst-6461	97	13	type	type	NOUN
ajst-6461	97	14	2	2	NUM
ajst-6461	97	15	distribution.p	distribution.p	NOUN
ajst-6461	97	16	;	;	PUNCT
ajst-6461	97	17	theorem3.3	theorem3.3	PRON
ajst-6461	97	18	:	:	PUNCT
ajst-6461	97	19	if	if	SCONJ
ajst-6461	97	20	the	the	DET
ajst-6461	97	21	p.d.f	p.d.f	NOUN
ajst-6461	97	22	of	of	ADP
ajst-6461	97	23	）	）	PROPN
ajst-6461	97	24	（	（	PROPN
ajst-6461	97	25	11,yx	11,yx	NUM
ajst-6461	97	26	is	be	AUX
ajst-6461	97	27	given	give	VERB
ajst-6461	97	28	by	by	ADP
ajst-6461	97	29	theorem	theorem	ADJ
ajst-6461	97	30	3.1	3.1	NUM
ajst-6461	97	31	,	,	PUNCT
ajst-6461	97	32	then	then	ADV
ajst-6461	97	33	the	the	DET
ajst-6461	97	34	density	density	NOUN
ajst-6461	97	35	of	of	ADP
ajst-6461	97	36	11s	11	NOUN
ajst-6461	97	37	yx	yx	PROPN
ajst-6461	97	38			PROPN
ajst-6461	97	39	is	be	AUX
ajst-6461	97	40	0	0	NUM
ajst-6461	97	41	,	,	PUNCT
ajst-6461	97	42	1	1	NUM
ajst-6461	97	43	;	;	PUNCT
ajst-6461	97	44	;	;	PUNCT
ajst-6461	97	45	)	)	PUNCT
ajst-6461	97	46	1	1	X
ajst-6461	97	47	)	)	PUNCT
ajst-6461	97	48	(	(	PUNCT
ajst-6461	97	49	,	,	PUNCT
ajst-6461	97	50	(	(	PUNCT
ajst-6461	97	51	e	e	NOUN
ajst-6461	97	52	11	11	NUM
ajst-6461	97	53	1	1	NUM
ajst-6461	97	54			NOUN
ajst-6461	97	55			NOUN
ajst-6461	98	1			PRON
ajst-6461	98	2			PROPN
ajst-6461	98	3			PROPN
ajst-6461	98	4			NOUN
ajst-6461	98	5			VERB
ajst-6461	98	6			PROPN
ajst-6461	98	7			PROPN
ajst-6461	98	8			PROPN
ajst-6461	98	9			NOUN
ajst-6461	98	10	s	s	NOUN
ajst-6461	98	11	s	s	NOUN
ajst-6461	98	12	ccbaf	ccbaf	NOUN
ajst-6461	98	13	scbab	scbab	PROPN
ajst-6461	98	14	s	s	PART
ajst-6461	98	15	cba	cba	PROPN
ajst-6461	98	16	ba	ba	PROPN
ajst-6461	98	17			PROPN
ajst-6461	98	18	.	.	PUNCT
ajst-6461	99	1	proof	proof	NOUN
ajst-6461	99	2	:	:	PUNCT
ajst-6461	99	3	by	by	ADP
ajst-6461	99	4	using	use	VERB
ajst-6461	99	5	the	the	DET
ajst-6461	99	6	convolution	convolution	NOUN
ajst-6461	99	7	formula	formula	NOUN
ajst-6461	99	8	,	,	PUNCT
ajst-6461	99	9	(	(	PUNCT
ajst-6461	99	10	3.3	3.3	NUM
ajst-6461	99	11	)	)	PUNCT
ajst-6461	99	12	is	be	AUX
ajst-6461	99	13	proved	prove	VERB
ajst-6461	99	14	.	.	PUNCT
ajst-6461	100	1	4	4	X
ajst-6461	100	2	.	.	X
ajst-6461	100	3	conclusion	conclusion	NOUN
ajst-6461	100	4	this	this	DET
ajst-6461	100	5	paper	paper	NOUN
ajst-6461	100	6	makes	make	VERB
ajst-6461	100	7	a	a	DET
ajst-6461	100	8	preliminary	preliminary	ADJ
ajst-6461	100	9	study	study	NOUN
ajst-6461	100	10	on	on	ADP
ajst-6461	100	11	two	two	NUM
ajst-6461	100	12	twodimensional	twodimensional	ADJ
ajst-6461	100	13	random	random	ADJ
ajst-6461	100	14	variables	variable	NOUN
ajst-6461	100	15	based	base	VERB
ajst-6461	100	16	on	on	ADP
ajst-6461	100	17	confluent	confluent	ADJ
ajst-6461	100	18	hypergeometic	hypergeometic	ADJ
ajst-6461	100	19	series	series	NOUN
ajst-6461	100	20	.	.	PUNCT
ajst-6461	101	1	from	from	ADP
ajst-6461	101	2	the	the	DET
ajst-6461	101	3	above	above	ADJ
ajst-6461	101	4	theorems	theorem	NOUN
ajst-6461	101	5	,	,	PUNCT
ajst-6461	101	6	we	we	PRON
ajst-6461	101	7	find	find	VERB
ajst-6461	101	8	that	that	PRON
ajst-6461	101	9	)	)	PUNCT
ajst-6461	101	10	,	,	PUNCT
ajst-6461	101	11	(	(	PUNCT
ajst-6461	101	12	yx	yx	NOUN
ajst-6461	101	13	and	and	CCONJ
ajst-6461	101	14	)	)	PUNCT
ajst-6461	101	15	,	,	PUNCT
ajst-6461	101	16	(	(	PUNCT
ajst-6461	101	17	11	11	NUM
ajst-6461	101	18	yx	yx	NOUN
ajst-6461	101	19	follow	follow	VERB
ajst-6461	101	20	the	the	DET
ajst-6461	101	21	generalized	generalized	ADJ
ajst-6461	101	22	dirichlet	dirichlet	NOUN
ajst-6461	101	23	type	type	NOUN
ajst-6461	101	24	1	1	NUM
ajst-6461	101	25	distribution	distribution	NOUN
ajst-6461	101	26	and	and	CCONJ
ajst-6461	101	27	generalized	generalized	ADJ
ajst-6461	101	28	dirichlet	dirichlet	NOUN
ajst-6461	101	29	type	type	NOUN
ajst-6461	101	30	2	2	NUM
ajst-6461	101	31	distribution	distribution	NOUN
ajst-6461	101	32	,	,	PUNCT
ajst-6461	101	33	which	which	PRON
ajst-6461	101	34	provides	provide	VERB
ajst-6461	101	35	new	new	ADJ
ajst-6461	101	36	methods	method	NOUN
ajst-6461	101	37	for	for	ADP
ajst-6461	101	38	the	the	DET
ajst-6461	101	39	future	future	ADJ
ajst-6461	101	40	study	study	NOUN
ajst-6461	101	41	of	of	ADP
ajst-6461	101	42	dirichlet	dirichlet	PROPN
ajst-6461	101	43	distribution	distribution	NOUN
ajst-6461	101	44	.	.	PUNCT
ajst-6461	102	1	references	reference	NOUN
ajst-6461	102	2	[	[	X
ajst-6461	102	3	1	1	NUM
ajst-6461	102	4	]	]	PUNCT
ajst-6461	102	5	kai	kai	PROPN
ajst-6461	102	6	wang	wang	PROPN
ajst-6461	102	7	ng	ng	PROPN
ajst-6461	102	8	,	,	PUNCT
ajst-6461	102	9	guo	guo	PROPN
ajst-6461	102	10	-	-	PUNCT
ajst-6461	102	11	liang	liang	PROPN
ajst-6461	102	12	tian	tian	PROPN
ajst-6461	102	13	,	,	PUNCT
ajst-6461	102	14	man	man	NOUN
ajst-6461	102	15	-	-	PUNCT
ajst-6461	102	16	lai	lai	PROPN
ajst-6461	102	17	tang	tang	PROPN
ajst-6461	102	18	.	.	PUNCT
ajst-6461	103	1	dirichlet	dirichlet	PROPN
ajst-6461	103	2	and	and	CCONJ
ajst-6461	103	3	related	related	ADJ
ajst-6461	103	4	distributions	distribution	NOUN
ajst-6461	103	5	:	:	PUNCT
ajst-6461	104	1	theory	theory	NOUN
ajst-6461	104	2	,	,	PUNCT
ajst-6461	104	3	methods	method	NOUN
ajst-6461	104	4	and	and	CCONJ
ajst-6461	104	5	applications	application	NOUN
ajst-6461	104	6	.	.	PUNCT
ajst-6461	105	1	new	new	PROPN
ajst-6461	105	2	york	york	PROPN
ajst-6461	105	3	:	:	PUNCT
ajst-6461	105	4	john	john	PROPN
ajst-6461	105	5	wiley	wiley	PROPN
ajst-6461	105	6	&	&	CCONJ
ajst-6461	105	7	sons	son	NOUN
ajst-6461	105	8	,	,	PUNCT
ajst-6461	105	9	2011	2011	NUM
ajst-6461	105	10	.	.	PUNCT
ajst-6461	106	1	[	[	X
ajst-6461	106	2	2	2	NUM
ajst-6461	106	3	]	]	PUNCT
ajst-6461	106	4	mohamed	mohamed	PROPN
ajst-6461	106	5	maher	maher	PROPN
ajst-6461	106	6	ben	ben	PROPN
ajst-6461	106	7	ismaila	ismaila	PROPN
ajst-6461	106	8	,	,	PUNCT
ajst-6461	106	9	hichem	hichem	NOUN
ajst-6461	106	10	friguib	friguib	NOUN
ajst-6461	106	11	.	.	PUNCT
ajst-6461	107	1	unsupervised	unsupervised	ADJ
ajst-6461	107	2	clustering	clustering	NOUN
ajst-6461	107	3	and	and	CCONJ
ajst-6461	107	4	feature	feature	NOUN
ajst-6461	107	5	weighting	weighting	NOUN
ajst-6461	107	6	based	base	VERB
ajst-6461	107	7	on	on	ADP
ajst-6461	107	8	generalized	generalized	ADJ
ajst-6461	107	9	dirichlet	dirichlet	PROPN
ajst-6461	107	10	mixture	mixture	NOUN
ajst-6461	107	11	modeling	modeling	NOUN
ajst-6461	107	12	.	.	PUNCT
ajst-6461	108	1	information	information	NOUN
ajst-6461	108	2	sciences	sciences	PROPN
ajst-6461	108	3	,	,	PUNCT
ajst-6461	108	4	2014	2014	NUM
ajst-6461	108	5	,	,	PUNCT
ajst-6461	108	6	274	274	NUM
ajst-6461	108	7	:	:	SYM
ajst-6461	108	8	35	35	NUM
ajst-6461	108	9	-	-	SYM
ajst-6461	108	10	54	54	NUM
ajst-6461	108	11	.	.	PUNCT
ajst-6461	109	1	[	[	X
ajst-6461	109	2	3	3	X
ajst-6461	109	3	]	]	X
ajst-6461	109	4	david	david	PROPN
ajst-6461	109	5	m.	m.	PROPN
ajst-6461	109	6	blei	blei	PROPN
ajst-6461	109	7	,	,	PUNCT
ajst-6461	109	8	andrew	andrew	PROPN
ajst-6461	109	9	y.	y.	PROPN
ajst-6461	109	10	ng	ng	PROPN
ajst-6461	109	11	,	,	PUNCT
ajst-6461	109	12	michael	michael	PROPN
ajst-6461	109	13	i.	i.	PROPN
ajst-6461	109	14	jordan	jordan	PROPN
ajst-6461	109	15	.	.	PUNCT
ajst-6461	110	1	latent	latent	PROPN
ajst-6461	110	2	dirichlet	dirichlet	PROPN
ajst-6461	110	3	allocation	allocation	NOUN
ajst-6461	110	4	.	.	PUNCT
ajst-6461	111	1	journal	journal	PROPN
ajst-6461	111	2	of	of	ADP
ajst-6461	111	3	machine	machine	NOUN
ajst-6461	111	4	learning	learn	VERB
ajst-6461	111	5	research	research	NOUN
ajst-6461	111	6	,	,	PUNCT
ajst-6461	111	7	2003	2003	NUM
ajst-6461	111	8	,	,	PUNCT
ajst-6461	111	9	3	3	NUM
ajst-6461	111	10	:	:	SYM
ajst-6461	111	11	993	993	NUM
ajst-6461	111	12	-	-	SYM
ajst-6461	111	13	1022	1022	NUM
ajst-6461	111	14	.	.	PUNCT
ajst-6461	112	1	[	[	X
ajst-6461	112	2	4	4	X
ajst-6461	112	3	]	]	X
ajst-6461	112	4	s.	s.	PROPN
ajst-6461	112	5	shivashankar	shivashankar	PROPN
ajst-6461	112	6	,	,	PUNCT
ajst-6461	112	7	s.	s.	PROPN
ajst-6461	112	8	srivathsan	srivathsan	PROPN
ajst-6461	112	9	,	,	PUNCT
ajst-6461	112	10	b.	b.	PROPN
ajst-6461	112	11	ravindran	ravindran	PROPN
ajst-6461	112	12	,	,	PUNCT
ajst-6461	112	13	ashish	ashish	PROPN
ajst-6461	112	14	v.	v.	ADP
ajst-6461	112	15	tendulkar	tendulkar	PROPN
ajst-6461	112	16	.	.	PUNCT
ajst-6461	113	1	multi	multi	ADJ
ajst-6461	113	2	-	-	ADJ
ajst-6461	113	3	view	view	ADJ
ajst-6461	113	4	methods	method	NOUN
ajst-6461	113	5	for	for	ADP
ajst-6461	113	6	protein	protein	NOUN
ajst-6461	113	7	structure	structure	NOUN
ajst-6461	113	8	comparison	comparison	NOUN
ajst-6461	113	9	using	use	VERB
ajst-6461	113	10	latent	latent	ADJ
ajst-6461	113	11	dirichlet	dirichlet	PROPN
ajst-6461	113	12	allocation	allocation	NOUN
ajst-6461	113	13	.	.	PUNCT
ajst-6461	114	1	bioinformatics	bioinformatic	NOUN
ajst-6461	114	2	,	,	PUNCT
ajst-6461	114	3	2011	2011	NUM
ajst-6461	114	4	,	,	PUNCT
ajst-6461	114	5	27	27	NUM
ajst-6461	114	6	:	:	PUNCT
ajst-6461	114	7	i61	i61	NOUN
ajst-6461	114	8	-	-	PUNCT
ajst-6461	114	9	i68	i68	PROPN
ajst-6461	114	10	.	.	PUNCT
ajst-6461	115	1	[	[	X
ajst-6461	115	2	5	5	X
ajst-6461	115	3	]	]	X
ajst-6461	115	4	arjun	arjun	PROPN
ajst-6461	115	5	k.	k.	PROPN
ajst-6461	115	6	gupta	gupta	PROPN
ajst-6461	115	7	,	,	PUNCT
ajst-6461	115	8	johanna	johanna	PROPN
ajst-6461	115	9	marcela	marcela	PROPN
ajst-6461	115	10	orozco	orozco	PROPN
ajst-6461	115	11	-	-	PUNCT
ajst-6461	115	12	castañeda	castañeda	PROPN
ajst-6461	115	13	,	,	PUNCT
ajst-6461	115	14	daya	daya	PROPN
ajst-6461	115	15	k.	k.	PROPN
ajst-6461	115	16	nagar	nagar	PROPN
ajst-6461	115	17	.	.	PUNCT
ajst-6461	116	1	non	non	ADJ
ajst-6461	116	2	-	-	ADJ
ajst-6461	116	3	central	central	ADJ
ajst-6461	116	4	bivariate	bivariate	ADJ
ajst-6461	116	5	beta	beta	ADJ
ajst-6461	116	6	distribution	distribution	NOUN
ajst-6461	116	7	.	.	PUNCT
ajst-6461	117	1	springer	springer	NOUN
ajst-6461	117	2	,	,	PUNCT
ajst-6461	117	3	2011	2011	NUM
ajst-6461	117	4	,	,	PUNCT
ajst-6461	117	5	52	52	NUM
ajst-6461	117	6	:	:	SYM
ajst-6461	117	7	139	139	NUM
ajst-6461	117	8	-	-	SYM
ajst-6461	117	9	152	152	NUM
ajst-6461	117	10	.	.	PUNCT
ajst-6461	118	1	[	[	X
ajst-6461	118	2	6	6	NUM
ajst-6461	118	3	]	]	PUNCT
ajst-6461	118	4	johanna	johanna	PROPN
ajst-6461	118	5	marcela	marcela	PROPN
ajst-6461	118	6	orozco	orozco	PROPN
ajst-6461	118	7	-	-	PUNCT
ajst-6461	118	8	castañeda	castañeda	PROPN
ajst-6461	118	9	,	,	PUNCT
ajst-6461	118	10	daya	daya	PROPN
ajst-6461	118	11	k.	k.	PROPN
ajst-6461	118	12	nagar	nagar	PROPN
ajst-6461	118	13	,	,	PUNCT
ajst-6461	118	14	arjun	arjun	PROPN
ajst-6461	118	15	k.	k.	PROPN
ajst-6461	118	16	gupta	gupta	PROPN
ajst-6461	118	17	.	.	PUNCT
ajst-6461	119	1	generalized	generalize	VERB
ajst-6461	119	2	bivariate	bivariate	ADJ
ajst-6461	119	3	beta	beta	NOUN
ajst-6461	119	4	distributions	distribution	NOUN
ajst-6461	119	5	involving	involve	VERB
ajst-6461	119	6	appell	appell	PROPN
ajst-6461	119	7	’s	’s	PART
ajst-6461	119	8	hypergeometric	hypergeometric	ADJ
ajst-6461	119	9	function	function	NOUN
ajst-6461	119	10	of	of	ADP
ajst-6461	119	11	the	the	DET
ajst-6461	119	12	second	second	ADJ
ajst-6461	119	13	kind	kind	NOUN
ajst-6461	119	14	.	.	PUNCT
ajst-6461	120	1	computers	computer	NOUN
ajst-6461	120	2	and	and	CCONJ
ajst-6461	120	3	mathematics	mathematic	NOUN
ajst-6461	120	4	with	with	ADP
ajst-6461	120	5	applications	application	NOUN
ajst-6461	120	6	,	,	PUNCT
ajst-6461	120	7	2012	2012	NUM
ajst-6461	120	8	,	,	PUNCT
ajst-6461	120	9	64	64	NUM
ajst-6461	120	10	:	:	SYM
ajst-6461	120	11	2507	2507	NUM
ajst-6461	120	12	-	-	SYM
ajst-6461	120	13	2519	2519	NUM
ajst-6461	120	14	.	.	PUNCT
ajst-6461	121	1	[	[	X
ajst-6461	121	2	7	7	X
ajst-6461	121	3	]	]	X
ajst-6461	121	4	yudell	yudell	PROPN
ajst-6461	121	5	l.	l.	PROPN
ajst-6461	121	6	luke	luke	PROPN
ajst-6461	121	7	.	.	PUNCT
ajst-6461	122	1	the	the	DET
ajst-6461	122	2	special	special	ADJ
ajst-6461	122	3	functions	function	NOUN
ajst-6461	122	4	and	and	CCONJ
ajst-6461	122	5	their	their	PRON
ajst-6461	122	6	approximations	approximation	NOUN
ajst-6461	122	7	.	.	PUNCT
ajst-6461	123	1	mathematics	mathematic	NOUN
ajst-6461	123	2	in	in	ADP
ajst-6461	123	3	science	science	NOUN
ajst-6461	123	4	and	and	CCONJ
ajst-6461	123	5	engineering	engineering	NOUN
ajst-6461	123	6	,	,	PUNCT
ajst-6461	123	7	1969,53	1969,53	NUM
ajst-6461	123	8	:	:	PUNCT
ajst-6461	123	9	1	1	NUM
ajst-6461	123	10	-	-	SYM
ajst-6461	123	11	349	349	NUM
ajst-6461	123	12	.	.	PUNCT
ajst-6461	124	1	[	[	X
ajst-6461	124	2	8	8	NUM
ajst-6461	124	3	]	]	X
ajst-6461	124	4	d.	d.	PROPN
ajst-6461	124	5	k.	k.	PROPN
ajst-6461	124	6	nagar	nagar	PROPN
ajst-6461	124	7	,	,	PUNCT
ajst-6461	124	8	johanna	johanna	PROPN
ajst-6461	124	9	marcela	marcela	PROPN
ajst-6461	124	10	orozco	orozco	PROPN
ajst-6461	124	11	-	-	PUNCT
ajst-6461	124	12	castañeda	castañeda	PROPN
ajst-6461	124	13	,	,	PUNCT
ajst-6461	124	14	arjun	arjun	PROPN
ajst-6461	124	15	k.	k.	PROPN
ajst-6461	124	16	gupta	gupta	PROPN
ajst-6461	124	17	.	.	PUNCT
ajst-6461	124	18	product	product	NOUN
ajst-6461	124	19	and	and	CCONJ
ajst-6461	124	20	quotient	quotient	NOUN
ajst-6461	124	21	of	of	ADP
ajst-6461	124	22	correlated	correlate	VERB
ajst-6461	124	23	beta	beta	ADJ
ajst-6461	124	24	variables	variable	NOUN
ajst-6461	124	25	.	.	PUNCT
ajst-6461	125	1	appl	appl	PROPN
ajst-6461	125	2	.	.	PROPN
ajst-6461	125	3	math	math	PROPN
ajst-6461	125	4	.	.	PUNCT
ajst-6461	126	1	lett	lett	PROPN
ajst-6461	126	2	.	.	PROPN
ajst-6461	126	3	,	,	PUNCT
ajst-6461	126	4	2009	2009	NUM
ajst-6461	126	5	,	,	PUNCT
ajst-6461	126	6	22	22	NUM
ajst-6461	126	7	:	:	PUNCT
ajst-6461	126	8	105	105	NUM
ajst-6461	126	9	-	-	SYM
ajst-6461	126	10	109	109	NUM
ajst-6461	126	11	.	.	PUNCT
ajst-6461	127	1	[	[	X
ajst-6461	127	2	9	9	NUM
ajst-6461	127	3	]	]	X
ajst-6461	127	4	ingram	ingram	PROPN
ajst-6461	127	5	olkin	olkin	PROPN
ajst-6461	127	6	,	,	PUNCT
ajst-6461	127	7	ruixue	ruixue	PROPN
ajst-6461	127	8	liu	liu	PROPN
ajst-6461	127	9	.	.	PUNCT
ajst-6461	128	1	a	a	DET
ajst-6461	128	2	bivariate	bivariate	ADJ
ajst-6461	128	3	beta	beta	ADJ
ajst-6461	128	4	distribution	distribution	NOUN
ajst-6461	128	5	.	.	PUNCT
ajst-6461	129	1	statistics	statistic	NOUN
ajst-6461	129	2	&	&	CCONJ
ajst-6461	129	3	probability	probability	NOUN
ajst-6461	129	4	letters	letter	NOUN
ajst-6461	129	5	,	,	PUNCT
ajst-6461	129	6	2003	2003	NUM
ajst-6461	129	7	,	,	PUNCT
ajst-6461	129	8	62	62	NUM
ajst-6461	129	9	:	:	PUNCT
ajst-6461	129	10	407	407	NUM
ajst-6461	129	11	-	-	SYM
ajst-6461	129	12	412	412	NUM
ajst-6461	129	13	.	.	PUNCT
ajst-6461	130	1	[	[	X
ajst-6461	130	2	10	10	NUM
ajst-6461	130	3	]	]	PUNCT
ajst-6461	130	4	saralees	saralee	NOUN
ajst-6461	130	5	nadarajah	nadarajah	PROPN
ajst-6461	130	6	,	,	PUNCT
ajst-6461	130	7	samuel	samuel	PROPN
ajst-6461	130	8	kotz	kotz	PROPN
ajst-6461	130	9	.	.	PUNCT
ajst-6461	131	1	some	some	DET
ajst-6461	131	2	bivariate	bivariate	ADJ
ajst-6461	131	3	beta	beta	ADJ
ajst-6461	131	4	distributions	distribution	NOUN
ajst-6461	131	5	.	.	PUNCT
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ajst-6461	132	2	,	,	PUNCT
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ajst-6461	132	4	,	,	PUNCT
ajst-6461	132	5	39	39	NUM
ajst-6461	132	6	:	:	PUNCT
ajst-6461	132	7	457	457	NUM
ajst-6461	132	8	-	-	SYM
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ajst-6461	133	3	]	]	X
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ajst-6461	133	9	r.	r.	PROPN
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ajst-6461	133	11	,	,	PUNCT
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ajst-6461	133	13	analysis	analysis	NOUN
ajst-6461	133	14	for	for	ADP
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ajst-6461	133	16	models	model	NOUN
ajst-6461	133	17	with	with	ADP
ajst-6461	133	18	generalized	generalize	VERB
ajst-6461	133	19	beta	beta	ADJ
ajst-6461	133	20	prior	prior	ADJ
ajst-6461	133	21	distributions	distribution	NOUN
ajst-6461	133	22	.	.	PUNCT
ajst-6461	134	1	journal	journal	NOUN
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ajst-6461	134	11	:	:	SYM
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ajst-6461	135	7	.	.	PUNCT
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ajst-6461	136	4	:	:	PUNCT
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ajst-6461	136	17	,	,	PUNCT
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ajst-6461	136	19	:	:	SYM
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ajst-6461	136	21	-	-	SYM
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ajst-6461	138	6	-	-	PUNCT
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ajst-6461	139	7	:	:	SYM
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ajst-6461	139	9	-	-	SYM
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ajst-6461	139	11	.	.	PUNCT
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ajst-6461	140	13	.	.	PUNCT
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ajst-6461	141	9	.	.	PUNCT
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ajst-6461	142	9	:	:	SYM
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ajst-6461	142	11	-	-	SYM
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ajst-6461	147	14	-	-	SYM
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ajst-6461	153	11	:	:	SYM
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