id	sid	tid	token	lemma	pos
ijassa-112	1	1	advances	advance	NOUN
ijassa-112	1	2	in	in	ADP
ijassa-112	1	3	systems	system	NOUN
ijassa-112	1	4	science	science	NOUN
ijassa-112	1	5	and	and	CCONJ
ijassa-112	1	6	applications	application	NOUN
ijassa-112	1	7	(	(	PUNCT
ijassa-112	1	8	2012	2012	NUM
ijassa-112	1	9	)	)	PUNCT
ijassa-112	1	10	vol.12	vol.12	NOUN
ijassa-112	1	11	no.3	no.3	VERB
ijassa-112	1	12	272	272	NUM
ijassa-112	1	13	-	-	SYM
ijassa-112	1	14	282	282	NUM
ijassa-112	1	15	improved	improved	ADJ
ijassa-112	1	16	airline	airline	NOUN
ijassa-112	1	17	seat	seat	NOUN
ijassa-112	1	18	inventory	inventory	NOUN
ijassa-112	1	19	control	control	NOUN
ijassa-112	1	20	policies	policy	NOUN
ijassa-112	1	21	under	under	ADP
ijassa-112	1	22	parametric	parametric	ADJ
ijassa-112	1	23	uncertainty	uncertainty	NOUN
ijassa-112	1	24	of	of	ADP
ijassa-112	1	25	customer	customer	NOUN
ijassa-112	1	26	demand	demand	NOUN
ijassa-112	1	27	models	model	NOUN
ijassa-112	1	28	nicholas	nicholas	PROPN
ijassa-112	1	29	a.	a.	PROPN
ijassa-112	1	30	nechval1	nechval1	PROPN
ijassa-112	1	31	,	,	PUNCT
ijassa-112	1	32	konstantin	konstantin	PROPN
ijassa-112	1	33	n.	n.	PROPN
ijassa-112	1	34	nechval2	nechval2	PROPN
ijassa-112	1	35	and	and	CCONJ
ijassa-112	1	36	maris	maris	PROPN
ijassa-112	1	37	purgailis1	purgailis1	PROPN
ijassa-112	1	38	1university	1university	NUM
ijassa-112	1	39	of	of	ADP
ijassa-112	1	40	latvia	latvia	PROPN
ijassa-112	1	41	,	,	PUNCT
ijassa-112	1	42	evf	evf	PROPN
ijassa-112	1	43	research	research	PROPN
ijassa-112	1	44	institute	institute	PROPN
ijassa-112	1	45	,	,	PUNCT
ijassa-112	1	46	statistics	statistics	PROPN
ijassa-112	1	47	department	department	PROPN
ijassa-112	1	48	,	,	PUNCT
ijassa-112	1	49	raina	raina	PROPN
ijassa-112	1	50	blvd	blvd	PROPN
ijassa-112	1	51	19	19	NUM
ijassa-112	1	52	,	,	PUNCT
ijassa-112	1	53	lv-1050	lv-1050	PROPN
ijassa-112	1	54	riga	riga	PROPN
ijassa-112	1	55	,	,	PUNCT
ijassa-112	1	56	latvia	latvia	PROPN
ijassa-112	1	57	2transport	2transport	NUM
ijassa-112	1	58	and	and	CCONJ
ijassa-112	1	59	telecommunication	telecommunication	NOUN
ijassa-112	1	60	institute	institute	NOUN
ijassa-112	1	61	,	,	PUNCT
ijassa-112	1	62	applied	apply	VERB
ijassa-112	1	63	mathematics	mathematics	PROPN
ijassa-112	1	64	department	department	NOUN
ijassa-112	1	65	,	,	PUNCT
ijassa-112	1	66	lomonosov	lomonosov	PROPN
ijassa-112	1	67	street	street	NOUN
ijassa-112	1	68	1	1	NUM
ijassa-112	1	69	,	,	PUNCT
ijassa-112	1	70	lv-1019	lv-1019	PROPN
ijassa-112	1	71	riga	riga	PROPN
ijassa-112	1	72	,	,	PUNCT
ijassa-112	1	73	latvia	latvia	PROPN
ijassa-112	1	74	abstract	abstract	ADJ
ijassa-112	1	75	most	most	ADJ
ijassa-112	1	76	models	model	NOUN
ijassa-112	1	77	,	,	PUNCT
ijassa-112	1	78	which	which	PRON
ijassa-112	1	79	are	be	AUX
ijassa-112	1	80	used	use	VERB
ijassa-112	1	81	for	for	ADP
ijassa-112	1	82	solving	solve	VERB
ijassa-112	1	83	airline	airline	NOUN
ijassa-112	1	84	seat	seat	NOUN
ijassa-112	1	85	inventory	inventory	NOUN
ijassa-112	1	86	control	control	NOUN
ijassa-112	1	87	problems	problem	NOUN
ijassa-112	1	88	,	,	PUNCT
ijassa-112	1	89	are	be	AUX
ijassa-112	1	90	developed	develop	VERB
ijassa-112	1	91	in	in	ADP
ijassa-112	1	92	the	the	DET
ijassa-112	1	93	literature	literature	NOUN
ijassa-112	1	94	under	under	ADP
ijassa-112	1	95	the	the	DET
ijassa-112	1	96	assumptions	assumption	NOUN
ijassa-112	1	97	that	that	SCONJ
ijassa-112	1	98	the	the	DET
ijassa-112	1	99	parameter	parameter	NOUN
ijassa-112	1	100	values	value	NOUN
ijassa-112	1	101	of	of	ADP
ijassa-112	1	102	the	the	DET
ijassa-112	1	103	models	model	NOUN
ijassa-112	1	104	are	be	AUX
ijassa-112	1	105	known	know	VERB
ijassa-112	1	106	with	with	ADP
ijassa-112	1	107	certainty	certainty	PROPN
ijassa-112	1	108	.	.	PUNCT
ijassa-112	2	1	when	when	SCONJ
ijassa-112	2	2	these	these	DET
ijassa-112	2	3	models	model	NOUN
ijassa-112	2	4	are	be	AUX
ijassa-112	2	5	applied	apply	VERB
ijassa-112	2	6	to	to	PART
ijassa-112	2	7	solve	solve	VERB
ijassa-112	2	8	real	real	ADJ
ijassa-112	2	9	-	-	PUNCT
ijassa-112	2	10	world	world	NOUN
ijassa-112	2	11	problems	problem	NOUN
ijassa-112	2	12	,	,	PUNCT
ijassa-112	2	13	the	the	DET
ijassa-112	2	14	parameters	parameter	NOUN
ijassa-112	2	15	are	be	AUX
ijassa-112	2	16	estimated	estimate	VERB
ijassa-112	2	17	and	and	CCONJ
ijassa-112	2	18	then	then	ADV
ijassa-112	2	19	treated	treat	VERB
ijassa-112	2	20	as	as	SCONJ
ijassa-112	2	21	if	if	SCONJ
ijassa-112	2	22	they	they	PRON
ijassa-112	2	23	were	be	AUX
ijassa-112	2	24	the	the	DET
ijassa-112	2	25	true	true	ADJ
ijassa-112	2	26	values	value	NOUN
ijassa-112	2	27	.	.	PUNCT
ijassa-112	3	1	the	the	DET
ijassa-112	3	2	risk	risk	NOUN
ijassa-112	3	3	associated	associate	VERB
ijassa-112	3	4	with	with	ADP
ijassa-112	3	5	using	use	VERB
ijassa-112	3	6	estimates	estimate	NOUN
ijassa-112	3	7	rather	rather	ADV
ijassa-112	3	8	than	than	ADP
ijassa-112	3	9	the	the	DET
ijassa-112	3	10	true	true	ADJ
ijassa-112	3	11	parameters	parameter	NOUN
ijassa-112	3	12	is	be	AUX
ijassa-112	3	13	called	call	VERB
ijassa-112	3	14	estimation	estimation	NOUN
ijassa-112	3	15	risk	risk	NOUN
ijassa-112	3	16	and	and	CCONJ
ijassa-112	3	17	is	be	AUX
ijassa-112	3	18	often	often	ADV
ijassa-112	3	19	ignored	ignore	VERB
ijassa-112	3	20	.	.	PUNCT
ijassa-112	4	1	when	when	SCONJ
ijassa-112	4	2	data	datum	NOUN
ijassa-112	4	3	are	be	AUX
ijassa-112	4	4	limited	limited	ADJ
ijassa-112	4	5	and/or	and/or	CCONJ
ijassa-112	4	6	unreliable	unreliable	ADJ
ijassa-112	4	7	,	,	PUNCT
ijassa-112	4	8	estimation	estimation	NOUN
ijassa-112	4	9	risk	risk	NOUN
ijassa-112	4	10	may	may	AUX
ijassa-112	4	11	be	be	AUX
ijassa-112	4	12	significant	significant	ADJ
ijassa-112	4	13	,	,	PUNCT
ijassa-112	4	14	and	and	CCONJ
ijassa-112	4	15	failure	failure	NOUN
ijassa-112	4	16	to	to	PART
ijassa-112	4	17	incorporate	incorporate	VERB
ijassa-112	4	18	it	it	PRON
ijassa-112	4	19	into	into	ADP
ijassa-112	4	20	the	the	DET
ijassa-112	4	21	model	model	NOUN
ijassa-112	4	22	design	design	NOUN
ijassa-112	4	23	may	may	AUX
ijassa-112	4	24	lead	lead	VERB
ijassa-112	4	25	to	to	ADP
ijassa-112	4	26	serious	serious	ADJ
ijassa-112	4	27	errors	error	NOUN
ijassa-112	4	28	.	.	PUNCT
ijassa-112	5	1	in	in	ADP
ijassa-112	5	2	this	this	DET
ijassa-112	5	3	paper	paper	NOUN
ijassa-112	5	4	,	,	PUNCT
ijassa-112	5	5	we	we	PRON
ijassa-112	5	6	consider	consider	VERB
ijassa-112	5	7	the	the	DET
ijassa-112	5	8	static	static	ADJ
ijassa-112	5	9	and	and	CCONJ
ijassa-112	5	10	dynamic	dynamic	ADJ
ijassa-112	5	11	problems	problem	NOUN
ijassa-112	5	12	of	of	ADP
ijassa-112	5	13	airline	airline	NOUN
ijassa-112	5	14	seat	seat	NOUN
ijassa-112	5	15	inventory	inventory	NOUN
ijassa-112	5	16	control	control	NOUN
ijassa-112	5	17	under	under	ADP
ijassa-112	5	18	parametric	parametric	ADJ
ijassa-112	5	19	uncertainty	uncertainty	NOUN
ijassa-112	5	20	,	,	PUNCT
ijassa-112	5	21	which	which	PRON
ijassa-112	5	22	are	be	AUX
ijassa-112	5	23	invariant	invariant	ADJ
ijassa-112	5	24	with	with	ADP
ijassa-112	5	25	respect	respect	NOUN
ijassa-112	5	26	to	to	ADP
ijassa-112	5	27	a	a	DET
ijassa-112	5	28	certain	certain	ADJ
ijassa-112	5	29	group	group	NOUN
ijassa-112	5	30	of	of	ADP
ijassa-112	5	31	transformations	transformation	NOUN
ijassa-112	5	32	.	.	PUNCT
ijassa-112	6	1	since	since	SCONJ
ijassa-112	6	2	common	common	ADJ
ijassa-112	6	3	practice	practice	NOUN
ijassa-112	6	4	for	for	ADP
ijassa-112	6	5	airlines	airline	NOUN
ijassa-112	6	6	is	be	AUX
ijassa-112	6	7	to	to	PART
ijassa-112	6	8	charge	charge	VERB
ijassa-112	6	9	several	several	ADJ
ijassa-112	6	10	different	different	ADJ
ijassa-112	6	11	fares	fare	NOUN
ijassa-112	6	12	for	for	ADP
ijassa-112	6	13	a	a	DET
ijassa-112	6	14	common	common	ADJ
ijassa-112	6	15	pool	pool	NOUN
ijassa-112	6	16	of	of	ADP
ijassa-112	6	17	seats	seat	NOUN
ijassa-112	6	18	,	,	PUNCT
ijassa-112	6	19	this	this	DET
ijassa-112	6	20	paper	paper	NOUN
ijassa-112	6	21	presents	present	VERB
ijassa-112	6	22	the	the	DET
ijassa-112	6	23	policies	policy	NOUN
ijassa-112	6	24	that	that	PRON
ijassa-112	6	25	have	have	AUX
ijassa-112	6	26	been	be	AUX
ijassa-112	6	27	used	use	VERB
ijassa-112	6	28	to	to	PART
ijassa-112	6	29	address	address	VERB
ijassa-112	6	30	the	the	DET
ijassa-112	6	31	problem	problem	NOUN
ijassa-112	6	32	of	of	ADP
ijassa-112	6	33	when	when	SCONJ
ijassa-112	6	34	to	to	PART
ijassa-112	6	35	refuse	refuse	VERB
ijassa-112	6	36	booking	booking	NOUN
ijassa-112	6	37	requests	request	NOUN
ijassa-112	6	38	for	for	ADP
ijassa-112	6	39	a	a	DET
ijassa-112	6	40	given	give	VERB
ijassa-112	6	41	fare	fare	NOUN
ijassa-112	6	42	level	level	NOUN
ijassa-112	6	43	to	to	PART
ijassa-112	6	44	save	save	VERB
ijassa-112	6	45	the	the	DET
ijassa-112	6	46	seat	seat	NOUN
ijassa-112	6	47	for	for	ADP
ijassa-112	6	48	a	a	DET
ijassa-112	6	49	potential	potential	ADJ
ijassa-112	6	50	request	request	NOUN
ijassa-112	6	51	at	at	ADP
ijassa-112	6	52	a	a	DET
ijassa-112	6	53	higher	high	ADJ
ijassa-112	6	54	fare	fare	NOUN
ijassa-112	6	55	level	level	NOUN
ijassa-112	6	56	.	.	PUNCT
ijassa-112	7	1	in	in	ADP
ijassa-112	7	2	this	this	DET
ijassa-112	7	3	paper	paper	NOUN
ijassa-112	7	4	,	,	PUNCT
ijassa-112	7	5	we	we	PRON
ijassa-112	7	6	present	present	VERB
ijassa-112	7	7	the	the	DET
ijassa-112	7	8	innovative	innovative	ADJ
ijassa-112	7	9	technologies	technology	NOUN
ijassa-112	7	10	for	for	ADP
ijassa-112	7	11	constructing	construct	VERB
ijassa-112	7	12	the	the	DET
ijassa-112	7	13	static	static	ADJ
ijassa-112	7	14	and	and	CCONJ
ijassa-112	7	15	dynamic	dynamic	ADJ
ijassa-112	7	16	policies	policy	NOUN
ijassa-112	7	17	of	of	ADP
ijassa-112	7	18	the	the	DET
ijassa-112	7	19	airline	airline	NOUN
ijassa-112	7	20	seat	seat	NOUN
ijassa-112	7	21	inventory	inventory	NOUN
ijassa-112	7	22	control.on	control.on	NOUN
ijassa-112	7	23	the	the	DET
ijassa-112	7	24	basis	basis	NOUN
ijassa-112	7	25	of	of	ADP
ijassa-112	7	26	the	the	DET
ijassa-112	7	27	‘	'	PUNCT
ijassa-112	7	28	unbiasedness	unbiasedness	ADJ
ijassa-112	7	29	performance	performance	NOUN
ijassa-112	7	30	index	index	NOUN
ijassa-112	7	31	’	'	PUNCT
ijassa-112	7	32	.	.	PUNCT
ijassa-112	8	1	the	the	DET
ijassa-112	8	2	idea	idea	NOUN
ijassa-112	8	3	of	of	ADP
ijassa-112	8	4	prediction	prediction	NOUN
ijassa-112	8	5	of	of	ADP
ijassa-112	8	6	a	a	DET
ijassa-112	8	7	future	future	ADJ
ijassa-112	8	8	cumulative	cumulative	ADJ
ijassa-112	8	9	customer	customer	NOUN
ijassa-112	8	10	demand	demand	NOUN
ijassa-112	8	11	for	for	ADP
ijassa-112	8	12	the	the	DET
ijassa-112	8	13	seats	seat	NOUN
ijassa-112	8	14	on	on	ADP
ijassa-112	8	15	a	a	DET
ijassa-112	8	16	flight	flight	NOUN
ijassa-112	8	17	via	via	ADP
ijassa-112	8	18	the	the	DET
ijassa-112	8	19	order	order	NOUN
ijassa-112	8	20	statistics	statistic	NOUN
ijassa-112	8	21	from	from	ADP
ijassa-112	8	22	the	the	DET
ijassa-112	8	23	underlying	underlie	VERB
ijassa-112	8	24	distribution	distribution	NOUN
ijassa-112	8	25	,	,	PUNCT
ijassa-112	8	26	introduced	introduce	VERB
ijassa-112	8	27	in	in	ADP
ijassa-112	8	28	the	the	DET
ijassa-112	8	29	paper	paper	NOUN
ijassa-112	8	30	,	,	PUNCT
ijassa-112	8	31	allows	allow	VERB
ijassa-112	8	32	one	one	PRON
ijassa-112	8	33	to	to	PART
ijassa-112	8	34	use	use	VERB
ijassa-112	8	35	the	the	DET
ijassa-112	8	36	invariant	invariant	ADJ
ijassa-112	8	37	embedding	embed	VERB
ijassa-112	8	38	technique	technique	NOUN
ijassa-112	8	39	in	in	ADP
ijassa-112	8	40	order	order	NOUN
ijassa-112	8	41	to	to	PART
ijassa-112	8	42	eliminate	eliminate	VERB
ijassa-112	8	43	the	the	DET
ijassa-112	8	44	unknown	unknown	ADJ
ijassa-112	8	45	parameters	parameter	NOUN
ijassa-112	8	46	from	from	ADP
ijassa-112	8	47	the	the	DET
ijassa-112	8	48	problem	problem	NOUN
ijassa-112	8	49	and	and	CCONJ
ijassa-112	8	50	to	to	PART
ijassa-112	8	51	use	use	VERB
ijassa-112	8	52	the	the	DET
ijassa-112	8	53	previous	previous	ADJ
ijassa-112	8	54	and	and	CCONJ
ijassa-112	8	55	current	current	ADJ
ijassa-112	8	56	sample	sample	NOUN
ijassa-112	8	57	data	datum	NOUN
ijassa-112	8	58	as	as	ADV
ijassa-112	8	59	completely	completely	ADV
ijassa-112	8	60	as	as	ADP
ijassa-112	8	61	possible	possible	ADJ
ijassa-112	8	62	.	.	PUNCT
ijassa-112	9	1	the	the	DET
ijassa-112	9	2	proposed	propose	VERB
ijassa-112	9	3	unbiased	unbiased	ADJ
ijassa-112	9	4	static	static	ADJ
ijassa-112	9	5	and	and	CCONJ
ijassa-112	9	6	dynamic	dynamic	ADJ
ijassa-112	9	7	policies	policy	NOUN
ijassa-112	9	8	are	be	AUX
ijassa-112	9	9	more	more	ADV
ijassa-112	9	10	efficient	efficient	ADJ
ijassa-112	9	11	as	as	SCONJ
ijassa-112	9	12	compared	compare	VERB
ijassa-112	9	13	with	with	ADP
ijassa-112	9	14	the	the	DET
ijassa-112	9	15	policies	policy	NOUN
ijassa-112	9	16	,	,	PUNCT
ijassa-112	9	17	where	where	SCONJ
ijassa-112	9	18	the	the	DET
ijassa-112	9	19	unknown	unknown	ADJ
ijassa-112	9	20	parameters	parameter	NOUN
ijassa-112	9	21	of	of	ADP
ijassa-112	9	22	the	the	DET
ijassa-112	9	23	airline	airline	NOUN
ijassa-112	9	24	customer	customer	NOUN
ijassa-112	9	25	demand	demand	NOUN
ijassa-112	9	26	models	model	NOUN
ijassa-112	9	27	are	be	AUX
ijassa-112	9	28	estimated	estimate	VERB
ijassa-112	9	29	and	and	CCONJ
ijassa-112	9	30	then	then	ADV
ijassa-112	9	31	treated	treat	VERB
ijassa-112	9	32	as	as	SCONJ
ijassa-112	9	33	if	if	SCONJ
ijassa-112	9	34	they	they	PRON
ijassa-112	9	35	were	be	AUX
ijassa-112	9	36	the	the	DET
ijassa-112	9	37	true	true	ADJ
ijassa-112	9	38	values	value	NOUN
ijassa-112	9	39	.	.	PUNCT
ijassa-112	10	1	an	an	DET
ijassa-112	10	2	illustrative	illustrative	ADJ
ijassa-112	10	3	example	example	NOUN
ijassa-112	10	4	is	be	AUX
ijassa-112	10	5	given	give	VERB
ijassa-112	10	6	.	.	PUNCT
ijassa-112	11	1	keywords	keyword	NOUN
ijassa-112	11	2	airlines	airline	NOUN
ijassa-112	11	3	,	,	PUNCT
ijassa-112	11	4	demand	demand	NOUN
ijassa-112	11	5	,	,	PUNCT
ijassa-112	11	6	uncertainty	uncertainty	NOUN
ijassa-112	11	7	,	,	PUNCT
ijassa-112	11	8	airline	airline	NOUN
ijassa-112	11	9	booking	booking	NOUN
ijassa-112	11	10	,	,	PUNCT
ijassa-112	11	11	optimization	optimization	NOUN
ijassa-112	11	12	1	1	NUM
ijassa-112	11	13	introduction	introduction	NOUN
ijassa-112	11	14	passenger	passenger	NOUN
ijassa-112	11	15	reservations	reservation	NOUN
ijassa-112	11	16	systems	system	NOUN
ijassa-112	11	17	have	have	AUX
ijassa-112	11	18	evolved	evolve	VERB
ijassa-112	11	19	from	from	ADP
ijassa-112	11	20	low	low	ADJ
ijassa-112	11	21	level	level	NOUN
ijassa-112	11	22	inventory	inventory	NOUN
ijassa-112	11	23	control	control	NOUN
ijassa-112	11	24	processes	process	NOUN
ijassa-112	11	25	to	to	ADP
ijassa-112	11	26	major	major	ADJ
ijassa-112	11	27	strategic	strategic	ADJ
ijassa-112	11	28	information	information	NOUN
ijassa-112	11	29	systems	system	NOUN
ijassa-112	11	30	.	.	PUNCT
ijassa-112	12	1	today	today	NOUN
ijassa-112	12	2	,	,	PUNCT
ijassa-112	12	3	airlines	airline	NOUN
ijassa-112	12	4	and	and	CCONJ
ijassa-112	12	5	other	other	ADJ
ijassa-112	12	6	transportation	transportation	NOUN
ijassa-112	12	7	companies	company	NOUN
ijassa-112	12	8	view	view	VERB
ijassa-112	12	9	revenue	revenue	NOUN
ijassa-112	12	10	management	management	NOUN
ijassa-112	12	11	systems	system	NOUN
ijassa-112	12	12	and	and	CCONJ
ijassa-112	12	13	related	relate	VERB
ijassa-112	12	14	information	information	NOUN
ijassa-112	12	15	advances	advance	NOUN
ijassa-112	12	16	in	in	ADP
ijassa-112	12	17	systems	system	NOUN
ijassa-112	12	18	science	science	NOUN
ijassa-112	12	19	and	and	CCONJ
ijassa-112	12	20	applications	application	NOUN
ijassa-112	12	21	(	(	PUNCT
ijassa-112	12	22	2012	2012	NUM
ijassa-112	12	23	)	)	PUNCT
ijassa-112	12	24	vol.12	vol.12	NOUN
ijassa-112	12	25	no.3	no.3	VERB
ijassa-112	12	26	273	273	NUM
ijassa-112	12	27	technologies	technology	NOUN
ijassa-112	12	28	as	as	ADP
ijassa-112	12	29	critical	critical	ADJ
ijassa-112	12	30	determinants	determinant	NOUN
ijassa-112	12	31	of	of	ADP
ijassa-112	12	32	future	future	ADJ
ijassa-112	12	33	success	success	NOUN
ijassa-112	12	34	.	.	PUNCT
ijassa-112	13	1	indeed	indeed	ADV
ijassa-112	13	2	,	,	PUNCT
ijassa-112	13	3	expectations	expectation	NOUN
ijassa-112	13	4	of	of	ADP
ijassa-112	13	5	revenue	revenue	NOUN
ijassa-112	13	6	gains	gain	NOUN
ijassa-112	13	7	that	that	PRON
ijassa-112	13	8	are	be	AUX
ijassa-112	13	9	possible	possible	ADJ
ijassa-112	13	10	with	with	ADP
ijassa-112	13	11	expanded	expand	VERB
ijassa-112	13	12	revenue	revenue	NOUN
ijassa-112	13	13	management	management	NOUN
ijassa-112	13	14	capabilities	capability	NOUN
ijassa-112	13	15	are	be	AUX
ijassa-112	13	16	now	now	ADV
ijassa-112	13	17	driving	drive	VERB
ijassa-112	13	18	the	the	DET
ijassa-112	13	19	acquisition	acquisition	NOUN
ijassa-112	13	20	of	of	ADP
ijassa-112	13	21	new	new	ADJ
ijassa-112	13	22	information	information	NOUN
ijassa-112	13	23	technology	technology	NOUN
ijassa-112	13	24	.	.	PUNCT
ijassa-112	14	1	each	each	DET
ijassa-112	14	2	advance	advance	NOUN
ijassa-112	14	3	in	in	ADP
ijassa-112	14	4	information	information	NOUN
ijassa-112	14	5	technology	technology	NOUN
ijassa-112	14	6	creates	create	VERB
ijassa-112	14	7	an	an	DET
ijassa-112	14	8	opportunity	opportunity	NOUN
ijassa-112	14	9	for	for	ADP
ijassa-112	14	10	more	more	ADV
ijassa-112	14	11	comprehensive	comprehensive	ADJ
ijassa-112	14	12	reservations	reservation	NOUN
ijassa-112	14	13	control	control	NOUN
ijassa-112	14	14	and	and	CCONJ
ijassa-112	14	15	greater	great	ADJ
ijassa-112	14	16	integration	integration	NOUN
ijassa-112	14	17	with	with	ADP
ijassa-112	14	18	other	other	ADJ
ijassa-112	14	19	important	important	ADJ
ijassa-112	14	20	transportation	transportation	NOUN
ijassa-112	14	21	planning	planning	NOUN
ijassa-112	14	22	functions	function	NOUN
ijassa-112	14	23	.	.	PUNCT
ijassa-112	15	1	the	the	DET
ijassa-112	15	2	airline	airline	NOUN
ijassa-112	15	3	seat	seat	NOUN
ijassa-112	15	4	inventory	inventory	NOUN
ijassa-112	15	5	control	control	NOUN
ijassa-112	15	6	problem	problem	NOUN
ijassa-112	15	7	lies	lie	VERB
ijassa-112	15	8	at	at	ADP
ijassa-112	15	9	the	the	DET
ijassa-112	15	10	heart	heart	NOUN
ijassa-112	15	11	of	of	ADP
ijassa-112	15	12	airline	airline	NOUN
ijassa-112	15	13	revenue	revenue	NOUN
ijassa-112	15	14	management	management	NOUN
ijassa-112	15	15	.	.	PUNCT
ijassa-112	16	1	it	it	PRON
ijassa-112	16	2	is	be	AUX
ijassa-112	16	3	common	common	ADJ
ijassa-112	16	4	practice	practice	NOUN
ijassa-112	16	5	for	for	SCONJ
ijassa-112	16	6	airlines	airline	NOUN
ijassa-112	16	7	to	to	PART
ijassa-112	16	8	sell	sell	VERB
ijassa-112	16	9	a	a	DET
ijassa-112	16	10	pool	pool	NOUN
ijassa-112	16	11	of	of	ADP
ijassa-112	16	12	identical	identical	ADJ
ijassa-112	16	13	seats	seat	NOUN
ijassa-112	16	14	at	at	ADP
ijassa-112	16	15	different	different	ADJ
ijassa-112	16	16	prices	price	NOUN
ijassa-112	16	17	according	accord	VERB
ijassa-112	16	18	to	to	ADP
ijassa-112	16	19	different	different	ADJ
ijassa-112	16	20	booking	booking	NOUN
ijassa-112	16	21	classes	class	NOUN
ijassa-112	16	22	to	to	PART
ijassa-112	16	23	improve	improve	VERB
ijassa-112	16	24	revenues	revenue	NOUN
ijassa-112	16	25	in	in	ADP
ijassa-112	16	26	a	a	DET
ijassa-112	16	27	very	very	ADV
ijassa-112	16	28	competitive	competitive	ADJ
ijassa-112	16	29	market	market	NOUN
ijassa-112	16	30	.	.	PUNCT
ijassa-112	17	1	in	in	ADP
ijassa-112	17	2	other	other	ADJ
ijassa-112	17	3	words	word	NOUN
ijassa-112	17	4	,	,	PUNCT
ijassa-112	17	5	airlines	airline	NOUN
ijassa-112	17	6	sell	sell	VERB
ijassa-112	17	7	the	the	DET
ijassa-112	17	8	same	same	ADJ
ijassa-112	17	9	seat	seat	NOUN
ijassa-112	17	10	at	at	ADP
ijassa-112	17	11	different	different	ADJ
ijassa-112	17	12	prices	price	NOUN
ijassa-112	17	13	according	accord	VERB
ijassa-112	17	14	to	to	ADP
ijassa-112	17	15	different	different	ADJ
ijassa-112	17	16	types	type	NOUN
ijassa-112	17	17	of	of	ADP
ijassa-112	17	18	travelers	traveler	NOUN
ijassa-112	17	19	(	(	PUNCT
ijassa-112	17	20	first	first	ADJ
ijassa-112	17	21	class	class	NOUN
ijassa-112	17	22	,	,	PUNCT
ijassa-112	17	23	business	business	NOUN
ijassa-112	17	24	and	and	CCONJ
ijassa-112	17	25	economy	economy	NOUN
ijassa-112	17	26	)	)	PUNCT
ijassa-112	17	27	and	and	CCONJ
ijassa-112	17	28	other	other	ADJ
ijassa-112	17	29	conditions	condition	NOUN
ijassa-112	17	30	.	.	PUNCT
ijassa-112	18	1	the	the	DET
ijassa-112	18	2	question	question	NOUN
ijassa-112	18	3	then	then	ADV
ijassa-112	18	4	arises	arise	VERB
ijassa-112	18	5	whether	whether	SCONJ
ijassa-112	18	6	to	to	PART
ijassa-112	18	7	offer	offer	VERB
ijassa-112	18	8	seats	seat	NOUN
ijassa-112	18	9	at	at	ADP
ijassa-112	18	10	a	a	DET
ijassa-112	18	11	relatively	relatively	ADV
ijassa-112	18	12	low	low	ADJ
ijassa-112	18	13	price	price	NOUN
ijassa-112	18	14	at	at	ADP
ijassa-112	18	15	a	a	DET
ijassa-112	18	16	given	give	VERB
ijassa-112	18	17	time	time	NOUN
ijassa-112	18	18	with	with	ADP
ijassa-112	18	19	a	a	DET
ijassa-112	18	20	given	give	VERB
ijassa-112	18	21	number	number	NOUN
ijassa-112	18	22	of	of	ADP
ijassa-112	18	23	seats	seat	NOUN
ijassa-112	18	24	remaining	remain	VERB
ijassa-112	18	25	or	or	CCONJ
ijassa-112	18	26	to	to	PART
ijassa-112	18	27	wait	wait	VERB
ijassa-112	18	28	for	for	ADP
ijassa-112	18	29	the	the	DET
ijassa-112	18	30	possible	possible	ADJ
ijassa-112	18	31	arrival	arrival	NOUN
ijassa-112	18	32	of	of	ADP
ijassa-112	18	33	a	a	DET
ijassa-112	18	34	higher	high	ADJ
ijassa-112	18	35	paying	pay	VERB
ijassa-112	18	36	customer	customer	NOUN
ijassa-112	18	37	.	.	PUNCT
ijassa-112	19	1	assigning	assign	VERB
ijassa-112	19	2	seats	seat	NOUN
ijassa-112	19	3	in	in	ADP
ijassa-112	19	4	the	the	DET
ijassa-112	19	5	same	same	ADJ
ijassa-112	19	6	compartment	compartment	NOUN
ijassa-112	19	7	to	to	ADP
ijassa-112	19	8	different	different	ADJ
ijassa-112	19	9	fare	fare	NOUN
ijassa-112	19	10	classes	class	NOUN
ijassa-112	19	11	of	of	ADP
ijassa-112	19	12	passengers	passenger	NOUN
ijassa-112	19	13	in	in	ADP
ijassa-112	19	14	order	order	NOUN
ijassa-112	19	15	to	to	PART
ijassa-112	19	16	improve	improve	VERB
ijassa-112	19	17	revenues	revenue	NOUN
ijassa-112	19	18	is	be	AUX
ijassa-112	19	19	a	a	DET
ijassa-112	19	20	major	major	ADJ
ijassa-112	19	21	problem	problem	NOUN
ijassa-112	19	22	of	of	ADP
ijassa-112	19	23	airline	airline	NOUN
ijassa-112	19	24	seat	seat	NOUN
ijassa-112	19	25	inventory	inventory	NOUN
ijassa-112	19	26	control	control	NOUN
ijassa-112	19	27	.	.	PUNCT
ijassa-112	20	1	this	this	DET
ijassa-112	20	2	problem	problem	NOUN
ijassa-112	20	3	has	have	AUX
ijassa-112	20	4	been	be	AUX
ijassa-112	20	5	considered	consider	VERB
ijassa-112	20	6	in	in	ADP
ijassa-112	20	7	numerous	numerous	ADJ
ijassa-112	20	8	papers	paper	NOUN
ijassa-112	20	9	.	.	PUNCT
ijassa-112	21	1	for	for	ADP
ijassa-112	21	2	details	detail	NOUN
ijassa-112	21	3	,	,	PUNCT
ijassa-112	21	4	the	the	DET
ijassa-112	21	5	reader	reader	NOUN
ijassa-112	21	6	is	be	AUX
ijassa-112	21	7	referred	refer	VERB
ijassa-112	21	8	to	to	ADP
ijassa-112	21	9	a	a	DET
ijassa-112	21	10	review	review	NOUN
ijassa-112	21	11	of	of	ADP
ijassa-112	21	12	yield	yield	NOUN
ijassa-112	21	13	management	management	NOUN
ijassa-112	21	14	,	,	PUNCT
ijassa-112	21	15	as	as	ADV
ijassa-112	21	16	well	well	ADV
ijassa-112	21	17	as	as	ADP
ijassa-112	21	18	perishable	perishable	ADJ
ijassa-112	21	19	asset	asset	NOUN
ijassa-112	21	20	revenue	revenue	NOUN
ijassa-112	21	21	management	management	NOUN
ijassa-112	21	22	,	,	PUNCT
ijassa-112	21	23	by	by	ADP
ijassa-112	21	24	weatherford	weatherford	PROPN
ijassa-112	21	25	et	et	PROPN
ijassa-112	21	26	al	al	PROPN
ijassa-112	21	27	.	.	PUNCT
ijassa-112	22	1	[	[	X
ijassa-112	22	2	1	1	NUM
ijassa-112	22	3	]	]	PUNCT
ijassa-112	22	4	,	,	PUNCT
ijassa-112	22	5	and	and	CCONJ
ijassa-112	22	6	a	a	DET
ijassa-112	22	7	review	review	NOUN
ijassa-112	22	8	of	of	ADP
ijassa-112	22	9	relevant	relevant	ADJ
ijassa-112	22	10	mathematical	mathematical	ADJ
ijassa-112	22	11	models	model	NOUN
ijassa-112	22	12	by	by	ADP
ijassa-112	22	13	belobaba	belobaba	NOUN
ijassa-112	22	14	[	[	X
ijassa-112	22	15	2	2	NUM
ijassa-112	22	16	]	]	PUNCT
ijassa-112	22	17	.	.	PUNCT
ijassa-112	23	1	this	this	DET
ijassa-112	23	2	paper	paper	NOUN
ijassa-112	23	3	deals	deal	NOUN
ijassa-112	23	4	with	with	ADP
ijassa-112	23	5	the	the	DET
ijassa-112	23	6	airline	airline	NOUN
ijassa-112	23	7	seat	seat	NOUN
ijassa-112	23	8	inventory	inventory	NOUN
ijassa-112	23	9	control	control	NOUN
ijassa-112	23	10	problem	problem	NOUN
ijassa-112	23	11	when	when	SCONJ
ijassa-112	23	12	customers	customer	NOUN
ijassa-112	23	13	for	for	ADP
ijassa-112	23	14	different	different	ADJ
ijassa-112	23	15	fare	fare	NOUN
ijassa-112	23	16	levels	level	NOUN
ijassa-112	23	17	are	be	AUX
ijassa-112	23	18	booked	book	VERB
ijassa-112	23	19	into	into	ADP
ijassa-112	23	20	a	a	DET
ijassa-112	23	21	common	common	ADJ
ijassa-112	23	22	seating	seating	NOUN
ijassa-112	23	23	pool	pool	NOUN
ijassa-112	23	24	in	in	ADP
ijassa-112	23	25	the	the	DET
ijassa-112	23	26	aircraft	aircraft	NOUN
ijassa-112	23	27	.	.	PUNCT
ijassa-112	24	1	the	the	DET
ijassa-112	24	2	following	follow	VERB
ijassa-112	24	3	assumptions	assumption	NOUN
ijassa-112	24	4	are	be	AUX
ijassa-112	24	5	made	make	VERB
ijassa-112	24	6	:	:	PUNCT
ijassa-112	24	7	(	(	PUNCT
ijassa-112	24	8	1	1	X
ijassa-112	24	9	)	)	PUNCT
ijassa-112	24	10	single	single	ADJ
ijassa-112	24	11	-	-	PUNCT
ijassa-112	24	12	leg	leg	NOUN
ijassa-112	24	13	flight	flight	NOUN
ijassa-112	24	14	:	:	PUNCT
ijassa-112	24	15	bookings	booking	NOUN
ijassa-112	24	16	are	be	AUX
ijassa-112	24	17	made	make	VERB
ijassa-112	24	18	on	on	ADP
ijassa-112	24	19	the	the	DET
ijassa-112	24	20	basis	basis	NOUN
ijassa-112	24	21	of	of	ADP
ijassa-112	24	22	a	a	DET
ijassa-112	24	23	single	single	ADJ
ijassa-112	24	24	departure	departure	NOUN
ijassa-112	24	25	and	and	CCONJ
ijassa-112	24	26	landing	landing	NOUN
ijassa-112	24	27	;	;	PUNCT
ijassa-112	24	28	no	no	DET
ijassa-112	24	29	allowance	allowance	NOUN
ijassa-112	24	30	is	be	AUX
ijassa-112	24	31	made	make	VERB
ijassa-112	24	32	for	for	ADP
ijassa-112	24	33	the	the	DET
ijassa-112	24	34	possibility	possibility	NOUN
ijassa-112	24	35	that	that	SCONJ
ijassa-112	24	36	bookings	booking	NOUN
ijassa-112	24	37	may	may	AUX
ijassa-112	24	38	be	be	AUX
ijassa-112	24	39	part	part	NOUN
ijassa-112	24	40	of	of	ADP
ijassa-112	24	41	larger	large	ADJ
ijassa-112	24	42	trip	trip	NOUN
ijassa-112	24	43	itineraries	itinerary	NOUN
ijassa-112	24	44	,	,	PUNCT
ijassa-112	24	45	(	(	PUNCT
ijassa-112	24	46	2	2	X
ijassa-112	24	47	)	)	PUNCT
ijassa-112	24	48	independent	independent	ADJ
ijassa-112	24	49	demands	demand	NOUN
ijassa-112	24	50	:	:	PUNCT
ijassa-112	24	51	the	the	DET
ijassa-112	24	52	demands	demand	NOUN
ijassa-112	24	53	for	for	ADP
ijassa-112	24	54	different	different	ADJ
ijassa-112	24	55	fare	fare	NOUN
ijassa-112	24	56	classes	class	NOUN
ijassa-112	24	57	are	be	AUX
ijassa-112	24	58	stochastically	stochastically	ADV
ijassa-112	24	59	independent	independent	ADJ
ijassa-112	24	60	,	,	PUNCT
ijassa-112	24	61	(	(	PUNCT
ijassa-112	24	62	3	3	X
ijassa-112	24	63	)	)	PUNCT
ijassa-112	24	64	low	low	ADJ
ijassa-112	24	65	before	before	ADP
ijassa-112	24	66	high	high	ADJ
ijassa-112	24	67	demands	demand	NOUN
ijassa-112	24	68	:	:	PUNCT
ijassa-112	24	69	the	the	DET
ijassa-112	24	70	lowest	low	ADJ
ijassa-112	24	71	fare	fare	NOUN
ijassa-112	24	72	reservations	reservation	NOUN
ijassa-112	24	73	requests	request	NOUN
ijassa-112	24	74	arrive	arrive	VERB
ijassa-112	24	75	first	first	ADV
ijassa-112	24	76	,	,	PUNCT
ijassa-112	24	77	followed	follow	VERB
ijassa-112	24	78	by	by	ADP
ijassa-112	24	79	the	the	DET
ijassa-112	24	80	next	next	ADJ
ijassa-112	24	81	lowest	low	ADJ
ijassa-112	24	82	,	,	PUNCT
ijassa-112	24	83	etc	etc	X
ijassa-112	24	84	.	.	X
ijassa-112	24	85	,	,	PUNCT
ijassa-112	24	86	(	(	PUNCT
ijassa-112	24	87	4	4	X
ijassa-112	24	88	)	)	PUNCT
ijassa-112	24	89	no	no	DET
ijassa-112	24	90	cancellations	cancellation	NOUN
ijassa-112	24	91	:	:	PUNCT
ijassa-112	24	92	cancellations	cancellation	NOUN
ijassa-112	24	93	,	,	PUNCT
ijassa-112	24	94	no	no	DET
ijassa-112	24	95	-	-	PUNCT
ijassa-112	24	96	shows	show	NOUN
ijassa-112	24	97	and	and	CCONJ
ijassa-112	24	98	overbooking	overbooking	NOUN
ijassa-112	24	99	are	be	AUX
ijassa-112	24	100	not	not	PART
ijassa-112	24	101	considered	consider	VERB
ijassa-112	24	102	,	,	PUNCT
ijassa-112	24	103	(	(	PUNCT
ijassa-112	24	104	5	5	X
ijassa-112	24	105	)	)	PUNCT
ijassa-112	24	106	nested	nested	ADJ
ijassa-112	24	107	classes	class	NOUN
ijassa-112	24	108	:	:	PUNCT
ijassa-112	24	109	any	any	DET
ijassa-112	24	110	fare	fare	NOUN
ijassa-112	24	111	class	class	NOUN
ijassa-112	24	112	can	can	AUX
ijassa-112	24	113	be	be	AUX
ijassa-112	24	114	booked	book	VERB
ijassa-112	24	115	into	into	ADP
ijassa-112	24	116	seats	seat	NOUN
ijassa-112	24	117	not	not	PART
ijassa-112	24	118	taken	take	VERB
ijassa-112	24	119	by	by	ADP
ijassa-112	24	120	bookings	booking	NOUN
ijassa-112	24	121	in	in	ADP
ijassa-112	24	122	lower	low	ADJ
ijassa-112	24	123	fare	fare	NOUN
ijassa-112	24	124	classes	class	NOUN
ijassa-112	24	125	,	,	PUNCT
ijassa-112	24	126	(	(	PUNCT
ijassa-112	24	127	6	6	X
ijassa-112	24	128	)	)	PUNCT
ijassa-112	24	129	fare	fare	NOUN
ijassa-112	24	130	classes	class	NOUN
ijassa-112	24	131	:	:	PUNCT
ijassa-112	24	132	the	the	DET
ijassa-112	24	133	business	business	NOUN
ijassa-112	24	134	and	and	CCONJ
ijassa-112	24	135	economy	economy	NOUN
ijassa-112	24	136	fare	fare	NOUN
ijassa-112	24	137	classes	class	NOUN
ijassa-112	24	138	are	be	AUX
ijassa-112	24	139	considered	consider	VERB
ijassa-112	24	140	.	.	PUNCT
ijassa-112	25	1	the	the	DET
ijassa-112	25	2	first	first	ADJ
ijassa-112	25	3	purpose	purpose	NOUN
ijassa-112	25	4	of	of	ADP
ijassa-112	25	5	this	this	DET
ijassa-112	25	6	paper	paper	NOUN
ijassa-112	25	7	is	be	AUX
ijassa-112	25	8	to	to	PART
ijassa-112	25	9	present	present	VERB
ijassa-112	25	10	the	the	DET
ijassa-112	25	11	innovative	innovative	ADJ
ijassa-112	25	12	information	information	NOUN
ijassa-112	25	13	technologies	technology	NOUN
ijassa-112	25	14	for	for	ADP
ijassa-112	25	15	constructing	construct	VERB
ijassa-112	25	16	the	the	DET
ijassa-112	25	17	static	static	ADJ
ijassa-112	25	18	and	and	CCONJ
ijassa-112	25	19	dynamic	dynamic	ADJ
ijassa-112	25	20	policies	policy	NOUN
ijassa-112	25	21	of	of	ADP
ijassa-112	25	22	the	the	DET
ijassa-112	25	23	airline	airline	NOUN
ijassa-112	25	24	seat	seat	NOUN
ijassa-112	25	25	inventory	inventory	NOUN
ijassa-112	25	26	control	control	NOUN
ijassa-112	25	27	on	on	ADP
ijassa-112	25	28	the	the	DET
ijassa-112	25	29	basis	basis	NOUN
ijassa-112	25	30	of	of	ADP
ijassa-112	25	31	the	the	DET
ijassa-112	25	32	‘	'	PUNCT
ijassa-112	25	33	unbiasedness	unbiasedness	ADJ
ijassa-112	25	34	performance	performance	NOUN
ijassa-112	25	35	index	index	NOUN
ijassa-112	25	36	’	'	PUNCT
ijassa-112	25	37	.	.	PUNCT
ijassa-112	26	1	the	the	DET
ijassa-112	26	2	static	static	ADJ
ijassa-112	26	3	and	and	CCONJ
ijassa-112	26	4	dynamic	dynamic	ADJ
ijassa-112	26	5	policies	policy	NOUN
ijassa-112	26	6	(	(	PUNCT
ijassa-112	26	7	unbiased	unbiased	ADJ
ijassa-112	26	8	)	)	PUNCT
ijassa-112	26	9	are	be	AUX
ijassa-112	26	10	more	more	ADV
ijassa-112	26	11	efficient	efficient	ADJ
ijassa-112	26	12	(	(	PUNCT
ijassa-112	26	13	from	from	ADP
ijassa-112	26	14	the	the	DET
ijassa-112	26	15	point	point	NOUN
ijassa-112	26	16	of	of	ADP
ijassa-112	26	17	view	view	NOUN
ijassa-112	26	18	of	of	ADP
ijassa-112	26	19	airline	airline	NOUN
ijassa-112	26	20	revenue	revenue	NOUN
ijassa-112	26	21	management	management	NOUN
ijassa-112	26	22	)	)	PUNCT
ijassa-112	26	23	as	as	SCONJ
ijassa-112	26	24	compared	compare	VERB
ijassa-112	26	25	with	with	ADP
ijassa-112	26	26	the	the	DET
ijassa-112	26	27	policies	policy	NOUN
ijassa-112	26	28	,	,	PUNCT
ijassa-112	26	29	where	where	SCONJ
ijassa-112	26	30	the	the	DET
ijassa-112	26	31	unknown	unknown	ADJ
ijassa-112	26	32	parameters	parameter	NOUN
ijassa-112	26	33	of	of	ADP
ijassa-112	26	34	the	the	DET
ijassa-112	26	35	airline	airline	NOUN
ijassa-112	26	36	customer	customer	NOUN
ijassa-112	26	37	demand	demand	NOUN
ijassa-112	26	38	models	model	NOUN
ijassa-112	26	39	are	be	AUX
ijassa-112	26	40	estimated	estimate	VERB
ijassa-112	26	41	and	and	CCONJ
ijassa-112	26	42	then	then	ADV
ijassa-112	26	43	treated	treat	VERB
ijassa-112	26	44	as	as	SCONJ
ijassa-112	26	45	if	if	SCONJ
ijassa-112	26	46	they	they	PRON
ijassa-112	26	47	were	be	AUX
ijassa-112	26	48	the	the	DET
ijassa-112	26	49	true	true	ADJ
ijassa-112	26	50	values	value	NOUN
ijassa-112	26	51	.	.	PUNCT
ijassa-112	27	1	the	the	DET
ijassa-112	27	2	second	second	ADJ
ijassa-112	27	3	purpose	purpose	NOUN
ijassa-112	27	4	of	of	ADP
ijassa-112	27	5	this	this	DET
ijassa-112	27	6	paper	paper	NOUN
ijassa-112	27	7	is	be	AUX
ijassa-112	27	8	to	to	PART
ijassa-112	27	9	introduce	introduce	VERB
ijassa-112	27	10	the	the	DET
ijassa-112	27	11	idea	idea	NOUN
ijassa-112	27	12	of	of	ADP
ijassa-112	27	13	prediction	prediction	NOUN
ijassa-112	27	14	of	of	ADP
ijassa-112	27	15	a	a	DET
ijassa-112	27	16	future	future	ADJ
ijassa-112	27	17	cumulative	cumulative	ADJ
ijassa-112	27	18	customer	customer	NOUN
ijassa-112	27	19	demand	demand	NOUN
ijassa-112	27	20	for	for	ADP
ijassa-112	27	21	the	the	DET
ijassa-112	27	22	seats	seat	NOUN
ijassa-112	27	23	on	on	ADP
ijassa-112	27	24	a	a	DET
ijassa-112	27	25	flight	flight	NOUN
ijassa-112	27	26	via	via	ADP
ijassa-112	27	27	the	the	DET
ijassa-112	27	28	order	order	NOUN
ijassa-112	27	29	statistics	statistic	NOUN
ijassa-112	27	30	from	from	ADP
ijassa-112	27	31	the	the	DET
ijassa-112	27	32	underlying	underlie	VERB
ijassa-112	27	33	distribution	distribution	NOUN
ijassa-112	27	34	,	,	PUNCT
ijassa-112	27	35	where	where	SCONJ
ijassa-112	27	36	only	only	ADV
ijassa-112	27	37	the	the	DET
ijassa-112	27	38	functional	functional	ADJ
ijassa-112	27	39	form	form	NOUN
ijassa-112	27	40	of	of	ADP
ijassa-112	27	41	the	the	DET
ijassa-112	27	42	274	274	NUM
ijassa-112	27	43	nicholas	nicholas	PROPN
ijassa-112	27	44	a.	a.	PROPN
ijassa-112	27	45	nechval	nechval	PROPN
ijassa-112	27	46	:	:	PUNCT
ijassa-112	27	47	improved	improved	ADJ
ijassa-112	27	48	airline	airline	NOUN
ijassa-112	27	49	seat	seat	NOUN
ijassa-112	27	50	inventory	inventory	NOUN
ijassa-112	27	51	control	control	NOUN
ijassa-112	27	52	policies	policy	NOUN
ijassa-112	27	53	under	under	ADP
ijassa-112	27	54	parametric	parametric	ADJ
ijassa-112	27	55	...	...	PUNCT
ijassa-112	27	56	distribution	distribution	NOUN
ijassa-112	27	57	is	be	AUX
ijassa-112	27	58	specified	specify	VERB
ijassa-112	27	59	,	,	PUNCT
ijassa-112	27	60	but	but	CCONJ
ijassa-112	27	61	some	some	PRON
ijassa-112	27	62	or	or	CCONJ
ijassa-112	27	63	all	all	PRON
ijassa-112	27	64	of	of	ADP
ijassa-112	27	65	its	its	PRON
ijassa-112	27	66	parameters	parameter	NOUN
ijassa-112	27	67	are	be	AUX
ijassa-112	27	68	unspecified	unspecified	ADJ
ijassa-112	27	69	.	.	PUNCT
ijassa-112	28	1	this	this	DET
ijassa-112	28	2	idea	idea	NOUN
ijassa-112	28	3	allows	allow	VERB
ijassa-112	28	4	one	one	NUM
ijassa-112	28	5	to	to	PART
ijassa-112	28	6	use	use	VERB
ijassa-112	28	7	the	the	DET
ijassa-112	28	8	technique	technique	NOUN
ijassa-112	28	9	of	of	ADP
ijassa-112	28	10	invariant	invariant	ADJ
ijassa-112	28	11	embedding	embedding	NOUN
ijassa-112	28	12	of	of	ADP
ijassa-112	28	13	sample	sample	NOUN
ijassa-112	28	14	statistics	statistic	NOUN
ijassa-112	28	15	in	in	ADP
ijassa-112	28	16	a	a	DET
ijassa-112	28	17	performance	performance	NOUN
ijassa-112	28	18	index	index	NOUN
ijassa-112	28	19	in	in	ADP
ijassa-112	28	20	order	order	NOUN
ijassa-112	28	21	to	to	PART
ijassa-112	28	22	eliminate	eliminate	VERB
ijassa-112	28	23	the	the	DET
ijassa-112	28	24	unknown	unknown	ADJ
ijassa-112	28	25	parameters	parameter	NOUN
ijassa-112	28	26	from	from	ADP
ijassa-112	28	27	the	the	DET
ijassa-112	28	28	problem	problem	NOUN
ijassa-112	28	29	[	[	X
ijassa-112	28	30	3	3	NUM
ijassa-112	28	31	-	-	SYM
ijassa-112	28	32	4	4	NUM
ijassa-112	28	33	]	]	PUNCT
ijassa-112	28	34	.	.	PUNCT
ijassa-112	29	1	the	the	DET
ijassa-112	29	2	technique	technique	NOUN
ijassa-112	29	3	represents	represent	VERB
ijassa-112	29	4	a	a	DET
ijassa-112	29	5	simple	simple	ADJ
ijassa-112	29	6	and	and	CCONJ
ijassa-112	29	7	computationally	computationally	ADV
ijassa-112	29	8	attractive	attractive	ADJ
ijassa-112	29	9	statistical	statistical	ADJ
ijassa-112	29	10	method	method	NOUN
ijassa-112	29	11	based	base	VERB
ijassa-112	29	12	on	on	ADP
ijassa-112	29	13	the	the	DET
ijassa-112	29	14	constructive	constructive	ADJ
ijassa-112	29	15	use	use	NOUN
ijassa-112	29	16	of	of	ADP
ijassa-112	29	17	the	the	DET
ijassa-112	29	18	invariance	invariance	NOUN
ijassa-112	29	19	principle	principle	NOUN
ijassa-112	29	20	in	in	ADP
ijassa-112	29	21	mathematical	mathematical	ADJ
ijassa-112	29	22	statistics	statistic	NOUN
ijassa-112	29	23	.	.	PUNCT
ijassa-112	30	1	unlike	unlike	ADP
ijassa-112	30	2	the	the	DET
ijassa-112	30	3	bayesian	bayesian	NOUN
ijassa-112	30	4	approach	approach	NOUN
ijassa-112	30	5	,	,	PUNCT
ijassa-112	30	6	an	an	DET
ijassa-112	30	7	invariant	invariant	ADJ
ijassa-112	30	8	embedding	embed	VERB
ijassa-112	30	9	technique	technique	NOUN
ijassa-112	30	10	is	be	AUX
ijassa-112	30	11	independent	independent	ADJ
ijassa-112	30	12	of	of	ADP
ijassa-112	30	13	the	the	DET
ijassa-112	30	14	choice	choice	NOUN
ijassa-112	30	15	of	of	ADP
ijassa-112	30	16	priors	prior	NOUN
ijassa-112	30	17	,	,	PUNCT
ijassa-112	30	18	i.e.	i.e.	X
ijassa-112	30	19	,	,	PUNCT
ijassa-112	30	20	subjectivity	subjectivity	NOUN
ijassa-112	30	21	of	of	ADP
ijassa-112	30	22	investigator	investigator	NOUN
ijassa-112	30	23	is	be	AUX
ijassa-112	30	24	eliminated	eliminate	VERB
ijassa-112	30	25	from	from	ADP
ijassa-112	30	26	the	the	DET
ijassa-112	30	27	problem	problem	NOUN
ijassa-112	30	28	.	.	PUNCT
ijassa-112	31	1	it	it	PRON
ijassa-112	31	2	allows	allow	VERB
ijassa-112	31	3	one	one	PRON
ijassa-112	31	4	to	to	PART
ijassa-112	31	5	find	find	VERB
ijassa-112	31	6	the	the	DET
ijassa-112	31	7	improved	improve	VERB
ijassa-112	31	8	invariant	invariant	ADJ
ijassa-112	31	9	statistical	statistical	ADJ
ijassa-112	31	10	decision	decision	NOUN
ijassa-112	31	11	rules	rule	NOUN
ijassa-112	31	12	,	,	PUNCT
ijassa-112	31	13	which	which	PRON
ijassa-112	31	14	have	have	VERB
ijassa-112	31	15	smaller	small	ADJ
ijassa-112	31	16	risk	risk	NOUN
ijassa-112	31	17	than	than	ADP
ijassa-112	31	18	any	any	PRON
ijassa-112	31	19	of	of	ADP
ijassa-112	31	20	the	the	DET
ijassa-112	31	21	well	well	ADV
ijassa-112	31	22	-	-	PUNCT
ijassa-112	31	23	known	know	VERB
ijassa-112	31	24	traditional	traditional	ADJ
ijassa-112	31	25	statistical	statistical	ADJ
ijassa-112	31	26	decision	decision	NOUN
ijassa-112	31	27	rules	rule	NOUN
ijassa-112	31	28	,	,	PUNCT
ijassa-112	31	29	and	and	CCONJ
ijassa-112	31	30	to	to	PART
ijassa-112	31	31	use	use	VERB
ijassa-112	31	32	the	the	DET
ijassa-112	31	33	previous	previous	ADJ
ijassa-112	31	34	and	and	CCONJ
ijassa-112	31	35	current	current	ADJ
ijassa-112	31	36	sample	sample	NOUN
ijassa-112	31	37	data	datum	NOUN
ijassa-112	31	38	as	as	ADV
ijassa-112	31	39	completely	completely	ADV
ijassa-112	31	40	as	as	ADP
ijassa-112	31	41	possible	possible	ADJ
ijassa-112	31	42	.	.	PUNCT
ijassa-112	32	1	2	2	NUM
ijassa-112	32	2	state	state	NOUN
ijassa-112	32	3	-	-	PUNCT
ijassa-112	32	4	of	of	ADP
ijassa-112	32	5	-	-	PUNCT
ijassa-112	32	6	the	the	DET
ijassa-112	32	7	-	-	PUNCT
ijassa-112	32	8	art	art	NOUN
ijassa-112	32	9	and	and	CCONJ
ijassa-112	32	10	progress	progress	NOUN
ijassa-112	32	11	beyond	beyond	ADP
ijassa-112	32	12	airline	airline	NOUN
ijassa-112	32	13	seat	seat	NOUN
ijassa-112	32	14	inventory	inventory	NOUN
ijassa-112	32	15	control	control	NOUN
ijassa-112	32	16	is	be	AUX
ijassa-112	32	17	a	a	DET
ijassa-112	32	18	very	very	ADV
ijassa-112	32	19	profitable	profitable	ADJ
ijassa-112	32	20	tool	tool	NOUN
ijassa-112	32	21	in	in	ADP
ijassa-112	32	22	the	the	DET
ijassa-112	32	23	airline	airline	NOUN
ijassa-112	32	24	industry	industry	NOUN
ijassa-112	32	25	.	.	PUNCT
ijassa-112	33	1	a	a	DET
ijassa-112	33	2	major	major	ADJ
ijassa-112	33	3	problem	problem	NOUN
ijassa-112	33	4	of	of	ADP
ijassa-112	33	5	airline	airline	NOUN
ijassa-112	33	6	seat	seat	NOUN
ijassa-112	33	7	inventory	inventory	NOUN
ijassa-112	33	8	control	control	NOUN
ijassa-112	33	9	is	be	AUX
ijassa-112	33	10	to	to	PART
ijassa-112	33	11	sell	sell	VERB
ijassa-112	33	12	the	the	DET
ijassa-112	33	13	same	same	ADJ
ijassa-112	33	14	seat	seat	NOUN
ijassa-112	33	15	at	at	ADP
ijassa-112	33	16	different	different	ADJ
ijassa-112	33	17	prices	price	NOUN
ijassa-112	33	18	according	accord	VERB
ijassa-112	33	19	to	to	ADP
ijassa-112	33	20	different	different	ADJ
ijassa-112	33	21	types	type	NOUN
ijassa-112	33	22	of	of	ADP
ijassa-112	33	23	travelers	traveler	NOUN
ijassa-112	33	24	(	(	PUNCT
ijassa-112	33	25	first	first	ADJ
ijassa-112	33	26	class	class	NOUN
ijassa-112	33	27	,	,	PUNCT
ijassa-112	33	28	business	business	NOUN
ijassa-112	33	29	and	and	CCONJ
ijassa-112	33	30	economy	economy	NOUN
ijassa-112	33	31	)	)	PUNCT
ijassa-112	33	32	and	and	CCONJ
ijassa-112	33	33	other	other	ADJ
ijassa-112	33	34	conditions	condition	NOUN
ijassa-112	33	35	in	in	ADP
ijassa-112	33	36	order	order	NOUN
ijassa-112	33	37	to	to	PART
ijassa-112	33	38	improve	improve	VERB
ijassa-112	33	39	revenues	revenue	NOUN
ijassa-112	33	40	.	.	PUNCT
ijassa-112	34	1	this	this	DET
ijassa-112	34	2	problem	problem	NOUN
ijassa-112	34	3	has	have	AUX
ijassa-112	34	4	been	be	AUX
ijassa-112	34	5	considered	consider	VERB
ijassa-112	34	6	in	in	ADP
ijassa-112	34	7	numerous	numerous	ADJ
ijassa-112	34	8	papers	paper	NOUN
ijassa-112	34	9	.	.	PUNCT
ijassa-112	35	1	littlewood	littlewood	PROPN
ijassa-112	36	1	[	[	X
ijassa-112	36	2	5	5	NUM
ijassa-112	36	3	]	]	PUNCT
ijassa-112	36	4	was	be	AUX
ijassa-112	36	5	the	the	DET
ijassa-112	36	6	first	first	ADJ
ijassa-112	36	7	to	to	PART
ijassa-112	36	8	propose	propose	VERB
ijassa-112	36	9	a	a	DET
ijassa-112	36	10	solution	solution	NOUN
ijassa-112	36	11	method	method	NOUN
ijassa-112	36	12	of	of	ADP
ijassa-112	36	13	the	the	DET
ijassa-112	36	14	seat	seat	NOUN
ijassa-112	36	15	inventory	inventory	NOUN
ijassa-112	36	16	control	control	NOUN
ijassa-112	36	17	problem	problem	NOUN
ijassa-112	36	18	for	for	ADP
ijassa-112	36	19	a	a	DET
ijassa-112	36	20	single	single	ADJ
ijassa-112	36	21	leg	leg	NOUN
ijassa-112	36	22	flight	flight	NOUN
ijassa-112	36	23	with	with	ADP
ijassa-112	36	24	two	two	NUM
ijassa-112	36	25	fare	fare	NOUN
ijassa-112	36	26	classes	class	NOUN
ijassa-112	36	27	.	.	PUNCT
ijassa-112	37	1	the	the	DET
ijassa-112	37	2	idea	idea	NOUN
ijassa-112	37	3	of	of	ADP
ijassa-112	37	4	his	his	PRON
ijassa-112	37	5	scheme	scheme	NOUN
ijassa-112	37	6	is	be	AUX
ijassa-112	37	7	to	to	PART
ijassa-112	37	8	equate	equate	VERB
ijassa-112	37	9	the	the	DET
ijassa-112	37	10	marginal	marginal	ADJ
ijassa-112	37	11	revenues	revenue	NOUN
ijassa-112	37	12	in	in	ADP
ijassa-112	37	13	each	each	PRON
ijassa-112	37	14	of	of	ADP
ijassa-112	37	15	the	the	DET
ijassa-112	37	16	two	two	NUM
ijassa-112	37	17	fare	fare	NOUN
ijassa-112	37	18	classes	class	NOUN
ijassa-112	37	19	.	.	PUNCT
ijassa-112	38	1	he	he	PRON
ijassa-112	38	2	suggests	suggest	VERB
ijassa-112	38	3	closing	close	VERB
ijassa-112	38	4	down	down	ADP
ijassa-112	38	5	the	the	DET
ijassa-112	38	6	low	low	ADJ
ijassa-112	38	7	fare	fare	NOUN
ijassa-112	38	8	class	class	NOUN
ijassa-112	38	9	when	when	SCONJ
ijassa-112	38	10	the	the	DET
ijassa-112	38	11	certain	certain	ADJ
ijassa-112	38	12	revenue	revenue	NOUN
ijassa-112	38	13	from	from	ADP
ijassa-112	38	14	selling	sell	VERB
ijassa-112	38	15	low	low	ADJ
ijassa-112	38	16	fare	fare	NOUN
ijassa-112	38	17	seat	seat	NOUN
ijassa-112	38	18	is	be	AUX
ijassa-112	38	19	exceeded	exceed	VERB
ijassa-112	38	20	by	by	ADP
ijassa-112	38	21	the	the	DET
ijassa-112	38	22	expected	expect	VERB
ijassa-112	38	23	revenue	revenue	NOUN
ijassa-112	38	24	of	of	ADP
ijassa-112	38	25	selling	sell	VERB
ijassa-112	38	26	the	the	DET
ijassa-112	38	27	same	same	ADJ
ijassa-112	38	28	seat	seat	NOUN
ijassa-112	38	29	at	at	ADP
ijassa-112	38	30	the	the	DET
ijassa-112	38	31	higher	high	ADJ
ijassa-112	38	32	fare	fare	NOUN
ijassa-112	38	33	.	.	PUNCT
ijassa-112	39	1	that	that	PRON
ijassa-112	39	2	is	be	AUX
ijassa-112	39	3	,	,	PUNCT
ijassa-112	39	4	low	low	ADJ
ijassa-112	39	5	fare	fare	NOUN
ijassa-112	39	6	booking	booking	NOUN
ijassa-112	39	7	requests	request	NOUN
ijassa-112	39	8	should	should	AUX
ijassa-112	39	9	be	be	AUX
ijassa-112	39	10	accepted	accept	VERB
ijassa-112	39	11	as	as	ADV
ijassa-112	39	12	long	long	ADV
ijassa-112	39	13	as	as	SCONJ
ijassa-112	39	14	c2	c2	PROPN
ijassa-112	39	15	≥	≥	PROPN
ijassa-112	39	16	c1pr{y1	c1pr{y1	PROPN
ijassa-112	39	17	>	>	SYM
ijassa-112	39	18	µ1	µ1	PROPN
ijassa-112	39	19	}	}	PUNCT
ijassa-112	39	20	,	,	PUNCT
ijassa-112	39	21	(	(	PUNCT
ijassa-112	39	22	1	1	X
ijassa-112	39	23	)	)	PUNCT
ijassa-112	39	24	where	where	SCONJ
ijassa-112	39	25	c1	c1	PROPN
ijassa-112	39	26	and	and	CCONJ
ijassa-112	39	27	c2	c2	PROPN
ijassa-112	39	28	are	be	AUX
ijassa-112	39	29	the	the	DET
ijassa-112	39	30	high	high	ADJ
ijassa-112	39	31	and	and	CCONJ
ijassa-112	39	32	low	low	ADJ
ijassa-112	39	33	fare	fare	NOUN
ijassa-112	39	34	levels	level	NOUN
ijassa-112	39	35	respectively	respectively	ADV
ijassa-112	39	36	,	,	PUNCT
ijassa-112	39	37	y1	y1	NOUN
ijassa-112	39	38	denotes	denote	VERB
ijassa-112	39	39	the	the	DET
ijassa-112	39	40	demand	demand	NOUN
ijassa-112	39	41	for	for	ADP
ijassa-112	39	42	the	the	DET
ijassa-112	39	43	high	high	ADJ
ijassa-112	39	44	fare	fare	NOUN
ijassa-112	39	45	(	(	PUNCT
ijassa-112	39	46	or	or	CCONJ
ijassa-112	39	47	business	business	NOUN
ijassa-112	39	48	)	)	PUNCT
ijassa-112	40	1	class,µ1	class,µ1	NOUN
ijassa-112	40	2	is	be	AUX
ijassa-112	40	3	the	the	DET
ijassa-112	40	4	number	number	NOUN
ijassa-112	40	5	of	of	ADP
ijassa-112	40	6	seats	seat	NOUN
ijassa-112	40	7	to	to	PART
ijassa-112	40	8	protect	protect	VERB
ijassa-112	40	9	for	for	ADP
ijassa-112	40	10	the	the	DET
ijassa-112	40	11	high	high	ADJ
ijassa-112	40	12	fare	fare	NOUN
ijassa-112	40	13	class	class	NOUN
ijassa-112	40	14	and	and	CCONJ
ijassa-112	40	15	pr{y1	pr{y1	NOUN
ijassa-112	40	16	>	>	X
ijassa-112	41	1	µ1	µ1	PROPN
ijassa-112	41	2	}	}	PUNCT
ijassa-112	41	3	is	be	AUX
ijassa-112	41	4	the	the	DET
ijassa-112	41	5	probability	probability	NOUN
ijassa-112	41	6	of	of	ADP
ijassa-112	41	7	selling	sell	VERB
ijassa-112	41	8	more	more	ADJ
ijassa-112	41	9	than	than	ADP
ijassa-112	41	10	µ1	µ1	PROPN
ijassa-112	41	11	protected	protect	VERB
ijassa-112	41	12	seats	seat	NOUN
ijassa-112	41	13	to	to	ADP
ijassa-112	41	14	high	high	ADJ
ijassa-112	41	15	fare	fare	NOUN
ijassa-112	41	16	class	class	NOUN
ijassa-112	41	17	customers	customer	NOUN
ijassa-112	41	18	.	.	PUNCT
ijassa-112	42	1	the	the	DET
ijassa-112	42	2	smallest	small	ADJ
ijassa-112	42	3	value	value	NOUN
ijassa-112	42	4	of	of	ADP
ijassa-112	42	5	µ1	µ1	PROPN
ijassa-112	42	6	that	that	PRON
ijassa-112	42	7	satisfies	satisfy	VERB
ijassa-112	42	8	the	the	DET
ijassa-112	42	9	above	above	ADJ
ijassa-112	42	10	condition	condition	NOUN
ijassa-112	42	11	is	be	AUX
ijassa-112	42	12	the	the	DET
ijassa-112	42	13	number	number	NOUN
ijassa-112	42	14	of	of	ADP
ijassa-112	42	15	seats	seat	NOUN
ijassa-112	42	16	to	to	PART
ijassa-112	42	17	protect	protect	VERB
ijassa-112	42	18	for	for	ADP
ijassa-112	42	19	the	the	DET
ijassa-112	42	20	high	high	ADJ
ijassa-112	42	21	fare	fare	NOUN
ijassa-112	42	22	class	class	NOUN
ijassa-112	42	23	,	,	PUNCT
ijassa-112	42	24	and	and	CCONJ
ijassa-112	42	25	is	be	AUX
ijassa-112	42	26	known	know	VERB
ijassa-112	42	27	as	as	ADP
ijassa-112	42	28	the	the	DET
ijassa-112	42	29	protection	protection	NOUN
ijassa-112	42	30	level	level	NOUN
ijassa-112	42	31	of	of	ADP
ijassa-112	42	32	the	the	DET
ijassa-112	42	33	high	high	ADJ
ijassa-112	42	34	fare	fare	NOUN
ijassa-112	42	35	class	class	NOUN
ijassa-112	42	36	customers	customer	NOUN
ijassa-112	42	37	.	.	PUNCT
ijassa-112	43	1	the	the	DET
ijassa-112	43	2	concept	concept	NOUN
ijassa-112	43	3	of	of	ADP
ijassa-112	43	4	determining	determine	VERB
ijassa-112	43	5	a	a	DET
ijassa-112	43	6	protection	protection	NOUN
ijassa-112	43	7	level	level	NOUN
ijassa-112	43	8	for	for	ADP
ijassa-112	43	9	the	the	DET
ijassa-112	43	10	high	high	ADJ
ijassa-112	43	11	fare	fare	NOUN
ijassa-112	43	12	class	class	NOUN
ijassa-112	43	13	can	can	AUX
ijassa-112	43	14	also	also	ADV
ijassa-112	43	15	be	be	AUX
ijassa-112	43	16	seen	see	VERB
ijassa-112	43	17	as	as	ADP
ijassa-112	43	18	setting	set	VERB
ijassa-112	43	19	a	a	DET
ijassa-112	43	20	booking	booking	NOUN
ijassa-112	43	21	limit	limit	NOUN
ijassa-112	43	22	,	,	PUNCT
ijassa-112	43	23	a	a	DET
ijassa-112	43	24	maximum	maximum	ADJ
ijassa-112	43	25	number	number	NOUN
ijassa-112	43	26	of	of	ADP
ijassa-112	43	27	bookings	booking	NOUN
ijassa-112	43	28	,	,	PUNCT
ijassa-112	43	29	for	for	ADP
ijassa-112	43	30	the	the	DET
ijassa-112	43	31	low	low	ADJ
ijassa-112	43	32	fare	fare	NOUN
ijassa-112	43	33	class	class	NOUN
ijassa-112	43	34	.	.	PUNCT
ijassa-112	44	1	both	both	DET
ijassa-112	44	2	concepts	concept	NOUN
ijassa-112	44	3	restrict	restrict	VERB
ijassa-112	44	4	the	the	DET
ijassa-112	44	5	number	number	NOUN
ijassa-112	44	6	of	of	ADP
ijassa-112	44	7	bookings	booking	NOUN
ijassa-112	44	8	for	for	ADP
ijassa-112	44	9	the	the	DET
ijassa-112	44	10	low	low	ADJ
ijassa-112	44	11	fare	fare	NOUN
ijassa-112	44	12	class	class	NOUN
ijassa-112	44	13	in	in	ADP
ijassa-112	44	14	order	order	NOUN
ijassa-112	44	15	to	to	PART
ijassa-112	44	16	accept	accept	VERB
ijassa-112	44	17	bookings	booking	NOUN
ijassa-112	44	18	for	for	ADP
ijassa-112	44	19	the	the	DET
ijassa-112	44	20	high	high	ADJ
ijassa-112	44	21	fare	fare	NOUN
ijassa-112	44	22	class	class	NOUN
ijassa-112	44	23	.	.	PUNCT
ijassa-112	45	1	it	it	PRON
ijassa-112	45	2	should	should	AUX
ijassa-112	45	3	be	be	AUX
ijassa-112	45	4	remarked	remark	VERB
ijassa-112	45	5	that	that	SCONJ
ijassa-112	45	6	there	there	PRON
ijassa-112	45	7	is	be	VERB
ijassa-112	45	8	no	no	DET
ijassa-112	45	9	protection	protection	NOUN
ijassa-112	45	10	level	level	NOUN
ijassa-112	45	11	for	for	ADP
ijassa-112	45	12	the	the	DET
ijassa-112	45	13	low	low	ADJ
ijassa-112	45	14	fare	fare	NOUN
ijassa-112	45	15	(	(	PUNCT
ijassa-112	45	16	or	or	CCONJ
ijassa-112	45	17	economy	economy	NOUN
ijassa-112	45	18	)	)	PUNCT
ijassa-112	45	19	class;µ2	class;µ2	PROPN
ijassa-112	45	20	is	be	AUX
ijassa-112	45	21	the	the	DET
ijassa-112	45	22	booking	booking	NOUN
ijassa-112	45	23	limit	limit	NOUN
ijassa-112	45	24	,	,	PUNCT
ijassa-112	45	25	or	or	CCONJ
ijassa-112	45	26	number	number	NOUN
ijassa-112	45	27	of	of	ADP
ijassa-112	45	28	seats	seat	NOUN
ijassa-112	45	29	available	available	ADJ
ijassa-112	45	30	,	,	PUNCT
ijassa-112	45	31	for	for	ADP
ijassa-112	45	32	the	the	DET
ijassa-112	45	33	low	low	ADJ
ijassa-112	45	34	fare	fare	NOUN
ijassa-112	45	35	class	class	NOUN
ijassa-112	45	36	;	;	PUNCT
ijassa-112	45	37	the	the	DET
ijassa-112	45	38	low	low	ADJ
ijassa-112	45	39	fare	fare	NOUN
ijassa-112	45	40	class	class	NOUN
ijassa-112	45	41	is	be	AUX
ijassa-112	45	42	open	open	ADJ
ijassa-112	45	43	as	as	ADV
ijassa-112	45	44	long	long	ADV
ijassa-112	45	45	as	as	SCONJ
ijassa-112	45	46	the	the	DET
ijassa-112	45	47	number	number	NOUN
ijassa-112	45	48	of	of	ADP
ijassa-112	45	49	bookings	booking	NOUN
ijassa-112	45	50	in	in	ADP
ijassa-112	45	51	this	this	DET
ijassa-112	45	52	class	class	NOUN
ijassa-112	45	53	remains	remain	VERB
ijassa-112	45	54	less	less	ADJ
ijassa-112	45	55	than	than	ADP
ijassa-112	45	56	this	this	DET
ijassa-112	45	57	limit	limit	NOUN
ijassa-112	45	58	.	.	PUNCT
ijassa-112	46	1	thus	thus	ADV
ijassa-112	46	2	,	,	PUNCT
ijassa-112	46	3	is	be	AUX
ijassa-112	46	4	the	the	DET
ijassa-112	46	5	booking	booking	NOUN
ijassa-112	46	6	limit	limit	NOUN
ijassa-112	46	7	,	,	PUNCT
ijassa-112	46	8	or	or	CCONJ
ijassa-112	46	9	number	number	NOUN
ijassa-112	46	10	of	of	ADP
ijassa-112	46	11	seats	seat	NOUN
ijassa-112	46	12	available	available	ADJ
ijassa-112	46	13	,	,	PUNCT
ijassa-112	46	14	for	for	ADP
ijassa-112	46	15	the	the	DET
ijassa-112	46	16	low	low	ADJ
ijassa-112	46	17	fare	fare	NOUN
ijassa-112	46	18	class	class	NOUN
ijassa-112	46	19	;	;	PUNCT
ijassa-112	46	20	the	the	DET
ijassa-112	46	21	low	low	ADJ
ijassa-112	46	22	fare	fare	NOUN
ijassa-112	46	23	class	class	NOUN
ijassa-112	46	24	is	be	AUX
ijassa-112	46	25	open	open	ADJ
ijassa-112	46	26	as	as	ADV
ijassa-112	46	27	long	long	ADV
ijassa-112	46	28	as	as	SCONJ
ijassa-112	46	29	the	the	DET
ijassa-112	46	30	number	number	NOUN
ijassa-112	46	31	advances	advance	VERB
ijassa-112	46	32	in	in	ADP
ijassa-112	46	33	systems	system	NOUN
ijassa-112	46	34	science	science	NOUN
ijassa-112	46	35	and	and	CCONJ
ijassa-112	46	36	applications	application	NOUN
ijassa-112	46	37	(	(	PUNCT
ijassa-112	46	38	2012	2012	NUM
ijassa-112	46	39	)	)	PUNCT
ijassa-112	46	40	vol.12	vol.12	NOUN
ijassa-112	46	41	no.3	no.3	VERB
ijassa-112	46	42	275	275	NUM
ijassa-112	46	43	of	of	ADP
ijassa-112	46	44	bookings	booking	NOUN
ijassa-112	46	45	in	in	ADP
ijassa-112	46	46	this	this	DET
ijassa-112	46	47	class	class	NOUN
ijassa-112	46	48	remains	remain	VERB
ijassa-112	46	49	less	less	ADJ
ijassa-112	46	50	than	than	ADP
ijassa-112	46	51	this	this	DET
ijassa-112	46	52	limit	limit	NOUN
ijassa-112	46	53	.	.	PUNCT
ijassa-112	47	1	thus	thus	ADV
ijassa-112	47	2	,	,	PUNCT
ijassa-112	47	3	µ1+µ2	µ1+µ2	PROPN
ijassa-112	47	4	is	be	AUX
ijassa-112	47	5	the	the	DET
ijassa-112	47	6	booking	booking	NOUN
ijassa-112	47	7	limit	limit	NOUN
ijassa-112	47	8	or	or	CCONJ
ijassa-112	47	9	number	number	NOUN
ijassa-112	47	10	of	of	ADP
ijassa-112	47	11	seats	seat	NOUN
ijassa-112	47	12	available	available	ADJ
ijassa-112	47	13	,	,	PUNCT
ijassa-112	47	14	for	for	ADP
ijassa-112	47	15	the	the	DET
ijassa-112	47	16	high	high	ADJ
ijassa-112	47	17	fare	fare	NOUN
ijassa-112	47	18	class	class	NOUN
ijassa-112	47	19	at	at	ADP
ijassa-112	47	20	time	time	NOUN
ijassa-112	47	21	.	.	PUNCT
ijassa-112	48	1	the	the	DET
ijassa-112	48	2	high	high	ADJ
ijassa-112	48	3	fare	fare	NOUN
ijassa-112	48	4	class	class	NOUN
ijassa-112	48	5	is	be	AUX
ijassa-112	48	6	open	open	ADJ
ijassa-112	48	7	as	as	ADV
ijassa-112	48	8	long	long	ADV
ijassa-112	48	9	as	as	SCONJ
ijassa-112	48	10	the	the	DET
ijassa-112	48	11	number	number	NOUN
ijassa-112	48	12	of	of	ADP
ijassa-112	48	13	bookings	booking	NOUN
ijassa-112	48	14	in	in	ADP
ijassa-112	48	15	this	this	DET
ijassa-112	48	16	and	and	CCONJ
ijassa-112	48	17	low	low	ADJ
ijassa-112	48	18	classes	class	NOUN
ijassa-112	48	19	remain	remain	VERB
ijassa-112	48	20	less	less	ADJ
ijassa-112	48	21	than	than	ADP
ijassa-112	48	22	this	this	DET
ijassa-112	48	23	limit	limit	NOUN
ijassa-112	48	24	.	.	PUNCT
ijassa-112	49	1	richter	richter	PROPN
ijassa-112	50	1	[	[	X
ijassa-112	50	2	6	6	NUM
ijassa-112	50	3	]	]	PUNCT
ijassa-112	50	4	gave	give	VERB
ijassa-112	50	5	a	a	DET
ijassa-112	50	6	marginal	marginal	ADJ
ijassa-112	50	7	analysis	analysis	NOUN
ijassa-112	50	8	,	,	PUNCT
ijassa-112	50	9	which	which	PRON
ijassa-112	50	10	proved	prove	VERB
ijassa-112	50	11	that	that	SCONJ
ijassa-112	50	12	(	(	PUNCT
ijassa-112	50	13	1	1	X
ijassa-112	50	14	)	)	PUNCT
ijassa-112	50	15	gives	give	VERB
ijassa-112	50	16	an	an	DET
ijassa-112	50	17	optimal	optimal	ADJ
ijassa-112	50	18	allocation	allocation	NOUN
ijassa-112	50	19	(	(	PUNCT
ijassa-112	50	20	assuming	assume	VERB
ijassa-112	50	21	certain	certain	ADJ
ijassa-112	50	22	continuity	continuity	NOUN
ijassa-112	50	23	conditions	condition	NOUN
ijassa-112	50	24	)	)	PUNCT
ijassa-112	50	25	.	.	PUNCT
ijassa-112	51	1	optimal	optimal	ADJ
ijassa-112	51	2	policies	policy	NOUN
ijassa-112	51	3	for	for	ADP
ijassa-112	51	4	more	more	ADJ
ijassa-112	51	5	than	than	ADP
ijassa-112	51	6	two	two	NUM
ijassa-112	51	7	classes	class	NOUN
ijassa-112	51	8	have	have	AUX
ijassa-112	51	9	been	be	AUX
ijassa-112	51	10	presented	present	VERB
ijassa-112	51	11	independently	independently	ADV
ijassa-112	51	12	by	by	ADP
ijassa-112	51	13	curry	curry	NOUN
ijassa-112	51	14	[	[	X
ijassa-112	51	15	7	7	NUM
ijassa-112	51	16	]	]	PUNCT
ijassa-112	51	17	,	,	PUNCT
ijassa-112	51	18	wollmer	wollmer	NOUN
ijassa-112	52	1	[	[	X
ijassa-112	52	2	8	8	NUM
ijassa-112	52	3	]	]	PUNCT
ijassa-112	52	4	,	,	PUNCT
ijassa-112	52	5	and	and	CCONJ
ijassa-112	52	6	brumelle	brumelle	PROPN
ijassa-112	52	7	&	&	CCONJ
ijassa-112	52	8	mcgill	mcgill	PROPN
ijassa-112	53	1	[	[	X
ijassa-112	53	2	9	9	NUM
ijassa-112	53	3	]	]	SYM
ijassa-112	53	4	.	.	PUNCT
ijassa-112	54	1	3	3	NUM
ijassa-112	54	2	airline	airline	NOUN
ijassa-112	54	3	booking	booking	NOUN
ijassa-112	54	4	policies	policy	NOUN
ijassa-112	54	5	which	which	PRON
ijassa-112	54	6	are	be	AUX
ijassa-112	54	7	used	use	VERB
ijassa-112	54	8	in	in	ADP
ijassa-112	54	9	practice	practice	NOUN
ijassa-112	54	10	3.1	3.1	NUM
ijassa-112	54	11	static	static	ADJ
ijassa-112	54	12	airline	airline	NOUN
ijassa-112	54	13	booking	booking	NOUN
ijassa-112	54	14	policy	policy	NOUN
ijassa-112	54	15	under	under	ADP
ijassa-112	54	16	complete	complete	ADJ
ijassa-112	54	17	information	information	NOUN
ijassa-112	54	18	it	it	PRON
ijassa-112	54	19	will	will	AUX
ijassa-112	54	20	be	be	AUX
ijassa-112	54	21	noted	note	VERB
ijassa-112	54	22	that	that	SCONJ
ijassa-112	54	23	(	(	PUNCT
ijassa-112	54	24	1	1	X
ijassa-112	54	25	)	)	PUNCT
ijassa-112	54	26	represents	represent	VERB
ijassa-112	54	27	the	the	DET
ijassa-112	54	28	static	static	ADJ
ijassa-112	54	29	policy	policy	NOUN
ijassa-112	54	30	of	of	ADP
ijassa-112	54	31	airline	airline	NOUN
ijassa-112	54	32	seat	seat	NOUN
ijassa-112	54	33	inventory	inventory	NOUN
ijassa-112	54	34	control	control	NOUN
ijassa-112	54	35	(	(	PUNCT
ijassa-112	54	36	or	or	CCONJ
ijassa-112	54	37	airline	airline	NOUN
ijassa-112	54	38	booking	booking	NOUN
ijassa-112	54	39	)	)	PUNCT
ijassa-112	54	40	under	under	ADP
ijassa-112	54	41	complete	complete	ADJ
ijassa-112	54	42	information	information	NOUN
ijassa-112	54	43	.	.	PUNCT
ijassa-112	55	1	if	if	SCONJ
ijassa-112	55	2	fθ	fθ	ADV
ijassa-112	55	3	,	,	PUNCT
ijassa-112	55	4	the	the	DET
ijassa-112	55	5	probability	probability	NOUN
ijassa-112	55	6	distribution	distribution	NOUN
ijassa-112	55	7	function	function	NOUN
ijassa-112	55	8	of	of	ADP
ijassa-112	55	9	y1	y1	NOUN
ijassa-112	55	10	with	with	ADP
ijassa-112	55	11	the	the	DET
ijassa-112	55	12	parameter	parameter	NOUN
ijassa-112	55	13	θ	θ	PROPN
ijassa-112	55	14	(	(	PUNCT
ijassa-112	55	15	in	in	ADP
ijassa-112	55	16	general	general	ADJ
ijassa-112	55	17	,	,	PUNCT
ijassa-112	55	18	vector	vector	NOUN
ijassa-112	55	19	)	)	PUNCT
ijassa-112	55	20	,	,	PUNCT
ijassa-112	55	21	is	be	AUX
ijassa-112	55	22	continuous	continuous	ADJ
ijassa-112	55	23	and	and	CCONJ
ijassa-112	55	24	strictly	strictly	ADV
ijassa-112	55	25	increasing	increase	VERB
ijassa-112	55	26	,	,	PUNCT
ijassa-112	55	27	the	the	DET
ijassa-112	55	28	definition	definition	NOUN
ijassa-112	55	29	(	(	PUNCT
ijassa-112	55	30	1	1	X
ijassa-112	55	31	)	)	PUNCT
ijassa-112	55	32	of	of	ADP
ijassa-112	55	33	µ1	µ1	PROPN
ijassa-112	55	34	is	be	AUX
ijassa-112	55	35	equivalent	equivalent	ADJ
ijassa-112	55	36	to	to	ADP
ijassa-112	55	37	µ1	µ1	NOUN
ijassa-112	55	38	=	=	SYM
ijassa-112	55	39	arg	arg	NOUN
ijassa-112	55	40	(	(	PUNCT
ijassa-112	55	41	f̄θ(µ1	f̄θ(µ1	ADJ
ijassa-112	55	42	)	)	PUNCT
ijassa-112	55	43	=	=	SYM
ijassa-112	55	44	γ	γ	X
ijassa-112	55	45	)	)	PUNCT
ijassa-112	55	46	(	(	PUNCT
ijassa-112	55	47	2	2	X
ijassa-112	55	48	)	)	PUNCT
ijassa-112	55	49	where	where	SCONJ
ijassa-112	55	50	γ	γ	PROPN
ijassa-112	55	51	=	=	PROPN
ijassa-112	55	52	c1	c1	PROPN
ijassa-112	55	53	/	/	SYM
ijassa-112	55	54	c2	c2	PROPN
ijassa-112	55	55	,	,	PUNCT
ijassa-112	55	56	(	(	PUNCT
ijassa-112	55	57	3	3	X
ijassa-112	55	58	)	)	PUNCT
ijassa-112	55	59	f̄θ(τj	f̄θ(τj	PROPN
ijassa-112	55	60	)	)	PUNCT
ijassa-112	55	61	=	=	SYM
ijassa-112	55	62	1−	1−	NUM
ijassa-112	55	63	fθ(τj	fθ(τj	NOUN
ijassa-112	55	64	)	)	PUNCT
ijassa-112	55	65	.	.	PUNCT
ijassa-112	56	1	(	(	PUNCT
ijassa-112	56	2	4	4	X
ijassa-112	56	3	)	)	PUNCT
ijassa-112	56	4	3.2	3.2	NUM
ijassa-112	56	5	static	static	ADJ
ijassa-112	56	6	airline	airline	NOUN
ijassa-112	56	7	booking	booking	NOUN
ijassa-112	56	8	policy	policy	NOUN
ijassa-112	56	9	under	under	ADP
ijassa-112	56	10	parametric	parametric	ADJ
ijassa-112	56	11	uncertainty	uncertainty	NOUN
ijassa-112	56	12	in	in	ADP
ijassa-112	56	13	practice	practice	NOUN
ijassa-112	56	14	,	,	PUNCT
ijassa-112	56	15	under	under	ADP
ijassa-112	56	16	parametric	parametric	ADJ
ijassa-112	56	17	uncertainty	uncertainty	NOUN
ijassa-112	56	18	,	,	PUNCT
ijassa-112	56	19	i.e.	i.e.	X
ijassa-112	56	20	when	when	SCONJ
ijassa-112	56	21	the	the	DET
ijassa-112	56	22	parameter	parameter	NOUN
ijassa-112	56	23	θ	θ	PROPN
ijassa-112	56	24	is	be	AUX
ijassa-112	56	25	unknown	unknown	ADJ
ijassa-112	56	26	,	,	PUNCT
ijassa-112	56	27	the	the	DET
ijassa-112	56	28	performance	performance	NOUN
ijassa-112	56	29	index	index	NOUN
ijassa-112	56	30	,	,	PUNCT
ijassa-112	56	31	f̄θ(µ1	f̄θ(µ1	ADJ
ijassa-112	56	32	)	)	PUNCT
ijassa-112	56	33	=	=	SYM
ijassa-112	57	1	γ	γ	X
ijassa-112	57	2	,	,	PUNCT
ijassa-112	57	3	(	(	PUNCT
ijassa-112	57	4	5	5	X
ijassa-112	57	5	)	)	PUNCT
ijassa-112	57	6	is	be	AUX
ijassa-112	57	7	usually	usually	ADV
ijassa-112	57	8	used	use	VERB
ijassa-112	57	9	to	to	PART
ijassa-112	57	10	construct	construct	VERB
ijassa-112	57	11	the	the	DET
ijassa-112	57	12	static	static	ADJ
ijassa-112	57	13	policy	policy	NOUN
ijassa-112	57	14	given	give	VERB
ijassa-112	57	15	by	by	ADP
ijassa-112	57	16	µ1	µ1	PROPN
ijassa-112	57	17	=	=	SYM
ijassa-112	57	18	arg	arg	NOUN
ijassa-112	57	19	(	(	PUNCT
ijassa-112	57	20	f̄θ̂(µ1	f̄θ̂(µ1	PROPN
ijassa-112	57	21	)	)	PUNCT
ijassa-112	57	22	=	=	SYM
ijassa-112	57	23	γ	γ	PROPN
ijassa-112	57	24	)	)	PUNCT
ijassa-112	57	25	,	,	PUNCT
ijassa-112	57	26	(	(	PUNCT
ijassa-112	57	27	6	6	NUM
ijassa-112	57	28	)	)	PUNCT
ijassa-112	57	29	where	where	SCONJ
ijassa-112	57	30	θ̂	θ̂	NUM
ijassa-112	57	31	represents	represent	VERB
ijassa-112	57	32	the	the	DET
ijassa-112	57	33	maximum	maximum	ADJ
ijassa-112	57	34	likelihood	likelihood	NOUN
ijassa-112	57	35	estimator	estimator	NOUN
ijassa-112	57	36	of	of	ADP
ijassa-112	57	37	θ	θ	PROPN
ijassa-112	57	38	.	.	PUNCT
ijassa-112	58	1	the	the	DET
ijassa-112	58	2	performance	performance	NOUN
ijassa-112	58	3	index	index	NOUN
ijassa-112	58	4	(	(	PUNCT
ijassa-112	58	5	5	5	NUM
ijassa-112	58	6	)	)	PUNCT
ijassa-112	58	7	is	be	AUX
ijassa-112	58	8	named	name	VERB
ijassa-112	58	9	as	as	ADP
ijassa-112	58	10	‘	'	PUNCT
ijassa-112	58	11	maximum	maximum	ADJ
ijassa-112	58	12	likelihood	likelihood	NOUN
ijassa-112	58	13	performance	performance	NOUN
ijassa-112	58	14	index	index	NOUN
ijassa-112	58	15	’	'	PUNCT
ijassa-112	58	16	.	.	PUNCT
ijassa-112	59	1	the	the	DET
ijassa-112	59	2	static	static	ADJ
ijassa-112	59	3	policy	policy	NOUN
ijassa-112	59	4	(	(	PUNCT
ijassa-112	59	5	6	6	NUM
ijassa-112	59	6	)	)	PUNCT
ijassa-112	59	7	based	base	VERB
ijassa-112	59	8	on	on	ADP
ijassa-112	59	9	(	(	PUNCT
ijassa-112	59	10	5	5	NUM
ijassa-112	59	11	)	)	PUNCT
ijassa-112	59	12	is	be	AUX
ijassa-112	59	13	named	name	VERB
ijassa-112	59	14	as	as	ADP
ijassa-112	59	15	‘	'	PUNCT
ijassa-112	59	16	static	static	ADJ
ijassa-112	59	17	maximum	maximum	ADJ
ijassa-112	59	18	likelihood	likelihood	NOUN
ijassa-112	59	19	airline	airline	NOUN
ijassa-112	59	20	booking	booking	NOUN
ijassa-112	59	21	policy	policy	NOUN
ijassa-112	59	22	’	'	PUNCT
ijassa-112	59	23	.	.	PUNCT
ijassa-112	60	1	3.3	3.3	NUM
ijassa-112	60	2	dynamic	dynamic	ADJ
ijassa-112	60	3	airline	airline	NOUN
ijassa-112	60	4	booking	booking	NOUN
ijassa-112	60	5	policy	policy	NOUN
ijassa-112	60	6	under	under	ADP
ijassa-112	60	7	parametric	parametric	ADJ
ijassa-112	60	8	uncertainty	uncertainty	NOUN
ijassa-112	60	9	the	the	DET
ijassa-112	60	10	static	static	ADJ
ijassa-112	60	11	policy	policy	NOUN
ijassa-112	60	12	of	of	ADP
ijassa-112	60	13	airline	airline	NOUN
ijassa-112	60	14	booking	booking	NOUN
ijassa-112	60	15	is	be	AUX
ijassa-112	60	16	optimal	optimal	ADJ
ijassa-112	60	17	as	as	ADV
ijassa-112	60	18	long	long	ADV
ijassa-112	60	19	as	as	SCONJ
ijassa-112	60	20	no	no	DET
ijassa-112	60	21	change	change	NOUN
ijassa-112	60	22	in	in	ADP
ijassa-112	60	23	the	the	DET
ijassa-112	60	24	probability	probability	NOUN
ijassa-112	60	25	distributions	distribution	NOUN
ijassa-112	60	26	of	of	ADP
ijassa-112	60	27	the	the	DET
ijassa-112	60	28	customer	customer	NOUN
ijassa-112	60	29	demand	demand	NOUN
ijassa-112	60	30	is	be	AUX
ijassa-112	60	31	foreseen	foresee	VERB
ijassa-112	60	32	.	.	PUNCT
ijassa-112	61	1	however	however	ADV
ijassa-112	61	2	,	,	PUNCT
ijassa-112	61	3	information	information	NOUN
ijassa-112	61	4	on	on	ADP
ijassa-112	61	5	the	the	DET
ijassa-112	61	6	actual	actual	ADJ
ijassa-112	61	7	customer	customer	NOUN
ijassa-112	61	8	demand	demand	NOUN
ijassa-112	61	9	process	process	NOUN
ijassa-112	61	10	can	can	AUX
ijassa-112	61	11	reduce	reduce	VERB
ijassa-112	61	12	the	the	DET
ijassa-112	61	13	uncertainty	uncertainty	NOUN
ijassa-112	61	14	associated	associate	VERB
ijassa-112	61	15	with	with	ADP
ijassa-112	61	16	the	the	DET
ijassa-112	61	17	estimates	estimate	NOUN
ijassa-112	61	18	of	of	ADP
ijassa-112	61	19	demand	demand	NOUN
ijassa-112	61	20	.	.	PUNCT
ijassa-112	62	1	hence	hence	ADV
ijassa-112	62	2	,	,	PUNCT
ijassa-112	62	3	repetitive	repetitive	ADJ
ijassa-112	62	4	use	use	NOUN
ijassa-112	62	5	of	of	ADP
ijassa-112	62	6	a	a	DET
ijassa-112	62	7	static	static	ADJ
ijassa-112	62	8	policy	policy	NOUN
ijassa-112	62	9	over	over	ADP
ijassa-112	62	10	the	the	DET
ijassa-112	62	11	booking	booking	NOUN
ijassa-112	62	12	period	period	NOUN
ijassa-112	62	13	,	,	PUNCT
ijassa-112	62	14	based	base	VERB
ijassa-112	62	15	on	on	ADP
ijassa-112	62	16	the	the	DET
ijassa-112	62	17	most	most	ADV
ijassa-112	62	18	recent	recent	ADJ
ijassa-112	62	19	demand	demand	NOUN
ijassa-112	62	20	and	and	CCONJ
ijassa-112	62	21	capacity	capacity	NOUN
ijassa-112	62	22	information	information	NOUN
ijassa-112	62	23	,	,	PUNCT
ijassa-112	62	24	is	be	AUX
ijassa-112	62	25	the	the	DET
ijassa-112	62	26	general	general	ADJ
ijassa-112	62	27	way	way	NOUN
ijassa-112	62	28	to	to	PART
ijassa-112	62	29	proceed	proceed	VERB
ijassa-112	62	30	.	.	PUNCT
ijassa-112	63	1	276	276	NUM
ijassa-112	63	2	nicholas	nicholas	PROPN
ijassa-112	63	3	a.	a.	PROPN
ijassa-112	63	4	nechval	nechval	PROPN
ijassa-112	63	5	:	:	PUNCT
ijassa-112	63	6	improved	improved	ADJ
ijassa-112	63	7	airline	airline	NOUN
ijassa-112	63	8	seat	seat	NOUN
ijassa-112	63	9	inventory	inventory	NOUN
ijassa-112	63	10	control	control	NOUN
ijassa-112	63	11	policies	policy	NOUN
ijassa-112	63	12	under	under	ADP
ijassa-112	63	13	parametric	parametric	ADJ
ijassa-112	63	14	...	...	PUNCT
ijassa-112	63	15	4	4	NUM
ijassa-112	63	16	improved	improve	VERB
ijassa-112	63	17	airline	airline	NOUN
ijassa-112	63	18	booking	booking	NOUN
ijassa-112	63	19	policies	policy	NOUN
ijassa-112	63	20	proposed	propose	VERB
ijassa-112	63	21	in	in	ADP
ijassa-112	63	22	the	the	DET
ijassa-112	63	23	paper	paper	NOUN
ijassa-112	63	24	4.1	4.1	NUM
ijassa-112	63	25	static	static	ADJ
ijassa-112	63	26	unbiased	unbiased	ADJ
ijassa-112	63	27	airline	airline	NOUN
ijassa-112	63	28	booking	booking	NOUN
ijassa-112	63	29	policy	policy	NOUN
ijassa-112	63	30	under	under	ADP
ijassa-112	63	31	parametric	parametric	ADJ
ijassa-112	63	32	uncertainty	uncertainty	NOUN
ijassa-112	63	33	this	this	DET
ijassa-112	63	34	policy	policy	NOUN
ijassa-112	63	35	is	be	AUX
ijassa-112	63	36	based	base	VERB
ijassa-112	63	37	on	on	ADP
ijassa-112	63	38	the	the	DET
ijassa-112	63	39	performance	performance	NOUN
ijassa-112	63	40	index	index	NOUN
ijassa-112	63	41	,	,	PUNCT
ijassa-112	63	42	eθ{f̄θ(µ1	eθ{f̄θ(µ1	PROPN
ijassa-112	63	43	)	)	PUNCT
ijassa-112	63	44	}	}	PUNCT
ijassa-112	63	45	=	=	SYM
ijassa-112	63	46	γ	γ	X
ijassa-112	63	47	,	,	PUNCT
ijassa-112	63	48	(	(	PUNCT
ijassa-112	63	49	7	7	X
ijassa-112	63	50	)	)	PUNCT
ijassa-112	63	51	which	which	PRON
ijassa-112	63	52	takes	take	VERB
ijassa-112	63	53	into	into	ADP
ijassa-112	63	54	account	account	NOUN
ijassa-112	63	55	(	(	PUNCT
ijassa-112	63	56	2	2	NUM
ijassa-112	63	57	)	)	PUNCT
ijassa-112	63	58	and	and	CCONJ
ijassa-112	63	59	the	the	DET
ijassa-112	63	60	previous	previous	ADJ
ijassa-112	63	61	data	datum	NOUN
ijassa-112	63	62	of	of	ADP
ijassa-112	63	63	cumulative	cumulative	ADJ
ijassa-112	63	64	customer	customer	NOUN
ijassa-112	63	65	demand	demand	NOUN
ijassa-112	63	66	y1	y1	NOUN
ijassa-112	63	67	for	for	ADP
ijassa-112	63	68	the	the	DET
ijassa-112	63	69	seats	seat	NOUN
ijassa-112	63	70	on	on	ADP
ijassa-112	63	71	a	a	DET
ijassa-112	63	72	flight	flight	NOUN
ijassa-112	63	73	.	.	PUNCT
ijassa-112	64	1	it	it	PRON
ijassa-112	64	2	allows	allow	VERB
ijassa-112	64	3	one	one	NUM
ijassa-112	64	4	to	to	PART
ijassa-112	64	5	construct	construct	VERB
ijassa-112	64	6	the	the	DET
ijassa-112	64	7	static	static	ADJ
ijassa-112	64	8	airline	airline	NOUN
ijassa-112	64	9	booking	booking	NOUN
ijassa-112	64	10	policy	policy	NOUN
ijassa-112	64	11	given	give	VERB
ijassa-112	64	12	by	by	ADP
ijassa-112	64	13	µ	µ	X
ijassa-112	64	14	(	(	PUNCT
ijassa-112	64	15	µnb	µnb	VERB
ijassa-112	64	16	)	)	PUNCT
ijassa-112	64	17	1	1	NUM
ijassa-112	64	18	=	=	SYM
ijassa-112	64	19	arg	arg	NOUN
ijassa-112	64	20	(	(	PUNCT
ijassa-112	64	21	eθ{f̄θ(µ1	eθ{f̄θ(µ1	PROPN
ijassa-112	64	22	)	)	PUNCT
ijassa-112	64	23	}	}	PUNCT
ijassa-112	64	24	=	=	SYM
ijassa-112	64	25	γ	γ	PROPN
ijassa-112	64	26	)	)	PUNCT
ijassa-112	64	27	,	,	PUNCT
ijassa-112	64	28	(	(	PUNCT
ijassa-112	64	29	8)	8)	NUM
ijassa-112	64	30	where	where	SCONJ
ijassa-112	64	31	µ1	µ1	PROPN
ijassa-112	64	32	≡	≡	PROPN
ijassa-112	64	33	µ1(θ̂),θ̂	µ1(θ̂),θ̂	PROPN
ijassa-112	64	34	represents	represent	VERB
ijassa-112	64	35	either	either	CCONJ
ijassa-112	64	36	the	the	DET
ijassa-112	64	37	maximum	maximum	ADJ
ijassa-112	64	38	likelihood	likelihood	NOUN
ijassa-112	64	39	estimator	estimator	NOUN
ijassa-112	64	40	of	of	ADP
ijassa-112	64	41	θ	θ	PROPN
ijassa-112	64	42	or	or	CCONJ
ijassa-112	64	43	sufficient	sufficient	ADJ
ijassa-112	64	44	statistic	statistic	NOUN
ijassa-112	64	45	s	s	NOUN
ijassa-112	64	46	for	for	ADP
ijassa-112	64	47	θ	θ	PROPN
ijassa-112	64	48	,	,	PUNCT
ijassa-112	64	49	i.e.	i.e.	X
ijassa-112	64	50	,	,	PUNCT
ijassa-112	64	51	µ1	µ1	PROPN
ijassa-112	64	52	≡	≡	PROPN
ijassa-112	64	53	µ1(s	µ1(s	PROPN
ijassa-112	64	54	)	)	PUNCT
ijassa-112	64	55	the	the	DET
ijassa-112	64	56	performance	performance	NOUN
ijassa-112	64	57	index	index	NOUN
ijassa-112	64	58	(	(	PUNCT
ijassa-112	64	59	7	7	NUM
ijassa-112	64	60	)	)	PUNCT
ijassa-112	64	61	is	be	AUX
ijassa-112	64	62	named	name	VERB
ijassa-112	64	63	as	as	ADP
ijassa-112	64	64	‘	'	PUNCT
ijassa-112	64	65	unbiasedness	unbiasedness	ADJ
ijassa-112	64	66	performance	performance	NOUN
ijassa-112	64	67	index’.the	index’.the	DET
ijassa-112	64	68	static	static	ADJ
ijassa-112	64	69	policy	policy	NOUN
ijassa-112	64	70	(	(	PUNCT
ijassa-112	64	71	8)	8)	NUM
ijassa-112	64	72	,	,	PUNCT
ijassa-112	64	73	which	which	PRON
ijassa-112	64	74	is	be	AUX
ijassa-112	64	75	based	base	VERB
ijassa-112	64	76	on	on	ADP
ijassa-112	64	77	(	(	PUNCT
ijassa-112	64	78	7	7	NUM
ijassa-112	64	79	)	)	PUNCT
ijassa-112	64	80	,	,	PUNCT
ijassa-112	64	81	is	be	AUX
ijassa-112	64	82	named	name	VERB
ijassa-112	64	83	as	as	ADP
ijassa-112	64	84	‘	'	PUNCT
ijassa-112	64	85	static	static	ADJ
ijassa-112	64	86	unbiased	unbiased	ADJ
ijassa-112	64	87	airline	airline	NOUN
ijassa-112	64	88	booking	booking	NOUN
ijassa-112	64	89	policy	policy	NOUN
ijassa-112	64	90	’	'	PUNCT
ijassa-112	64	91	.	.	PUNCT
ijassa-112	65	1	the	the	DET
ijassa-112	65	2	relative	relative	ADJ
ijassa-112	65	3	bias	bias	NOUN
ijassa-112	65	4	of	of	ADP
ijassa-112	65	5	the	the	DET
ijassa-112	65	6	static	static	ADJ
ijassa-112	65	7	airline	airline	NOUN
ijassa-112	65	8	booking	booking	NOUN
ijassa-112	65	9	policy	policy	NOUN
ijassa-112	65	10	is	be	AUX
ijassa-112	65	11	given	give	VERB
ijassa-112	65	12	by	by	ADP
ijassa-112	65	13	γ(µ1	γ(µ1	NOUN
ijassa-112	65	14	)	)	PUNCT
ijassa-112	65	15	=	=	SYM
ijassa-112	65	16	∣∣eθ{f̄θ(µ1	∣∣eθ{f̄θ(µ1	NOUN
ijassa-112	65	17	)	)	PUNCT
ijassa-112	65	18	}	}	PUNCT
ijassa-112	65	19	−	−	PROPN
ijassa-112	65	20	γ	γ	X
ijassa-112	65	21	∣∣	∣∣	NUM
ijassa-112	65	22	γ	γ	X
ijassa-112	65	23	100	100	NUM
ijassa-112	65	24	%	%	NOUN
ijassa-112	65	25	(	(	PUNCT
ijassa-112	65	26	9	9	NUM
ijassa-112	65	27	)	)	SYM
ijassa-112	65	28	4.2	4.2	NUM
ijassa-112	65	29	dynamic	dynamic	ADJ
ijassa-112	65	30	airline	airline	NOUN
ijassa-112	65	31	booking	booking	NOUN
ijassa-112	65	32	policy	policy	NOUN
ijassa-112	65	33	under	under	ADP
ijassa-112	65	34	complete	complete	ADJ
ijassa-112	65	35	information	information	NOUN
ijassa-112	65	36	in	in	ADP
ijassa-112	65	37	this	this	DET
ijassa-112	65	38	section	section	NOUN
ijassa-112	65	39	,	,	PUNCT
ijassa-112	65	40	we	we	PRON
ijassa-112	65	41	consider	consider	VERB
ijassa-112	65	42	a	a	DET
ijassa-112	65	43	flight	flight	NOUN
ijassa-112	65	44	for	for	ADP
ijassa-112	65	45	a	a	DET
ijassa-112	65	46	single	single	ADJ
ijassa-112	65	47	departure	departure	NOUN
ijassa-112	65	48	date	date	NOUN
ijassa-112	65	49	with	with	ADP
ijassa-112	65	50	m	m	ADP
ijassa-112	65	51	predefined	predefine	VERB
ijassa-112	65	52	reading	reading	NOUN
ijassa-112	65	53	dates	date	NOUN
ijassa-112	65	54	at	at	ADP
ijassa-112	65	55	which	which	PRON
ijassa-112	65	56	the	the	DET
ijassa-112	65	57	dynamic	dynamic	ADJ
ijassa-112	65	58	policy	policy	NOUN
ijassa-112	65	59	is	be	AUX
ijassa-112	65	60	to	to	PART
ijassa-112	65	61	be	be	AUX
ijassa-112	65	62	updated	update	VERB
ijassa-112	65	63	,	,	PUNCT
ijassa-112	65	64	i.e.	i.e.	X
ijassa-112	65	65	,	,	PUNCT
ijassa-112	65	66	the	the	DET
ijassa-112	65	67	booking	booking	NOUN
ijassa-112	65	68	period	period	NOUN
ijassa-112	65	69	before	before	ADP
ijassa-112	65	70	departure	departure	NOUN
ijassa-112	65	71	is	be	AUX
ijassa-112	65	72	divided	divide	VERB
ijassa-112	65	73	intom	intom	ADJ
ijassa-112	65	74	readings	reading	NOUN
ijassa-112	65	75	periods:(0	periods:(0	PROPN
ijassa-112	65	76	,	,	PUNCT
ijassa-112	65	77	τ1	τ1	NOUN
ijassa-112	65	78	]	]	PUNCT
ijassa-112	65	79	,	,	PUNCT
ijassa-112	65	80	(	(	PUNCT
ijassa-112	65	81	τ1	τ1	NOUN
ijassa-112	65	82	,	,	PUNCT
ijassa-112	65	83	τ2	τ2	PROPN
ijassa-112	65	84	]	]	PUNCT
ijassa-112	65	85	,	,	PUNCT
ijassa-112	65	86	.	.	PUNCT
ijassa-112	65	87	.	.	PUNCT
ijassa-112	65	88	.	.	PUNCT
ijassa-112	66	1	,	,	PUNCT
ijassa-112	66	2	(	(	PUNCT
ijassa-112	66	3	τm−1	τm−1	PROPN
ijassa-112	66	4	,	,	PUNCT
ijassa-112	66	5	τm	τm	PROPN
ijassa-112	66	6	]	]	PUNCT
ijassa-112	66	7	determined	determine	VERB
ijassa-112	66	8	by	by	ADP
ijassa-112	66	9	them	they	PRON
ijassa-112	66	10	reading	read	VERB
ijassa-112	66	11	dates	date	NOUN
ijassa-112	66	12	:	:	PUNCT
ijassa-112	66	13	τ1	τ1	NOUN
ijassa-112	66	14	,	,	PUNCT
ijassa-112	66	15	τ2	τ2	NOUN
ijassa-112	66	16	,	,	PUNCT
ijassa-112	66	17	.	.	PUNCT
ijassa-112	66	18	.	.	PUNCT
ijassa-112	66	19	.	.	PUNCT
ijassa-112	67	1	,	,	PUNCT
ijassa-112	67	2	τm	τm	PROPN
ijassa-112	67	3	.	.	PUNCT
ijassa-112	68	1	these	these	DET
ijassa-112	68	2	reading	reading	NOUN
ijassa-112	68	3	dates	date	NOUN
ijassa-112	68	4	are	be	AUX
ijassa-112	68	5	indexed	index	VERB
ijassa-112	68	6	in	in	ADP
ijassa-112	68	7	increasing	increase	VERB
ijassa-112	68	8	order:0	order:0	NUM
ijassa-112	68	9	<	<	X
ijassa-112	68	10	τ1	τ1	NOUN
ijassa-112	68	11	<	<	X
ijassa-112	68	12	τ2	τ2	NOUN
ijassa-112	68	13	<	<	X
ijassa-112	68	14	.	.	PUNCT
ijassa-112	68	15	.	.	PUNCT
ijassa-112	68	16	.	.	PUNCT
ijassa-112	69	1	<	<	X
ijassa-112	69	2	τm	τm	PROPN
ijassa-112	69	3	,	,	PUNCT
ijassa-112	69	4	where	where	SCONJ
ijassa-112	69	5	(	(	PUNCT
ijassa-112	69	6	τm−1	τm−1	PROPN
ijassa-112	69	7	,	,	PUNCT
ijassa-112	69	8	τm	τm	ADP
ijassa-112	69	9	]	]	X
ijassa-112	69	10	denotes	denote	VERB
ijassa-112	69	11	the	the	DET
ijassa-112	69	12	reading	reading	NOUN
ijassa-112	69	13	period	period	NOUN
ijassa-112	69	14	immediately	immediately	ADV
ijassa-112	69	15	preceding	precede	VERB
ijassa-112	69	16	departure	departure	NOUN
ijassa-112	69	17	,	,	PUNCT
ijassa-112	69	18	and	and	CCONJ
ijassa-112	69	19	τm	τm	PRON
ijassa-112	69	20	]	]	PUNCT
ijassa-112	69	21	is	be	AUX
ijassa-112	69	22	at	at	ADP
ijassa-112	69	23	departure	departure	NOUN
ijassa-112	69	24	.	.	PUNCT
ijassa-112	70	1	typically	typically	ADV
ijassa-112	70	2	,	,	PUNCT
ijassa-112	70	3	the	the	DET
ijassa-112	70	4	reading	reading	NOUN
ijassa-112	70	5	periods	period	NOUN
ijassa-112	70	6	that	that	PRON
ijassa-112	70	7	are	be	AUX
ijassa-112	70	8	closer	close	ADJ
ijassa-112	70	9	to	to	ADP
ijassa-112	70	10	departure	departure	NOUN
ijassa-112	70	11	cover	cover	VERB
ijassa-112	70	12	much	much	ADV
ijassa-112	70	13	shorter	short	ADJ
ijassa-112	70	14	periods	period	NOUN
ijassa-112	70	15	of	of	ADP
ijassa-112	70	16	time	time	NOUN
ijassa-112	70	17	than	than	ADP
ijassa-112	70	18	those	those	PRON
ijassa-112	70	19	further	far	ADV
ijassa-112	70	20	from	from	ADP
ijassa-112	70	21	departure	departure	NOUN
ijassa-112	70	22	.	.	PUNCT
ijassa-112	71	1	for	for	ADP
ijassa-112	71	2	example	example	NOUN
ijassa-112	71	3	,	,	PUNCT
ijassa-112	71	4	the	the	DET
ijassa-112	71	5	reading	reading	NOUN
ijassa-112	71	6	period	period	NOUN
ijassa-112	71	7	immediately	immediately	ADV
ijassa-112	71	8	preceding	precede	VERB
ijassa-112	71	9	departure	departure	NOUN
ijassa-112	71	10	may	may	AUX
ijassa-112	71	11	cover	cover	VERB
ijassa-112	71	12	1	1	NUM
ijassa-112	71	13	day	day	NOUN
ijassa-112	71	14	whereas	whereas	SCONJ
ijassa-112	71	15	the	the	DET
ijassa-112	71	16	reading	reading	NOUN
ijassa-112	71	17	period	period	NOUN
ijassa-112	71	18	1	1	NUM
ijassa-112	71	19	-	-	PUNCT
ijassa-112	71	20	month	month	NOUN
ijassa-112	71	21	from	from	ADP
ijassa-112	71	22	departure	departure	NOUN
ijassa-112	71	23	may	may	AUX
ijassa-112	71	24	cover	cover	VERB
ijassa-112	71	25	1	1	NUM
ijassa-112	71	26	week	week	NOUN
ijassa-112	71	27	.	.	PUNCT
ijassa-112	72	1	let	let	VERB
ijassa-112	72	2	us	we	PRON
ijassa-112	72	3	suppose	suppose	VERB
ijassa-112	72	4	that	that	SCONJ
ijassa-112	72	5	the	the	DET
ijassa-112	72	6	cumulative	cumulative	ADJ
ijassa-112	72	7	passenger	passenger	NOUN
ijassa-112	72	8	demand	demand	NOUN
ijassa-112	72	9	for	for	ADP
ijassa-112	72	10	the	the	DET
ijassa-112	72	11	high	high	ADJ
ijassa-112	72	12	fare	fare	NOUN
ijassa-112	72	13	class	class	NOUN
ijassa-112	72	14	at	at	ADP
ijassa-112	72	15	the	the	DET
ijassa-112	72	16	kth	kth	PROPN
ijassa-112	72	17	reading	reading	NOUN
ijassa-112	72	18	date	date	NOUN
ijassa-112	72	19	(	(	PUNCT
ijassa-112	72	20	time	time	NOUN
ijassa-112	72	21	τk	τk	ADP
ijassa-112	72	22	,	,	PUNCT
ijassa-112	72	23	1	1	NUM
ijassa-112	72	24	≤	≤	NUM
ijassa-112	72	25	k	k	X
ijassa-112	72	26	≤	≤	NUM
ijassa-112	72	27	m	m	VERB
ijassa-112	72	28	)	)	PUNCT
ijassa-112	72	29	is	be	AUX
ijassa-112	72	30	y1k	y1k	PROPN
ijassa-112	72	31	representing	represent	VERB
ijassa-112	72	32	the	the	DET
ijassa-112	72	33	kth	kth	PROPN
ijassa-112	72	34	order	order	NOUN
ijassa-112	72	35	statistic	statistic	NOUN
ijassa-112	72	36	from	from	ADP
ijassa-112	72	37	the	the	DET
ijassa-112	72	38	underlying	underlie	VERB
ijassa-112	72	39	distribution	distribution	NOUN
ijassa-112	72	40	with	with	ADP
ijassa-112	72	41	the	the	DET
ijassa-112	72	42	probability	probability	NOUN
ijassa-112	72	43	distribution	distribution	NOUN
ijassa-112	72	44	function	function	NOUN
ijassa-112	72	45	gθ(y1k	gθ(y1k	PROPN
ijassa-112	72	46	)	)	PUNCT
ijassa-112	72	47	,	,	PUNCT
ijassa-112	72	48	where	where	SCONJ
ijassa-112	72	49	θ	θ	PROPN
ijassa-112	72	50	is	be	AUX
ijassa-112	72	51	a	a	DET
ijassa-112	72	52	parameter	parameter	NOUN
ijassa-112	72	53	(	(	PUNCT
ijassa-112	72	54	in	in	ADP
ijassa-112	72	55	general	general	ADJ
ijassa-112	72	56	,	,	PUNCT
ijassa-112	72	57	vector	vector	NOUN
ijassa-112	72	58	)	)	PUNCT
ijassa-112	72	59	.	.	PUNCT
ijassa-112	73	1	in	in	ADP
ijassa-112	73	2	other	other	ADJ
ijassa-112	73	3	words	word	NOUN
ijassa-112	73	4	,	,	PUNCT
ijassa-112	73	5	y1k	y1k	PROPN
ijassa-112	73	6	represents	represent	VERB
ijassa-112	73	7	the	the	DET
ijassa-112	73	8	number	number	NOUN
ijassa-112	73	9	of	of	ADP
ijassa-112	73	10	seats	seat	NOUN
ijassa-112	73	11	sold	sell	VERB
ijassa-112	73	12	for	for	ADP
ijassa-112	73	13	the	the	DET
ijassa-112	73	14	customers	customer	NOUN
ijassa-112	73	15	of	of	ADP
ijassa-112	73	16	the	the	DET
ijassa-112	73	17	high	high	ADJ
ijassa-112	73	18	fare	fare	NOUN
ijassa-112	73	19	class	class	NOUN
ijassa-112	73	20	at	at	ADP
ijassa-112	73	21	the	the	DET
ijassa-112	73	22	kth	kth	PROPN
ijassa-112	73	23	reading	reading	NOUN
ijassa-112	73	24	date	date	NOUN
ijassa-112	73	25	.	.	PUNCT
ijassa-112	74	1	we	we	PRON
ijassa-112	74	2	assume	assume	VERB
ijassa-112	74	3	that	that	SCONJ
ijassa-112	74	4	the	the	DET
ijassa-112	74	5	cumulative	cumulative	ADJ
ijassa-112	74	6	passenger	passenger	NOUN
ijassa-112	74	7	demands	demand	NOUN
ijassa-112	74	8	for	for	ADP
ijassa-112	74	9	the	the	DET
ijassa-112	74	10	high	high	ADJ
ijassa-112	74	11	and	and	CCONJ
ijassa-112	74	12	low	low	ADJ
ijassa-112	74	13	fare	fare	NOUN
ijassa-112	74	14	classes	class	NOUN
ijassa-112	74	15	are	be	AUX
ijassa-112	74	16	stochastically	stochastically	ADV
ijassa-112	74	17	independent	independent	ADJ
ijassa-112	74	18	.	.	PUNCT
ijassa-112	75	1	each	each	DET
ijassa-112	75	2	booking	booking	NOUN
ijassa-112	75	3	of	of	ADP
ijassa-112	75	4	a	a	DET
ijassa-112	75	5	seat	seat	NOUN
ijassa-112	75	6	of	of	ADP
ijassa-112	75	7	the	the	DET
ijassa-112	75	8	high	high	ADJ
ijassa-112	75	9	fare	fare	NOUN
ijassa-112	75	10	class	class	NOUN
ijassa-112	75	11	generates	generate	VERB
ijassa-112	75	12	average	average	ADJ
ijassa-112	75	13	revenue	revenue	NOUN
ijassa-112	75	14	of	of	ADP
ijassa-112	75	15	c1	c1	PROPN
ijassa-112	75	16	.	.	PUNCT
ijassa-112	76	1	each	each	DET
ijassa-112	76	2	booking	booking	NOUN
ijassa-112	76	3	of	of	ADP
ijassa-112	76	4	a	a	DET
ijassa-112	76	5	seat	seat	NOUN
ijassa-112	76	6	of	of	ADP
ijassa-112	76	7	the	the	DET
ijassa-112	76	8	low	low	ADJ
ijassa-112	76	9	fare	fare	NOUN
ijassa-112	76	10	class	class	NOUN
ijassa-112	76	11	generates	generate	VERB
ijassa-112	76	12	average	average	ADJ
ijassa-112	76	13	revenue	revenue	NOUN
ijassa-112	76	14	of	of	ADP
ijassa-112	76	15	c2	c2	PROPN
ijassa-112	76	16	,	,	PUNCT
ijassa-112	76	17	where	where	SCONJ
ijassa-112	76	18	c2	c2	PROPN
ijassa-112	76	19	<	<	X
ijassa-112	76	20	c1.let	c1.let	PROPN
ijassa-112	76	21	µ1k	µ1k	PART
ijassa-112	76	22	be	be	AUX
ijassa-112	76	23	an	an	DET
ijassa-112	76	24	individual	individual	ADJ
ijassa-112	76	25	protection	protection	NOUN
ijassa-112	76	26	level	level	NOUN
ijassa-112	76	27	for	for	ADP
ijassa-112	76	28	the	the	DET
ijassa-112	76	29	high	high	ADJ
ijassa-112	76	30	fare	fare	NOUN
ijassa-112	76	31	class	class	NOUN
ijassa-112	76	32	at	at	ADP
ijassa-112	76	33	time	time	NOUN
ijassa-112	76	34	τk	τk	SCONJ
ijassa-112	76	35	(	(	PUNCT
ijassa-112	76	36	the	the	DET
ijassa-112	76	37	kth	kth	PROPN
ijassa-112	76	38	advances	advance	VERB
ijassa-112	76	39	in	in	ADP
ijassa-112	76	40	systems	system	NOUN
ijassa-112	76	41	science	science	NOUN
ijassa-112	76	42	and	and	CCONJ
ijassa-112	76	43	applications	application	NOUN
ijassa-112	76	44	(	(	PUNCT
ijassa-112	76	45	2012	2012	NUM
ijassa-112	76	46	)	)	PUNCT
ijassa-112	77	1	vol.12	vol.12	NOUN
ijassa-112	77	2	no.3	no.3	VERB
ijassa-112	77	3	277	277	NUM
ijassa-112	77	4	reading	reading	NOUN
ijassa-112	77	5	date).this	date).this	VERB
ijassa-112	77	6	many	many	ADJ
ijassa-112	77	7	seats	seat	NOUN
ijassa-112	77	8	are	be	AUX
ijassa-112	77	9	protected	protect	VERB
ijassa-112	77	10	for	for	ADP
ijassa-112	77	11	the	the	DET
ijassa-112	77	12	high	high	ADJ
ijassa-112	77	13	fare	fare	NOUN
ijassa-112	77	14	class	class	NOUN
ijassa-112	77	15	from	from	ADP
ijassa-112	77	16	the	the	DET
ijassa-112	77	17	low	low	ADJ
ijassa-112	77	18	fare	fare	NOUN
ijassa-112	77	19	class	class	NOUN
ijassa-112	77	20	.	.	PUNCT
ijassa-112	78	1	there	there	PRON
ijassa-112	78	2	is	be	VERB
ijassa-112	78	3	no	no	DET
ijassa-112	78	4	protection	protection	NOUN
ijassa-112	78	5	level	level	NOUN
ijassa-112	78	6	for	for	ADP
ijassa-112	78	7	the	the	DET
ijassa-112	78	8	low	low	ADJ
ijassa-112	78	9	fare	fare	NOUN
ijassa-112	78	10	class;µ2k	class;µ2k	NOUN
ijassa-112	78	11	is	be	AUX
ijassa-112	78	12	the	the	DET
ijassa-112	78	13	booking	booking	NOUN
ijassa-112	78	14	limit	limit	NOUN
ijassa-112	78	15	for	for	ADP
ijassa-112	78	16	the	the	DET
ijassa-112	78	17	low	low	ADJ
ijassa-112	78	18	fare	fare	NOUN
ijassa-112	78	19	class	class	NOUN
ijassa-112	78	20	at	at	ADP
ijassa-112	78	21	time	time	NOUN
ijassa-112	78	22	τk	τk	ADP
ijassa-112	78	23	;	;	PUNCT
ijassa-112	78	24	the	the	DET
ijassa-112	78	25	low	low	ADJ
ijassa-112	78	26	fare	fare	NOUN
ijassa-112	78	27	class	class	NOUN
ijassa-112	78	28	is	be	AUX
ijassa-112	78	29	open	open	ADJ
ijassa-112	78	30	as	as	ADV
ijassa-112	78	31	long	long	ADV
ijassa-112	78	32	as	as	SCONJ
ijassa-112	78	33	the	the	DET
ijassa-112	78	34	number	number	NOUN
ijassa-112	78	35	of	of	ADP
ijassa-112	78	36	bookings	booking	NOUN
ijassa-112	78	37	in	in	ADP
ijassa-112	78	38	this	this	DET
ijassa-112	78	39	class	class	NOUN
ijassa-112	78	40	remains	remain	VERB
ijassa-112	78	41	less	less	ADJ
ijassa-112	78	42	than	than	ADP
ijassa-112	78	43	this	this	DET
ijassa-112	78	44	limit	limit	NOUN
ijassa-112	78	45	.	.	PUNCT
ijassa-112	79	1	thus,µ1k	thus,µ1k	NOUN
ijassa-112	80	1	+	+	CCONJ
ijassa-112	80	2	µ2k	µ2k	NOUN
ijassa-112	80	3	is	be	AUX
ijassa-112	80	4	the	the	DET
ijassa-112	80	5	booking	booking	NOUN
ijassa-112	80	6	limit	limit	NOUN
ijassa-112	80	7	for	for	ADP
ijassa-112	80	8	the	the	DET
ijassa-112	80	9	high	high	ADJ
ijassa-112	80	10	fare	fare	NOUN
ijassa-112	80	11	class	class	NOUN
ijassa-112	80	12	at	at	ADP
ijassa-112	80	13	time	time	NOUN
ijassa-112	80	14	τk	τk	ADP
ijassa-112	80	15	the	the	DET
ijassa-112	80	16	high	high	ADJ
ijassa-112	80	17	fare	fare	NOUN
ijassa-112	80	18	class	class	NOUN
ijassa-112	80	19	is	be	AUX
ijassa-112	80	20	open	open	ADJ
ijassa-112	80	21	as	as	ADV
ijassa-112	80	22	long	long	ADV
ijassa-112	80	23	as	as	SCONJ
ijassa-112	80	24	the	the	DET
ijassa-112	80	25	number	number	NOUN
ijassa-112	80	26	of	of	ADP
ijassa-112	80	27	bookings	booking	NOUN
ijassa-112	80	28	in	in	ADP
ijassa-112	80	29	this	this	DET
ijassa-112	80	30	and	and	CCONJ
ijassa-112	80	31	low	low	ADJ
ijassa-112	80	32	classes	class	NOUN
ijassa-112	80	33	remain	remain	VERB
ijassa-112	80	34	less	less	ADJ
ijassa-112	80	35	than	than	ADP
ijassa-112	80	36	this	this	DET
ijassa-112	80	37	limit	limit	NOUN
ijassa-112	80	38	.	.	PUNCT
ijassa-112	81	1	the	the	DET
ijassa-112	81	2	maximum	maximum	ADJ
ijassa-112	81	3	number	number	NOUN
ijassa-112	81	4	of	of	ADP
ijassa-112	81	5	seats	seat	NOUN
ijassa-112	81	6	that	that	PRON
ijassa-112	81	7	may	may	AUX
ijassa-112	81	8	be	be	AUX
ijassa-112	81	9	booked	book	VERB
ijassa-112	81	10	by	by	ADP
ijassa-112	81	11	fare	fare	NOUN
ijassa-112	81	12	classes	class	NOUN
ijassa-112	81	13	in	in	ADP
ijassa-112	81	14	the	the	DET
ijassa-112	81	15	next	next	ADJ
ijassa-112	81	16	at	at	ADP
ijassa-112	81	17	time	time	NOUN
ijassa-112	81	18	τk	τk	ADP
ijassa-112	81	19	prior	prior	ADV
ijassa-112	81	20	to	to	ADP
ijassa-112	81	21	flight	flight	NOUN
ijassa-112	81	22	departure	departure	NOUN
ijassa-112	81	23	is	be	AUX
ijassa-112	81	24	the	the	DET
ijassa-112	81	25	number	number	NOUN
ijassa-112	81	26	of	of	ADP
ijassa-112	81	27	unsold	unsold	ADJ
ijassa-112	81	28	seats	seat	NOUN
ijassa-112	81	29	µ	µ	PRON
ijassa-112	81	30	◦	◦	NOUN
ijassa-112	81	31	k.	k.	NOUN
ijassa-112	81	32	under	under	ADP
ijassa-112	81	33	the	the	DET
ijassa-112	81	34	complete	complete	ADJ
ijassa-112	81	35	information	information	NOUN
ijassa-112	81	36	,	,	PUNCT
ijassa-112	81	37	the	the	DET
ijassa-112	81	38	dynamic	dynamic	ADJ
ijassa-112	81	39	airline	airline	NOUN
ijassa-112	81	40	booking	booking	NOUN
ijassa-112	81	41	policy	policy	NOUN
ijassa-112	81	42	is	be	AUX
ijassa-112	81	43	given	give	VERB
ijassa-112	81	44	by	by	ADP
ijassa-112	81	45	µ1k	µ1k	PUNCT
ijassa-112	81	46	=	=	PUNCT
ijassa-112	81	47	arg	arg	X
ijassa-112	81	48	(	(	PUNCT
ijassa-112	81	49	ḡθ(µ1k|y1k	ḡθ(µ1k|y1k	PROPN
ijassa-112	81	50	)	)	PUNCT
ijassa-112	81	51	=	=	SYM
ijassa-112	81	52	γ	γ	PROPN
ijassa-112	81	53	)	)	PUNCT
ijassa-112	81	54	,	,	PUNCT
ijassa-112	81	55	k	k	X
ijassa-112	81	56	=	=	SYM
ijassa-112	81	57	1	1	NUM
ijassa-112	81	58	,	,	PUNCT
ijassa-112	81	59	2	2	NUM
ijassa-112	81	60	,	,	PUNCT
ijassa-112	81	61	.	.	PUNCT
ijassa-112	81	62	.	.	PUNCT
ijassa-112	81	63	.	.	PUNCT
ijassa-112	82	1	,	,	PUNCT
ijassa-112	82	2	m−	m−	PROPN
ijassa-112	82	3	1	1	NUM
ijassa-112	82	4	,	,	PUNCT
ijassa-112	82	5	(	(	PUNCT
ijassa-112	82	6	10	10	NUM
ijassa-112	82	7	)	)	PUNCT
ijassa-112	82	8	where	where	SCONJ
ijassa-112	82	9	ḡθ(µ1k|y1k	ḡθ(µ1k|y1k	NOUN
ijassa-112	82	10	)	)	PUNCT
ijassa-112	82	11	=	=	SYM
ijassa-112	82	12	1−gθ(µ1k|y1k	1−gθ(µ1k|y1k	NOUN
ijassa-112	82	13	)	)	PUNCT
ijassa-112	82	14	,	,	PUNCT
ijassa-112	82	15	(	(	PUNCT
ijassa-112	82	16	11	11	X
ijassa-112	82	17	)	)	PUNCT
ijassa-112	82	18	gθ(µ1k|y1k	gθ(µ1k|y1k	NOUN
ijassa-112	82	19	)	)	PUNCT
ijassa-112	82	20	represents	represent	VERB
ijassa-112	82	21	the	the	DET
ijassa-112	82	22	conditional	conditional	ADJ
ijassa-112	82	23	probability	probability	NOUN
ijassa-112	82	24	distribution	distribution	NOUN
ijassa-112	82	25	function	function	NOUN
ijassa-112	82	26	of	of	ADP
ijassa-112	82	27	the	the	DET
ijassa-112	82	28	mth	mth	NOUN
ijassa-112	82	29	order	order	NOUN
ijassa-112	82	30	statistic	statistic	PROPN
ijassa-112	82	31	y1	y1	X
ijassa-112	82	32	m	m	NOUN
ijassa-112	82	33	.	.	PUNCT
ijassa-112	83	1	the	the	DET
ijassa-112	83	2	number	number	NOUN
ijassa-112	83	3	of	of	ADP
ijassa-112	83	4	unsold	unsold	ADJ
ijassa-112	83	5	seats	seat	NOUN
ijassa-112	83	6	protected	protect	VERB
ijassa-112	83	7	for	for	ADP
ijassa-112	83	8	the	the	DET
ijassa-112	83	9	high	high	ADJ
ijassa-112	83	10	fare	fare	NOUN
ijassa-112	83	11	class	class	NOUN
ijassa-112	83	12	from	from	ADP
ijassa-112	83	13	the	the	DET
ijassa-112	83	14	low	low	ADJ
ijassa-112	83	15	fare	fare	NOUN
ijassa-112	83	16	class	class	NOUN
ijassa-112	83	17	in	in	ADP
ijassa-112	83	18	the	the	DET
ijassa-112	83	19	next	next	ADJ
ijassa-112	83	20	at	at	ADP
ijassa-112	83	21	time	time	NOUN
ijassa-112	83	22	τk	τk	ADP
ijassa-112	83	23	prior	prior	ADV
ijassa-112	83	24	to	to	ADP
ijassa-112	83	25	flight	flight	NOUN
ijassa-112	83	26	departure	departure	NOUN
ijassa-112	83	27	is	be	AUX
ijassa-112	83	28	the	the	DET
ijassa-112	83	29	number	number	NOUN
ijassa-112	83	30	of	of	ADP
ijassa-112	83	31	unsold	unsold	ADJ
ijassa-112	83	32	seats,µ	seats,µ	NUM
ijassa-112	83	33	◦	◦	NOUN
ijassa-112	83	34	1k	1k	NOUN
ijassa-112	83	35	,	,	PUNCT
ijassa-112	83	36	which	which	PRON
ijassa-112	83	37	is	be	AUX
ijassa-112	83	38	given	give	VERB
ijassa-112	83	39	by	by	ADP
ijassa-112	83	40	µ	µ	NUM
ijassa-112	83	41	◦	◦	NOUN
ijassa-112	83	42	1k	1k	NUM
ijassa-112	83	43	=	=	SYM
ijassa-112	83	44	min(µ	min(µ	PROPN
ijassa-112	83	45	◦	◦	NOUN
ijassa-112	83	46	k	k	NOUN
ijassa-112	83	47	,	,	PUNCT
ijassa-112	83	48	µ1k	µ1k	SYM
ijassa-112	83	49	−	−	PROPN
ijassa-112	83	50	y1k	y1k	NOUN
ijassa-112	83	51	)	)	PUNCT
ijassa-112	83	52	.	.	PUNCT
ijassa-112	84	1	(	(	PUNCT
ijassa-112	84	2	12	12	NUM
ijassa-112	84	3	)	)	PUNCT
ijassa-112	84	4	4.3	4.3	NUM
ijassa-112	84	5	dynamic	dynamic	ADJ
ijassa-112	84	6	unbiased	unbiased	ADJ
ijassa-112	84	7	airline	airline	NOUN
ijassa-112	84	8	booking	booking	NOUN
ijassa-112	84	9	policy	policy	NOUN
ijassa-112	84	10	under	under	ADP
ijassa-112	84	11	parametric	parametric	ADJ
ijassa-112	84	12	uncertainty	uncertainty	NOUN
ijassa-112	84	13	under	under	ADP
ijassa-112	84	14	the	the	DET
ijassa-112	84	15	parametric	parametric	ADJ
ijassa-112	84	16	uncertainty	uncertainty	NOUN
ijassa-112	84	17	,	,	PUNCT
ijassa-112	84	18	the	the	DET
ijassa-112	84	19	dynamic	dynamic	ADJ
ijassa-112	84	20	unbiased	unbiased	ADJ
ijassa-112	84	21	airline	airline	NOUN
ijassa-112	84	22	booking	booking	NOUN
ijassa-112	84	23	policy	policy	NOUN
ijassa-112	84	24	is	be	AUX
ijassa-112	84	25	given	give	VERB
ijassa-112	84	26	by	by	ADP
ijassa-112	84	27	µunb	µunb	NOUN
ijassa-112	84	28	1k	1k	NUM
ijassa-112	84	29	=	=	PUNCT
ijassa-112	84	30	arg	arg	NOUN
ijassa-112	84	31	(	(	PUNCT
ijassa-112	84	32	eθ{ḡθ(µ1k|y1k	eθ{ḡθ(µ1k|y1k	NOUN
ijassa-112	84	33	)	)	PUNCT
ijassa-112	84	34	}	}	PUNCT
ijassa-112	84	35	=	=	SYM
ijassa-112	84	36	γ	γ	X
ijassa-112	84	37	)	)	PUNCT
ijassa-112	84	38	,	,	PUNCT
ijassa-112	84	39	k	k	X
ijassa-112	85	1	=	=	SYM
ijassa-112	85	2	1	1	NUM
ijassa-112	85	3	,	,	PUNCT
ijassa-112	85	4	2	2	NUM
ijassa-112	85	5	,	,	PUNCT
ijassa-112	85	6	.	.	PUNCT
ijassa-112	85	7	.	.	PUNCT
ijassa-112	86	1	.	.	PUNCT
ijassa-112	87	1	,	,	PUNCT
ijassa-112	87	2	m−	m−	PROPN
ijassa-112	87	3	1	1	NUM
ijassa-112	87	4	,	,	PUNCT
ijassa-112	87	5	(	(	PUNCT
ijassa-112	87	6	13	13	NUM
ijassa-112	87	7	)	)	PUNCT
ijassa-112	87	8	where	where	SCONJ
ijassa-112	87	9	µ1k	µ1k	SYM
ijassa-112	87	10	≡	≡	PROPN
ijassa-112	87	11	µ1k(θ̂),θ̂	µ1k(θ̂),θ̂	PROPN
ijassa-112	87	12	represents	represent	VERB
ijassa-112	87	13	either	either	CCONJ
ijassa-112	87	14	the	the	DET
ijassa-112	87	15	maximum	maximum	ADJ
ijassa-112	87	16	likelihood	likelihood	NOUN
ijassa-112	87	17	estimator	estimator	NOUN
ijassa-112	87	18	of	of	ADP
ijassa-112	87	19	θ	θ	PROPN
ijassa-112	87	20	or	or	CCONJ
ijassa-112	87	21	sufficient	sufficient	ADJ
ijassa-112	87	22	statistic	statistic	NOUN
ijassa-112	87	23	s	s	NOUN
ijassa-112	87	24	for	for	ADP
ijassa-112	87	25	θ	θ	PROPN
ijassa-112	87	26	,	,	PUNCT
ijassa-112	87	27	i.e.	i.e.	X
ijassa-112	87	28	,µ1k	,µ1k	PUNCT
ijassa-112	87	29	≡	≡	ADJ
ijassa-112	87	30	µ1k(s).the	µ1k(s).the	DET
ijassa-112	87	31	number	number	NOUN
ijassa-112	87	32	of	of	ADP
ijassa-112	87	33	unsold	unsold	ADJ
ijassa-112	87	34	seats	seat	NOUN
ijassa-112	87	35	protected	protect	VERB
ijassa-112	87	36	for	for	ADP
ijassa-112	87	37	the	the	DET
ijassa-112	87	38	high	high	ADJ
ijassa-112	87	39	fare	fare	NOUN
ijassa-112	87	40	class	class	NOUN
ijassa-112	87	41	from	from	ADP
ijassa-112	87	42	the	the	DET
ijassa-112	87	43	low	low	ADJ
ijassa-112	87	44	fare	fare	NOUN
ijassa-112	87	45	class	class	NOUN
ijassa-112	87	46	in	in	ADP
ijassa-112	87	47	the	the	DET
ijassa-112	87	48	next	next	ADJ
ijassa-112	87	49	at	at	ADP
ijassa-112	87	50	time	time	NOUN
ijassa-112	87	51	τk	τk	ADP
ijassa-112	87	52	prior	prior	ADV
ijassa-112	87	53	to	to	ADP
ijassa-112	87	54	flight	flight	NOUN
ijassa-112	87	55	departure	departure	NOUN
ijassa-112	87	56	is	be	AUX
ijassa-112	87	57	the	the	DET
ijassa-112	87	58	number	number	NOUN
ijassa-112	87	59	of	of	ADP
ijassa-112	87	60	unsold	unsold	ADJ
ijassa-112	87	61	seats	seat	NOUN
ijassa-112	87	62	µ	µ	PRON
ijassa-112	87	63	◦	◦	NOUN
ijassa-112	87	64	1k	1k	NOUN
ijassa-112	87	65	,	,	PUNCT
ijassa-112	87	66	which	which	PRON
ijassa-112	87	67	is	be	AUX
ijassa-112	87	68	given	give	VERB
ijassa-112	87	69	by	by	ADP
ijassa-112	87	70	µ	µ	PRON
ijassa-112	87	71	◦	◦	NOUN
ijassa-112	87	72	(	(	PUNCT
ijassa-112	87	73	unb	unb	NOUN
ijassa-112	87	74	)	)	PUNCT
ijassa-112	87	75	1k	1k	NOUN
ijassa-112	87	76	=	=	SYM
ijassa-112	87	77	min(µ	min(µ	PROPN
ijassa-112	87	78	◦	◦	NOUN
ijassa-112	87	79	k	k	NOUN
ijassa-112	87	80	,	,	PUNCT
ijassa-112	87	81	µ	µ	X
ijassa-112	87	82	unb	unb	NOUN
ijassa-112	87	83	1k	1k	PROPN
ijassa-112	87	84	−	−	PROPN
ijassa-112	87	85	y1k	y1k	NOUN
ijassa-112	87	86	)	)	PUNCT
ijassa-112	87	87	.	.	PUNCT
ijassa-112	88	1	(	(	PUNCT
ijassa-112	88	2	14	14	NUM
ijassa-112	88	3	)	)	SYM
ijassa-112	88	4	5	5	NUM
ijassa-112	88	5	mathematical	mathematical	ADJ
ijassa-112	88	6	preliminaries	preliminary	NOUN
ijassa-112	88	7	theorem	theorem	VERB
ijassa-112	88	8	1	1	NUM
ijassa-112	88	9	let	let	VERB
ijassa-112	88	10	x1	x1	NOUN
ijassa-112	88	11	≤	≤	NUM
ijassa-112	88	12	.	.	PUNCT
ijassa-112	88	13	.	.	PUNCT
ijassa-112	88	14	.	.	PUNCT
ijassa-112	89	1	≤	≤	NUM
ijassa-112	89	2	xk	xk	PROPN
ijassa-112	89	3	be	be	AUX
ijassa-112	89	4	the	the	DET
ijassa-112	89	5	first	first	ADJ
ijassa-112	89	6	k	k	PROPN
ijassa-112	89	7	ordered	order	VERB
ijassa-112	89	8	observations	observation	NOUN
ijassa-112	89	9	(	(	PUNCT
ijassa-112	89	10	order	order	NOUN
ijassa-112	89	11	statistics	statistic	NOUN
ijassa-112	89	12	)	)	PUNCT
ijassa-112	89	13	in	in	ADP
ijassa-112	89	14	a	a	DET
ijassa-112	89	15	sample	sample	NOUN
ijassa-112	89	16	of	of	ADP
ijassa-112	89	17	size	size	NOUN
ijassa-112	89	18	m	m	VERB
ijassa-112	89	19	from	from	ADP
ijassa-112	89	20	a	a	DET
ijassa-112	89	21	continuous	continuous	ADJ
ijassa-112	89	22	distribution	distribution	NOUN
ijassa-112	89	23	with	with	ADP
ijassa-112	89	24	some	some	DET
ijassa-112	89	25	probability	probability	NOUN
ijassa-112	89	26	density	density	NOUN
ijassa-112	89	27	function	function	NOUN
ijassa-112	89	28	fθ(x	fθ(x	PUNCT
ijassa-112	89	29	)	)	PUNCT
ijassa-112	89	30	and	and	CCONJ
ijassa-112	89	31	distribution	distribution	NOUN
ijassa-112	89	32	function	function	NOUN
ijassa-112	89	33	fθ(x	fθ(x	PUNCT
ijassa-112	89	34	)	)	PUNCT
ijassa-112	89	35	where	where	SCONJ
ijassa-112	89	36	θ	θ	PROPN
ijassa-112	89	37	is	be	AUX
ijassa-112	89	38	a	a	DET
ijassa-112	89	39	parameter	parameter	NOUN
ijassa-112	89	40	(	(	PUNCT
ijassa-112	89	41	in	in	ADP
ijassa-112	89	42	general	general	ADJ
ijassa-112	89	43	,	,	PUNCT
ijassa-112	89	44	vector	vector	NOUN
ijassa-112	89	45	)	)	PUNCT
ijassa-112	89	46	.	.	PUNCT
ijassa-112	90	1	then	then	ADV
ijassa-112	90	2	the	the	DET
ijassa-112	90	3	joint	joint	ADJ
ijassa-112	90	4	probability	probability	NOUN
ijassa-112	90	5	density	density	NOUN
ijassa-112	90	6	function	function	NOUN
ijassa-112	90	7	of	of	ADP
ijassa-112	90	8	x1	x1	ADJ
ijassa-112	90	9	≤	≤	PROPN
ijassa-112	90	10	.	.	PUNCT
ijassa-112	90	11	.	.	PUNCT
ijassa-112	90	12	.	.	PUNCT
ijassa-112	91	1	≤	≤	NUM
ijassa-112	91	2	xk	xk	PROPN
ijassa-112	91	3	and	and	CCONJ
ijassa-112	91	4	the	the	DET
ijassa-112	91	5	lth	lth	NOUN
ijassa-112	91	6	order	order	NOUN
ijassa-112	91	7	statistics	statistic	NOUN
ijassa-112	91	8	xl(1	xl(1	PROPN
ijassa-112	91	9	≤	≤	ADV
ijassa-112	91	10	k	k	X
ijassa-112	91	11	≤	≤	NUM
ijassa-112	91	12	l	l	NOUN
ijassa-112	91	13	≤	≤	NUM
ijassa-112	91	14	m	m	VERB
ijassa-112	91	15	)	)	PUNCT
ijassa-112	91	16	is	be	AUX
ijassa-112	91	17	given	give	VERB
ijassa-112	91	18	by	by	ADP
ijassa-112	91	19	gθ(x1	gθ(x1	NOUN
ijassa-112	91	20	,	,	PUNCT
ijassa-112	91	21	.	.	PUNCT
ijassa-112	91	22	.	.	PUNCT
ijassa-112	91	23	.	.	PUNCT
ijassa-112	92	1	,	,	PUNCT
ijassa-112	92	2	xk	xk	PROPN
ijassa-112	92	3	,	,	PUNCT
ijassa-112	92	4	xl	xl	PROPN
ijassa-112	92	5	)	)	PUNCT
ijassa-112	92	6	=	=	SYM
ijassa-112	92	7	gθ(x1	gθ(x1	NOUN
ijassa-112	92	8	,	,	PUNCT
ijassa-112	92	9	.	.	PUNCT
ijassa-112	92	10	.	.	PUNCT
ijassa-112	93	1	.	.	PUNCT
ijassa-112	94	1	,	,	PUNCT
ijassa-112	94	2	xk)gθ(xl|xk	xk)gθ(xl|xk	PROPN
ijassa-112	94	3	)	)	PUNCT
ijassa-112	94	4	,	,	PUNCT
ijassa-112	94	5	(	(	PUNCT
ijassa-112	94	6	15	15	X
ijassa-112	94	7	)	)	PUNCT
ijassa-112	94	8	278	278	NUM
ijassa-112	94	9	nicholas	nicholas	PROPN
ijassa-112	94	10	a.	a.	PROPN
ijassa-112	94	11	nechval	nechval	PROPN
ijassa-112	94	12	:	:	PUNCT
ijassa-112	94	13	improved	improved	ADJ
ijassa-112	94	14	airline	airline	NOUN
ijassa-112	94	15	seat	seat	NOUN
ijassa-112	94	16	inventory	inventory	NOUN
ijassa-112	94	17	control	control	NOUN
ijassa-112	94	18	policies	policy	NOUN
ijassa-112	94	19	under	under	ADP
ijassa-112	94	20	parametric	parametric	NOUN
ijassa-112	94	21	...	...	PUNCT
ijassa-112	94	22	where	where	SCONJ
ijassa-112	94	23	gθ(x1	gθ(x1	NOUN
ijassa-112	94	24	,	,	PUNCT
ijassa-112	94	25	.	.	PUNCT
ijassa-112	94	26	.	.	PUNCT
ijassa-112	94	27	.	.	PUNCT
ijassa-112	95	1	,	,	PUNCT
ijassa-112	95	2	xk	xk	PROPN
ijassa-112	95	3	)	)	PUNCT
ijassa-112	95	4	=	=	PUNCT
ijassa-112	95	5	m	m	PROPN
ijassa-112	95	6	!	!	PUNCT
ijassa-112	96	1	(	(	PUNCT
ijassa-112	96	2	m−	m−	PROPN
ijassa-112	96	3	k	k	NOUN
ijassa-112	96	4	)	)	PUNCT
ijassa-112	96	5	!	!	PUNCT
ijassa-112	97	1	k∏	k∏	PROPN
ijassa-112	97	2	i=1	i=1	PROPN
ijassa-112	97	3	fθ(xi	fθ(xi	PROPN
ijassa-112	97	4	)	)	PUNCT
ijassa-112	98	1	[	[	PUNCT
ijassa-112	98	2	1−	1−	NUM
ijassa-112	98	3	fθ(xk	fθ(xk	NOUN
ijassa-112	98	4	)	)	PUNCT
ijassa-112	99	1	]	]	PUNCT
ijassa-112	99	2	m−k	m−k	NOUN
ijassa-112	99	3	,	,	PUNCT
ijassa-112	99	4	(	(	PUNCT
ijassa-112	99	5	16	16	NUM
ijassa-112	99	6	)	)	PUNCT
ijassa-112	99	7	gθ(xl|xk	gθ(xl|xk	PROPN
ijassa-112	99	8	)	)	PUNCT
ijassa-112	99	9	=	=	PUNCT
ijassa-112	99	10	(	(	PUNCT
ijassa-112	99	11	m−	m−	PROPN
ijassa-112	99	12	k	k	PROPN
ijassa-112	99	13	)	)	PUNCT
ijassa-112	99	14	!	!	PUNCT
ijassa-112	100	1	(	(	PUNCT
ijassa-112	100	2	l	l	NOUN
ijassa-112	100	3	−	−	PROPN
ijassa-112	101	1	k	k	PROPN
ijassa-112	101	2	−	−	PROPN
ijassa-112	101	3	1)!(m−	1)!(m−	NUM
ijassa-112	101	4	l	l	NOUN
ijassa-112	101	5	)	)	PUNCT
ijassa-112	101	6	!	!	PUNCT
ijassa-112	102	1	[	[	X
ijassa-112	102	2	fθ(xl)−	fθ(xl)−	PROPN
ijassa-112	102	3	fθ(xk	fθ(xk	PROPN
ijassa-112	102	4	)	)	PUNCT
ijassa-112	102	5	1−	1−	NUM
ijassa-112	102	6	fθ(xk	fθ(xk	PROPN
ijassa-112	102	7	)	)	PUNCT
ijassa-112	102	8	]	]	X
ijassa-112	102	9	l−k−1	l−k−1	PROPN
ijassa-112	102	10	[	[	PUNCT
ijassa-112	102	11	1−	1−	NUM
ijassa-112	102	12	fθ(xl)−	fθ(xl)−	PROPN
ijassa-112	102	13	fθ(xk	fθ(xk	PROPN
ijassa-112	102	14	)	)	PUNCT
ijassa-112	102	15	1−	1−	NUM
ijassa-112	102	16	fθ(xk	fθ(xk	PROPN
ijassa-112	102	17	)	)	PUNCT
ijassa-112	102	18	]	]	PUNCT
ijassa-112	102	19	m−l	m−l	PROPN
ijassa-112	102	20	fθ(xl	fθ(xl	VERB
ijassa-112	102	21	)	)	PUNCT
ijassa-112	102	22	1−	1−	NUM
ijassa-112	102	23	fθ(xk	fθ(xk	PROPN
ijassa-112	102	24	)	)	PUNCT
ijassa-112	102	25	=	=	PUNCT
ijassa-112	102	26	(	(	PUNCT
ijassa-112	102	27	m−	m−	PROPN
ijassa-112	102	28	k	k	PROPN
ijassa-112	102	29	)	)	PUNCT
ijassa-112	102	30	!	!	PUNCT
ijassa-112	103	1	(	(	PUNCT
ijassa-112	103	2	l	l	NOUN
ijassa-112	103	3	−	−	PROPN
ijassa-112	104	1	k	k	PROPN
ijassa-112	104	2	−	−	PROPN
ijassa-112	104	3	1)!(m−	1)!(m−	NUM
ijassa-112	104	4	l	l	NOUN
ijassa-112	104	5	)	)	PUNCT
ijassa-112	104	6	!	!	PUNCT
ijassa-112	105	1	k−l−1∑	k−l−1∑	PROPN
ijassa-112	105	2	j=0	j=0	PROPN
ijassa-112	105	3	(	(	PUNCT
ijassa-112	105	4	l	l	NOUN
ijassa-112	105	5	−	−	PROPN
ijassa-112	106	1	k	k	NOUN
ijassa-112	107	1	−	−	PROPN
ijassa-112	107	2	1	1	NUM
ijassa-112	107	3	j	j	NOUN
ijassa-112	107	4	)	)	PUNCT
ijassa-112	107	5	(	(	PUNCT
ijassa-112	107	6	−1)j	−1)j	X
ijassa-112	107	7	[	[	PUNCT
ijassa-112	107	8	1−	1−	NUM
ijassa-112	107	9	fθ(xl	fθ(xl	NOUN
ijassa-112	107	10	)	)	PUNCT
ijassa-112	107	11	1−	1−	NUM
ijassa-112	107	12	fθ(xk	fθ(xk	PROPN
ijassa-112	107	13	)	)	PUNCT
ijassa-112	107	14	]	]	PUNCT
ijassa-112	107	15	m−l+j	m−l+j	ADJ
ijassa-112	107	16	fθ(xl	fθ(xl	VERB
ijassa-112	107	17	)	)	PUNCT
ijassa-112	107	18	1−	1−	NUM
ijassa-112	107	19	fθ(xk	fθ(xk	PROPN
ijassa-112	107	20	)	)	PUNCT
ijassa-112	107	21	=	=	PUNCT
ijassa-112	107	22	(	(	PUNCT
ijassa-112	107	23	m−	m−	PROPN
ijassa-112	107	24	k	k	PROPN
ijassa-112	107	25	)	)	PUNCT
ijassa-112	107	26	!	!	PUNCT
ijassa-112	108	1	(	(	PUNCT
ijassa-112	108	2	l	l	NOUN
ijassa-112	108	3	−	−	PROPN
ijassa-112	109	1	k	k	PROPN
ijassa-112	109	2	−	−	PROPN
ijassa-112	109	3	1)!(m−	1)!(m−	NUM
ijassa-112	109	4	l	l	NOUN
ijassa-112	109	5	)	)	PUNCT
ijassa-112	109	6	!	!	PUNCT
ijassa-112	110	1	m−l∑	m−l∑	PRON
ijassa-112	111	1	j=0	j=0	PROPN
ijassa-112	111	2	(	(	PUNCT
ijassa-112	111	3	m−	m−	PROPN
ijassa-112	111	4	l	l	PROPN
ijassa-112	111	5	j	j	PROPN
ijassa-112	111	6	)	)	PUNCT
ijassa-112	111	7	(	(	PUNCT
ijassa-112	111	8	−1)j	−1)j	X
ijassa-112	112	1	[	[	X
ijassa-112	112	2	fθ(xl)−	fθ(xl)−	PROPN
ijassa-112	112	3	fθ(xk	fθ(xk	PROPN
ijassa-112	112	4	)	)	PUNCT
ijassa-112	112	5	1−	1−	NUM
ijassa-112	112	6	fθ(xk	fθ(xk	PROPN
ijassa-112	112	7	)	)	PUNCT
ijassa-112	112	8	]	]	PUNCT
ijassa-112	112	9	l−k−1+j	l−k−1+j	PROPN
ijassa-112	112	10	fθ(xl	fθ(xl	VERB
ijassa-112	112	11	)	)	PUNCT
ijassa-112	112	12	1−	1−	NUM
ijassa-112	112	13	fθ(xk	fθ(xk	PROPN
ijassa-112	112	14	)	)	PUNCT
ijassa-112	112	15	(	(	PUNCT
ijassa-112	112	16	17	17	NUM
ijassa-112	112	17	)	)	PUNCT
ijassa-112	112	18	represents	represent	VERB
ijassa-112	112	19	the	the	DET
ijassa-112	112	20	conditional	conditional	ADJ
ijassa-112	112	21	probability	probability	NOUN
ijassa-112	112	22	density	density	NOUN
ijassa-112	112	23	function	function	NOUN
ijassa-112	112	24	of	of	ADP
ijassa-112	112	25	xl	xl	PROPN
ijassa-112	112	26	given	give	VERB
ijassa-112	112	27	xk	xk	PROPN
ijassa-112	112	28	=	=	PUNCT
ijassa-112	112	29	xk	xk	PROPN
ijassa-112	112	30	.	.	PUNCT
ijassa-112	112	31	proof	proof	NOUN
ijassa-112	112	32	.	.	PUNCT
ijassa-112	113	1	the	the	DET
ijassa-112	113	2	joint	joint	ADJ
ijassa-112	113	3	density	density	NOUN
ijassa-112	113	4	of	of	ADP
ijassa-112	113	5	x1	x1	ADJ
ijassa-112	113	6	≤	≤	NOUN
ijassa-112	113	7	.	.	PUNCT
ijassa-112	113	8	.	.	PUNCT
ijassa-112	113	9	.	.	PUNCT
ijassa-112	114	1	≤	≤	NUM
ijassa-112	114	2	xk	xk	PROPN
ijassa-112	114	3	and	and	CCONJ
ijassa-112	114	4	xl	xl	PROPN
ijassa-112	114	5	is	be	AUX
ijassa-112	114	6	given	give	VERB
ijassa-112	114	7	by	by	ADP
ijassa-112	114	8	gθ(x1	gθ(x1	NOUN
ijassa-112	114	9	,	,	PUNCT
ijassa-112	114	10	.	.	PUNCT
ijassa-112	114	11	.	.	PUNCT
ijassa-112	114	12	.	.	PUNCT
ijassa-112	115	1	,	,	PUNCT
ijassa-112	115	2	xk	xk	PROPN
ijassa-112	115	3	,	,	PUNCT
ijassa-112	115	4	xl	xl	PROPN
ijassa-112	115	5	)	)	PUNCT
ijassa-112	116	1	=	=	PUNCT
ijassa-112	116	2	m	m	PROPN
ijassa-112	116	3	!	!	PUNCT
ijassa-112	117	1	(	(	PUNCT
ijassa-112	117	2	l	l	NOUN
ijassa-112	117	3	−	−	PROPN
ijassa-112	118	1	k	k	PROPN
ijassa-112	118	2	−	−	PROPN
ijassa-112	118	3	1)!(m−	1)!(m−	NUM
ijassa-112	118	4	l	l	NOUN
ijassa-112	118	5	)	)	PUNCT
ijassa-112	118	6	!	!	PUNCT
ijassa-112	119	1	k∏	k∏	PROPN
ijassa-112	119	2	i=1	i=1	PROPN
ijassa-112	119	3	fθ(xi	fθ(xi	PROPN
ijassa-112	119	4	)	)	PUNCT
ijassa-112	120	1	[	[	PUNCT
ijassa-112	120	2	fθ(xl)−	fθ(xl)−	PROPN
ijassa-112	120	3	fθ(xk	fθ(xk	PROPN
ijassa-112	120	4	)	)	PUNCT
ijassa-112	121	1	]	]	PUNCT
ijassa-112	121	2	l−k−1	l−k−1	PROPN
ijassa-112	121	3	fθ(xl	fθ(xl	PROPN
ijassa-112	121	4	)	)	PUNCT
ijassa-112	122	1	[	[	PUNCT
ijassa-112	122	2	1−	1−	NUM
ijassa-112	122	3	fθ(xl	fθ(xl	NOUN
ijassa-112	122	4	)	)	PUNCT
ijassa-112	123	1	]	]	PUNCT
ijassa-112	123	2	m−l	m−l	NOUN
ijassa-112	123	3	=	=	SYM
ijassa-112	123	4	gθ(x1	gθ(x1	PROPN
ijassa-112	123	5	,	,	PUNCT
ijassa-112	123	6	.	.	PUNCT
ijassa-112	123	7	.	.	PUNCT
ijassa-112	124	1	.	.	PUNCT
ijassa-112	124	2	,	,	PUNCT
ijassa-112	124	3	xk)gθ(xl|xk	xk)gθ(xl|xk	PROPN
ijassa-112	124	4	)	)	PUNCT
ijassa-112	124	5	.	.	PUNCT
ijassa-112	125	1	(	(	PUNCT
ijassa-112	125	2	18	18	NUM
ijassa-112	125	3	)	)	PUNCT
ijassa-112	125	4	it	it	PRON
ijassa-112	125	5	follows	follow	VERB
ijassa-112	125	6	from	from	ADP
ijassa-112	125	7	(	(	PUNCT
ijassa-112	125	8	4	4	NUM
ijassa-112	125	9	)	)	PUNCT
ijassa-112	125	10	that	that	PRON
ijassa-112	125	11	gθ(xl|x1	gθ(xl|x1	VERB
ijassa-112	125	12	,	,	PUNCT
ijassa-112	125	13	.	.	PUNCT
ijassa-112	125	14	.	.	PUNCT
ijassa-112	125	15	.	.	PUNCT
ijassa-112	126	1	,	,	PUNCT
ijassa-112	126	2	xk	xk	PROPN
ijassa-112	126	3	)	)	PUNCT
ijassa-112	126	4	=	=	SYM
ijassa-112	126	5	gθ(x1	gθ(x1	NOUN
ijassa-112	126	6	,	,	PUNCT
ijassa-112	126	7	.	.	PUNCT
ijassa-112	126	8	.	.	PUNCT
ijassa-112	126	9	.	.	PUNCT
ijassa-112	127	1	,	,	PUNCT
ijassa-112	127	2	xk	xk	PROPN
ijassa-112	127	3	,	,	PUNCT
ijassa-112	127	4	xl	xl	PROPN
ijassa-112	127	5	)	)	PUNCT
ijassa-112	127	6	gθ(x1	gθ(x1	NOUN
ijassa-112	127	7	,	,	PUNCT
ijassa-112	127	8	.	.	PUNCT
ijassa-112	127	9	.	.	PUNCT
ijassa-112	127	10	.	.	PUNCT
ijassa-112	128	1	,	,	PUNCT
ijassa-112	128	2	xk	xk	PROPN
ijassa-112	128	3	)	)	PUNCT
ijassa-112	128	4	=	=	SYM
ijassa-112	128	5	gθ(xl|xk	gθ(xl|xk	PROPN
ijassa-112	128	6	)	)	PUNCT
ijassa-112	128	7	,	,	PUNCT
ijassa-112	128	8	(	(	PUNCT
ijassa-112	128	9	19	19	NUM
ijassa-112	128	10	)	)	PUNCT
ijassa-112	128	11	i.e.	i.e.	X
ijassa-112	128	12	,	,	PUNCT
ijassa-112	128	13	the	the	DET
ijassa-112	128	14	conditional	conditional	ADJ
ijassa-112	128	15	distribution	distribution	NOUN
ijassa-112	128	16	of	of	ADP
ijassa-112	128	17	xl	xl	PROPN
ijassa-112	128	18	,	,	PUNCT
ijassa-112	128	19	given	give	VERB
ijassa-112	128	20	xi	xi	X
ijassa-112	128	21	=	=	PUNCT
ijassa-112	128	22	xi	xi	PROPN
ijassa-112	128	23	for	for	ADP
ijassa-112	128	24	all	all	DET
ijassa-112	128	25	i	i	PRON
ijassa-112	128	26	=	=	NOUN
ijassa-112	129	1	1	1	NUM
ijassa-112	129	2	,	,	PUNCT
ijassa-112	129	3	.	.	PUNCT
ijassa-112	129	4	.	.	PUNCT
ijassa-112	130	1	.	.	PUNCT
ijassa-112	131	1	,	,	PUNCT
ijassa-112	131	2	k	k	NOUN
ijassa-112	131	3	,	,	PUNCT
ijassa-112	131	4	is	be	AUX
ijassa-112	131	5	the	the	DET
ijassa-112	131	6	same	same	ADJ
ijassa-112	131	7	as	as	ADP
ijassa-112	131	8	the	the	DET
ijassa-112	131	9	conditional	conditional	ADJ
ijassa-112	131	10	distribution	distribution	NOUN
ijassa-112	131	11	of	of	ADP
ijassa-112	131	12	xl	xl	PROPN
ijassa-112	131	13	,	,	PUNCT
ijassa-112	131	14	given	give	VERB
ijassa-112	131	15	only	only	ADV
ijassa-112	131	16	xk	xk	PROPN
ijassa-112	131	17	=	=	SYM
ijassa-112	131	18	xk	xk	PROPN
ijassa-112	131	19	,	,	PUNCT
ijassa-112	131	20	which	which	PRON
ijassa-112	131	21	is	be	AUX
ijassa-112	131	22	given	give	VERB
ijassa-112	131	23	by	by	ADP
ijassa-112	131	24	(	(	PUNCT
ijassa-112	131	25	17	17	NUM
ijassa-112	131	26	)	)	PUNCT
ijassa-112	131	27	.	.	PUNCT
ijassa-112	132	1	this	this	PRON
ijassa-112	132	2	ends	end	VERB
ijassa-112	132	3	the	the	DET
ijassa-112	132	4	proof	proof	NOUN
ijassa-112	132	5	.	.	PUNCT
ijassa-112	133	1	corollary	corollary	ADJ
ijassa-112	133	2	1.1	1.1	NUM
ijassa-112	133	3	.	.	PUNCT
ijassa-112	134	1	the	the	DET
ijassa-112	134	2	conditional	conditional	ADJ
ijassa-112	134	3	probability	probability	NOUN
ijassa-112	134	4	distribution	distribution	NOUN
ijassa-112	134	5	function	function	NOUN
ijassa-112	134	6	of	of	ADP
ijassa-112	134	7	xl	xl	PROPN
ijassa-112	134	8	given	give	VERB
ijassa-112	134	9	xk	xk	PROPN
ijassa-112	134	10	=	=	PUNCT
ijassa-112	134	11	xk	xk	PROPN
ijassa-112	134	12	is	be	AUX
ijassa-112	134	13	pθ{xl	pθ{xl	ADJ
ijassa-112	134	14	≤	≤	X
ijassa-112	134	15	xl|xk	xl|xk	PUNCT
ijassa-112	135	1	=	=	PUNCT
ijassa-112	135	2	xk	xk	ADJ
ijassa-112	135	3	}	}	PUNCT
ijassa-112	135	4	=	=	ADJ
ijassa-112	135	5	1−	1−	NUM
ijassa-112	135	6	(	(	PUNCT
ijassa-112	135	7	m−	m−	PROPN
ijassa-112	135	8	k	k	PROPN
ijassa-112	135	9	)	)	PUNCT
ijassa-112	135	10	!	!	PUNCT
ijassa-112	136	1	(	(	PUNCT
ijassa-112	136	2	l	l	NOUN
ijassa-112	136	3	−	−	PROPN
ijassa-112	137	1	k	k	PROPN
ijassa-112	137	2	−	−	PROPN
ijassa-112	137	3	1)!(m−	1)!(m−	NUM
ijassa-112	137	4	l	l	NOUN
ijassa-112	137	5	)	)	PUNCT
ijassa-112	137	6	!	!	PUNCT
ijassa-112	138	1	l−k−1∑	l−k−1∑	PROPN
ijassa-112	138	2	j=0	j=0	PROPN
ijassa-112	138	3	(	(	PUNCT
ijassa-112	138	4	l	l	NOUN
ijassa-112	138	5	−	−	PROPN
ijassa-112	138	6	k	k	NOUN
ijassa-112	138	7	−	−	PROPN
ijassa-112	138	8	1	1	NUM
ijassa-112	138	9	j	j	NOUN
ijassa-112	138	10	)	)	PUNCT
ijassa-112	138	11	(	(	PUNCT
ijassa-112	138	12	−1)j	−1)j	NOUN
ijassa-112	138	13	m−	m−	PROPN
ijassa-112	138	14	l	l	PROPN
ijassa-112	139	1	+	+	CCONJ
ijassa-112	139	2	1	1	NUM
ijassa-112	139	3	+	+	NUM
ijassa-112	139	4	j	j	X
ijassa-112	139	5	[	[	PUNCT
ijassa-112	139	6	1−	1−	NUM
ijassa-112	139	7	fθ(xl	fθ(xl	NOUN
ijassa-112	139	8	)	)	PUNCT
ijassa-112	139	9	1−	1−	NUM
ijassa-112	139	10	fθ(xk	fθ(xk	PROPN
ijassa-112	139	11	)	)	PUNCT
ijassa-112	139	12	]	]	PUNCT
ijassa-112	139	13	m−l+1+j	m−l+1+j	NOUN
ijassa-112	139	14	=	=	SYM
ijassa-112	139	15	(	(	PUNCT
ijassa-112	139	16	m−	m−	PROPN
ijassa-112	139	17	k	k	PROPN
ijassa-112	139	18	)	)	PUNCT
ijassa-112	139	19	!	!	PUNCT
ijassa-112	140	1	(	(	PUNCT
ijassa-112	140	2	l	l	NOUN
ijassa-112	140	3	−	−	PROPN
ijassa-112	141	1	k	k	PROPN
ijassa-112	141	2	−	−	PROPN
ijassa-112	141	3	1)!(m−	1)!(m−	NUM
ijassa-112	141	4	l	l	NOUN
ijassa-112	141	5	)	)	PUNCT
ijassa-112	141	6	!	!	PUNCT
ijassa-112	142	1	m−k∑	m−k∑	X
ijassa-112	142	2	j=0	j=0	PROPN
ijassa-112	142	3	(	(	PUNCT
ijassa-112	142	4	m−	m−	PROPN
ijassa-112	142	5	l	l	PROPN
ijassa-112	142	6	j	j	PROPN
ijassa-112	142	7	)	)	PUNCT
ijassa-112	143	1	[	[	X
ijassa-112	143	2	fθ(xl)−	fθ(xl)−	PROPN
ijassa-112	143	3	fθ(xk	fθ(xk	PROPN
ijassa-112	143	4	)	)	PUNCT
ijassa-112	143	5	1−	1−	NUM
ijassa-112	143	6	fθ(xk	fθ(xk	PROPN
ijassa-112	143	7	)	)	PUNCT
ijassa-112	143	8	]	]	PUNCT
ijassa-112	143	9	l−k+j	l−k+j	PUNCT
ijassa-112	143	10	.	.	PUNCT
ijassa-112	144	1	(	(	PUNCT
ijassa-112	144	2	20	20	X
ijassa-112	144	3	)	)	PUNCT
ijassa-112	144	4	advances	advance	NOUN
ijassa-112	144	5	in	in	ADP
ijassa-112	144	6	systems	system	NOUN
ijassa-112	144	7	science	science	NOUN
ijassa-112	144	8	and	and	CCONJ
ijassa-112	144	9	applications	application	NOUN
ijassa-112	144	10	(	(	PUNCT
ijassa-112	144	11	2012	2012	NUM
ijassa-112	144	12	)	)	PUNCT
ijassa-112	144	13	vol.12	vol.12	NOUN
ijassa-112	144	14	no.3	no.3	VERB
ijassa-112	144	15	279	279	NUM
ijassa-112	144	16	corollary	corollary	ADJ
ijassa-112	144	17	1.2.let	1.2.let	NUM
ijassa-112	144	18	x1	x1	PROPN
ijassa-112	144	19	≤	≤	PROPN
ijassa-112	144	20	.	.	PUNCT
ijassa-112	144	21	.	.	PUNCT
ijassa-112	144	22	.	.	PUNCT
ijassa-112	145	1	≤	≤	NUM
ijassa-112	145	2	xk	xk	PROPN
ijassa-112	145	3	be	be	AUX
ijassa-112	145	4	the	the	DET
ijassa-112	145	5	first	first	ADJ
ijassa-112	145	6	k	k	PROPN
ijassa-112	145	7	order	order	NOUN
ijassa-112	145	8	statistics	statistic	NOUN
ijassa-112	145	9	in	in	ADP
ijassa-112	145	10	a	a	DET
ijassa-112	145	11	sample	sample	NOUN
ijassa-112	145	12	of	of	ADP
ijassa-112	145	13	size	size	NOUN
ijassa-112	145	14	m	m	PROPN
ijassa-112	145	15	from	from	ADP
ijassa-112	145	16	the	the	DET
ijassa-112	145	17	two	two	NUM
ijassa-112	145	18	-	-	PUNCT
ijassa-112	145	19	parameter	parameter	NOUN
ijassa-112	145	20	weibull	weibull	NOUN
ijassa-112	145	21	distribution	distribution	NOUN
ijassa-112	145	22	with	with	ADP
ijassa-112	145	23	the	the	DET
ijassa-112	145	24	probability	probability	NOUN
ijassa-112	145	25	density	density	NOUN
ijassa-112	145	26	function	function	NOUN
ijassa-112	145	27	fθ(x	fθ(x	PUNCT
ijassa-112	145	28	)	)	PUNCT
ijassa-112	145	29	=	=	SYM
ijassa-112	145	30	δ	δ	X
ijassa-112	145	31	β	β	X
ijassa-112	145	32	(	(	PUNCT
ijassa-112	145	33	x	x	X
ijassa-112	145	34	β	β	X
ijassa-112	145	35	)	)	PUNCT
ijassa-112	145	36	δ−1	δ−1	PROPN
ijassa-112	145	37	exp	exp	NOUN
ijassa-112	145	38	[	[	PUNCT
ijassa-112	145	39	−	−	PROPN
ijassa-112	145	40	(	(	PUNCT
ijassa-112	145	41	x	x	X
ijassa-112	145	42	β	β	X
ijassa-112	145	43	)	)	PUNCT
ijassa-112	145	44	δ	δ	NOUN
ijassa-112	145	45	]	]	PUNCT
ijassa-112	145	46	(	(	PUNCT
ijassa-112	145	47	x	x	X
ijassa-112	145	48	>	>	X
ijassa-112	145	49	0	0	NUM
ijassa-112	145	50	)	)	PUNCT
ijassa-112	145	51	,	,	PUNCT
ijassa-112	145	52	(	(	PUNCT
ijassa-112	145	53	21	21	NUM
ijassa-112	145	54	)	)	PUNCT
ijassa-112	145	55	where	where	SCONJ
ijassa-112	145	56	θ	θ	NOUN
ijassa-112	145	57	=	=	SYM
ijassa-112	145	58	(	(	PUNCT
ijassa-112	145	59	β	β	X
ijassa-112	145	60	,	,	PUNCT
ijassa-112	145	61	δ	δ	PROPN
ijassa-112	145	62	)	)	PUNCT
ijassa-112	145	63	,	,	PUNCT
ijassa-112	145	64	β	β	X
ijassa-112	145	65	>	>	X
ijassa-112	145	66	0	0	PUNCT
ijassa-112	145	67	and	and	CCONJ
ijassa-112	145	68	δ	δ	PROPN
ijassa-112	145	69	>	>	X
ijassa-112	145	70	0	0	NUM
ijassa-112	145	71	are	be	AUX
ijassa-112	145	72	the	the	DET
ijassa-112	145	73	scale	scale	NOUN
ijassa-112	145	74	and	and	CCONJ
ijassa-112	145	75	shape	shape	NOUN
ijassa-112	145	76	parameters	parameter	NOUN
ijassa-112	145	77	,	,	PUNCT
ijassa-112	145	78	respectively	respectively	ADV
ijassa-112	145	79	.	.	PUNCT
ijassa-112	146	1	then	then	ADV
ijassa-112	146	2	the	the	DET
ijassa-112	146	3	conditional	conditional	ADJ
ijassa-112	146	4	probability	probability	NOUN
ijassa-112	146	5	distribution	distribution	NOUN
ijassa-112	146	6	function	function	NOUN
ijassa-112	146	7	of	of	ADP
ijassa-112	146	8	xl	xl	PROPN
ijassa-112	146	9	given	give	VERB
ijassa-112	146	10	xk	xk	PROPN
ijassa-112	146	11	=	=	PUNCT
ijassa-112	146	12	xk	xk	PROPN
ijassa-112	146	13	is	be	AUX
ijassa-112	146	14	pθ{xl	pθ{xl	ADJ
ijassa-112	146	15	≤	≤	X
ijassa-112	146	16	xl|xk	xl|xk	PUNCT
ijassa-112	147	1	=	=	PUNCT
ijassa-112	147	2	xk	xk	ADJ
ijassa-112	147	3	}	}	PUNCT
ijassa-112	147	4	=	=	SYM
ijassa-112	147	5	1−	1−	NUM
ijassa-112	147	6	(	(	PUNCT
ijassa-112	147	7	m−	m−	PROPN
ijassa-112	147	8	k	k	PROPN
ijassa-112	147	9	)	)	PUNCT
ijassa-112	147	10	!	!	PUNCT
ijassa-112	148	1	(	(	PUNCT
ijassa-112	148	2	l	l	NOUN
ijassa-112	148	3	−	−	PROPN
ijassa-112	149	1	k	k	PROPN
ijassa-112	149	2	−	−	PROPN
ijassa-112	149	3	1)!(m−	1)!(m−	NUM
ijassa-112	149	4	l	l	NOUN
ijassa-112	149	5	)	)	PUNCT
ijassa-112	149	6	!	!	PUNCT
ijassa-112	150	1	l−k−1∑	l−k−1∑	PROPN
ijassa-112	150	2	j=0	j=0	PROPN
ijassa-112	150	3	(	(	PUNCT
ijassa-112	150	4	l	l	NOUN
ijassa-112	150	5	−	−	PROPN
ijassa-112	150	6	k	k	NOUN
ijassa-112	150	7	−	−	PROPN
ijassa-112	150	8	1	1	NUM
ijassa-112	150	9	j	j	NOUN
ijassa-112	150	10	)	)	PUNCT
ijassa-112	150	11	(	(	PUNCT
ijassa-112	150	12	−1)j	−1)j	NOUN
ijassa-112	150	13	m−	m−	PROPN
ijassa-112	150	14	l	l	PROPN
ijassa-112	151	1	+	+	CCONJ
ijassa-112	151	2	1	1	NUM
ijassa-112	151	3	+	+	NUM
ijassa-112	151	4	j	j	X
ijassa-112	151	5	[	[	PUNCT
ijassa-112	151	6	exp(−	exp(−	PROPN
ijassa-112	151	7	xδl	xδl	PROPN
ijassa-112	151	8	−	−	PROPN
ijassa-112	151	9	xδk	xδk	NOUN
ijassa-112	151	10	βδ	βδ	PROPN
ijassa-112	151	11	)	)	PUNCT
ijassa-112	151	12	]	]	X
ijassa-112	151	13	m−l+1+j	m−l+1+j	NOUN
ijassa-112	151	14	.	.	PUNCT
ijassa-112	152	1	(	(	PUNCT
ijassa-112	152	2	22	22	NUM
ijassa-112	152	3	)	)	PUNCT
ijassa-112	152	4	theorem	theorem	NOUN
ijassa-112	152	5	2	2	NUM
ijassa-112	152	6	if	if	SCONJ
ijassa-112	152	7	in	in	ADP
ijassa-112	152	8	(	(	PUNCT
ijassa-112	152	9	22	22	NUM
ijassa-112	152	10	)	)	PUNCT
ijassa-112	152	11	the	the	DET
ijassa-112	152	12	scale	scale	NOUN
ijassa-112	152	13	parameter	parameter	NOUN
ijassa-112	152	14	β	β	PROPN
ijassa-112	152	15	is	be	AUX
ijassa-112	152	16	unknown	unknown	ADJ
ijassa-112	152	17	,	,	PUNCT
ijassa-112	152	18	then	then	ADV
ijassa-112	152	19	the	the	DET
ijassa-112	152	20	predictive	predictive	ADJ
ijassa-112	152	21	probability	probability	NOUN
ijassa-112	152	22	distribution	distribution	NOUN
ijassa-112	152	23	function	function	NOUN
ijassa-112	152	24	of	of	ADP
ijassa-112	152	25	xl	xl	PROPN
ijassa-112	152	26	based	base	VERB
ijassa-112	152	27	on	on	ADP
ijassa-112	152	28	(	(	PUNCT
ijassa-112	152	29	xk	xk	PROPN
ijassa-112	152	30	,	,	PUNCT
ijassa-112	152	31	δ	δ	PROPN
ijassa-112	152	32	)	)	PUNCT
ijassa-112	152	33	is	be	AUX
ijassa-112	152	34	given	give	VERB
ijassa-112	152	35	by	by	ADP
ijassa-112	152	36	pδ	pδ	PROPN
ijassa-112	152	37	{	{	PUNCT
ijassa-112	152	38	(	(	PUNCT
ijassa-112	152	39	xl	xl	PROPN
ijassa-112	152	40	xk	xk	PROPN
ijassa-112	152	41	)	)	PUNCT
ijassa-112	152	42	δ	δ	PROPN
ijassa-112	152	43	≤	≤	PROPN
ijassa-112	152	44	(	(	PUNCT
ijassa-112	152	45	xl	xl	PROPN
ijassa-112	152	46	xk	xk	PROPN
ijassa-112	152	47	)	)	PUNCT
ijassa-112	152	48	δ	δ	PROPN
ijassa-112	152	49	)	)	PUNCT
ijassa-112	152	50	}	}	PUNCT
ijassa-112	152	51	=	=	PUNCT
ijassa-112	152	52	1−	1−	NUM
ijassa-112	152	53	m	m	NOUN
ijassa-112	152	54	!	!	PUNCT
ijassa-112	153	1	(	(	PUNCT
ijassa-112	153	2	l	l	NOUN
ijassa-112	153	3	−	−	PROPN
ijassa-112	154	1	k	k	PROPN
ijassa-112	154	2	−	−	PROPN
ijassa-112	154	3	1)!(m−	1)!(m−	NUM
ijassa-112	154	4	l	l	NOUN
ijassa-112	154	5	)	)	PUNCT
ijassa-112	154	6	!	!	PUNCT
ijassa-112	155	1	×	×	NOUN
ijassa-112	155	2	l−k−1∑	l−k−1∑	PROPN
ijassa-112	155	3	j=0	j=0	PROPN
ijassa-112	155	4	(	(	PUNCT
ijassa-112	155	5	l	l	NOUN
ijassa-112	155	6	−	−	PROPN
ijassa-112	156	1	k	k	NOUN
ijassa-112	156	2	−	−	PROPN
ijassa-112	156	3	1	1	NUM
ijassa-112	156	4	j	j	NOUN
ijassa-112	156	5	)	)	PUNCT
ijassa-112	156	6	(	(	PUNCT
ijassa-112	156	7	−1)j	−1)j	NOUN
ijassa-112	156	8	m−	m−	PROPN
ijassa-112	156	9	l	l	PROPN
ijassa-112	157	1	+	+	CCONJ
ijassa-112	157	2	1	1	NUM
ijassa-112	157	3	+	+	CCONJ
ijassa-112	157	4	j	j	PROPN
ijassa-112	157	5	(	(	PUNCT
ijassa-112	157	6	πk−1	πk−1	PROPN
ijassa-112	157	7	s=0	s=0	X
ijassa-112	158	1	[	[	X
ijassa-112	158	2	(	(	PUNCT
ijassa-112	158	3	(	(	PUNCT
ijassa-112	158	4	xl	xl	PROPN
ijassa-112	158	5	xk	xk	PROPN
ijassa-112	158	6	)	)	PUNCT
ijassa-112	158	7	δ	δ	PROPN
ijassa-112	158	8	−	−	NOUN
ijassa-112	158	9	1	1	NUM
ijassa-112	158	10	)	)	PUNCT
ijassa-112	158	11	(	(	PUNCT
ijassa-112	158	12	m−	m−	PROPN
ijassa-112	158	13	j	j	PROPN
ijassa-112	158	14	+1	+1	PROPN
ijassa-112	158	15	+	+	PROPN
ijassa-112	158	16	j	j	NOUN
ijassa-112	158	17	)	)	PUNCT
ijassa-112	159	1	+	+	CCONJ
ijassa-112	159	2	(	(	PUNCT
ijassa-112	159	3	m−	m−	PROPN
ijassa-112	159	4	k+1	k+1	PROPN
ijassa-112	159	5	+	+	PROPN
ijassa-112	159	6	s	s	NOUN
ijassa-112	159	7	)	)	PUNCT
ijassa-112	159	8	]	]	PUNCT
ijassa-112	159	9	)	)	PUNCT
ijassa-112	159	10	−1	−1	NOUN
ijassa-112	159	11	.	.	PUNCT
ijassa-112	160	1	(	(	PUNCT
ijassa-112	160	2	23	23	X
ijassa-112	160	3	)	)	PUNCT
ijassa-112	160	4	proof.we	proof.we	NOUN
ijassa-112	160	5	reduce	reduce	VERB
ijassa-112	160	6	(	(	PUNCT
ijassa-112	160	7	22	22	NUM
ijassa-112	160	8	)	)	PUNCT
ijassa-112	160	9	to	to	PART
ijassa-112	160	10	pθ	pθ	VERB
ijassa-112	160	11	{	{	PUNCT
ijassa-112	160	12	(	(	PUNCT
ijassa-112	160	13	xl	xl	PROPN
ijassa-112	160	14	xk	xk	PROPN
ijassa-112	160	15	)	)	PUNCT
ijassa-112	160	16	δ	δ	PROPN
ijassa-112	160	17	≤	≤	PROPN
ijassa-112	160	18	(	(	PUNCT
ijassa-112	160	19	xl	xl	PROPN
ijassa-112	160	20	xk	xk	PROPN
ijassa-112	160	21	)	)	PUNCT
ijassa-112	160	22	δ	δ	PROPN
ijassa-112	161	1	|	|	ADV
ijassa-112	161	2	(	(	PUNCT
ijassa-112	161	3	xk	xk	X
ijassa-112	161	4	β	β	X
ijassa-112	161	5	)	)	PUNCT
ijassa-112	161	6	δ	δ	PROPN
ijassa-112	161	7	=	=	PRON
ijassa-112	161	8	(	(	PUNCT
ijassa-112	161	9	xk	xk	X
ijassa-112	161	10	β	β	X
ijassa-112	161	11	)	)	PUNCT
ijassa-112	161	12	δ	δ	PROPN
ijassa-112	161	13	}	}	PUNCT
ijassa-112	161	14	=	=	SYM
ijassa-112	161	15	1−	1−	NUM
ijassa-112	161	16	(	(	PUNCT
ijassa-112	161	17	m−	m−	PROPN
ijassa-112	161	18	k	k	PROPN
ijassa-112	161	19	)	)	PUNCT
ijassa-112	161	20	!	!	PUNCT
ijassa-112	162	1	(	(	PUNCT
ijassa-112	162	2	l	l	NOUN
ijassa-112	162	3	−	−	PROPN
ijassa-112	163	1	k	k	PROPN
ijassa-112	163	2	−	−	PROPN
ijassa-112	163	3	1)!(m−	1)!(m−	NUM
ijassa-112	163	4	l	l	NOUN
ijassa-112	163	5	)	)	PUNCT
ijassa-112	163	6	!	!	PUNCT
ijassa-112	164	1	l−k−1∑	l−k−1∑	PROPN
ijassa-112	164	2	j=0	j=0	PROPN
ijassa-112	164	3	(	(	PUNCT
ijassa-112	164	4	l	l	NOUN
ijassa-112	164	5	−	−	PROPN
ijassa-112	164	6	k	k	NOUN
ijassa-112	164	7	−	−	PROPN
ijassa-112	164	8	1	1	NUM
ijassa-112	164	9	j	j	PROPN
ijassa-112	164	10	)	)	PUNCT
ijassa-112	164	11	×	×	NOUN
ijassa-112	164	12	(	(	PUNCT
ijassa-112	164	13	−1)j	−1)j	NOUN
ijassa-112	164	14	m−	m−	PROPN
ijassa-112	164	15	l	l	PROPN
ijassa-112	165	1	+	+	CCONJ
ijassa-112	165	2	1	1	NUM
ijassa-112	165	3	+	+	NUM
ijassa-112	165	4	j	j	X
ijassa-112	165	5	[	[	PUNCT
ijassa-112	165	6	exp	exp	NOUN
ijassa-112	165	7	(	(	PUNCT
ijassa-112	165	8	−	−	PROPN
ijassa-112	165	9	ω[νδ	ω[νδ	ADV
ijassa-112	165	10	−	−	PROPN
ijassa-112	165	11	1	1	NUM
ijassa-112	165	12	]	]	PUNCT
ijassa-112	165	13	)	)	PUNCT
ijassa-112	165	14	]	]	X
ijassa-112	165	15	m−l+1+j	m−l+1+j	NOUN
ijassa-112	165	16	=	=	PROPN
ijassa-112	165	17	pδ{v	pδ{v	PROPN
ijassa-112	165	18	δ	δ	PROPN
ijassa-112	165	19	≤	≤	NOUN
ijassa-112	165	20	νδ|w	νδ|w	NOUN
ijassa-112	165	21	=	=	SYM
ijassa-112	165	22	ω	ω	PROPN
ijassa-112	165	23	}	}	PUNCT
ijassa-112	165	24	(	(	PUNCT
ijassa-112	165	25	24	24	NUM
ijassa-112	165	26	)	)	PUNCT
ijassa-112	165	27	where	where	SCONJ
ijassa-112	165	28	v	v	NOUN
ijassa-112	165	29	=	=	SYM
ijassa-112	165	30	xl	xl	PROPN
ijassa-112	165	31	/	/	SYM
ijassa-112	165	32	xk	xk	PROPN
ijassa-112	165	33	is	be	AUX
ijassa-112	165	34	the	the	DET
ijassa-112	165	35	ancillary	ancillary	ADJ
ijassa-112	165	36	statistic	statistic	NOUN
ijassa-112	165	37	whose	whose	DET
ijassa-112	165	38	distribution	distribution	NOUN
ijassa-112	165	39	does	do	AUX
ijassa-112	165	40	not	not	PART
ijassa-112	165	41	depend	depend	VERB
ijassa-112	165	42	on	on	ADP
ijassa-112	165	43	the	the	DET
ijassa-112	165	44	parameter	parameter	NOUN
ijassa-112	165	45	β	β	PROPN
ijassa-112	165	46	.	.	PUNCT
ijassa-112	166	1	since	since	SCONJ
ijassa-112	166	2	xk	xk	PROPN
ijassa-112	166	3	does	do	AUX
ijassa-112	166	4	not	not	PART
ijassa-112	166	5	depend	depend	VERB
ijassa-112	166	6	on	on	ADP
ijassa-112	166	7	v	v	NUM
ijassa-112	166	8	,	,	PUNCT
ijassa-112	166	9	w	w	PROPN
ijassa-112	166	10	=	=	SYM
ijassa-112	166	11	(	(	PUNCT
ijassa-112	166	12	xk	xk	PROPN
ijassa-112	166	13	/	/	SYM
ijassa-112	166	14	β	β	NOUN
ijassa-112	166	15	)	)	PUNCT
ijassa-112	166	16	δ	δ	PROPN
ijassa-112	166	17	is	be	AUX
ijassa-112	166	18	the	the	DET
ijassa-112	166	19	pivotal	pivotal	ADJ
ijassa-112	166	20	quantity	quantity	NOUN
ijassa-112	166	21	,	,	PUNCT
ijassa-112	166	22	whose	whose	DET
ijassa-112	166	23	distribution	distribution	NOUN
ijassa-112	166	24	is	be	AUX
ijassa-112	166	25	known	know	VERB
ijassa-112	166	26	and	and	CCONJ
ijassa-112	166	27	does	do	AUX
ijassa-112	166	28	not	not	PART
ijassa-112	166	29	depend	depend	VERB
ijassa-112	166	30	on	on	ADP
ijassa-112	166	31	the	the	DET
ijassa-112	166	32	parameters	parameter	NOUN
ijassa-112	166	33	β	β	X
ijassa-112	166	34	and	and	CCONJ
ijassa-112	166	35	δ	δ	PROPN
ijassa-112	166	36	,	,	PUNCT
ijassa-112	166	37	we	we	PRON
ijassa-112	166	38	eliminate	eliminate	VERB
ijassa-112	166	39	the	the	DET
ijassa-112	166	40	parameter	parameter	NOUN
ijassa-112	166	41	β	β	PROPN
ijassa-112	166	42	from	from	ADP
ijassa-112	166	43	the	the	DET
ijassa-112	166	44	problem	problem	NOUN
ijassa-112	166	45	as	as	ADP
ijassa-112	166	46	pδ{xl	pδ{xl	PROPN
ijassa-112	166	47	≤	≤	NUM
ijassa-112	166	48	xl	xl	PROPN
ijassa-112	166	49	}	}	PUNCT
ijassa-112	166	50	=	=	SYM
ijassa-112	166	51	∫	∫	PROPN
ijassa-112	166	52	∞	∞	NUM
ijassa-112	166	53	0	0	NUM
ijassa-112	167	1	pθ{xl	pθ{xl	ADJ
ijassa-112	167	2	≤	≤	X
ijassa-112	167	3	xl|xk	xl|xk	PUNCT
ijassa-112	168	1	=	=	SYM
ijassa-112	168	2	xk}gθ(xk)dxk	xk}gθ(xk)dxk	PROPN
ijassa-112	168	3	,	,	PUNCT
ijassa-112	168	4	(	(	PUNCT
ijassa-112	168	5	25	25	NUM
ijassa-112	168	6	)	)	PUNCT
ijassa-112	168	7	where	where	SCONJ
ijassa-112	168	8	gθ(xk	gθ(xk	NOUN
ijassa-112	168	9	)	)	PUNCT
ijassa-112	168	10	=	=	PUNCT
ijassa-112	169	1	m	m	PROPN
ijassa-112	169	2	!	!	PUNCT
ijassa-112	170	1	(	(	PUNCT
ijassa-112	170	2	k	k	PROPN
ijassa-112	170	3	−	−	PROPN
ijassa-112	170	4	1)!(m−	1)!(m−	NUM
ijassa-112	170	5	k	k	NOUN
ijassa-112	170	6	)	)	PUNCT
ijassa-112	170	7	!	!	PUNCT
ijassa-112	171	1	f	f	PROPN
ijassa-112	171	2	k−1	k−1	PROPN
ijassa-112	171	3	θ	θ	PROPN
ijassa-112	171	4	(	(	PUNCT
ijassa-112	171	5	xk	xk	PROPN
ijassa-112	171	6	)	)	PUNCT
ijassa-112	171	7	[	[	PUNCT
ijassa-112	171	8	1−	1−	NUM
ijassa-112	171	9	fθ(xk	fθ(xk	NOUN
ijassa-112	171	10	)	)	PUNCT
ijassa-112	171	11	]	]	PUNCT
ijassa-112	171	12	m−k	m−k	NOUN
ijassa-112	171	13	fθ(xk	fθ(xk	PROPN
ijassa-112	171	14	)	)	PUNCT
ijassa-112	171	15	,	,	PUNCT
ijassa-112	171	16	xk	xk	PROPN
ijassa-112	171	17	∈	∈	PROPN
ijassa-112	171	18	(	(	PUNCT
ijassa-112	171	19	0,∞	0,∞	NOUN
ijassa-112	171	20	)	)	PUNCT
ijassa-112	171	21	,	,	PUNCT
ijassa-112	171	22	(	(	PUNCT
ijassa-112	171	23	26	26	NUM
ijassa-112	171	24	)	)	PUNCT
ijassa-112	171	25	280	280	NUM
ijassa-112	171	26	nicholas	nicholas	PROPN
ijassa-112	171	27	a.	a.	PROPN
ijassa-112	171	28	nechval	nechval	PROPN
ijassa-112	171	29	:	:	PUNCT
ijassa-112	171	30	improved	improved	ADJ
ijassa-112	171	31	airline	airline	NOUN
ijassa-112	171	32	seat	seat	NOUN
ijassa-112	171	33	inventory	inventory	NOUN
ijassa-112	171	34	control	control	NOUN
ijassa-112	171	35	policies	policy	NOUN
ijassa-112	171	36	under	under	ADP
ijassa-112	171	37	parametric	parametric	NOUN
ijassa-112	171	38	...	...	PUNCT
ijassa-112	171	39	represents	represent	VERB
ijassa-112	171	40	the	the	DET
ijassa-112	171	41	probability	probability	NOUN
ijassa-112	171	42	density	density	NOUN
ijassa-112	171	43	function	function	NOUN
ijassa-112	171	44	of	of	ADP
ijassa-112	171	45	the	the	DET
ijassa-112	171	46	kth	kth	PROPN
ijassa-112	171	47	order	order	NOUN
ijassa-112	171	48	statistic	statistic	VERB
ijassa-112	171	49	xk.indeed	xk.indeed	NOUN
ijassa-112	171	50	,	,	PUNCT
ijassa-112	171	51	it	it	PRON
ijassa-112	171	52	follows	follow	VERB
ijassa-112	171	53	from	from	ADP
ijassa-112	171	54	(	(	PUNCT
ijassa-112	171	55	26	26	NUM
ijassa-112	171	56	)	)	PUNCT
ijassa-112	172	1	that	that	DET
ijassa-112	172	2	gθ(xk)dxk	gθ(xk)dxk	NOUN
ijassa-112	172	3	=	=	PUNCT
ijassa-112	172	4	m	m	PROPN
ijassa-112	172	5	!	!	PUNCT
ijassa-112	173	1	(	(	PUNCT
ijassa-112	173	2	k	k	PROPN
ijassa-112	173	3	−	−	PROPN
ijassa-112	173	4	1)!(m−	1)!(m−	NUM
ijassa-112	173	5	k	k	NOUN
ijassa-112	173	6	)	)	PUNCT
ijassa-112	173	7	!	!	PUNCT
ijassa-112	174	1	[	[	PUNCT
ijassa-112	174	2	1−	1−	NUM
ijassa-112	174	3	exp	exp	NOUN
ijassa-112	174	4	(	(	PUNCT
ijassa-112	174	5	−	−	PROPN
ijassa-112	174	6	(	(	PUNCT
ijassa-112	174	7	xk	xk	X
ijassa-112	174	8	β	β	X
ijassa-112	174	9	)	)	PUNCT
ijassa-112	174	10	δ)]k−1	δ)]k−1	NUM
ijassa-112	174	11	exp	exp	NOUN
ijassa-112	174	12	(	(	PUNCT
ijassa-112	174	13	−	−	PROPN
ijassa-112	174	14	(	(	PUNCT
ijassa-112	174	15	xk	xk	X
ijassa-112	174	16	β	β	X
ijassa-112	174	17	)	)	PUNCT
ijassa-112	174	18	δ(m−k	δ(m−k	PROPN
ijassa-112	174	19	)	)	PUNCT
ijassa-112	174	20	)	)	PUNCT
ijassa-112	174	21	exp	exp	NOUN
ijassa-112	174	22	(	(	PUNCT
ijassa-112	175	1	−	−	PROPN
ijassa-112	175	2	(	(	PUNCT
ijassa-112	175	3	x	x	X
ijassa-112	175	4	β	β	X
ijassa-112	175	5	)	)	PUNCT
ijassa-112	175	6	δ	δ	PROPN
ijassa-112	175	7	)	)	PUNCT
ijassa-112	175	8	d	d	NOUN
ijassa-112	175	9	(	(	PUNCT
ijassa-112	175	10	x	x	NOUN
ijassa-112	175	11	β	β	X
ijassa-112	175	12	)	)	PUNCT
ijassa-112	175	13	δ	δ	PROPN
ijassa-112	175	14	=	=	PUNCT
ijassa-112	175	15	m	m	PROPN
ijassa-112	175	16	!	!	PUNCT
ijassa-112	176	1	(	(	PUNCT
ijassa-112	176	2	k	k	PROPN
ijassa-112	176	3	−	−	PROPN
ijassa-112	176	4	1)!(m−	1)!(m−	NUM
ijassa-112	176	5	k	k	NOUN
ijassa-112	176	6	)	)	PUNCT
ijassa-112	176	7	!	!	PUNCT
ijassa-112	177	1	[	[	PUNCT
ijassa-112	177	2	1−	1−	NUM
ijassa-112	177	3	e−ω	e−ω	NOUN
ijassa-112	177	4	]	]	PUNCT
ijassa-112	177	5	k−1	k−1	PROPN
ijassa-112	177	6	e−ω(m−k+1)dω	e−ω(m−k+1)dω	PROPN
ijassa-112	177	7	=	=	SYM
ijassa-112	177	8	g(ω)dω	g(ω)dω	NOUN
ijassa-112	177	9	.	.	PUNCT
ijassa-112	178	1	(	(	PUNCT
ijassa-112	178	2	27	27	NUM
ijassa-112	178	3	)	)	PUNCT
ijassa-112	178	4	it	it	PRON
ijassa-112	178	5	follows	follow	VERB
ijassa-112	178	6	from	from	ADP
ijassa-112	178	7	(	(	PUNCT
ijassa-112	178	8	24	24	NUM
ijassa-112	178	9	)	)	PUNCT
ijassa-112	178	10	and	and	CCONJ
ijassa-112	178	11	(	(	PUNCT
ijassa-112	178	12	27	27	NUM
ijassa-112	178	13	)	)	PUNCT
ijassa-112	178	14	that	that	PRON
ijassa-112	178	15	pδ{v	pδ{v	PROPN
ijassa-112	178	16	δ	δ	PROPN
ijassa-112	178	17	≤	≤	NUM
ijassa-112	178	18	νδ	νδ	VERB
ijassa-112	178	19	}	}	PUNCT
ijassa-112	178	20	=	=	SYM
ijassa-112	178	21	∫	∫	PROPN
ijassa-112	179	1	∞	∞	NOUN
ijassa-112	179	2	0	0	X
ijassa-112	180	1	pδ{v	pδ{v	PROPN
ijassa-112	180	2	δ	δ	PROPN
ijassa-112	180	3	≤	≤	NOUN
ijassa-112	180	4	νδ|w	νδ|w	NOUN
ijassa-112	180	5	=	=	SYM
ijassa-112	180	6	ω}g(ω)d(ω	ω}g(ω)d(ω	X
ijassa-112	180	7	)	)	PUNCT
ijassa-112	180	8	=	=	NOUN
ijassa-112	180	9	1−	1−	NUM
ijassa-112	180	10	m	m	NOUN
ijassa-112	180	11	!	!	PUNCT
ijassa-112	181	1	(	(	PUNCT
ijassa-112	181	2	l	l	NOUN
ijassa-112	181	3	−	−	PROPN
ijassa-112	182	1	k	k	PROPN
ijassa-112	182	2	−	−	PROPN
ijassa-112	182	3	1)!(m−	1)!(m−	NUM
ijassa-112	182	4	l	l	NOUN
ijassa-112	182	5	)	)	PUNCT
ijassa-112	182	6	!	!	PUNCT
ijassa-112	183	1	l−k−1∑	l−k−1∑	PROPN
ijassa-112	183	2	j=0	j=0	PROPN
ijassa-112	183	3	(	(	PUNCT
ijassa-112	183	4	l	l	NOUN
ijassa-112	183	5	−	−	PROPN
ijassa-112	183	6	k	k	NOUN
ijassa-112	183	7	−	−	PROPN
ijassa-112	183	8	1	1	NUM
ijassa-112	183	9	j	j	NOUN
ijassa-112	183	10	)	)	PUNCT
ijassa-112	183	11	(	(	PUNCT
ijassa-112	183	12	−1)j	−1)j	NOUN
ijassa-112	183	13	m−	m−	PROPN
ijassa-112	183	14	l	l	PROPN
ijassa-112	184	1	+	+	CCONJ
ijassa-112	184	2	1	1	NUM
ijassa-112	184	3	+	+	SYM
ijassa-112	184	4	j	j	PROPN
ijassa-112	184	5	(	(	PUNCT
ijassa-112	184	6	πk−1	πk−1	PROPN
ijassa-112	184	7	s=0	s=0	X
ijassa-112	184	8	[	[	PUNCT
ijassa-112	184	9	(	(	PUNCT
ijassa-112	184	10	νδ	νδ	NOUN
ijassa-112	184	11	−	−	PROPN
ijassa-112	184	12	1)(m−	1)(m−	NUM
ijassa-112	184	13	l	l	NOUN
ijassa-112	185	1	+	+	CCONJ
ijassa-112	185	2	1	1	NUM
ijassa-112	185	3	+	+	SYM
ijassa-112	185	4	j	j	NOUN
ijassa-112	185	5	)	)	PUNCT
ijassa-112	186	1	+	+	CCONJ
ijassa-112	186	2	(	(	PUNCT
ijassa-112	186	3	m−	m−	PROPN
ijassa-112	186	4	k	k	PROPN
ijassa-112	187	1	+	+	CCONJ
ijassa-112	187	2	1	1	NUM
ijassa-112	187	3	+	+	NUM
ijassa-112	187	4	s	s	NOUN
ijassa-112	187	5	)	)	PUNCT
ijassa-112	187	6	]	]	PUNCT
ijassa-112	187	7	)	)	PUNCT
ijassa-112	187	8	−1	−1	NOUN
ijassa-112	187	9	.	.	PUNCT
ijassa-112	188	1	(	(	PUNCT
ijassa-112	188	2	28	28	NUM
ijassa-112	188	3	)	)	PUNCT
ijassa-112	188	4	now	now	ADV
ijassa-112	188	5	(	(	PUNCT
ijassa-112	188	6	23	23	NUM
ijassa-112	188	7	)	)	PUNCT
ijassa-112	188	8	follows	follow	VERB
ijassa-112	188	9	from	from	ADP
ijassa-112	188	10	(	(	PUNCT
ijassa-112	188	11	28	28	NUM
ijassa-112	188	12	)	)	PUNCT
ijassa-112	188	13	.	.	PUNCT
ijassa-112	189	1	this	this	PRON
ijassa-112	189	2	ends	end	VERB
ijassa-112	189	3	the	the	DET
ijassa-112	189	4	proof	proof	NOUN
ijassa-112	189	5	.	.	PUNCT
ijassa-112	190	1	corollary	corollary	ADJ
ijassa-112	190	2	2.1.if	2.1.if	PROPN
ijassa-112	191	1	the	the	DET
ijassa-112	191	2	parameter	parameter	NOUN
ijassa-112	191	3	δ	δ	PROPN
ijassa-112	191	4	=	=	NOUN
ijassa-112	191	5	1	1	NUM
ijassa-112	191	6	,	,	PUNCT
ijassa-112	191	7	i.e.	i.e.	X
ijassa-112	191	8	,	,	PUNCT
ijassa-112	191	9	we	we	PRON
ijassa-112	191	10	deal	deal	VERB
ijassa-112	191	11	with	with	ADP
ijassa-112	191	12	the	the	DET
ijassa-112	191	13	exponential	exponential	ADJ
ijassa-112	191	14	distribution	distribution	NOUN
ijassa-112	191	15	,	,	PUNCT
ijassa-112	191	16	then	then	ADV
ijassa-112	191	17	the	the	DET
ijassa-112	191	18	predictive	predictive	ADJ
ijassa-112	191	19	probability	probability	NOUN
ijassa-112	191	20	distribution	distribution	NOUN
ijassa-112	191	21	function	function	NOUN
ijassa-112	191	22	of	of	ADP
ijassa-112	191	23	xl	xl	PROPN
ijassa-112	191	24	based	base	VERB
ijassa-112	191	25	on	on	ADP
ijassa-112	191	26	xk	xk	PROPN
ijassa-112	191	27	is	be	AUX
ijassa-112	191	28	given	give	VERB
ijassa-112	191	29	by	by	ADP
ijassa-112	191	30	p	p	X
ijassa-112	191	31	{	{	PUNCT
ijassa-112	191	32	(	(	PUNCT
ijassa-112	191	33	xl	xl	PROPN
ijassa-112	191	34	xk	xk	PROPN
ijassa-112	191	35	≤	≤	PROPN
ijassa-112	191	36	xlxk	xlxk	PROPN
ijassa-112	191	37	)	)	PUNCT
ijassa-112	191	38	}	}	PUNCT
ijassa-112	192	1	=	=	NOUN
ijassa-112	192	2	1−	1−	NUM
ijassa-112	192	3	m	m	NOUN
ijassa-112	192	4	!	!	PUNCT
ijassa-112	193	1	(	(	PUNCT
ijassa-112	193	2	l	l	NOUN
ijassa-112	193	3	−	−	PROPN
ijassa-112	194	1	k	k	PROPN
ijassa-112	194	2	−	−	PROPN
ijassa-112	194	3	1)!(m−	1)!(m−	NUM
ijassa-112	194	4	l	l	NOUN
ijassa-112	194	5	)	)	PUNCT
ijassa-112	194	6	!	!	PUNCT
ijassa-112	195	1	×	×	NOUN
ijassa-112	195	2	l−k−1∑	l−k−1∑	PROPN
ijassa-112	195	3	j=0	j=0	PROPN
ijassa-112	195	4	(	(	PUNCT
ijassa-112	195	5	l	l	NOUN
ijassa-112	195	6	−	−	PROPN
ijassa-112	196	1	k	k	NOUN
ijassa-112	196	2	−	−	PROPN
ijassa-112	196	3	1	1	NUM
ijassa-112	196	4	j	j	NOUN
ijassa-112	196	5	)	)	PUNCT
ijassa-112	196	6	(	(	PUNCT
ijassa-112	196	7	−1)j	−1)j	NOUN
ijassa-112	196	8	m−	m−	PROPN
ijassa-112	196	9	l	l	PROPN
ijassa-112	197	1	+	+	CCONJ
ijassa-112	197	2	1	1	NUM
ijassa-112	197	3	+	+	SYM
ijassa-112	197	4	j	j	PROPN
ijassa-112	197	5	(	(	PUNCT
ijassa-112	197	6	πk−1	πk−1	PROPN
ijassa-112	197	7	s=0	s=0	PUNCT
ijassa-112	198	1	[	[	X
ijassa-112	198	2	(	(	PUNCT
ijassa-112	198	3	xl	xl	PROPN
ijassa-112	198	4	xk	xk	PROPN
ijassa-112	198	5	−	−	PROPN
ijassa-112	198	6	1	1	NUM
ijassa-112	198	7	)	)	PUNCT
ijassa-112	198	8	(	(	PUNCT
ijassa-112	198	9	m−	m−	PROPN
ijassa-112	198	10	l	l	PROPN
ijassa-112	199	1	+	+	CCONJ
ijassa-112	199	2	1	1	NUM
ijassa-112	199	3	+	+	SYM
ijassa-112	199	4	j	j	NOUN
ijassa-112	199	5	)	)	PUNCT
ijassa-112	200	1	+	+	CCONJ
ijassa-112	200	2	(	(	PUNCT
ijassa-112	200	3	m−	m−	PROPN
ijassa-112	200	4	k	k	PROPN
ijassa-112	201	1	+	+	CCONJ
ijassa-112	201	2	1	1	NUM
ijassa-112	201	3	+	+	NUM
ijassa-112	201	4	s	s	NOUN
ijassa-112	201	5	)	)	PUNCT
ijassa-112	201	6	]	]	PUNCT
ijassa-112	201	7	)	)	PUNCT
ijassa-112	201	8	−1	−1	NOUN
ijassa-112	201	9	.	.	PUNCT
ijassa-112	202	1	(	(	PUNCT
ijassa-112	202	2	29	29	NUM
ijassa-112	202	3	)	)	PUNCT
ijassa-112	202	4	6	6	NUM
ijassa-112	202	5	illustrative	illustrative	ADJ
ijassa-112	202	6	example	example	NOUN
ijassa-112	202	7	of	of	ADP
ijassa-112	202	8	airline	airline	NOUN
ijassa-112	202	9	booking	booking	NOUN
ijassa-112	202	10	policies	policy	NOUN
ijassa-112	202	11	let	let	VERB
ijassa-112	202	12	x1	x1	PROPN
ijassa-112	202	13	,	,	PUNCT
ijassa-112	202	14	.	.	PUNCT
ijassa-112	202	15	.	.	PUNCT
ijassa-112	203	1	.	.	PUNCT
ijassa-112	204	1	,	,	PUNCT
ijassa-112	204	2	xn	xn	PROPN
ijassa-112	204	3	be	be	AUX
ijassa-112	204	4	the	the	DET
ijassa-112	204	5	random	random	ADJ
ijassa-112	204	6	sample	sample	NOUN
ijassa-112	204	7	of	of	ADP
ijassa-112	204	8	the	the	DET
ijassa-112	204	9	previous	previous	ADJ
ijassa-112	204	10	independent	independent	ADJ
ijassa-112	204	11	observations	observation	NOUN
ijassa-112	204	12	of	of	ADP
ijassa-112	204	13	the	the	DET
ijassa-112	204	14	cumulative	cumulative	ADJ
ijassa-112	204	15	customer	customer	NOUN
ijassa-112	204	16	demand	demand	NOUN
ijassa-112	204	17	for	for	ADP
ijassa-112	204	18	the	the	DET
ijassa-112	204	19	high	high	ADJ
ijassa-112	204	20	fare	fare	NOUN
ijassa-112	204	21	class	class	NOUN
ijassa-112	204	22	,	,	PUNCT
ijassa-112	204	23	which	which	PRON
ijassa-112	204	24	follow	follow	VERB
ijassa-112	204	25	the	the	DET
ijassa-112	204	26	exponential	exponential	ADJ
ijassa-112	204	27	distribution	distribution	NOUN
ijassa-112	204	28	with	with	ADP
ijassa-112	204	29	the	the	DET
ijassa-112	204	30	probability	probability	NOUN
ijassa-112	204	31	density	density	NOUN
ijassa-112	204	32	function	function	NOUN
ijassa-112	204	33	(	(	PUNCT
ijassa-112	204	34	21)(δ	21)(δ	NOUN
ijassa-112	204	35	=	=	SYM
ijassa-112	204	36	1	1	NUM
ijassa-112	204	37	)	)	PUNCT
ijassa-112	204	38	,	,	PUNCT
ijassa-112	204	39	where	where	SCONJ
ijassa-112	204	40	the	the	DET
ijassa-112	204	41	parameter	parameter	NOUN
ijassa-112	204	42	β	β	PROPN
ijassa-112	204	43	is	be	AUX
ijassa-112	204	44	unknown	unknown	ADJ
ijassa-112	204	45	.	.	PUNCT
ijassa-112	205	1	then	then	ADV
ijassa-112	205	2	the	the	DET
ijassa-112	205	3	static	static	ADJ
ijassa-112	205	4	policies	policy	NOUN
ijassa-112	205	5	of	of	ADP
ijassa-112	205	6	airline	airline	NOUN
ijassa-112	205	7	booking	booking	NOUN
ijassa-112	205	8	under	under	ADP
ijassa-112	205	9	parametric	parametric	ADJ
ijassa-112	205	10	uncertainty	uncertainty	NOUN
ijassa-112	205	11	are	be	AUX
ijassa-112	205	12	given	give	VERB
ijassa-112	205	13	as	as	SCONJ
ijassa-112	205	14	follows	follow	VERB
ijassa-112	205	15	.	.	PUNCT
ijassa-112	206	1	advances	advance	NOUN
ijassa-112	206	2	in	in	ADP
ijassa-112	206	3	systems	system	NOUN
ijassa-112	206	4	science	science	NOUN
ijassa-112	206	5	and	and	CCONJ
ijassa-112	206	6	applications	application	NOUN
ijassa-112	206	7	(	(	PUNCT
ijassa-112	206	8	2012	2012	NUM
ijassa-112	206	9	)	)	PUNCT
ijassa-112	206	10	vol.12	vol.12	NOUN
ijassa-112	206	11	no.3	no.3	VERB
ijassa-112	206	12	281	281	NUM
ijassa-112	206	13	the	the	DET
ijassa-112	206	14	static	static	ADJ
ijassa-112	206	15	maximum	maximum	ADJ
ijassa-112	206	16	likelihood	likelihood	NOUN
ijassa-112	206	17	airline	airline	NOUN
ijassa-112	206	18	booking	booking	NOUN
ijassa-112	206	19	policy	policy	NOUN
ijassa-112	206	20	follows	follow	VERB
ijassa-112	206	21	from	from	ADP
ijassa-112	206	22	(	(	PUNCT
ijassa-112	206	23	6	6	NUM
ijassa-112	206	24	):	):	PUNCT
ijassa-112	206	25	µml	µml	NOUN
ijassa-112	206	26	1	1	NUM
ijassa-112	206	27	=	=	SYM
ijassa-112	206	28	ln	ln	ADJ
ijassa-112	206	29	γ−s	γ−s	PROPN
ijassa-112	206	30	/	/	SYM
ijassa-112	206	31	n	n	CCONJ
ijassa-112	206	32	,	,	PUNCT
ijassa-112	206	33	(	(	PUNCT
ijassa-112	206	34	30	30	NUM
ijassa-112	206	35	)	)	PUNCT
ijassa-112	206	36	where	where	SCONJ
ijassa-112	206	37	s	s	VERB
ijassa-112	206	38	=	=	PUNCT
ijassa-112	206	39	∑n	∑n	PROPN
ijassa-112	206	40	i=1xi	i=1xi	NOUN
ijassa-112	206	41	is	be	AUX
ijassa-112	206	42	the	the	DET
ijassa-112	206	43	sufficient	sufficient	ADJ
ijassa-112	206	44	statistic	statistic	NOUN
ijassa-112	206	45	for	for	ADP
ijassa-112	206	46	β	β	X
ijassa-112	206	47	,	,	PUNCT
ijassa-112	206	48	with	with	ADP
ijassa-112	206	49	v	v	NOUN
ijassa-112	206	50	=	=	SYM
ijassa-112	206	51	s	s	NOUN
ijassa-112	206	52	/	/	SYM
ijassa-112	206	53	β	β	X
ijassa-112	206	54	∼	∼	NOUN
ijassa-112	206	55	f(ν	f(ν	NOUN
ijassa-112	206	56	)	)	PUNCT
ijassa-112	206	57	=	=	SYM
ijassa-112	206	58	1	1	NUM
ijassa-112	206	59	γ(n	γ(n	X
ijassa-112	206	60	)	)	PUNCT
ijassa-112	206	61	νn−1	νn−1	PROPN
ijassa-112	206	62	exp(−ν	exp(−ν	PROPN
ijassa-112	206	63	)	)	PUNCT
ijassa-112	206	64	,	,	PUNCT
ijassa-112	206	65	ν	ν	X
ijassa-112	206	66	≥	≥	NOUN
ijassa-112	206	67	0	0	NUM
ijassa-112	206	68	,	,	PUNCT
ijassa-112	206	69	(	(	PUNCT
ijassa-112	206	70	31	31	NUM
ijassa-112	206	71	)	)	PUNCT
ijassa-112	206	72	and	and	CCONJ
ijassa-112	206	73	the	the	DET
ijassa-112	206	74	relative	relative	ADJ
ijassa-112	206	75	bias	bias	NOUN
ijassa-112	206	76	,	,	PUNCT
ijassa-112	206	77	r(µml	r(µml	NOUN
ijassa-112	206	78	1	1	NUM
ijassa-112	206	79	)	)	PUNCT
ijassa-112	206	80	=	=	NOUN
ijassa-112	206	81	∣∣eθ{f̄θ(µ	∣∣eθ{f̄θ(µ	NOUN
ijassa-112	206	82	ml	ml	VERB
ijassa-112	206	83	1	1	NUM
ijassa-112	206	84	)	)	PUNCT
ijassa-112	206	85	}	}	PUNCT
ijassa-112	206	86	−	−	PROPN
ijassa-112	206	87	γ	γ	X
ijassa-112	206	88	∣∣	∣∣	NUM
ijassa-112	206	89	γ	γ	X
ijassa-112	206	90	100	100	NUM
ijassa-112	206	91	%	%	NOUN
ijassa-112	206	92	=	=	SYM
ijassa-112	206	93	1	1	NUM
ijassa-112	206	94	+	+	CCONJ
ijassa-112	206	95	(	(	PUNCT
ijassa-112	206	96	1	1	NUM
ijassa-112	206	97	+	+	CCONJ
ijassa-112	206	98	ln	ln	ADJ
ijassa-112	206	99	γ−1	γ−1	ADJ
ijassa-112	206	100	/	/	SYM
ijassa-112	206	101	n)−1	n)−1	NOUN
ijassa-112	206	102	−	−	NOUN
ijassa-112	206	103	γ	γ	PROPN
ijassa-112	206	104	γ	γ	X
ijassa-112	206	105	100	100	NUM
ijassa-112	206	106	%	%	NOUN
ijassa-112	206	107	.	.	PUNCT
ijassa-112	207	1	(	(	PUNCT
ijassa-112	207	2	32	32	NUM
ijassa-112	207	3	)	)	PUNCT
ijassa-112	207	4	if	if	SCONJ
ijassa-112	207	5	,	,	PUNCT
ijassa-112	207	6	say	say	INTJ
ijassa-112	207	7	,	,	PUNCT
ijassa-112	207	8	n	n	NOUN
ijassa-112	207	9	=	=	SYM
ijassa-112	207	10	1	1	NUM
ijassa-112	207	11	and	and	CCONJ
ijassa-112	207	12	γ	γ	X
ijassa-112	207	13	=	=	SYM
ijassa-112	207	14	0.4	0.4	NUM
ijassa-112	208	1	,	,	PUNCT
ijassa-112	208	2	then	then	ADV
ijassa-112	208	3	rrb(µ	rrb(µ	PROPN
ijassa-112	208	4	ml	ml	PROPN
ijassa-112	208	5	1	1	NUM
ijassa-112	208	6	)	)	PUNCT
ijassa-112	208	7	=	=	SYM
ijassa-112	208	8	30%.thus	30%.thus	NUM
ijassa-112	208	9	,	,	PUNCT
ijassa-112	208	10	in	in	ADP
ijassa-112	208	11	this	this	DET
ijassa-112	208	12	example	example	NOUN
ijassa-112	208	13	the	the	DET
ijassa-112	208	14	static	static	ADJ
ijassa-112	208	15	maximum	maximum	ADJ
ijassa-112	208	16	likelihood	likelihood	NOUN
ijassa-112	208	17	airline	airline	NOUN
ijassa-112	208	18	booking	booking	NOUN
ijassa-112	208	19	policy	policy	NOUN
ijassa-112	208	20	has	have	AUX
ijassa-112	208	21	the	the	DET
ijassa-112	208	22	relative	relative	ADJ
ijassa-112	208	23	bias	bias	NOUN
ijassa-112	208	24	equal	equal	ADJ
ijassa-112	208	25	to	to	ADP
ijassa-112	208	26	30%.it	30%.it	PROPN
ijassa-112	208	27	follows	follow	VERB
ijassa-112	208	28	that	that	SCONJ
ijassa-112	208	29	the	the	DET
ijassa-112	208	30	protection	protection	NOUN
ijassa-112	208	31	level	level	NOUN
ijassa-112	208	32	for	for	ADP
ijassa-112	208	33	customers	customer	NOUN
ijassa-112	208	34	of	of	ADP
ijassa-112	208	35	the	the	DET
ijassa-112	208	36	high	high	ADJ
ijassa-112	208	37	fare	fare	NOUN
ijassa-112	208	38	class	class	NOUN
ijassa-112	208	39	will	will	AUX
ijassa-112	208	40	be	be	AUX
ijassa-112	208	41	determined	determine	VERB
ijassa-112	208	42	incorrectly	incorrectly	ADV
ijassa-112	208	43	.	.	PUNCT
ijassa-112	209	1	this	this	PRON
ijassa-112	209	2	may	may	AUX
ijassa-112	209	3	lead	lead	VERB
ijassa-112	209	4	to	to	ADP
ijassa-112	209	5	serious	serious	ADJ
ijassa-112	209	6	loss	loss	NOUN
ijassa-112	209	7	.	.	PUNCT
ijassa-112	210	1	the	the	DET
ijassa-112	210	2	static	static	ADJ
ijassa-112	210	3	unbiased	unbiased	ADJ
ijassa-112	210	4	airline	airline	NOUN
ijassa-112	210	5	booking	booking	NOUN
ijassa-112	210	6	policyfollows	policyfollow	VERB
ijassa-112	210	7	from	from	ADP
ijassa-112	210	8	(	(	PUNCT
ijassa-112	210	9	8)	8)	NUM
ijassa-112	210	10	:	:	PUNCT
ijassa-112	210	11	µunb	µunb	NOUN
ijassa-112	210	12	1	1	NUM
ijassa-112	211	1	=	=	SYM
ijassa-112	212	1	[	[	X
ijassa-112	212	2	γ−1	γ−1	ADJ
ijassa-112	212	3	/	/	SYM
ijassa-112	212	4	n	n	CCONJ
ijassa-112	212	5	−	−	PROPN
ijassa-112	212	6	1]s	1]s	NOUN
ijassa-112	212	7	,	,	PUNCT
ijassa-112	212	8	(	(	PUNCT
ijassa-112	212	9	33	33	NUM
ijassa-112	212	10	)	)	PUNCT
ijassa-112	212	11	where	where	SCONJ
ijassa-112	212	12	the	the	DET
ijassa-112	212	13	relative	relative	ADJ
ijassa-112	212	14	bias	bias	NOUN
ijassa-112	212	15	r(µunb	r(µunb	NOUN
ijassa-112	212	16	1	1	NUM
ijassa-112	212	17	)	)	PUNCT
ijassa-112	212	18	=	=	SYM
ijassa-112	212	19	0	0	X
ijassa-112	212	20	.	.	PUNCT
ijassa-112	213	1	the	the	DET
ijassa-112	213	2	dynamic	dynamic	ADJ
ijassa-112	213	3	unbiased	unbiased	ADJ
ijassa-112	213	4	airline	airline	NOUN
ijassa-112	213	5	booking	booking	NOUN
ijassa-112	213	6	policyfollows	policyfollow	VERB
ijassa-112	213	7	from	from	ADP
ijassa-112	213	8	(	(	PUNCT
ijassa-112	213	9	13	13	NUM
ijassa-112	213	10	)	)	PUNCT
ijassa-112	213	11	and	and	CCONJ
ijassa-112	213	12	(	(	PUNCT
ijassa-112	213	13	29	29	NUM
ijassa-112	213	14	):	):	PUNCT
ijassa-112	213	15	µunb	µunb	NOUN
ijassa-112	213	16	1k	1k	PROPN
ijassa-112	213	17	=	=	PUNCT
ijassa-112	213	18	arg	arg	NOUN
ijassa-112	213	19	(	(	PUNCT
ijassa-112	213	20	m	m	NOUN
ijassa-112	213	21	!	!	PUNCT
ijassa-112	214	1	(	(	PUNCT
ijassa-112	214	2	m−	m−	PROPN
ijassa-112	214	3	k	k	NOUN
ijassa-112	214	4	−	−	PROPN
ijassa-112	214	5	1	1	NUM
ijassa-112	214	6	)	)	PUNCT
ijassa-112	214	7	!	!	PUNCT
ijassa-112	215	1	m−k−1∑	m−k−1∑	PROPN
ijassa-112	215	2	j=0	j=0	PROPN
ijassa-112	215	3	(	(	PUNCT
ijassa-112	215	4	m−	m−	PROPN
ijassa-112	215	5	k	k	NOUN
ijassa-112	215	6	−	−	PROPN
ijassa-112	215	7	1	1	NUM
ijassa-112	215	8	j	j	NOUN
ijassa-112	215	9	)	)	PUNCT
ijassa-112	215	10	(	(	PUNCT
ijassa-112	215	11	−1)j	−1)j	NOUN
ijassa-112	215	12	1	1	NUM
ijassa-112	215	13	+	+	NUM
ijassa-112	215	14	j	j	PROPN
ijassa-112	215	15	(	(	PUNCT
ijassa-112	215	16	πk−1	πk−1	PROPN
ijassa-112	215	17	s=0	s=0	X
ijassa-112	216	1	[	[	X
ijassa-112	216	2	(	(	PUNCT
ijassa-112	216	3	µ1k	µ1k	PROPN
ijassa-112	216	4	y1k	y1k	PROPN
ijassa-112	216	5	−	−	PROPN
ijassa-112	216	6	1	1	NUM
ijassa-112	216	7	)	)	PUNCT
ijassa-112	216	8	(	(	PUNCT
ijassa-112	216	9	1	1	NUM
ijassa-112	216	10	+	+	CCONJ
ijassa-112	216	11	j	j	NOUN
ijassa-112	216	12	)	)	PUNCT
ijassa-112	216	13	+	+	CCONJ
ijassa-112	216	14	(	(	PUNCT
ijassa-112	216	15	m−	m−	PROPN
ijassa-112	216	16	k	k	PROPN
ijassa-112	217	1	+	+	CCONJ
ijassa-112	217	2	1	1	NUM
ijassa-112	217	3	+	+	NUM
ijassa-112	217	4	s	s	NOUN
ijassa-112	217	5	)	)	PUNCT
ijassa-112	217	6	]	]	PUNCT
ijassa-112	217	7	)	)	PUNCT
ijassa-112	217	8	−1	−1	NOUN
ijassa-112	217	9	=	=	SYM
ijassa-112	217	10	γ	γ	PROPN
ijassa-112	217	11	)	)	PUNCT
ijassa-112	217	12	,	,	PUNCT
ijassa-112	217	13	k	k	X
ijassa-112	217	14	=	=	SYM
ijassa-112	217	15	1	1	NUM
ijassa-112	217	16	,	,	PUNCT
ijassa-112	217	17	2	2	NUM
ijassa-112	217	18	.	.	PUNCT
ijassa-112	217	19	.	.	PUNCT
ijassa-112	217	20	.	.	PUNCT
ijassa-112	218	1	,	,	PUNCT
ijassa-112	218	2	m−	m−	PROPN
ijassa-112	218	3	1	1	NUM
ijassa-112	218	4	,	,	PUNCT
ijassa-112	218	5	(	(	PUNCT
ijassa-112	218	6	34	34	NUM
ijassa-112	218	7	)	)	PUNCT
ijassa-112	218	8	µ	µ	PRON
ijassa-112	218	9	◦	◦	NOUN
ijassa-112	218	10	(	(	PUNCT
ijassa-112	218	11	unb	unb	NOUN
ijassa-112	218	12	)	)	PUNCT
ijassa-112	218	13	1k	1k	PROPN
ijassa-112	218	14	=	=	SYM
ijassa-112	218	15	min	min	PROPN
ijassa-112	218	16	(	(	PUNCT
ijassa-112	218	17	µ	µ	NUM
ijassa-112	218	18	◦	◦	NOUN
ijassa-112	218	19	k	k	PROPN
ijassa-112	218	20	,	,	PUNCT
ijassa-112	218	21	µ	µ	X
ijassa-112	218	22	unb	unb	PROPN
ijassa-112	218	23	1k	1k	NOUN
ijassa-112	218	24	,	,	PUNCT
ijassa-112	218	25	−y1k	−y1k	PUNCT
ijassa-112	218	26	)	)	PUNCT
ijassa-112	218	27	.	.	PUNCT
ijassa-112	219	1	(	(	PUNCT
ijassa-112	219	2	35	35	NUM
ijassa-112	219	3	)	)	PUNCT
ijassa-112	219	4	7	7	NUM
ijassa-112	219	5	conclusion	conclusion	NOUN
ijassa-112	219	6	the	the	DET
ijassa-112	219	7	methodology	methodology	NOUN
ijassa-112	219	8	,	,	PUNCT
ijassa-112	219	9	which	which	PRON
ijassa-112	219	10	is	be	AUX
ijassa-112	219	11	developed	develop	VERB
ijassa-112	219	12	in	in	ADP
ijassa-112	219	13	this	this	DET
ijassa-112	219	14	paper	paper	NOUN
ijassa-112	219	15	for	for	ADP
ijassa-112	219	16	the	the	DET
ijassa-112	219	17	use	use	NOUN
ijassa-112	219	18	in	in	ADP
ijassa-112	219	19	the	the	DET
ijassa-112	219	20	airline	airline	NOUN
ijassa-112	219	21	industry	industry	NOUN
ijassa-112	219	22	under	under	ADP
ijassa-112	219	23	parametric	parametric	ADJ
ijassa-112	219	24	uncertainty	uncertainty	NOUN
ijassa-112	219	25	of	of	ADP
ijassa-112	219	26	airline	airline	NOUN
ijassa-112	219	27	customer	customer	NOUN
ijassa-112	219	28	demand	demand	NOUN
ijassa-112	219	29	models	model	NOUN
ijassa-112	219	30	,	,	PUNCT
ijassa-112	219	31	may	may	AUX
ijassa-112	219	32	be	be	AUX
ijassa-112	219	33	found	find	VERB
ijassa-112	219	34	to	to	PART
ijassa-112	219	35	be	be	AUX
ijassa-112	219	36	useful	useful	ADJ
ijassa-112	219	37	in	in	ADP
ijassa-112	219	38	other	other	ADJ
ijassa-112	219	39	industries	industry	NOUN
ijassa-112	219	40	such	such	ADJ
ijassa-112	219	41	as	as	ADP
ijassa-112	219	42	hotels	hotel	NOUN
ijassa-112	219	43	,	,	PUNCT
ijassa-112	219	44	car	car	NOUN
ijassa-112	219	45	rental	rental	NOUN
ijassa-112	219	46	companies	company	NOUN
ijassa-112	219	47	,	,	PUNCT
ijassa-112	219	48	shipping	shipping	NOUN
ijassa-112	219	49	companies	company	NOUN
ijassa-112	219	50	,	,	PUNCT
ijassa-112	219	51	etc	etc	X
ijassa-112	219	52	.	.	X
ijassa-112	219	53	while	while	SCONJ
ijassa-112	219	54	the	the	DET
ijassa-112	219	55	details	detail	NOUN
ijassa-112	219	56	of	of	ADP
ijassa-112	219	57	problems	problem	NOUN
ijassa-112	219	58	considered	consider	VERB
ijassa-112	219	59	in	in	ADP
ijassa-112	219	60	this	this	DET
ijassa-112	219	61	project	project	NOUN
ijassa-112	219	62	can	can	AUX
ijassa-112	219	63	change	change	VERB
ijassa-112	219	64	significantly	significantly	ADV
ijassa-112	219	65	from	from	ADP
ijassa-112	219	66	one	one	NUM
ijassa-112	219	67	industry	industry	NOUN
ijassa-112	219	68	to	to	ADP
ijassa-112	219	69	the	the	DET
ijassa-112	219	70	next	next	ADJ
ijassa-112	219	71	,	,	PUNCT
ijassa-112	219	72	the	the	DET
ijassa-112	219	73	focus	focus	NOUN
ijassa-112	219	74	is	be	AUX
ijassa-112	219	75	always	always	ADV
ijassa-112	219	76	on	on	ADP
ijassa-112	219	77	making	make	VERB
ijassa-112	219	78	better	well	ADJ
ijassa-112	219	79	demand	demand	NOUN
ijassa-112	219	80	decisions	decision	NOUN
ijassa-112	219	81	and	and	CCONJ
ijassa-112	219	82	not	not	PART
ijassa-112	219	83	manually	manually	ADV
ijassa-112	219	84	with	with	ADP
ijassa-112	219	85	guess	guess	NOUN
ijassa-112	219	86	work	work	NOUN
ijassa-112	219	87	and	and	CCONJ
ijassa-112	219	88	intuition	intuition	NOUN
ijassa-112	219	89	but	but	CCONJ
ijassa-112	219	90	rather	rather	ADV
ijassa-112	219	91	scientifically	scientifically	ADV
ijassa-112	219	92	with	with	ADP
ijassa-112	219	93	models	model	NOUN
ijassa-112	219	94	and	and	CCONJ
ijassa-112	219	95	technology	technology	NOUN
ijassa-112	219	96	,	,	PUNCT
ijassa-112	219	97	all	all	PRON
ijassa-112	219	98	implemented	implement	VERB
ijassa-112	219	99	with	with	ADP
ijassa-112	219	100	disciplined	discipline	VERB
ijassa-112	219	101	processes	process	NOUN
ijassa-112	219	102	and	and	CCONJ
ijassa-112	219	103	systems	system	NOUN
ijassa-112	219	104	.	.	PUNCT
ijassa-112	220	1	282	282	NUM
ijassa-112	220	2	nicholas	nicholas	PROPN
ijassa-112	220	3	a.	a.	PROPN
ijassa-112	220	4	nechval	nechval	PROPN
ijassa-112	220	5	:	:	PUNCT
ijassa-112	220	6	improved	improved	ADJ
ijassa-112	220	7	airline	airline	NOUN
ijassa-112	220	8	seat	seat	NOUN
ijassa-112	220	9	inventory	inventory	NOUN
ijassa-112	220	10	control	control	NOUN
ijassa-112	220	11	policies	policy	NOUN
ijassa-112	220	12	under	under	ADP
ijassa-112	220	13	parametric	parametric	ADJ
ijassa-112	220	14	...	...	PUNCT
ijassa-112	220	15	acknowledgements	acknowledgement	NOUN
ijassa-112	220	16	this	this	DET
ijassa-112	220	17	research	research	NOUN
ijassa-112	220	18	was	be	AUX
ijassa-112	220	19	supported	support	VERB
ijassa-112	220	20	in	in	ADP
ijassa-112	220	21	part	part	NOUN
ijassa-112	220	22	by	by	ADP
ijassa-112	220	23	grant	grant	NOUN
ijassa-112	220	24	no	no	PROPN
ijassa-112	220	25	.	.	PROPN
ijassa-112	220	26	06.1936	06.1936	NUM
ijassa-112	220	27	,	,	PUNCT
ijassa-112	220	28	grant	grant	VERB
ijassa-112	220	29	no	no	DET
ijassa-112	220	30	.	.	NOUN
ijassa-112	220	31	09.1014	09.1014	NUM
ijassa-112	220	32	,	,	PUNCT
ijassa-112	220	33	and	and	CCONJ
ijassa-112	220	34	grant	grant	VERB
ijassa-112	220	35	no	no	DET
ijassa-112	220	36	.	.	PROPN
ijassa-112	220	37	09.1544	09.1544	NUM
ijassa-112	220	38	from	from	ADP
ijassa-112	220	39	the	the	DET
ijassa-112	220	40	latvian	latvian	ADJ
ijassa-112	220	41	council	council	PROPN
ijassa-112	220	42	of	of	ADP
ijassa-112	220	43	science	science	PROPN
ijassa-112	220	44	and	and	CCONJ
ijassa-112	220	45	the	the	DET
ijassa-112	220	46	national	national	PROPN
ijassa-112	220	47	institute	institute	PROPN
ijassa-112	220	48	of	of	ADP
ijassa-112	220	49	mathematics	mathematics	PROPN
ijassa-112	220	50	and	and	CCONJ
ijassa-112	220	51	informatics	informatic	NOUN
ijassa-112	220	52	of	of	ADP
ijassa-112	220	53	latvia	latvia	PROPN
ijassa-112	220	54	.	.	PUNCT
ijassa-112	221	1	references	reference	NOUN
ijassa-112	221	2	[	[	X
ijassa-112	221	3	1	1	X
ijassa-112	221	4	]	]	PUNCT
ijassa-112	221	5	weatherford	weatherford	PROPN
ijassa-112	221	6	l.r	l.r	PROPN
ijassa-112	221	7	.	.	PROPN
ijassa-112	221	8	,	,	PUNCT
ijassa-112	221	9	bodily	bodily	PROPN
ijassa-112	221	10	s.e	s.e	PROPN
ijassa-112	221	11	.	.	PROPN
ijassa-112	221	12	and	and	CCONJ
ijassa-112	221	13	pfeifer	pfeifer	PROPN
ijassa-112	221	14	p.e	p.e	PROPN
ijassa-112	221	15	.	.	PROPN
ijassa-112	221	16	(	(	PUNCT
ijassa-112	221	17	1993	1993	NUM
ijassa-112	221	18	)	)	PUNCT
ijassa-112	221	19	,	,	PUNCT
ijassa-112	221	20	“	"	PUNCT
ijassa-112	221	21	modeling	model	VERB
ijassa-112	221	22	the	the	DET
ijassa-112	221	23	customer	customer	NOUN
ijassa-112	221	24	arrival	arrival	NOUN
ijassa-112	221	25	process	process	NOUN
ijassa-112	221	26	and	and	CCONJ
ijassa-112	221	27	comparing	compare	VERB
ijassa-112	221	28	decision	decision	NOUN
ijassa-112	221	29	rules	rule	NOUN
ijassa-112	221	30	in	in	ADP
ijassa-112	221	31	perishable	perishable	ADJ
ijassa-112	221	32	asset	asset	NOUN
ijassa-112	221	33	revenue	revenue	NOUN
ijassa-112	221	34	management	management	NOUN
ijassa-112	221	35	situation	situation	NOUN
ijassa-112	221	36	”	"	PUNCT
ijassa-112	221	37	,	,	PUNCT
ijassa-112	221	38	transportation	transportation	NOUN
ijassa-112	221	39	science	science	NOUN
ijassa-112	221	40	,	,	PUNCT
ijassa-112	221	41	vol.27	vol.27	NOUN
ijassa-112	221	42	,	,	PUNCT
ijassa-112	221	43	pp.239	pp.239	PROPN
ijassa-112	221	44	-	-	PUNCT
ijassa-112	221	45	251	251	NUM
ijassa-112	221	46	.	.	PUNCT
ijassa-112	222	1	[	[	X
ijassa-112	222	2	2	2	X
ijassa-112	222	3	]	]	X
ijassa-112	222	4	belobaba	belobaba	PROPN
ijassa-112	222	5	p.p	p.p	PROPN
ijassa-112	222	6	.	.	PROPN
ijassa-112	222	7	(	(	PUNCT
ijassa-112	222	8	1987	1987	NUM
ijassa-112	222	9	)	)	PUNCT
ijassa-112	222	10	,	,	PUNCT
ijassa-112	222	11	“	"	PUNCT
ijassa-112	222	12	airline	airline	NOUN
ijassa-112	222	13	yield	yield	NOUN
ijassa-112	222	14	management	management	NOUN
ijassa-112	222	15	:	:	PUNCT
ijassa-112	222	16	an	an	DET
ijassa-112	222	17	overview	overview	NOUN
ijassa-112	222	18	of	of	ADP
ijassa-112	222	19	seat	seat	NOUN
ijassa-112	222	20	inventory	inventory	NOUN
ijassa-112	222	21	control	control	NOUN
ijassa-112	222	22	”	"	PUNCT
ijassa-112	222	23	,	,	PUNCT
ijassa-112	222	24	transportation	transportation	NOUN
ijassa-112	222	25	science	science	NOUN
ijassa-112	222	26	,	,	PUNCT
ijassa-112	222	27	vol.21	vol.21	NOUN
ijassa-112	222	28	,	,	PUNCT
ijassa-112	222	29	pp.66	pp.66	NOUN
ijassa-112	222	30	-	-	PUNCT
ijassa-112	222	31	73	73	NUM
ijassa-112	222	32	.	.	PUNCT
ijassa-112	223	1	[	[	X
ijassa-112	223	2	3	3	X
ijassa-112	223	3	]	]	X
ijassa-112	223	4	nechval	nechval	PROPN
ijassa-112	223	5	n.a	n.a	PROPN
ijassa-112	223	6	.	.	PROPN
ijassa-112	223	7	,	,	PUNCT
ijassa-112	223	8	berzins	berzin	NOUN
ijassa-112	223	9	g.	g.	PROPN
ijassa-112	223	10	,	,	PUNCT
ijassa-112	223	11	purgailis	purgailis	PROPN
ijassa-112	223	12	m.	m.	PROPN
ijassa-112	223	13	,	,	PUNCT
ijassa-112	223	14	nechval	nechval	PROPN
ijassa-112	223	15	k.n	k.n	PROPN
ijassa-112	223	16	.	.	PROPN
ijassa-112	223	17	(	(	PUNCT
ijassa-112	223	18	2008	2008	NUM
ijassa-112	223	19	)	)	PUNCT
ijassa-112	223	20	,	,	PUNCT
ijassa-112	223	21	“	"	PUNCT
ijassa-112	223	22	improved	improved	ADJ
ijassa-112	223	23	estimation	estimation	NOUN
ijassa-112	223	24	of	of	ADP
ijassa-112	223	25	state	state	NOUN
ijassa-112	223	26	of	of	ADP
ijassa-112	223	27	stochastic	stochastic	ADJ
ijassa-112	223	28	systems	system	NOUN
ijassa-112	223	29	via	via	ADP
ijassa-112	223	30	invariant	invariant	ADJ
ijassa-112	223	31	embedding	embed	VERB
ijassa-112	223	32	technique	technique	NOUN
ijassa-112	223	33	”	"	PUNCT
ijassa-112	223	34	,	,	PUNCT
ijassa-112	223	35	wseas	wsea	VERB
ijassa-112	223	36	transactions	transaction	NOUN
ijassa-112	223	37	on	on	ADP
ijassa-112	223	38	mathematics	mathematic	NOUN
ijassa-112	223	39	,	,	PUNCT
ijassa-112	223	40	vol.7	vol.7	PROPN
ijassa-112	223	41	,	,	PUNCT
ijassa-112	223	42	pp.141	pp.141	NOUN
ijassa-112	223	43	-	-	X
ijassa-112	223	44	159	159	NUM
ijassa-112	223	45	.	.	PUNCT
ijassa-112	224	1	[	[	X
ijassa-112	224	2	4	4	NUM
ijassa-112	224	3	]	]	X
ijassa-112	224	4	nechval	nechval	PROPN
ijassa-112	224	5	n.a	n.a	PROPN
ijassa-112	224	6	.	.	PROPN
ijassa-112	224	7	,	,	PUNCT
ijassa-112	224	8	nechval	nechval	PROPN
ijassa-112	224	9	k.n	k.n	PROPN
ijassa-112	224	10	.	.	PROPN
ijassa-112	224	11	,	,	PUNCT
ijassa-112	224	12	purgailis	purgailis	PROPN
ijassa-112	224	13	m.	m.	PROPN
ijassa-112	224	14	,	,	PUNCT
ijassa-112	224	15	rozevskis	rozevskis	PROPN
ijassa-112	224	16	u.	u.	PROPN
ijassa-112	224	17	(	(	PUNCT
ijassa-112	224	18	2011	2011	NUM
ijassa-112	224	19	)	)	PUNCT
ijassa-112	224	20	,	,	PUNCT
ijassa-112	224	21	“	"	PUNCT
ijassa-112	224	22	improvement	improvement	NOUN
ijassa-112	224	23	of	of	ADP
ijassa-112	224	24	inventory	inventory	NOUN
ijassa-112	224	25	control	control	NOUN
ijassa-112	224	26	under	under	ADP
ijassa-112	224	27	parametric	parametric	ADJ
ijassa-112	224	28	uncertainty	uncertainty	NOUN
ijassa-112	224	29	and	and	CCONJ
ijassa-112	224	30	constraints	constraint	NOUN
ijassa-112	224	31	”	"	PUNCT
ijassa-112	224	32	,	,	PUNCT
ijassa-112	224	33	in	in	ADP
ijassa-112	224	34	:	:	PUNCT
ijassa-112	224	35	dobnikar	dobnikar	PROPN
ijassa-112	224	36	,	,	PUNCT
ijassa-112	224	37	a.	a.	NOUN
ijassa-112	224	38	,	,	PUNCT
ijassa-112	224	39	lotric	lotric	NOUN
ijassa-112	224	40	,	,	PUNCT
ijassa-112	224	41	u.	u.	PROPN
ijassa-112	224	42	,	,	PUNCT
ijassa-112	224	43	ster	ster	PROPN
ijassa-112	224	44	,	,	PUNCT
ijassa-112	224	45	b.	b.	PROPN
ijassa-112	224	46	(	(	PUNCT
ijassa-112	224	47	eds	eds	PROPN
ijassa-112	224	48	.	.	PUNCT
ijassa-112	224	49	)	)	PUNCT
ijassa-112	224	50	,	,	PUNCT
ijassa-112	224	51	adaptive	adaptive	ADJ
ijassa-112	224	52	and	and	CCONJ
ijassa-112	224	53	natural	natural	ADJ
ijassa-112	224	54	computing	compute	VERB
ijassa-112	224	55	algorithms	algorithm	NOUN
ijassa-112	224	56	,	,	PUNCT
ijassa-112	224	57	lncs	lnc	NOUN
ijassa-112	224	58	,	,	PUNCT
ijassa-112	224	59	vol.6594	vol.6594	X
ijassa-112	224	60	,	,	PUNCT
ijassa-112	224	61	part	part	PROPN
ijassa-112	224	62	ii	ii	PROPN
ijassa-112	224	63	,	,	PUNCT
ijassa-112	224	64	pp.136	pp.136	PROPN
ijassa-112	224	65	-	-	PUNCT
ijassa-112	224	66	146	146	NUM
ijassa-112	224	67	,	,	PUNCT
ijassa-112	224	68	springer	springer	NOUN
ijassa-112	224	69	,	,	PUNCT
ijassa-112	224	70	heidelberg	heidelberg	NOUN
ijassa-112	224	71	.	.	PUNCT
ijassa-112	225	1	[	[	X
ijassa-112	225	2	5	5	X
ijassa-112	225	3	]	]	X
ijassa-112	225	4	littlewood	littlewood	PROPN
ijassa-112	225	5	k.	k.	PROPN
ijassa-112	225	6	(	(	PUNCT
ijassa-112	225	7	1972	1972	NUM
ijassa-112	225	8	)	)	PUNCT
ijassa-112	225	9	,	,	PUNCT
ijassa-112	225	10	“	"	PUNCT
ijassa-112	225	11	forecasting	forecasting	NOUN
ijassa-112	225	12	and	and	CCONJ
ijassa-112	225	13	control	control	NOUN
ijassa-112	225	14	of	of	ADP
ijassa-112	225	15	passenger	passenger	NOUN
ijassa-112	225	16	bookings	booking	NOUN
ijassa-112	225	17	”	"	PUNCT
ijassa-112	225	18	,	,	PUNCT
ijassa-112	225	19	in	in	ADP
ijassa-112	225	20	:	:	PUNCT
ijassa-112	225	21	proceedings	proceeding	NOUN
ijassa-112	225	22	of	of	ADP
ijassa-112	225	23	the	the	DET
ijassa-112	225	24	12th	12th	ADJ
ijassa-112	225	25	agifors	agifors	PROPN
ijassa-112	225	26	symposium	symposium	NOUN
ijassa-112	225	27	,	,	PUNCT
ijassa-112	225	28	pp.95	pp.95	NOUN
ijassa-112	225	29	-	-	PUNCT
ijassa-112	225	30	117	117	NUM
ijassa-112	225	31	,	,	PUNCT
ijassa-112	225	32	american	american	PROPN
ijassa-112	225	33	airlines	airlines	PROPN
ijassa-112	225	34	,	,	PUNCT
ijassa-112	225	35	new	new	PROPN
ijassa-112	225	36	york	york	PROPN
ijassa-112	225	37	.	.	PUNCT
ijassa-112	226	1	[	[	X
ijassa-112	226	2	6	6	NUM
ijassa-112	226	3	]	]	X
ijassa-112	226	4	i	i	PRON
ijassa-112	226	5	richter	richter	PROPN
ijassa-112	226	6	h.	h.	PROPN
ijassa-112	226	7	(	(	PUNCT
ijassa-112	226	8	1982	1982	NUM
ijassa-112	226	9	)	)	PUNCT
ijassa-112	226	10	,	,	PUNCT
ijassa-112	226	11	“	"	PUNCT
ijassa-112	226	12	the	the	DET
ijassa-112	226	13	differential	differential	ADJ
ijassa-112	226	14	revenue	revenue	NOUN
ijassa-112	226	15	method	method	NOUN
ijassa-112	226	16	to	to	PART
ijassa-112	226	17	determine	determine	VERB
ijassa-112	226	18	optimal	optimal	ADJ
ijassa-112	226	19	seat	seat	NOUN
ijassa-112	226	20	allotments	allotment	NOUN
ijassa-112	226	21	by	by	ADP
ijassa-112	226	22	fare	fare	NOUN
ijassa-112	226	23	type	type	NOUN
ijassa-112	226	24	”	"	PUNCT
ijassa-112	226	25	,	,	PUNCT
ijassa-112	226	26	in	in	ADP
ijassa-112	226	27	:	:	PUNCT
ijassa-112	226	28	proceedings	proceeding	NOUN
ijassa-112	226	29	of	of	ADP
ijassa-112	226	30	the	the	DET
ijassa-112	226	31	xxii	xxii	PROPN
ijassa-112	226	32	agifors	agifors	PROPN
ijassa-112	226	33	symposium	symposium	NOUN
ijassa-112	226	34	,	,	PUNCT
ijassa-112	226	35	pp.339	pp.339	PROPN
ijassa-112	226	36	-	-	PUNCT
ijassa-112	226	37	362	362	NUM
ijassa-112	226	38	,	,	PUNCT
ijassa-112	226	39	american	american	PROPN
ijassa-112	226	40	airlines	airlines	PROPN
ijassa-112	226	41	,	,	PUNCT
ijassa-112	226	42	new	new	PROPN
ijassa-112	226	43	york	york	PROPN
ijassa-112	226	44	.	.	PUNCT
ijassa-112	227	1	[	[	X
ijassa-112	227	2	7	7	NUM
ijassa-112	227	3	]	]	X
ijassa-112	227	4	curry	curry	NOUN
ijassa-112	227	5	,	,	PUNCT
ijassa-112	227	6	r.e	r.e	PROPN
ijassa-112	227	7	.	.	PROPN
ijassa-112	227	8	(	(	PUNCT
ijassa-112	227	9	1990	1990	NUM
ijassa-112	227	10	)	)	PUNCT
ijassa-112	227	11	,	,	PUNCT
ijassa-112	227	12	“	"	PUNCT
ijassa-112	227	13	optimal	optimal	ADJ
ijassa-112	227	14	airline	airline	NOUN
ijassa-112	227	15	beat	beat	VERB
ijassa-112	227	16	allocation	allocation	NOUN
ijassa-112	227	17	with	with	ADP
ijassa-112	227	18	fare	fare	ADJ
ijassa-112	227	19	classes	class	NOUN
ijassa-112	227	20	nested	nest	VERB
ijassa-112	227	21	by	by	ADP
ijassa-112	227	22	origins	origin	NOUN
ijassa-112	227	23	and	and	CCONJ
ijassa-112	227	24	destinations	destination	NOUN
ijassa-112	227	25	”	"	PUNCT
ijassa-112	227	26	,	,	PUNCT
ijassa-112	227	27	transportation	transportation	NOUN
ijassa-112	227	28	science	science	NOUN
ijassa-112	227	29	,	,	PUNCT
ijassa-112	227	30	vol.24	vol.24	NOUN
ijassa-112	227	31	,	,	PUNCT
ijassa-112	227	32	pp.193	pp.193	NOUN
ijassa-112	227	33	-	-	PUNCT
ijassa-112	227	34	203	203	NUM
ijassa-112	227	35	.	.	PUNCT
ijassa-112	228	1	[	[	X
ijassa-112	228	2	8	8	NUM
ijassa-112	228	3	]	]	PUNCT
ijassa-112	228	4	wollmer	wollmer	NOUN
ijassa-112	228	5	,	,	PUNCT
ijassa-112	228	6	r.d	r.d	PROPN
ijassa-112	228	7	.	.	PROPN
ijassa-112	228	8	(	(	PUNCT
ijassa-112	228	9	1992	1992	NUM
ijassa-112	228	10	)	)	PUNCT
ijassa-112	228	11	,	,	PUNCT
ijassa-112	228	12	“	"	PUNCT
ijassa-112	228	13	an	an	DET
ijassa-112	228	14	airline	airline	NOUN
ijassa-112	228	15	seat	seat	NOUN
ijassa-112	228	16	management	management	NOUN
ijassa-112	228	17	model	model	NOUN
ijassa-112	228	18	for	for	ADP
ijassa-112	228	19	a	a	DET
ijassa-112	228	20	single	single	ADJ
ijassa-112	228	21	leg	leg	NOUN
ijassa-112	228	22	route	route	NOUN
ijassa-112	228	23	when	when	SCONJ
ijassa-112	228	24	lower	low	ADJ
ijassa-112	228	25	fare	fare	NOUN
ijassa-112	228	26	classes	class	NOUN
ijassa-112	228	27	book	book	NOUN
ijassa-112	228	28	first	first	ADV
ijassa-112	228	29	”	"	PUNCT
ijassa-112	228	30	,	,	PUNCT
ijassa-112	228	31	operations	operation	NOUN
ijassa-112	228	32	research	research	NOUN
ijassa-112	228	33	,	,	PUNCT
ijassa-112	228	34	vol.40	vol.40	NOUN
ijassa-112	228	35	,	,	PUNCT
ijassa-112	228	36	pp.2637	pp.2637	PROPN
ijassa-112	228	37	.	.	PUNCT
ijassa-112	229	1	[	[	X
ijassa-112	229	2	9	9	NUM
ijassa-112	229	3	]	]	PUNCT
ijassa-112	229	4	brumelle	brumelle	PROPN
ijassa-112	229	5	,	,	PUNCT
ijassa-112	229	6	s.l	s.l	PROPN
ijassa-112	229	7	.	.	PROPN
ijassa-112	229	8	and	and	CCONJ
ijassa-112	229	9	mcgill	mcgill	PROPN
ijassa-112	229	10	,	,	PUNCT
ijassa-112	229	11	j.i	j.i	PROPN
ijassa-112	229	12	.	.	PROPN
ijassa-112	229	13	(	(	PUNCT
ijassa-112	229	14	1993	1993	NUM
ijassa-112	229	15	)	)	PUNCT
ijassa-112	229	16	,	,	PUNCT
ijassa-112	229	17	“	"	PUNCT
ijassa-112	229	18	airline	airline	NOUN
ijassa-112	229	19	seat	seat	NOUN
ijassa-112	229	20	allocation	allocation	NOUN
ijassa-112	229	21	with	with	ADP
ijassa-112	229	22	multiple	multiple	ADJ
ijassa-112	229	23	nested	nest	VERB
ijassa-112	229	24	fare	fare	NOUN
ijassa-112	229	25	classes	class	NOUN
ijassa-112	229	26	”	"	PUNCT
ijassa-112	229	27	,	,	PUNCT
ijassa-112	229	28	operations	operation	NOUN
ijassa-112	229	29	research	research	NOUN
ijassa-112	229	30	,	,	PUNCT
ijassa-112	229	31	vol.41	vol.41	NOUN
ijassa-112	229	32	,	,	PUNCT
ijassa-112	229	33	pp.127	pp.127	PROPN
ijassa-112	229	34	-	-	PUNCT
ijassa-112	229	35	137	137	NUM
ijassa-112	229	36	.	.	PUNCT
ijassa-112	229	37	corresponding	correspond	VERB
ijassa-112	229	38	author	author	NOUN
ijassa-112	229	39	nicholas	nicholas	PROPN
ijassa-112	229	40	nechval	nechval	PROPN
ijassa-112	229	41	can	can	AUX
ijassa-112	229	42	be	be	AUX
ijassa-112	229	43	contacted	contact	VERB
ijassa-112	229	44	at:jnechval@junik.lv	at:jnechval@junik.lv	PROPN