id	sid	tid	token	lemma	pos
iajs-2434	1	1	microsoft	microsoft	PROPN
iajs-2434	1	2	word	word	NOUN
iajs-2434	1	3	128	128	NUM
iajs-2434	1	4	-	-	SYM
iajs-2434	1	5	139	139	NUM
iajs-2434	1	6	  	  	SPACE
iajs-2434	1	7	128	128	NUM
iajs-2434	1	8	  	  	SPACE
iajs-2434	1	9	ibn	ibn	PROPN
iajs-2434	1	10	al	al	PROPN
iajs-2434	1	11	-	-	PUNCT
iajs-2434	1	12	haitham	haitham	PROPN
iajs-2434	1	13	jour	jour	X
iajs-2434	1	14	.	.	PROPN
iajs-2434	2	1	for	for	ADP
iajs-2434	2	2	pure	pure	ADJ
iajs-2434	2	3	&	&	CCONJ
iajs-2434	2	4	appl	appl	PROPN
iajs-2434	2	5	.	.	PUNCT
iajs-2434	3	1	sci	sci	PROPN
iajs-2434	3	2	.	.	PROPN
iajs-2434	4	1	33	33	NUM
iajs-2434	4	2	(	(	PUNCT
iajs-2434	4	3	1	1	NUM
iajs-2434	4	4	)	)	PUNCT
iajs-2434	4	5	2020	2020	NUM
iajs-2434	4	6	      	      	SPACE
iajs-2434	4	7	bayesian	bayesian	NOUN
iajs-2434	4	8	estimators	estimator	NOUN
iajs-2434	4	9	of	of	ADP
iajs-2434	4	10	the	the	DET
iajs-2434	4	11	parameter	parameter	NOUN
iajs-2434	4	12	and	and	CCONJ
iajs-2434	4	13	reliability	reliability	NOUN
iajs-2434	4	14	function	function	NOUN
iajs-2434	4	15	of	of	ADP
iajs-2434	4	16	inverse	inverse	NOUN
iajs-2434	4	17	rayleigh	rayleigh	PROPN
iajs-2434	4	18	distribution"a	distribution"a	PROPN
iajs-2434	4	19	comparison	comparison	NOUN
iajs-2434	4	20	study	study	PROPN
iajs-2434	4	21	”	"	PUNCT
iajs-2434	4	22	masooma	masooma	PROPN
iajs-2434	4	23	ali	ali	PROPN
iajs-2434	4	24	abod	abod	PROPN
iajs-2434	4	25	hazim	hazim	PROPN
iajs-2434	4	26	mansoor	mansoor	PROPN
iajs-2434	4	27	gorgee	gorgee	PROPN
iajs-2434	4	28	    	    	SPACE
iajs-2434	4	29	article	article	NOUN
iajs-2434	4	30	history	history	NOUN
iajs-2434	4	31	:	:	PUNCT
iajs-2434	4	32	received	receive	VERB
iajs-2434	4	33	2	2	NUM
iajs-2434	4	34	july	july	PROPN
iajs-2434	4	35	2019	2019	NUM
iajs-2434	4	36	,	,	PUNCT
iajs-2434	4	37	accepted	accept	VERB
iajs-2434	4	38	19	19	NUM
iajs-2434	4	39	august	august	PROPN
iajs-2434	4	40	2019	2019	NUM
iajs-2434	4	41	,	,	PUNCT
iajs-2434	4	42	published	publish	VERB
iajs-2434	4	43	in	in	ADP
iajs-2434	4	44	april	april	PROPN
iajs-2434	4	45	2020	2020	NUM
iajs-2434	4	46	.	.	PUNCT
iajs-2434	5	1	abstract	abstract	ADJ
iajs-2434	5	2	in	in	ADP
iajs-2434	5	3	this	this	DET
iajs-2434	5	4	paper	paper	NOUN
iajs-2434	5	5	,	,	PUNCT
iajs-2434	5	6	bayesian	bayesian	NOUN
iajs-2434	5	7	estimator	estimator	NOUN
iajs-2434	5	8	for	for	ADP
iajs-2434	5	9	the	the	DET
iajs-2434	5	10	parameter	parameter	NOUN
iajs-2434	5	11	and	and	CCONJ
iajs-2434	5	12	reliability	reliability	NOUN
iajs-2434	5	13	function	function	NOUN
iajs-2434	5	14	of	of	ADP
iajs-2434	5	15	inverse	inverse	NOUN
iajs-2434	5	16	rayleigh	rayleigh	NOUN
iajs-2434	5	17	distribution	distribution	NOUN
iajs-2434	5	18	(	(	PUNCT
iajs-2434	5	19	ird	ird	PROPN
iajs-2434	5	20	)	)	PUNCT
iajs-2434	5	21	were	be	AUX
iajs-2434	5	22	obtained	obtain	VERB
iajs-2434	5	23	under	under	ADP
iajs-2434	5	24	three	three	NUM
iajs-2434	5	25	types	type	NOUN
iajs-2434	5	26	of	of	ADP
iajs-2434	5	27	loss	loss	NOUN
iajs-2434	5	28	function	function	NOUN
iajs-2434	5	29	,	,	PUNCT
iajs-2434	5	30	namely	namely	ADV
iajs-2434	5	31	,	,	PUNCT
iajs-2434	5	32	square	square	ADJ
iajs-2434	5	33	error	error	NOUN
iajs-2434	5	34	loss	loss	NOUN
iajs-2434	5	35	function	function	NOUN
iajs-2434	5	36	(	(	PUNCT
iajs-2434	5	37	self	self	NOUN
iajs-2434	5	38	)	)	PUNCT
iajs-2434	5	39	,	,	PUNCT
iajs-2434	5	40	modified	modify	VERB
iajs-2434	5	41	square	square	ADJ
iajs-2434	5	42	error	error	NOUN
iajs-2434	5	43	loss	loss	NOUN
iajs-2434	5	44	function	function	NOUN
iajs-2434	5	45	(	(	PUNCT
iajs-2434	5	46	mself	mself	NUM
iajs-2434	5	47	)	)	PUNCT
iajs-2434	5	48	and	and	CCONJ
iajs-2434	5	49	precautionary	precautionary	ADJ
iajs-2434	5	50	loss	loss	NOUN
iajs-2434	5	51	function	function	NOUN
iajs-2434	5	52	(	(	PUNCT
iajs-2434	5	53	plf	plf	NOUN
iajs-2434	5	54	)	)	PUNCT
iajs-2434	5	55	,	,	PUNCT
iajs-2434	5	56	taking	take	VERB
iajs-2434	5	57	into	into	ADP
iajs-2434	5	58	consideration	consideration	NOUN
iajs-2434	5	59	the	the	DET
iajs-2434	5	60	informative	informative	ADJ
iajs-2434	5	61	and	and	CCONJ
iajs-2434	5	62	noninformative	noninformative	ADJ
iajs-2434	5	63	prior	prior	ADV
iajs-2434	5	64	.	.	PUNCT
iajs-2434	6	1	the	the	DET
iajs-2434	6	2	performance	performance	NOUN
iajs-2434	6	3	of	of	ADP
iajs-2434	6	4	such	such	ADJ
iajs-2434	6	5	estimators	estimator	NOUN
iajs-2434	6	6	was	be	AUX
iajs-2434	6	7	assessed	assess	VERB
iajs-2434	6	8	on	on	ADP
iajs-2434	6	9	the	the	DET
iajs-2434	6	10	basis	basis	NOUN
iajs-2434	6	11	of	of	ADP
iajs-2434	6	12	mean	mean	ADJ
iajs-2434	6	13	square	square	ADJ
iajs-2434	6	14	error	error	NOUN
iajs-2434	6	15	(	(	PUNCT
iajs-2434	6	16	mse	mse	NOUN
iajs-2434	6	17	)	)	PUNCT
iajs-2434	6	18	criterion	criterion	NOUN
iajs-2434	6	19	by	by	ADP
iajs-2434	6	20	performing	perform	VERB
iajs-2434	6	21	a	a	DET
iajs-2434	6	22	monte	monte	PROPN
iajs-2434	6	23	carlo	carlo	PROPN
iajs-2434	6	24	simulation	simulation	NOUN
iajs-2434	6	25	technique	technique	NOUN
iajs-2434	6	26	.	.	PUNCT
iajs-2434	7	1	keywords	keyword	NOUN
iajs-2434	7	2	:	:	PUNCT
iajs-2434	7	3	inverse	inverse	ADJ
iajs-2434	7	4	rayleigh	rayleigh	NOUN
iajs-2434	7	5	distribution	distribution	NOUN
iajs-2434	7	6	,	,	PUNCT
iajs-2434	7	7	loss	loss	NOUN
iajs-2434	7	8	function	function	NOUN
iajs-2434	7	9	,	,	PUNCT
iajs-2434	7	10	risk	risk	NOUN
iajs-2434	7	11	function	function	NOUN
iajs-2434	7	12	prior	prior	ADJ
iajs-2434	7	13	information	information	NOUN
iajs-2434	7	14	,	,	PUNCT
iajs-2434	7	15	posterior	posterior	ADJ
iajs-2434	7	16	distribution	distribution	NOUN
iajs-2434	7	17	.	.	PUNCT
iajs-2434	8	1	1	1	X
iajs-2434	8	2	.	.	X
iajs-2434	8	3	introduction	introduction	NOUN
iajs-2434	8	4	in	in	ADP
iajs-2434	8	5	reliability	reliability	NOUN
iajs-2434	8	6	studies	study	NOUN
iajs-2434	8	7	,	,	PUNCT
iajs-2434	8	8	most	most	ADJ
iajs-2434	8	9	of	of	ADP
iajs-2434	8	10	the	the	DET
iajs-2434	8	11	life	life	NOUN
iajs-2434	8	12	time	time	NOUN
iajs-2434	8	13	distributions	distribution	NOUN
iajs-2434	8	14	used	use	VERB
iajs-2434	8	15	are	be	AUX
iajs-2434	8	16	characterized	characterize	VERB
iajs-2434	8	17	by	by	ADP
iajs-2434	8	18	a	a	DET
iajs-2434	8	19	monotone	monotone	ADJ
iajs-2434	8	20	failure	failure	NOUN
iajs-2434	8	21	rate	rate	NOUN
iajs-2434	8	22	,	,	PUNCT
iajs-2434	8	23	however	however	ADV
iajs-2434	8	24	,	,	PUNCT
iajs-2434	8	25	one	one	NUM
iajs-2434	8	26	parameter	parameter	NOUN
iajs-2434	8	27	inverse	inverse	NOUN
iajs-2434	8	28	rayleigh	rayleigh	PROPN
iajs-2434	8	29	distribution	distribution	NOUN
iajs-2434	8	30	has	have	AUX
iajs-2434	8	31	also	also	ADV
iajs-2434	8	32	been	be	AUX
iajs-2434	8	33	used	use	VERB
iajs-2434	8	34	as	as	ADP
iajs-2434	8	35	a	a	DET
iajs-2434	8	36	failure	failure	NOUN
iajs-2434	8	37	time	time	NOUN
iajs-2434	8	38	distribution	distribution	NOUN
iajs-2434	8	39	.	.	PUNCT
iajs-2434	9	1	recently	recently	ADV
iajs-2434	9	2	,	,	PUNCT
iajs-2434	9	3	many	many	ADJ
iajs-2434	9	4	researchers	researcher	NOUN
iajs-2434	9	5	interested	interested	ADJ
iajs-2434	9	6	in	in	ADP
iajs-2434	9	7	studying	study	VERB
iajs-2434	9	8	inverse	inverse	ADJ
iajs-2434	9	9	rayleigh	rayleigh	NOUN
iajs-2434	9	10	distribution	distribution	NOUN
iajs-2434	9	11	in	in	ADP
iajs-2434	9	12	various	various	ADJ
iajs-2434	9	13	aspects	aspect	NOUN
iajs-2434	9	14	,	,	PUNCT
iajs-2434	9	15	for	for	ADP
iajs-2434	9	16	example	example	NOUN
iajs-2434	9	17	:	:	PUNCT
iajs-2434	9	18	mukherjee	mukherjee	PROPN
iajs-2434	9	19	and	and	CCONJ
iajs-2434	9	20	saran	saran	PROPN
iajs-2434	9	21	(	(	PUNCT
iajs-2434	9	22	1984	1984	NUM
iajs-2434	9	23	)	)	PUNCT
iajs-2434	9	24	demonstrated	demonstrate	VERB
iajs-2434	9	25	that	that	SCONJ
iajs-2434	9	26	for	for	ADP
iajs-2434	9	27	a	a	DET
iajs-2434	9	28	given	give	VERB
iajs-2434	9	29	parameter	parameter	NOUN
iajs-2434	9	30	𝜃	𝜃	NOUN
iajs-2434	9	31	the	the	DET
iajs-2434	9	32	distribution	distribution	NOUN
iajs-2434	9	33	is	be	AUX
iajs-2434	9	34	increasing	increase	VERB
iajs-2434	9	35	(	(	PUNCT
iajs-2434	9	36	or	or	CCONJ
iajs-2434	9	37	decreasing	decrease	VERB
iajs-2434	9	38	)	)	PUNCT
iajs-2434	9	39	failure	failure	NOUN
iajs-2434	9	40	rate	rate	NOUN
iajs-2434	9	41	according	accord	VERB
iajs-2434	9	42	as	as	SCONJ
iajs-2434	9	43	the	the	DET
iajs-2434	9	44	distribution	distribution	NOUN
iajs-2434	9	45	variety	variety	NOUN
iajs-2434	9	46	is	be	AUX
iajs-2434	9	47	less	less	ADJ
iajs-2434	9	48	than	than	ADP
iajs-2434	9	49	or	or	CCONJ
iajs-2434	9	50	more	more	ADJ
iajs-2434	9	51	than	than	ADP
iajs-2434	9	52	1.069543/√𝜃	1.069543/√𝜃	ADV
iajs-2434	9	53	.	.	PUNCT
iajs-2434	10	1	[	[	X
iajs-2434	10	2	1	1	NUM
iajs-2434	10	3	]	]	PUNCT
iajs-2434	10	4	.	.	PUNCT
iajs-2434	11	1	gharraph	gharraph	NOUN
iajs-2434	11	2	(	(	PUNCT
iajs-2434	11	3	1993	1993	NUM
iajs-2434	11	4	)	)	PUNCT
iajs-2434	11	5	0btained	0btained	NUM
iajs-2434	11	6	five	five	NUM
iajs-2434	11	7	measures	measure	NOUN
iajs-2434	11	8	of	of	ADP
iajs-2434	11	9	the	the	DET
iajs-2434	11	10	parameter	parameter	NOUN
iajs-2434	11	11	of	of	ADP
iajs-2434	11	12	(	(	PUNCT
iajs-2434	11	13	ird	ird	PROPN
iajs-2434	11	14	)	)	PUNCT
iajs-2434	11	15	.	.	PUNCT
iajs-2434	12	1	moreover	moreover	ADV
iajs-2434	12	2	,	,	PUNCT
iajs-2434	12	3	he	he	PRON
iajs-2434	12	4	estimated	estimate	VERB
iajs-2434	12	5	the	the	DET
iajs-2434	12	6	parameter	parameter	NOUN
iajs-2434	12	7	by	by	ADP
iajs-2434	12	8	using	use	VERB
iajs-2434	12	9	different	different	ADJ
iajs-2434	12	10	methods	method	NOUN
iajs-2434	12	11	of	of	ADP
iajs-2434	12	12	estimation	estimation	NOUN
iajs-2434	12	13	[	[	X
iajs-2434	12	14	2	2	NUM
iajs-2434	12	15	]	]	PUNCT
iajs-2434	12	16	.	.	PUNCT
iajs-2434	13	1	mukherjee	mukherjee	PROPN
iajs-2434	13	2	and	and	CCONJ
iajs-2434	13	3	maiti	maiti	PROPN
iajs-2434	13	4	(	(	PUNCT
iajs-2434	13	5	1996	1996	NUM
iajs-2434	13	6	)	)	PUNCT
iajs-2434	13	7	derived	derive	VERB
iajs-2434	13	8	percentile	percentile	ADJ
iajs-2434	13	9	estimator	estimator	NOUN
iajs-2434	13	10	of	of	ADP
iajs-2434	13	11	the	the	DET
iajs-2434	13	12	parameter	parameter	NOUN
iajs-2434	13	13	𝜃	𝜃	NOUN
iajs-2434	13	14	and	and	CCONJ
iajs-2434	13	15	its	its	PRON
iajs-2434	13	16	asymptotic	asymptotic	ADJ
iajs-2434	13	17	efficiency	efficiency	NOUN
iajs-2434	13	18	[	[	X
iajs-2434	13	19	3	3	NUM
iajs-2434	13	20	]	]	PUNCT
iajs-2434	13	21	.	.	PUNCT
iajs-2434	14	1	abdel	abdel	PROPN
iajs-2434	14	2	monem	monem	PROPN
iajs-2434	14	3	(	(	PUNCT
iajs-2434	14	4	2003	2003	NUM
iajs-2434	14	5	)	)	PUNCT
iajs-2434	14	6	discussed	discuss	VERB
iajs-2434	14	7	some	some	DET
iajs-2434	14	8	estimation	estimation	NOUN
iajs-2434	14	9	and	and	CCONJ
iajs-2434	14	10	prediction	prediction	NOUN
iajs-2434	14	11	results	result	NOUN
iajs-2434	14	12	for	for	ADP
iajs-2434	14	13	(	(	PUNCT
iajs-2434	14	14	ird	ird	PROPN
iajs-2434	14	15	)	)	PUNCT
iajs-2434	15	1	[	[	X
iajs-2434	15	2	4	4	NUM
iajs-2434	15	3	]	]	PUNCT
iajs-2434	15	4	.	.	PUNCT
iajs-2434	16	1	el	el	PROPN
iajs-2434	16	2	-	-	PUNCT
iajs-2434	16	3	helbawy	helbawy	PROPN
iajs-2434	16	4	and	and	CCONJ
iajs-2434	16	5	abdel	abdel	PROPN
iajs-2434	16	6	-	-	PUNCT
iajs-2434	16	7	monem	monem	PROPN
iajs-2434	16	8	(	(	PUNCT
iajs-2434	16	9	2005	2005	NUM
iajs-2434	16	10	)	)	PUNCT
iajs-2434	16	11	used	use	VERB
iajs-2434	16	12	bayesian	bayesian	NOUN
iajs-2434	16	13	approach	approach	NOUN
iajs-2434	16	14	to	to	PART
iajs-2434	16	15	estimate	estimate	VERB
iajs-2434	16	16	the	the	DET
iajs-2434	16	17	parameter	parameter	NOUN
iajs-2434	16	18	of	of	ADP
iajs-2434	16	19	ird	ird	PROPN
iajs-2434	16	20	under	under	ADP
iajs-2434	16	21	four	four	NUM
iajs-2434	16	22	loss	loss	NOUN
iajs-2434	16	23	functions	function	NOUN
iajs-2434	16	24	[	[	X
iajs-2434	16	25	5	5	NUM
iajs-2434	16	26	]	]	PUNCT
iajs-2434	16	27	.	.	PUNCT
iajs-2434	17	1	soleman	soleman	PROPN
iajs-2434	17	2	et	et	PROPN
iajs-2434	17	3	-	-	PUNCT
iajs-2434	17	4	al	al	PROPN
iajs-2434	17	5	.	.	PUNCT
iajs-2434	18	1	(	(	PUNCT
iajs-2434	18	2	2010	2010	NUM
iajs-2434	18	3	)	)	PUNCT
iajs-2434	18	4	discussed	discuss	VERB
iajs-2434	18	5	bayesian	bayesian	NOUN
iajs-2434	18	6	and	and	CCONJ
iajs-2434	18	7	non	non	ADJ
iajs-2434	18	8	-	-	ADJ
iajs-2434	18	9	bayesian	bayesian	ADJ
iajs-2434	18	10	estimation	estimation	NOUN
iajs-2434	18	11	of	of	ADP
iajs-2434	18	12	the	the	DET
iajs-2434	18	13	parameter	parameter	NOUN
iajs-2434	18	14	of	of	ADP
iajs-2434	18	15	ird	ird	PROPN
iajs-2434	18	16	along	along	ADV
iajs-2434	18	17	with	with	ADP
iajs-2434	18	18	bayesian	bayesian	NOUN
iajs-2434	18	19	prediction	prediction	NOUN
iajs-2434	18	20	on	on	ADP
iajs-2434	18	21	the	the	DET
iajs-2434	18	22	basis	basis	NOUN
iajs-2434	18	23	of	of	ADP
iajs-2434	18	24	lower	low	ADJ
iajs-2434	18	25	ibn	ibn	PROPN
iajs-2434	18	26	al	al	PROPN
iajs-2434	18	27	haitham	haitham	PROPN
iajs-2434	18	28	journal	journal	PROPN
iajs-2434	18	29	for	for	ADP
iajs-2434	18	30	pure	pure	ADJ
iajs-2434	18	31	and	and	CCONJ
iajs-2434	18	32	applied	apply	VERB
iajs-2434	18	33	science	science	NOUN
iajs-2434	18	34	journal	journal	PROPN
iajs-2434	18	35	homepage	homepage	NOUN
iajs-2434	18	36	:	:	PUNCT
iajs-2434	18	37	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2434	18	38	doi	doi	NOUN
iajs-2434	18	39	:	:	PUNCT
iajs-2434	18	40	10.30526/33.2.2434	10.30526/33.2.2434	NUM
iajs-2434	18	41	masoomaailabod@gmail.com	masoomaailabod@gmail.com	NOUN
iajs-2434	18	42	  	  	SPACE
iajs-2434	18	43	hazim5656@yahoo.com	hazim5656@yahoo.com	NOUN
iajs-2434	18	44	record	record	NOUN
iajs-2434	18	45	values	value	NOUN
iajs-2434	18	46	.	.	PUNCT
iajs-2434	19	1	[	[	X
iajs-2434	19	2	6	6	NUM
iajs-2434	19	3	]	]	PUNCT
iajs-2434	19	4	.	.	PUNCT
iajs-2434	19	5	  	  	SPACE
iajs-2434	19	6	department	department	NOUN
iajs-2434	19	7	of	of	ADP
iajs-2434	19	8	mathematics	mathematics	PROPN
iajs-2434	19	9	,	,	PUNCT
iajs-2434	19	10	college	college	NOUN
iajs-2434	19	11	of	of	ADP
iajs-2434	19	12	education	education	NOUN
iajs-2434	19	13	for	for	ADP
iajs-2434	19	14	pure	pure	ADJ
iajs-2434	19	15	science	science	NOUN
iajs-2434	19	16	ibn	ibn	PROPN
iajs-2434	19	17	al	al	PROPN
iajs-2434	19	18	-	-	PUNCT
iajs-2434	19	19	haitham	haitham	PROPN
iajs-2434	19	20	,	,	PUNCT
iajs-2434	19	21	university	university	NOUN
iajs-2434	19	22	of	of	ADP
iajs-2434	19	23	baghdad	baghdad	PROPN
iajs-2434	19	24	,	,	PUNCT
iajs-2434	19	25	baghdad	baghdad	PROPN
iajs-2434	19	26	,	,	PUNCT
iajs-2434	19	27	iraq	iraq	PROPN
iajs-2434	19	28	.	.	PUNCT
iajs-2434	19	29	  	  	SPACE
iajs-2434	20	1	129	129	NUM
iajs-2434	20	2	  	  	SPACE
iajs-2434	20	3	ibn	ibn	PROPN
iajs-2434	20	4	al	al	PROPN
iajs-2434	20	5	-	-	PUNCT
iajs-2434	20	6	haitham	haitham	PROPN
iajs-2434	20	7	jour	jour	X
iajs-2434	20	8	.	.	PROPN
iajs-2434	20	9	for	for	ADP
iajs-2434	20	10	pure	pure	ADJ
iajs-2434	20	11	&	&	CCONJ
iajs-2434	20	12	appl	appl	PROPN
iajs-2434	20	13	.	.	PUNCT
iajs-2434	21	1	sci	sci	PROPN
iajs-2434	21	2	.	.	PROPN
iajs-2434	22	1	33	33	NUM
iajs-2434	22	2	(	(	PUNCT
iajs-2434	22	3	1	1	NUM
iajs-2434	22	4	)	)	PUNCT
iajs-2434	22	5	2020	2020	NUM
iajs-2434	23	1	2	2	NUM
iajs-2434	23	2	.	.	PUNCT
iajs-2434	23	3	inverse	inverse	PROPN
iajs-2434	23	4	rayleigh	rayleigh	NOUN
iajs-2434	23	5	distribution	distribution	NOUN
iajs-2434	23	6	(	(	PUNCT
iajs-2434	23	7	ird	ird	PROPN
iajs-2434	23	8	)	)	PUNCT
iajs-2434	23	9	the	the	DET
iajs-2434	23	10	continuous	continuous	ADJ
iajs-2434	23	11	random	random	ADJ
iajs-2434	23	12	variable	variable	NOUN
iajs-2434	23	13	t	t	PROPN
iajs-2434	23	14	is	be	AUX
iajs-2434	23	15	said	say	VERB
iajs-2434	23	16	to	to	PART
iajs-2434	23	17	have	have	VERB
iajs-2434	23	18	inverse	inverse	NOUN
iajs-2434	23	19	rayleigh	rayleigh	NOUN
iajs-2434	23	20	distribution	distribution	NOUN
iajs-2434	23	21	with	with	ADP
iajs-2434	23	22	scale	scale	NOUN
iajs-2434	23	23	parameter	parameter	NOUN
iajs-2434	23	24	𝜃	𝜃	NOUN
iajs-2434	24	1	if	if	SCONJ
iajs-2434	24	2	it	it	PRON
iajs-2434	24	3	has	have	VERB
iajs-2434	24	4	the	the	DET
iajs-2434	24	5	probability	probability	NOUN
iajs-2434	24	6	density	density	NOUN
iajs-2434	24	7	function	function	VERB
iajs-2434	24	8	𝑓	𝑓	DET
iajs-2434	24	9	𝑡	𝑡	NOUN
iajs-2434	24	10	,	,	PUNCT
iajs-2434	24	11	𝜃	𝜃	NUM
iajs-2434	24	12	exp	exp	NOUN
iajs-2434	24	13	,	,	PUNCT
iajs-2434	24	14	𝑡	𝑡	PROPN
iajs-2434	24	15	0	0	NUM
iajs-2434	24	16	,	,	PUNCT
iajs-2434	24	17	𝜃	𝜃	NOUN
iajs-2434	24	18	0	0	NUM
iajs-2434	24	19	1	1	NUM
iajs-2434	24	20	the	the	DET
iajs-2434	24	21	corresponding	corresponding	ADJ
iajs-2434	24	22	cumulative	cumulative	ADJ
iajs-2434	24	23	distribution	distribution	NOUN
iajs-2434	24	24	function	function	NOUN
iajs-2434	24	25	is	be	AUX
iajs-2434	24	26	𝐹	𝐹	PROPN
iajs-2434	24	27	𝑡	𝑡	PROPN
iajs-2434	24	28	,	,	PUNCT
iajs-2434	24	29	𝜃	𝜃	NOUN
iajs-2434	24	30	exp	exp	NOUN
iajs-2434	24	31	𝜃	𝜃	X
iajs-2434	24	32	𝑡	𝑡	PROPN
iajs-2434	24	33	,	,	PUNCT
iajs-2434	24	34	𝑡	𝑡	PROPN
iajs-2434	24	35	0	0	NUM
iajs-2434	24	36	,	,	PUNCT
iajs-2434	24	37	𝜃	𝜃	NOUN
iajs-2434	24	38	0	0	NUM
iajs-2434	24	39	2	2	NUM
iajs-2434	24	40	therefore	therefore	ADV
iajs-2434	24	41	,	,	PUNCT
iajs-2434	24	42	the	the	DET
iajs-2434	24	43	reliably	reliably	ADJ
iajs-2434	24	44	function	function	NOUN
iajs-2434	24	45	of	of	ADP
iajs-2434	24	46	ird	ird	PROPN
iajs-2434	24	47	is	be	AUX
iajs-2434	24	48	given	give	VERB
iajs-2434	24	49	by	by	ADP
iajs-2434	24	50	𝑅	𝑅	PROPN
iajs-2434	24	51	𝑡	𝑡	PROPN
iajs-2434	24	52	,	,	PUNCT
iajs-2434	24	53	𝜃	𝜃	PRON
iajs-2434	24	54	1	1	NUM
iajs-2434	24	55	𝐹	𝐹	PROPN
iajs-2434	24	56	𝑡	𝑡	PROPN
iajs-2434	24	57	,	,	PUNCT
iajs-2434	24	58	𝜃	𝜃	NOUN
iajs-2434	24	59	1	1	NUM
iajs-2434	24	60	exp	exp	NOUN
iajs-2434	24	61	,	,	PUNCT
iajs-2434	24	62	𝑡	𝑡	PROPN
iajs-2434	24	63	0	0	NUM
iajs-2434	24	64	,	,	PUNCT
iajs-2434	24	65	𝜃	𝜃	NOUN
iajs-2434	24	66	0	0	NUM
iajs-2434	24	67	(	(	PUNCT
iajs-2434	24	68	3	3	NUM
iajs-2434	24	69	)	)	PUNCT
iajs-2434	24	70	a	a	DET
iajs-2434	24	71	variance	variance	NOUN
iajs-2434	24	72	and	and	CCONJ
iajs-2434	24	73	higher	high	ADJ
iajs-2434	24	74	order	order	NOUN
iajs-2434	24	75	moments	moment	NOUN
iajs-2434	24	76	do	do	AUX
iajs-2434	24	77	not	not	PART
iajs-2434	24	78	exist	exist	VERB
iajs-2434	24	79	for	for	ADP
iajs-2434	24	80	this	this	DET
iajs-2434	24	81	distribution	distribution	NOUN
iajs-2434	24	82	,	,	PUNCT
iajs-2434	24	83	moreover	moreover	ADV
iajs-2434	24	84	,	,	PUNCT
iajs-2434	24	85	it	it	PRON
iajs-2434	24	86	can	can	AUX
iajs-2434	24	87	be	be	AUX
iajs-2434	24	88	shown	show	VERB
iajs-2434	24	89	that	that	SCONJ
iajs-2434	24	90	ird	ird	PROPN
iajs-2434	24	91	is	be	AUX
iajs-2434	24	92	special	special	ADJ
iajs-2434	24	93	case	case	NOUN
iajs-2434	24	94	of	of	ADP
iajs-2434	24	95	inverse	inverse	ADJ
iajs-2434	24	96	weibull	weibull	NOUN
iajs-2434	24	97	distribution	distribution	NOUN
iajs-2434	24	98	with	with	ADP
iajs-2434	24	99	parameters	parameter	NOUN
iajs-2434	24	100	𝜃	𝜃	PROPN
iajs-2434	24	101	,	,	PUNCT
iajs-2434	24	102	𝛽	𝛽	NOUN
iajs-2434	24	103	when	when	SCONJ
iajs-2434	24	104	𝛽	𝛽	NOUN
iajs-2434	24	105	2	2	NUM
iajs-2434	24	106	[	[	X
iajs-2434	24	107	7	7	NUM
iajs-2434	24	108	]	]	PUNCT
iajs-2434	24	109	.	.	PUNCT
iajs-2434	25	1	3	3	X
iajs-2434	25	2	.	.	X
iajs-2434	25	3	prior	prior	ADJ
iajs-2434	25	4	information	information	NOUN
iajs-2434	25	5	's	be	AUX
iajs-2434	25	6	a	a	DET
iajs-2434	25	7	convenient	convenient	ADJ
iajs-2434	25	8	choice	choice	NOUN
iajs-2434	25	9	of	of	ADP
iajs-2434	25	10	priors	prior	NOUN
iajs-2434	25	11	is	be	AUX
iajs-2434	25	12	indispensable	indispensable	ADJ
iajs-2434	25	13	for	for	ADP
iajs-2434	25	14	bayesian	bayesian	NOUN
iajs-2434	25	15	analysis	analysis	NOUN
iajs-2434	25	16	.	.	PUNCT
iajs-2434	26	1	many	many	ADJ
iajs-2434	26	2	researchers	researcher	NOUN
iajs-2434	26	3	choose	choose	VERB
iajs-2434	26	4	priors	prior	NOUN
iajs-2434	26	5	on	on	ADP
iajs-2434	26	6	the	the	DET
iajs-2434	26	7	basis	basis	NOUN
iajs-2434	26	8	of	of	ADP
iajs-2434	26	9	their	their	PRON
iajs-2434	26	10	subjective	subjective	ADJ
iajs-2434	26	11	beliefs	belief	NOUN
iajs-2434	26	12	and	and	CCONJ
iajs-2434	26	13	knowledge	knowledge	NOUN
iajs-2434	26	14	's	's	PART
iajs-2434	26	15	.	.	PUNCT
iajs-2434	27	1	however	however	ADV
iajs-2434	27	2	,	,	PUNCT
iajs-2434	27	3	if	if	SCONJ
iajs-2434	27	4	enough	enough	ADJ
iajs-2434	27	5	information	information	NOUN
iajs-2434	27	6	about	about	ADP
iajs-2434	27	7	parameter	parameter	NOUN
iajs-2434	27	8	is	be	AUX
iajs-2434	27	9	presented	present	VERB
iajs-2434	27	10	,	,	PUNCT
iajs-2434	27	11	we	we	PRON
iajs-2434	27	12	should	should	AUX
iajs-2434	27	13	use	use	VERB
iajs-2434	27	14	informative	informative	ADJ
iajs-2434	27	15	priors	prior	NOUN
iajs-2434	27	16	;	;	PUNCT
iajs-2434	27	17	otherwise	otherwise	ADV
iajs-2434	27	18	,	,	PUNCT
iajs-2434	27	19	it	it	PRON
iajs-2434	27	20	is	be	AUX
iajs-2434	27	21	better	well	ADJ
iajs-2434	27	22	to	to	PART
iajs-2434	27	23	employ	employ	VERB
iajs-2434	27	24	vague	vague	ADJ
iajs-2434	27	25	or	or	CCONJ
iajs-2434	27	26	non	non	ADJ
iajs-2434	27	27	-	-	ADJ
iajs-2434	27	28	informative	informative	ADJ
iajs-2434	27	29	priors	prior	NOUN
iajs-2434	27	30	.	.	PUNCT
iajs-2434	28	1	in	in	ADP
iajs-2434	28	2	this	this	DET
iajs-2434	28	3	paper	paper	NOUN
iajs-2434	28	4	,	,	PUNCT
iajs-2434	28	5	we	we	PRON
iajs-2434	28	6	consider	consider	VERB
iajs-2434	28	7	the	the	DET
iajs-2434	28	8	general	general	ADJ
iajs-2434	28	9	rule	rule	NOUN
iajs-2434	28	10	developed	develop	VERB
iajs-2434	28	11	by	by	ADP
iajs-2434	28	12	jeffrey	jeffrey	PROPN
iajs-2434	28	13	(	(	PUNCT
iajs-2434	28	14	1961	1961	NUM
iajs-2434	28	15	)	)	PUNCT
iajs-2434	28	16	to	to	PART
iajs-2434	28	17	obtain	obtain	VERB
iajs-2434	28	18	the	the	DET
iajs-2434	28	19	non	non	ADJ
iajs-2434	28	20	–	–	PUNCT
iajs-2434	28	21	informative	informative	ADJ
iajs-2434	28	22	prior	prior	ADV
iajs-2434	28	23	.	.	PUNCT
iajs-2434	29	1	he	he	PRON
iajs-2434	29	2	established	establish	VERB
iajs-2434	29	3	that	that	SCONJ
iajs-2434	29	4	the	the	DET
iajs-2434	29	5	single	single	ADJ
iajs-2434	29	6	unknown	unknown	ADJ
iajs-2434	29	7	parameter	parameter	NOUN
iajs-2434	29	8	𝜃	𝜃	PRON
iajs-2434	29	9	which	which	PRON
iajs-2434	29	10	is	be	AUX
iajs-2434	29	11	regarded	regard	VERB
iajs-2434	29	12	as	as	ADP
iajs-2434	29	13	a	a	DET
iajs-2434	29	14	random	random	ADJ
iajs-2434	29	15	variable	variable	NOUN
iajs-2434	29	16	follows	follow	VERB
iajs-2434	29	17	such	such	DET
iajs-2434	29	18	a	a	DET
iajs-2434	29	19	distribution	distribution	NOUN
iajs-2434	29	20	that	that	PRON
iajs-2434	29	21	is	be	AUX
iajs-2434	29	22	proportional	proportional	ADJ
iajs-2434	29	23	to	to	ADP
iajs-2434	29	24	the	the	DET
iajs-2434	29	25	square	square	ADJ
iajs-2434	29	26	root	root	NOUN
iajs-2434	29	27	of	of	ADP
iajs-2434	29	28	fisher	fisher	PROPN
iajs-2434	29	29	information	information	NOUN
iajs-2434	29	30	𝐼	𝐼	ADP
iajs-2434	29	31	𝜃	𝜃	PROPN
iajs-2434	29	32	,	,	PUNCT
iajs-2434	29	33	that	that	PRON
iajs-2434	29	34	is	be	AUX
iajs-2434	29	35	𝑔	𝑔	PROPN
iajs-2434	29	36	𝜃	𝜃	NOUN
iajs-2434	29	37	∝	∝	NOUN
iajs-2434	29	38	𝐼	𝐼	ADP
iajs-2434	29	39	𝜃	𝜃	PROPN
iajs-2434	29	40	where	where	SCONJ
iajs-2434	29	41	𝑔	𝑔	PROPN
iajs-2434	29	42	𝜃	𝜃	PROPN
iajs-2434	29	43	denotes	denote	VERB
iajs-2434	29	44	the	the	DET
iajs-2434	29	45	prior	prior	ADJ
iajs-2434	29	46	information	information	NOUN
iajs-2434	29	47	.	.	PUNCT
iajs-2434	30	1	equivalently	equivalently	ADV
iajs-2434	30	2	,	,	PUNCT
iajs-2434	30	3	𝑔	𝑔	PROPN
iajs-2434	30	4	𝜃	𝜃	PROPN
iajs-2434	30	5	𝑐	𝑐	NOUN
iajs-2434	30	6	𝐼	𝐼	ADP
iajs-2434	30	7	𝜃	𝜃	X
iajs-2434	30	8	(	(	PUNCT
iajs-2434	30	9	4	4	NUM
iajs-2434	30	10	)	)	PUNCT
iajs-2434	30	11	where	where	SCONJ
iajs-2434	30	12	c	c	NOUN
iajs-2434	30	13	is	be	AUX
iajs-2434	30	14	a	a	DET
iajs-2434	30	15	constant	constant	NOUN
iajs-2434	30	16	of	of	ADP
iajs-2434	30	17	proportionality	proportionality	NOUN
iajs-2434	30	18	and	and	CCONJ
iajs-2434	30	19	,	,	PUNCT
iajs-2434	30	20	𝐼	𝐼	PROPN
iajs-2434	30	21	𝜃	𝜃	PROPN
iajs-2434	30	22	𝑛𝐸	𝑛𝐸	PROPN
iajs-2434	30	23	,	,	PUNCT
iajs-2434	30	24	]	]	PUNCT
iajs-2434	30	25	(	(	PUNCT
iajs-2434	30	26	5	5	X
iajs-2434	30	27	)	)	PUNCT
iajs-2434	30	28	it	it	PRON
iajs-2434	30	29	follows	follow	VERB
iajs-2434	30	30	that	that	SCONJ
iajs-2434	30	31	:	:	PUNCT
iajs-2434	30	32	𝑔	𝑔	PROPN
iajs-2434	30	33	𝜃	𝜃	PUNCT
iajs-2434	30	34	𝑐	𝑐	PROPN
iajs-2434	30	35	𝑛𝐸	𝑛𝐸	PROPN
iajs-2434	30	36	,	,	PUNCT
iajs-2434	30	37	(	(	PUNCT
iajs-2434	30	38	6	6	NUM
iajs-2434	30	39	)	)	SYM
iajs-2434	30	40	4	4	NUM
iajs-2434	30	41	.	.	PUNCT
iajs-2434	30	42	posterior	posterior	ADJ
iajs-2434	30	43	density	density	NOUN
iajs-2434	30	44	of	of	ADP
iajs-2434	30	45	inverse	inverse	NOUN
iajs-2434	30	46	rayleigh	rayleigh	PROPN
iajs-2434	30	47	parameter	parameter	NOUN
iajs-2434	30	48	based	base	VERB
iajs-2434	30	49	on	on	ADP
iajs-2434	30	50	jeffrey	jeffrey	PROPN
iajs-2434	30	51	's	's	PART
iajs-2434	30	52	prior	prior	ADJ
iajs-2434	30	53	information	information	NOUN
iajs-2434	30	54	from	from	ADP
iajs-2434	30	55	equation	equation	NOUN
iajs-2434	30	56	(	(	PUNCT
iajs-2434	30	57	1	1	NUM
iajs-2434	30	58	)	)	PUNCT
iajs-2434	30	59	,	,	PUNCT
iajs-2434	30	60	we	we	PRON
iajs-2434	30	61	have	have	VERB
iajs-2434	30	62	:	:	PUNCT
iajs-2434	30	63	𝑙𝑛𝑓	𝑙𝑛𝑓	PROPN
iajs-2434	30	64	𝑡	𝑡	PROPN
iajs-2434	30	65	,	,	PUNCT
iajs-2434	30	66	𝜃	𝜃	NOUN
iajs-2434	30	67	𝑙𝑛2	𝑙𝑛2	NOUN
iajs-2434	30	68	𝑙𝑛𝜃	𝑙𝑛𝜃	PROPN
iajs-2434	30	69	3𝑙𝑛𝑡	3𝑙𝑛𝑡	NUM
iajs-2434	30	70	,	,	PUNCT
iajs-2434	30	71	it	it	PRON
iajs-2434	30	72	follows	follow	VERB
iajs-2434	30	73	that	that	PRON
iajs-2434	30	74	,	,	PUNCT
iajs-2434	30	75	=	=	PUNCT
iajs-2434	30	76	  	  	SPACE
iajs-2434	30	77	130	130	NUM
iajs-2434	30	78	  	  	SPACE
iajs-2434	30	79	ibn	ibn	PROPN
iajs-2434	30	80	al	al	PROPN
iajs-2434	30	81	-	-	PUNCT
iajs-2434	30	82	haitham	haitham	PROPN
iajs-2434	30	83	jour	jour	X
iajs-2434	30	84	.	.	PROPN
iajs-2434	31	1	for	for	ADP
iajs-2434	31	2	pure	pure	ADJ
iajs-2434	31	3	&	&	CCONJ
iajs-2434	31	4	appl	appl	PROPN
iajs-2434	31	5	.	.	PUNCT
iajs-2434	32	1	sci	sci	PROPN
iajs-2434	32	2	.	.	PROPN
iajs-2434	33	1	33	33	NUM
iajs-2434	33	2	(	(	PUNCT
iajs-2434	33	3	1	1	NUM
iajs-2434	33	4	)	)	PUNCT
iajs-2434	33	5	2020	2020	NUM
iajs-2434	34	1	𝑔	𝑔	PROPN
iajs-2434	34	2	𝜃	𝜃	PROPN
iajs-2434	34	3	√𝑛	√𝑛	X
iajs-2434	34	4	(	(	PUNCT
iajs-2434	34	5	7	7	NUM
iajs-2434	34	6	)	)	PUNCT
iajs-2434	34	7	from	from	ADP
iajs-2434	34	8	bayesian	bayesian	NOUN
iajs-2434	34	9	perspective	perspective	NOUN
iajs-2434	34	10	,	,	PUNCT
iajs-2434	34	11	the	the	DET
iajs-2434	34	12	posterior	posterior	ADJ
iajs-2434	34	13	density	density	NOUN
iajs-2434	34	14	denoted	denote	VERB
iajs-2434	34	15	by	by	ADP
iajs-2434	34	16	ℎ	ℎ	NOUN
iajs-2434	34	17	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	34	18	can	can	AUX
iajs-2434	34	19	be	be	AUX
iajs-2434	34	20	determined	determine	VERB
iajs-2434	34	21	by	by	ADP
iajs-2434	34	22	combining	combine	VERB
iajs-2434	34	23	the	the	DET
iajs-2434	34	24	prior	prior	ADJ
iajs-2434	34	25	distribution	distribution	NOUN
iajs-2434	34	26	𝑔	𝑔	PROPN
iajs-2434	34	27	𝜃	𝜃	NOUN
iajs-2434	34	28	with	with	ADP
iajs-2434	34	29	the	the	DET
iajs-2434	34	30	likelihood	likelihood	NOUN
iajs-2434	34	31	function	function	NOUN
iajs-2434	34	32	𝐿	𝐿	PROPN
iajs-2434	34	33	𝑡	𝑡	PROPN
iajs-2434	34	34	|𝜃	|𝜃	X
iajs-2434	34	35	,	,	PUNCT
iajs-2434	34	36	as	as	SCONJ
iajs-2434	34	37	follows	follow	VERB
iajs-2434	34	38	:	:	PUNCT
iajs-2434	34	39	ℎ	ℎ	X
iajs-2434	34	40	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	35	1	=	=	PUNCT
iajs-2434	35	2	|	|	ADV
iajs-2434	35	3	|	|	ADV
iajs-2434	35	4	(	(	PUNCT
iajs-2434	35	5	8)	8)	NUM
iajs-2434	35	6	let	let	VERB
iajs-2434	35	7	𝑡	𝑡	X
iajs-2434	35	8	=	=	SYM
iajs-2434	35	9	(	(	PUNCT
iajs-2434	35	10	𝑡	𝑡	PROPN
iajs-2434	35	11	,	,	PUNCT
iajs-2434	35	12	𝑡	𝑡	PROPN
iajs-2434	35	13	,	,	PUNCT
iajs-2434	35	14	…	…	PUNCT
iajs-2434	35	15	…	…	PUNCT
iajs-2434	35	16	𝑡	𝑡	PRON
iajs-2434	35	17	be	be	VERB
iajs-2434	35	18	a	a	DET
iajs-2434	35	19	random	random	ADJ
iajs-2434	35	20	sample	sample	NOUN
iajs-2434	35	21	drawn	draw	VERB
iajs-2434	35	22	from	from	ADP
iajs-2434	35	23	inverse	inverse	ADJ
iajs-2434	35	24	rayleigh	rayleigh	NOUN
iajs-2434	35	25	distribution	distribution	NOUN
iajs-2434	35	26	,	,	PUNCT
iajs-2434	35	27	then	then	ADV
iajs-2434	35	28	the	the	DET
iajs-2434	35	29	likelihood	likelihood	NOUN
iajs-2434	35	30	function	function	NOUN
iajs-2434	35	31	is	be	AUX
iajs-2434	35	32	:	:	PUNCT
iajs-2434	35	33	𝐿	𝐿	NOUN
iajs-2434	35	34	𝑡|𝜃	𝑡|𝜃	PUNCT
iajs-2434	35	35	=	=	SYM
iajs-2434	36	1	∏	∏	PROPN
iajs-2434	36	2	𝑓	𝑓	PRON
iajs-2434	36	3	𝑡	𝑡	PROPN
iajs-2434	36	4	,	,	PUNCT
iajs-2434	36	5	𝜃	𝜃	NOUN
iajs-2434	36	6	2	2	NUM
iajs-2434	36	7	𝜃	𝜃	SYM
iajs-2434	36	8	∏	∏	NUM
iajs-2434	36	9	𝑒𝑥𝑝	𝑒𝑥𝑝	INTJ
iajs-2434	36	10	𝜃	𝜃	X
iajs-2434	36	11	∑	∑	PROPN
iajs-2434	36	12	(	(	PUNCT
iajs-2434	36	13	9	9	X
iajs-2434	36	14	)	)	PUNCT
iajs-2434	36	15	let	let	VERB
iajs-2434	36	16	ℎ	ℎ	PROPN
iajs-2434	36	17	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	36	18	denote	denote	VERB
iajs-2434	36	19	the	the	DET
iajs-2434	36	20	posterior	posterior	ADJ
iajs-2434	36	21	density	density	NOUN
iajs-2434	36	22	based	base	VERB
iajs-2434	36	23	on	on	ADP
iajs-2434	36	24	jeffrey	jeffrey	PROPN
iajs-2434	36	25	's	's	PART
iajs-2434	36	26	prior	prior	ADJ
iajs-2434	36	27	distribution	distribution	NOUN
iajs-2434	36	28	𝑔	𝑔	PROPN
iajs-2434	36	29	𝜃	𝜃	PROPN
iajs-2434	36	30	for	for	ADP
iajs-2434	36	31	inverse	inverse	NOUN
iajs-2434	36	32	rayleigh	rayleigh	PROPN
iajs-2434	36	33	parameter	parameter	PROPN
iajs-2434	36	34	𝜃	𝜃	PROPN
iajs-2434	36	35	,	,	PUNCT
iajs-2434	36	36	then	then	ADV
iajs-2434	36	37	by	by	ADP
iajs-2434	36	38	substituting	substitute	VERB
iajs-2434	36	39	equations	equation	NOUN
iajs-2434	36	40	(	(	PUNCT
iajs-2434	36	41	7	7	NUM
iajs-2434	36	42	)	)	PUNCT
iajs-2434	36	43	and	and	CCONJ
iajs-2434	36	44	(	(	PUNCT
iajs-2434	36	45	9	9	NUM
iajs-2434	36	46	)	)	PUNCT
iajs-2434	36	47	into	into	ADP
iajs-2434	36	48	equation	equation	NOUN
iajs-2434	36	49	(	(	PUNCT
iajs-2434	36	50	8)	8)	NUM
iajs-2434	36	51	with	with	ADP
iajs-2434	36	52	simplification	simplification	NOUN
iajs-2434	36	53	,	,	PUNCT
iajs-2434	36	54	we	we	PRON
iajs-2434	36	55	get	get	VERB
iajs-2434	36	56	:	:	PUNCT
iajs-2434	36	57	ℎ	ℎ	X
iajs-2434	36	58	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	36	59	where	where	SCONJ
iajs-2434	36	60	𝑇	𝑇	PROPN
iajs-2434	36	61	∑	∑	PUNCT
iajs-2434	36	62	it	it	PRON
iajs-2434	36	63	follows	follow	VERB
iajs-2434	36	64	that	that	SCONJ
iajs-2434	36	65	ℎ	ℎ	VERB
iajs-2434	36	66	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	36	67	(	(	PUNCT
iajs-2434	36	68	10	10	NUM
iajs-2434	36	69	)	)	PUNCT
iajs-2434	36	70	the	the	DET
iajs-2434	36	71	posterior	posterior	ADJ
iajs-2434	36	72	density	density	NOUN
iajs-2434	36	73	function	function	NOUN
iajs-2434	36	74	in	in	ADP
iajs-2434	36	75	equation	equation	NOUN
iajs-2434	36	76	(	(	PUNCT
iajs-2434	36	77	10	10	NUM
iajs-2434	36	78	)	)	PUNCT
iajs-2434	36	79	is	be	AUX
iajs-2434	36	80	recognized	recognize	VERB
iajs-2434	36	81	as	as	ADP
iajs-2434	36	82	the	the	DET
iajs-2434	36	83	density	density	NOUN
iajs-2434	36	84	of	of	ADP
iajs-2434	36	85	gamma	gamma	NOUN
iajs-2434	36	86	distribution	distribution	NOUN
iajs-2434	36	87	,	,	PUNCT
iajs-2434	36	88	that	that	PRON
iajs-2434	36	89	is	be	AUX
iajs-2434	36	90	:	:	PUNCT
iajs-2434	36	91	𝜃|𝑡~	𝜃|𝑡~	NOUN
iajs-2434	36	92	gamma	gamma	PROPN
iajs-2434	36	93	𝑛	𝑛	PROPN
iajs-2434	36	94	,	,	PUNCT
iajs-2434	36	95	hence	hence	ADV
iajs-2434	36	96	,	,	PUNCT
iajs-2434	36	97	𝐸	𝐸	PROPN
iajs-2434	36	98	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	36	99	(	(	PUNCT
iajs-2434	36	100	11	11	NUM
iajs-2434	36	101	)	)	SYM
iajs-2434	36	102	5	5	NUM
iajs-2434	36	103	.	.	PUNCT
iajs-2434	36	104	posterior	posterior	ADJ
iajs-2434	36	105	density	density	NOUN
iajs-2434	36	106	of	of	ADP
iajs-2434	36	107	inverse	inverse	NOUN
iajs-2434	36	108	rayleigh	rayleigh	PROPN
iajs-2434	36	109	parameter	parameter	NOUN
iajs-2434	36	110	based	base	VERB
iajs-2434	36	111	on	on	ADP
iajs-2434	36	112	exponential	exponential	ADJ
iajs-2434	36	113	prior	prior	ADJ
iajs-2434	36	114	distribution	distribution	NOUN
iajs-2434	36	115	assuming	assume	VERB
iajs-2434	36	116	that	that	SCONJ
iajs-2434	36	117	the	the	DET
iajs-2434	36	118	inverse	inverse	NOUN
iajs-2434	36	119	rayleigh	rayleigh	PROPN
iajs-2434	36	120	parameter	parameter	PROPN
iajs-2434	36	121	𝜃	𝜃	PROPN
iajs-2434	36	122	follows	follow	VERB
iajs-2434	36	123	exponential	exponential	ADJ
iajs-2434	36	124	prior	prior	ADJ
iajs-2434	36	125	distribution	distribution	NOUN
iajs-2434	36	126	with	with	ADP
iajs-2434	36	127	parameter	parameter	NOUN
iajs-2434	36	128	,	,	PUNCT
iajs-2434	36	129	that	that	PRON
iajs-2434	36	130	is	be	AUX
iajs-2434	36	131	:	:	PUNCT
iajs-2434	36	132	𝑔	𝑔	PROPN
iajs-2434	36	133	𝜃	𝜃	X
iajs-2434	36	134	𝜆𝑒	𝜆𝑒	NOUN
iajs-2434	36	135	,	,	PUNCT
iajs-2434	36	136	λ	λ	PROPN
iajs-2434	36	137	0	0	NUM
iajs-2434	36	138	,	,	PUNCT
iajs-2434	36	139	𝜃	𝜃	NOUN
iajs-2434	36	140	0	0	NUM
iajs-2434	36	141	(	(	PUNCT
iajs-2434	36	142	12	12	NUM
iajs-2434	36	143	)	)	PUNCT
iajs-2434	36	144	where	where	SCONJ
iajs-2434	36	145	𝑔	𝑔	PROPN
iajs-2434	36	146	𝜃	𝜃	PROPN
iajs-2434	36	147	denotes	denote	VERB
iajs-2434	36	148	the	the	DET
iajs-2434	36	149	exponential	exponential	ADJ
iajs-2434	36	150	prior	prior	ADJ
iajs-2434	36	151	distribution	distribution	NOUN
iajs-2434	36	152	of	of	ADP
iajs-2434	36	153	the	the	DET
iajs-2434	36	154	inverse	inverse	NOUN
iajs-2434	36	155	rayleigh	rayleigh	PROPN
iajs-2434	36	156	parameter	parameter	PROPN
iajs-2434	36	157	𝜃.	𝜃.	ADV
iajs-2434	36	158	by	by	ADP
iajs-2434	36	159	substituting	substitute	VERB
iajs-2434	36	160	equations	equation	NOUN
iajs-2434	36	161	(	(	PUNCT
iajs-2434	36	162	9	9	NUM
iajs-2434	36	163	)	)	PUNCT
iajs-2434	36	164	and	and	CCONJ
iajs-2434	36	165	(	(	PUNCT
iajs-2434	36	166	12	12	NUM
iajs-2434	36	167	)	)	PUNCT
iajs-2434	36	168	into	into	ADP
iajs-2434	36	169	equation	equation	NOUN
iajs-2434	36	170	(	(	PUNCT
iajs-2434	36	171	8)	8)	NUM
iajs-2434	36	172	with	with	ADP
iajs-2434	36	173	simplification	simplification	NOUN
iajs-2434	36	174	,	,	PUNCT
iajs-2434	36	175	we	we	PRON
iajs-2434	36	176	get	get	VERB
iajs-2434	36	177	:	:	PUNCT
iajs-2434	36	178	ℎ	ℎ	PROPN
iajs-2434	36	179	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	36	180	(	(	PUNCT
iajs-2434	36	181	13	13	NUM
iajs-2434	36	182	)	)	PUNCT
iajs-2434	36	183	  	  	SPACE
iajs-2434	36	184	131	131	NUM
iajs-2434	36	185	  	  	SPACE
iajs-2434	36	186	ibn	ibn	PROPN
iajs-2434	36	187	al	al	PROPN
iajs-2434	36	188	-	-	PUNCT
iajs-2434	36	189	haitham	haitham	PROPN
iajs-2434	36	190	jour	jour	X
iajs-2434	36	191	.	.	PROPN
iajs-2434	37	1	for	for	ADP
iajs-2434	37	2	pure	pure	ADJ
iajs-2434	37	3	&	&	CCONJ
iajs-2434	37	4	appl	appl	PROPN
iajs-2434	37	5	.	.	PUNCT
iajs-2434	38	1	sci	sci	PROPN
iajs-2434	38	2	.	.	PROPN
iajs-2434	39	1	33	33	NUM
iajs-2434	39	2	(	(	PUNCT
iajs-2434	39	3	1	1	NUM
iajs-2434	39	4	)	)	PUNCT
iajs-2434	39	5	2020	2020	NUM
iajs-2434	40	1	where	where	SCONJ
iajs-2434	40	2	ℎ	ℎ	NOUN
iajs-2434	40	3	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	40	4	denotes	denote	VERB
iajs-2434	40	5	the	the	DET
iajs-2434	40	6	posterior	posterior	ADJ
iajs-2434	40	7	density	density	NOUN
iajs-2434	40	8	based	base	VERB
iajs-2434	40	9	on	on	ADP
iajs-2434	40	10	exponential	exponential	ADJ
iajs-2434	40	11	prior	prior	ADJ
iajs-2434	40	12	distribution	distribution	NOUN
iajs-2434	40	13	and	and	CCONJ
iajs-2434	40	14	𝑝	𝑝	NOUN
iajs-2434	40	15	𝑇	𝑇	PROPN
iajs-2434	40	16	𝜆	𝜆	PROPN
iajs-2434	40	17	.	.	PUNCT
iajs-2434	41	1	from	from	ADP
iajs-2434	41	2	equation	equation	NOUN
iajs-2434	41	3	(	(	PUNCT
iajs-2434	41	4	13	13	NUM
iajs-2434	41	5	)	)	PUNCT
iajs-2434	41	6	,	,	PUNCT
iajs-2434	41	7	it	it	PRON
iajs-2434	41	8	can	can	AUX
iajs-2434	41	9	be	be	AUX
iajs-2434	41	10	easily	easily	ADV
iajs-2434	41	11	noted	note	VERB
iajs-2434	41	12	that	that	SCONJ
iajs-2434	41	13	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	41	14	distributed	distribute	VERB
iajs-2434	41	15	as	as	ADP
iajs-2434	41	16	gamma	gamma	NOUN
iajs-2434	41	17	with	with	ADP
iajs-2434	41	18	parameter	parameter	NOUN
iajs-2434	41	19	𝑛	𝑛	PRON
iajs-2434	41	20	1	1	NUM
iajs-2434	41	21	,	,	PUNCT
iajs-2434	41	22	.	.	PUNCT
iajs-2434	42	1	it	it	PRON
iajs-2434	42	2	follows	follow	VERB
iajs-2434	42	3	that	that	SCONJ
iajs-2434	42	4	:	:	PUNCT
iajs-2434	42	5	𝐸	𝐸	ADJ
iajs-2434	42	6	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	42	7	(	(	PUNCT
iajs-2434	42	8	14	14	NUM
iajs-2434	42	9	)	)	PUNCT
iajs-2434	42	10	6	6	NUM
iajs-2434	42	11	.	.	PUNCT
iajs-2434	42	12	types	type	NOUN
iajs-2434	42	13	of	of	ADP
iajs-2434	42	14	loss	loss	NOUN
iajs-2434	42	15	functions	function	NOUN
iajs-2434	42	16	from	from	ADP
iajs-2434	42	17	bayesian	bayesian	NOUN
iajs-2434	42	18	viewpoint	viewpoint	NOUN
iajs-2434	42	19	,	,	PUNCT
iajs-2434	42	20	[	[	X
iajs-2434	42	21	8	8	NUM
iajs-2434	42	22	]	]	PUNCT
iajs-2434	42	23	.	.	PUNCT
iajs-2434	43	1	the	the	DET
iajs-2434	43	2	essential	essential	ADJ
iajs-2434	43	3	step	step	NOUN
iajs-2434	43	4	in	in	ADP
iajs-2434	43	5	the	the	DET
iajs-2434	43	6	estimation	estimation	NOUN
iajs-2434	43	7	and	and	CCONJ
iajs-2434	43	8	prediction	prediction	NOUN
iajs-2434	43	9	problems	problem	NOUN
iajs-2434	43	10	represented	represent	VERB
iajs-2434	43	11	by	by	ADP
iajs-2434	43	12	choosing	choose	VERB
iajs-2434	43	13	the	the	DET
iajs-2434	43	14	loss	loss	NOUN
iajs-2434	43	15	function	function	NOUN
iajs-2434	43	16	.	.	PUNCT
iajs-2434	44	1	in	in	ADP
iajs-2434	44	2	fact	fact	NOUN
iajs-2434	44	3	,	,	PUNCT
iajs-2434	44	4	there	there	PRON
iajs-2434	44	5	is	be	VERB
iajs-2434	44	6	no	no	DET
iajs-2434	44	7	specific	specific	ADJ
iajs-2434	44	8	analytical	analytical	ADJ
iajs-2434	44	9	procedure	procedure	NOUN
iajs-2434	44	10	to	to	PART
iajs-2434	44	11	determine	determine	VERB
iajs-2434	44	12	the	the	DET
iajs-2434	44	13	suitable	suitable	ADJ
iajs-2434	44	14	loss	loss	NOUN
iajs-2434	44	15	function	function	NOUN
iajs-2434	44	16	to	to	PART
iajs-2434	44	17	be	be	AUX
iajs-2434	44	18	employed	employ	VERB
iajs-2434	44	19	.	.	PUNCT
iajs-2434	45	1	in	in	ADP
iajs-2434	45	2	most	most	ADJ
iajs-2434	45	3	of	of	ADP
iajs-2434	45	4	studies	study	NOUN
iajs-2434	45	5	concerning	concern	VERB
iajs-2434	45	6	bayesian	bayesian	NOUN
iajs-2434	45	7	estimation	estimation	NOUN
iajs-2434	45	8	problem	problem	NOUN
iajs-2434	45	9	,	,	PUNCT
iajs-2434	45	10	the	the	DET
iajs-2434	45	11	researchers	researcher	NOUN
iajs-2434	45	12	consider	consider	VERB
iajs-2434	45	13	the	the	DET
iajs-2434	45	14	underlying	underlie	VERB
iajs-2434	45	15	loss	loss	NOUN
iajs-2434	45	16	function	function	NOUN
iajs-2434	45	17	to	to	PART
iajs-2434	45	18	be	be	AUX
iajs-2434	45	19	squared	square	VERB
iajs-2434	45	20	error	error	NOUN
iajs-2434	45	21	loss	loss	NOUN
iajs-2434	45	22	function	function	NOUN
iajs-2434	45	23	(	(	PUNCT
iajs-2434	45	24	self	self	NOUN
iajs-2434	45	25	)	)	PUNCT
iajs-2434	45	26	which	which	PRON
iajs-2434	45	27	is	be	AUX
iajs-2434	45	28	symmetric	symmetric	ADJ
iajs-2434	45	29	in	in	ADP
iajs-2434	45	30	nature	nature	NOUN
iajs-2434	45	31	.	.	PUNCT
iajs-2434	46	1	however	however	ADV
iajs-2434	46	2	,	,	PUNCT
iajs-2434	46	3	in	in	ADP
iajs-2434	46	4	many	many	ADJ
iajs-2434	46	5	cases	case	NOUN
iajs-2434	46	6	,	,	PUNCT
iajs-2434	46	7	using	use	VERB
iajs-2434	46	8	the	the	DET
iajs-2434	46	9	squared	square	VERB
iajs-2434	46	10	error	error	NOUN
iajs-2434	46	11	loss	loss	NOUN
iajs-2434	46	12	function	function	NOUN
iajs-2434	46	13	is	be	AUX
iajs-2434	46	14	not	not	PART
iajs-2434	46	15	appropriate	appropriate	ADJ
iajs-2434	46	16	,	,	PUNCT
iajs-2434	46	17	especially	especially	ADV
iajs-2434	46	18	in	in	ADP
iajs-2434	46	19	those	those	DET
iajs-2434	46	20	cases	case	NOUN
iajs-2434	46	21	where	where	SCONJ
iajs-2434	46	22	the	the	DET
iajs-2434	46	23	losses	loss	NOUN
iajs-2434	46	24	are	be	AUX
iajs-2434	46	25	not	not	PART
iajs-2434	46	26	symmetric	symmetric	ADJ
iajs-2434	46	27	.	.	PUNCT
iajs-2434	47	1	accordingly	accordingly	ADV
iajs-2434	47	2	,	,	PUNCT
iajs-2434	47	3	in	in	ADP
iajs-2434	47	4	order	order	NOUN
iajs-2434	47	5	to	to	PART
iajs-2434	47	6	make	make	VERB
iajs-2434	47	7	the	the	DET
iajs-2434	47	8	statistical	statistical	ADJ
iajs-2434	47	9	inferences	inference	NOUN
iajs-2434	47	10	more	more	ADV
iajs-2434	47	11	practical	practical	ADJ
iajs-2434	47	12	and	and	CCONJ
iajs-2434	47	13	applicable	applicable	ADJ
iajs-2434	47	14	,	,	PUNCT
iajs-2434	47	15	we	we	PRON
iajs-2434	47	16	often	often	ADV
iajs-2434	47	17	need	need	VERB
iajs-2434	47	18	to	to	PART
iajs-2434	47	19	choose	choose	VERB
iajs-2434	47	20	an	an	DET
iajs-2434	47	21	asymmetric	asymmetric	ADJ
iajs-2434	47	22	loss	loss	NOUN
iajs-2434	47	23	function	function	NOUN
iajs-2434	47	24	.	.	PUNCT
iajs-2434	48	1	in	in	ADP
iajs-2434	48	2	this	this	DET
iajs-2434	48	3	paper	paper	NOUN
iajs-2434	48	4	,	,	PUNCT
iajs-2434	48	5	we	we	PRON
iajs-2434	48	6	consider	consider	VERB
iajs-2434	48	7	both	both	CCONJ
iajs-2434	48	8	symmetric	symmetric	ADJ
iajs-2434	48	9	and	and	CCONJ
iajs-2434	48	10	asymmetric	asymmetric	ADJ
iajs-2434	48	11	loss	loss	NOUN
iajs-2434	48	12	functions	function	NOUN
iajs-2434	48	13	for	for	ADP
iajs-2434	48	14	better	well	ADJ
iajs-2434	48	15	realization	realization	NOUN
iajs-2434	48	16	of	of	ADP
iajs-2434	48	17	bayesian	bayesian	NOUN
iajs-2434	48	18	analysis	analysis	NOUN
iajs-2434	48	19	.	.	PUNCT
iajs-2434	49	1	in	in	ADP
iajs-2434	49	2	particular	particular	ADJ
iajs-2434	49	3	,	,	PUNCT
iajs-2434	49	4	the	the	DET
iajs-2434	49	5	following	follow	VERB
iajs-2434	49	6	loss	loss	NOUN
iajs-2434	49	7	functions	function	NOUN
iajs-2434	49	8	have	have	AUX
iajs-2434	49	9	been	be	AUX
iajs-2434	49	10	considered	consider	VERB
iajs-2434	49	11	assuming	assume	VERB
iajs-2434	49	12	that	that	SCONJ
iajs-2434	49	13	𝜃	𝜃	NOUN
iajs-2434	49	14	is	be	AUX
iajs-2434	49	15	an	an	DET
iajs-2434	49	16	estimate	estimate	NOUN
iajs-2434	49	17	of	of	ADP
iajs-2434	49	18	𝜃	𝜃	NOUN
iajs-2434	49	19	,	,	PUNCT
iajs-2434	49	20	and	and	CCONJ
iajs-2434	49	21	l	l	NOUN
iajs-2434	49	22	θ	θ	PROPN
iajs-2434	49	23	,	,	PUNCT
iajs-2434	49	24	θ	θ	PROPN
iajs-2434	49	25	symbolizes	symbolize	VERB
iajs-2434	49	26	the	the	DET
iajs-2434	49	27	loss	loss	NOUN
iajs-2434	49	28	function	function	NOUN
iajs-2434	49	29	.	.	PUNCT
iajs-2434	50	1	i	i	PRON
iajs-2434	50	2	)	)	PUNCT
iajs-2434	50	3	the	the	DET
iajs-2434	50	4	squared	square	VERB
iajs-2434	50	5	error	error	NOUN
iajs-2434	50	6	loss	loss	NOUN
iajs-2434	50	7	function	function	NOUN
iajs-2434	50	8	(	(	PUNCT
iajs-2434	50	9	self	self	NOUN
iajs-2434	50	10	)	)	PUNCT
iajs-2434	50	11	is	be	AUX
iajs-2434	50	12	defined	define	VERB
iajs-2434	50	13	as	as	ADP
iajs-2434	50	14	:	:	PUNCT
iajs-2434	50	15	𝐿	𝐿	PROPN
iajs-2434	50	16	𝜃	𝜃	PROPN
iajs-2434	50	17	,	,	PUNCT
iajs-2434	50	18	𝜃	𝜃	X
iajs-2434	51	1	𝜃	𝜃	NOUN
iajs-2434	51	2	𝜃	𝜃	X
iajs-2434	51	3	(	(	PUNCT
iajs-2434	51	4	15	15	NUM
iajs-2434	51	5	)	)	PUNCT
iajs-2434	51	6	ii	ii	NOUN
iajs-2434	51	7	)	)	PUNCT
iajs-2434	51	8	modified	modify	VERB
iajs-2434	51	9	squared	square	VERB
iajs-2434	51	10	error	error	NOUN
iajs-2434	51	11	loss	loss	NOUN
iajs-2434	51	12	function	function	NOUN
iajs-2434	51	13	(	(	PUNCT
iajs-2434	51	14	mself	mself	PRON
iajs-2434	51	15	)	)	PUNCT
iajs-2434	51	16	is	be	AUX
iajs-2434	51	17	defined	define	VERB
iajs-2434	51	18	as	as	ADP
iajs-2434	51	19	:	:	PUNCT
iajs-2434	51	20	𝐿	𝐿	PROPN
iajs-2434	51	21	𝜃	𝜃	PROPN
iajs-2434	51	22	,	,	PUNCT
iajs-2434	51	23	𝜃	𝜃	NOUN
iajs-2434	52	1	𝜃	𝜃	NOUN
iajs-2434	52	2	𝜃	𝜃	NOUN
iajs-2434	52	3	𝜃	𝜃	NOUN
iajs-2434	52	4	r=1	r=1	NOUN
iajs-2434	52	5	,	,	PUNCT
iajs-2434	52	6	2	2	NUM
iajs-2434	52	7	,	,	PUNCT
iajs-2434	52	8	3	3	NUM
iajs-2434	52	9	(	(	PUNCT
iajs-2434	52	10	16	16	NUM
iajs-2434	52	11	)	)	PUNCT
iajs-2434	52	12	iii\	iii\	PROPN
iajs-2434	52	13	)	)	PUNCT
iajs-2434	52	14	precautionary	precautionary	ADJ
iajs-2434	52	15	loss	loss	NOUN
iajs-2434	52	16	function	function	NOUN
iajs-2434	52	17	(	(	PUNCT
iajs-2434	52	18	plf	plf	NOUN
iajs-2434	52	19	)	)	PUNCT
iajs-2434	52	20	is	be	AUX
iajs-2434	52	21	defined	define	VERB
iajs-2434	52	22	as	as	ADP
iajs-2434	52	23	:	:	PUNCT
iajs-2434	52	24	𝐿	𝐿	PROPN
iajs-2434	52	25	𝜃	𝜃	PROPN
iajs-2434	52	26	,	,	PUNCT
iajs-2434	52	27	𝜃	𝜃	X
iajs-2434	52	28	(	(	PUNCT
iajs-2434	52	29	17	17	NUM
iajs-2434	52	30	)	)	PUNCT
iajs-2434	52	31	7	7	NUM
iajs-2434	52	32	.	.	PUNCT
iajs-2434	52	33	bayesian	bayesian	NOUN
iajs-2434	52	34	estimation	estimation	NOUN
iajs-2434	52	35	the	the	DET
iajs-2434	52	36	bayes	bayes	PROPN
iajs-2434	52	37	estimator	estimator	NOUN
iajs-2434	52	38	of	of	ADP
iajs-2434	52	39	the	the	DET
iajs-2434	52	40	parameter	parameter	NOUN
iajs-2434	53	1	𝜃	𝜃	NOUN
iajs-2434	53	2	is	be	AUX
iajs-2434	53	3	the	the	DET
iajs-2434	53	4	value	value	NOUN
iajs-2434	53	5	of	of	ADP
iajs-2434	53	6	𝜃	𝜃	PRON
iajs-2434	53	7	that	that	PRON
iajs-2434	53	8	minimizes	minimize	VERB
iajs-2434	53	9	the	the	DET
iajs-2434	53	10	posterior	posterior	ADJ
iajs-2434	53	11	expectation	expectation	NOUN
iajs-2434	53	12	known	know	VERB
iajs-2434	53	13	as	as	ADP
iajs-2434	53	14	the	the	DET
iajs-2434	53	15	risk	risk	NOUN
iajs-2434	53	16	function	function	NOUN
iajs-2434	53	17	and	and	CCONJ
iajs-2434	53	18	denotes	denote	NOUN
iajs-2434	53	19	𝑅	𝑅	PROPN
iajs-2434	53	20	𝜃	𝜃	PROPN
iajs-2434	53	21	,	,	PUNCT
iajs-2434	53	22	𝜃	𝜃	INTJ
iajs-2434	53	23	,	,	PUNCT
iajs-2434	53	24	that	that	PRON
iajs-2434	53	25	is	be	AUX
iajs-2434	53	26	:	:	PUNCT
iajs-2434	53	27	𝑅	𝑅	PROPN
iajs-2434	53	28	𝜃	𝜃	PROPN
iajs-2434	53	29	,	,	PUNCT
iajs-2434	53	30	𝜃	𝜃	VERB
iajs-2434	53	31	𝐸	𝐸	NOUN
iajs-2434	53	32	𝐿	𝐿	PROPN
iajs-2434	53	33	𝜃	𝜃	PROPN
iajs-2434	53	34	,	,	PUNCT
iajs-2434	53	35	𝜃	𝜃	PROPN
iajs-2434	53	36	𝐿	𝐿	PROPN
iajs-2434	53	37	𝜃	𝜃	PROPN
iajs-2434	53	38	,	,	PUNCT
iajs-2434	53	39	𝜃	𝜃	NUM
iajs-2434	53	40	ℎ	ℎ	NOUN
iajs-2434	53	41	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	53	42	𝑑𝜃	𝑑𝜃	PROPN
iajs-2434	53	43	(	(	PUNCT
iajs-2434	53	44	18	18	NUM
iajs-2434	53	45	)	)	PUNCT
iajs-2434	53	46	where	where	SCONJ
iajs-2434	53	47	ℎ	ℎ	NOUN
iajs-2434	53	48	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	53	49	is	be	AUX
iajs-2434	53	50	the	the	DET
iajs-2434	53	51	posterior	posterior	ADJ
iajs-2434	53	52	density	density	NOUN
iajs-2434	53	53	of	of	ADP
iajs-2434	53	54	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	53	55	8	8	NUM
iajs-2434	53	56	.	.	PUNCT
iajs-2434	54	1	bayes	bayes	PROPN
iajs-2434	54	2	estimator	estimator	NOUN
iajs-2434	54	3	of	of	ADP
iajs-2434	54	4	the	the	DET
iajs-2434	54	5	parameter	parameter	NOUN
iajs-2434	54	6	𝜽	𝜽	PROPN
iajs-2434	54	7	of	of	ADP
iajs-2434	54	8	ird	ird	PROPN
iajs-2434	54	9	under	under	ADP
iajs-2434	54	10	self	self	NOUN
iajs-2434	54	11	in	in	ADP
iajs-2434	54	12	general	general	ADJ
iajs-2434	54	13	,	,	PUNCT
iajs-2434	54	14	if	if	SCONJ
iajs-2434	54	15	self	self	NOUN
iajs-2434	54	16	is	be	AUX
iajs-2434	54	17	chosen	choose	VERB
iajs-2434	54	18	,	,	PUNCT
iajs-2434	54	19	then	then	ADV
iajs-2434	54	20	according	accord	VERB
iajs-2434	54	21	to	to	ADP
iajs-2434	54	22	equation	equation	NOUN
iajs-2434	54	23	(	(	PUNCT
iajs-2434	54	24	18	18	NUM
iajs-2434	54	25	)	)	PUNCT
iajs-2434	54	26	,	,	PUNCT
iajs-2434	54	27	we	we	PRON
iajs-2434	54	28	have	have	VERB
iajs-2434	54	29	:	:	PUNCT
iajs-2434	54	30	𝑅	𝑅	PROPN
iajs-2434	54	31	𝜃	𝜃	PROPN
iajs-2434	54	32	,	,	PUNCT
iajs-2434	54	33	𝜃	𝜃	NOUN
iajs-2434	54	34	𝜃	𝜃	NOUN
iajs-2434	54	35	𝜃	𝜃	NOUN
iajs-2434	54	36	ℎ	ℎ	NOUN
iajs-2434	54	37	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	54	38	𝑑𝜃	𝑑𝜃	ADP
iajs-2434	54	39	𝜃	𝜃	NUM
iajs-2434	54	40	ℎ	ℎ	NOUN
iajs-2434	54	41	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	55	1	𝑑𝜃	𝑑𝜃	ADP
iajs-2434	55	2	2𝜃	2𝜃	NUM
iajs-2434	55	3	𝜃ℎ	𝜃ℎ	NOUN
iajs-2434	55	4	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	55	5	𝑑𝜃	𝑑𝜃	ADP
iajs-2434	55	6	𝜃	𝜃	PRON
iajs-2434	55	7	ℎ	ℎ	NOUN
iajs-2434	55	8	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	55	9	𝑑𝜃	𝑑𝜃	ADP
iajs-2434	55	10	it	it	PRON
iajs-2434	55	11	follows	follow	VERB
iajs-2434	55	12	that	that	SCONJ
iajs-2434	55	13	:	:	PUNCT
iajs-2434	55	14	  	  	SPACE
iajs-2434	55	15	132	132	NUM
iajs-2434	55	16	  	  	SPACE
iajs-2434	55	17	ibn	ibn	PROPN
iajs-2434	55	18	al	al	PROPN
iajs-2434	55	19	-	-	PUNCT
iajs-2434	55	20	haitham	haitham	PROPN
iajs-2434	55	21	jour	jour	X
iajs-2434	55	22	.	.	PROPN
iajs-2434	56	1	for	for	ADP
iajs-2434	56	2	pure	pure	ADJ
iajs-2434	56	3	&	&	CCONJ
iajs-2434	56	4	appl	appl	PROPN
iajs-2434	56	5	.	.	PUNCT
iajs-2434	57	1	sci	sci	PROPN
iajs-2434	57	2	.	.	PROPN
iajs-2434	58	1	33	33	NUM
iajs-2434	58	2	(	(	PUNCT
iajs-2434	58	3	1	1	NUM
iajs-2434	58	4	)	)	PUNCT
iajs-2434	58	5	2020	2020	NUM
iajs-2434	58	6	𝑅	𝑅	PROPN
iajs-2434	58	7	𝜃	𝜃	PROPN
iajs-2434	58	8	,	,	PUNCT
iajs-2434	58	9	𝜃	𝜃	PRON
iajs-2434	58	10	𝜃	𝜃	NUM
iajs-2434	58	11	2𝜃𝐸	2𝜃𝐸	NUM
iajs-2434	58	12	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	58	13	𝐸	𝐸	PROPN
iajs-2434	58	14	𝜃	𝜃	X
iajs-2434	58	15	|𝑡	|𝑡	X
iajs-2434	58	16	by	by	ADP
iajs-2434	58	17	differentiating	differentiate	VERB
iajs-2434	58	18	𝑅	𝑅	PROPN
iajs-2434	58	19	𝜃	𝜃	PROPN
iajs-2434	58	20	,	,	PUNCT
iajs-2434	58	21	𝜃	𝜃	NOUN
iajs-2434	58	22	with	with	ADP
iajs-2434	58	23	respect	respect	NOUN
iajs-2434	58	24	to	to	ADP
iajs-2434	58	25	𝜃	𝜃	NOUN
iajs-2434	58	26	and	and	CCONJ
iajs-2434	58	27	setting	set	VERB
iajs-2434	58	28	the	the	DET
iajs-2434	58	29	resultant	resultant	NOUN
iajs-2434	58	30	derivative	derivative	NOUN
iajs-2434	58	31	equal	equal	ADJ
iajs-2434	58	32	to	to	ADP
iajs-2434	58	33	zero	zero	NUM
iajs-2434	58	34	,	,	PUNCT
iajs-2434	58	35	we	we	PRON
iajs-2434	58	36	get	get	VERB
iajs-2434	58	37	:	:	PUNCT
iajs-2434	58	38	2𝜃	2𝜃	NUM
iajs-2434	58	39	2𝐸	2𝐸	ADJ
iajs-2434	58	40	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	58	41	0	0	NUM
iajs-2434	58	42	by	by	ADP
iajs-2434	58	43	solving	solve	VERB
iajs-2434	58	44	for	for	ADP
iajs-2434	58	45	𝜃	𝜃	PROPN
iajs-2434	58	46	,	,	PUNCT
iajs-2434	58	47	we	we	PRON
iajs-2434	58	48	obtain	obtain	VERB
iajs-2434	58	49	the	the	DET
iajs-2434	58	50	bayes	bayes	PROPN
iajs-2434	58	51	estimator	estimator	NOUN
iajs-2434	58	52	of	of	ADP
iajs-2434	58	53	𝜃	𝜃	PROPN
iajs-2434	58	54	under	under	ADP
iajs-2434	58	55	self	self	NOUN
iajs-2434	58	56	denoted	denote	VERB
iajs-2434	58	57	by	by	ADP
iajs-2434	58	58	𝜃	𝜃	DET
iajs-2434	58	59	𝐸	𝐸	PROPN
iajs-2434	58	60	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	58	61	(	(	PUNCT
iajs-2434	58	62	19	19	NUM
iajs-2434	58	63	)	)	PUNCT
iajs-2434	58	64	from	from	ADP
iajs-2434	58	65	equation	equation	NOUN
iajs-2434	58	66	(	(	PUNCT
iajs-2434	58	67	11	11	NUM
iajs-2434	58	68	)	)	PUNCT
iajs-2434	58	69	and	and	CCONJ
iajs-2434	58	70	on	on	ADP
iajs-2434	58	71	the	the	DET
iajs-2434	58	72	basis	basis	NOUN
iajs-2434	58	73	of	of	ADP
iajs-2434	58	74	non	non	ADJ
iajs-2434	58	75	-	-	ADJ
iajs-2434	58	76	informative	informative	ADJ
iajs-2434	58	77	prior	prior	NOUN
iajs-2434	58	78	,	,	PUNCT
iajs-2434	58	79	the	the	DET
iajs-2434	58	80	bayes	bayes	PROPN
iajs-2434	58	81	estimator	estimator	NOUN
iajs-2434	58	82	of	of	ADP
iajs-2434	58	83	inverse	inverse	PROPN
iajs-2434	58	84	rayleigh	rayleigh	PROPN
iajs-2434	58	85	parameter	parameter	PROPN
iajs-2434	58	86	𝜃	𝜃	PRON
iajs-2434	58	87	denoted	denote	VERB
iajs-2434	58	88	as	as	SCONJ
iajs-2434	58	89	𝜃	𝜃	PRON
iajs-2434	58	90	is	be	AUX
iajs-2434	58	91	given	give	VERB
iajs-2434	58	92	by	by	ADP
iajs-2434	58	93	.	.	PUNCT
iajs-2434	59	1	𝜃	𝜃	X
iajs-2434	59	2	(	(	PUNCT
iajs-2434	59	3	20	20	NUM
iajs-2434	59	4	)	)	PUNCT
iajs-2434	59	5	where	where	SCONJ
iajs-2434	59	6	𝜃	𝜃	PRON
iajs-2434	59	7	denotes	denote	VERB
iajs-2434	59	8	the	the	DET
iajs-2434	59	9	bayes	bayes	PROPN
iajs-2434	59	10	estimate	estimate	NOUN
iajs-2434	59	11	of	of	ADP
iajs-2434	59	12	𝜃	𝜃	PRON
iajs-2434	59	13	based	base	VERB
iajs-2434	59	14	on	on	ADP
iajs-2434	59	15	jeffrey	jeffrey	PROPN
iajs-2434	59	16	's	's	PART
iajs-2434	59	17	prior	prior	ADJ
iajs-2434	59	18	information	information	NOUN
iajs-2434	59	19	.	.	PUNCT
iajs-2434	60	1	if	if	SCONJ
iajs-2434	60	2	the	the	DET
iajs-2434	60	3	inverse	inverse	NOUN
iajs-2434	60	4	rayleigh	rayleigh	PROPN
iajs-2434	60	5	parameter	parameter	PROPN
iajs-2434	60	6	follows	follow	VERB
iajs-2434	60	7	the	the	DET
iajs-2434	60	8	exponential	exponential	ADJ
iajs-2434	60	9	prior	prior	ADJ
iajs-2434	60	10	distribution	distribution	NOUN
iajs-2434	60	11	,	,	PUNCT
iajs-2434	60	12	then	then	ADV
iajs-2434	60	13	by	by	ADP
iajs-2434	60	14	equation	equation	NOUN
iajs-2434	60	15	(	(	PUNCT
iajs-2434	60	16	14	14	NUM
iajs-2434	60	17	)	)	PUNCT
iajs-2434	60	18	,	,	PUNCT
iajs-2434	60	19	we	we	PRON
iajs-2434	60	20	conclude	conclude	VERB
iajs-2434	60	21	that	that	SCONJ
iajs-2434	61	1	𝜃	𝜃	X
iajs-2434	61	2	(	(	PUNCT
iajs-2434	61	3	21	21	NUM
iajs-2434	61	4	)	)	PUNCT
iajs-2434	61	5	where	where	SCONJ
iajs-2434	61	6	𝜃	𝜃	PRON
iajs-2434	61	7	denotes	denote	VERB
iajs-2434	61	8	the	the	DET
iajs-2434	61	9	bayes	bayes	PROPN
iajs-2434	61	10	estimate	estimate	NOUN
iajs-2434	61	11	of	of	ADP
iajs-2434	61	12	𝜃	𝜃	PRON
iajs-2434	61	13	based	base	VERB
iajs-2434	61	14	on	on	ADP
iajs-2434	61	15	exponential	exponential	ADJ
iajs-2434	61	16	prior	prior	ADJ
iajs-2434	61	17	distribution	distribution	NOUN
iajs-2434	61	18	.	.	PUNCT
iajs-2434	62	1	9	9	X
iajs-2434	62	2	.	.	X
iajs-2434	62	3	bayes	bayes	PROPN
iajs-2434	62	4	estimator	estimator	NOUN
iajs-2434	62	5	of	of	ADP
iajs-2434	62	6	the	the	DET
iajs-2434	62	7	inverse	inverse	NOUN
iajs-2434	62	8	rayleigh	rayleigh	PROPN
iajs-2434	62	9	parameter	parameter	NOUN
iajs-2434	63	1	𝜽	𝜽	PROPN
iajs-2434	63	2	under	under	ADP
iajs-2434	63	3	mself	mself	PRON
iajs-2434	63	4	by	by	ADP
iajs-2434	63	5	substituting	substitute	VERB
iajs-2434	63	6	𝐿	𝐿	PROPN
iajs-2434	63	7	𝜃	𝜃	PROPN
iajs-2434	63	8	,	,	PUNCT
iajs-2434	63	9	𝜃	𝜃	PRON
iajs-2434	63	10	given	give	VERB
iajs-2434	63	11	in	in	ADP
iajs-2434	63	12	equation	equation	NOUN
iajs-2434	63	13	(	(	PUNCT
iajs-2434	63	14	16	16	NUM
iajs-2434	63	15	)	)	PUNCT
iajs-2434	63	16	into	into	ADP
iajs-2434	63	17	equation	equation	NOUN
iajs-2434	63	18	(	(	PUNCT
iajs-2434	63	19	18	18	NUM
iajs-2434	63	20	)	)	PUNCT
iajs-2434	63	21	,	,	PUNCT
iajs-2434	63	22	we	we	PRON
iajs-2434	63	23	get	get	VERB
iajs-2434	63	24	𝑅	𝑅	PROPN
iajs-2434	63	25	𝜃	𝜃	PROPN
iajs-2434	63	26	,	,	PUNCT
iajs-2434	63	27	𝜃	𝜃	NOUN
iajs-2434	63	28	𝜃	𝜃	NOUN
iajs-2434	63	29	𝜃	𝜃	NOUN
iajs-2434	63	30	𝜃	𝜃	NOUN
iajs-2434	63	31	ℎ	ℎ	NOUN
iajs-2434	63	32	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	63	33	𝑑𝜃	𝑑𝜃	NOUN
iajs-2434	63	34	by	by	ADP
iajs-2434	63	35	evaluating	evaluate	VERB
iajs-2434	63	36	the	the	DET
iajs-2434	63	37	integral	integral	ADJ
iajs-2434	63	38	,	,	PUNCT
iajs-2434	63	39	we	we	PRON
iajs-2434	63	40	get	get	VERB
iajs-2434	63	41	𝑅	𝑅	PROPN
iajs-2434	63	42	𝜃	𝜃	PROPN
iajs-2434	63	43	,	,	PUNCT
iajs-2434	63	44	𝜃	𝜃	PROPN
iajs-2434	63	45	𝜃	𝜃	X
iajs-2434	63	46	𝐸	𝐸	VERB
iajs-2434	63	47	𝜃	𝜃	X
iajs-2434	63	48	|𝑡	|𝑡	NOUN
iajs-2434	63	49	2𝜃𝐸	2𝜃𝐸	PROPN
iajs-2434	63	50	𝜃	𝜃	NUM
iajs-2434	63	51	|𝑡	|𝑡	X
iajs-2434	63	52	𝐸	𝐸	PROPN
iajs-2434	63	53	𝜃	𝜃	X
iajs-2434	63	54	|𝑡	|𝑡	X
iajs-2434	63	55	by	by	ADP
iajs-2434	63	56	differentiating	differentiate	VERB
iajs-2434	63	57	𝑅	𝑅	PROPN
iajs-2434	63	58	𝜃	𝜃	PROPN
iajs-2434	63	59	,	,	PUNCT
iajs-2434	63	60	𝜃	𝜃	NOUN
iajs-2434	63	61	with	with	ADP
iajs-2434	63	62	respect	respect	NOUN
iajs-2434	63	63	to	to	ADP
iajs-2434	63	64	θ	θ	PROPN
iajs-2434	63	65	,	,	PUNCT
iajs-2434	63	66	then	then	ADV
iajs-2434	63	67	equating	equate	VERB
iajs-2434	63	68	the	the	DET
iajs-2434	63	69	resultant	resultant	NOUN
iajs-2434	63	70	derivative	derivative	NOUN
iajs-2434	63	71	to	to	ADP
iajs-2434	63	72	zero	zero	NUM
iajs-2434	63	73	and	and	CCONJ
iajs-2434	63	74	solving	solve	VERB
iajs-2434	63	75	for	for	ADP
iajs-2434	63	76	𝜃	𝜃	NOUN
iajs-2434	63	77	,	,	PUNCT
iajs-2434	63	78	we	we	PRON
iajs-2434	63	79	get	get	VERB
iajs-2434	63	80	the	the	DET
iajs-2434	63	81	bayes	bayes	PROPN
iajs-2434	63	82	estimator	estimator	NOUN
iajs-2434	63	83	of	of	ADP
iajs-2434	63	84	𝜃	𝜃	NUM
iajs-2434	63	85	under	under	ADP
iajs-2434	63	86	modified	modify	VERB
iajs-2434	63	87	squared	square	VERB
iajs-2434	63	88	error	error	NOUN
iajs-2434	63	89	loss	loss	NOUN
iajs-2434	63	90	function	function	NOUN
iajs-2434	63	91	denoted	denote	VERB
iajs-2434	63	92	by	by	ADP
iajs-2434	63	93	𝜃	𝜃	PRON
iajs-2434	63	94	as	as	SCONJ
iajs-2434	63	95	follows	follow	VERB
iajs-2434	63	96	.	.	PUNCT
iajs-2434	64	1	𝜃	𝜃	X
iajs-2434	64	2	|	|	ADV
iajs-2434	64	3	|	|	ADV
iajs-2434	64	4	r=1,2	r=1,2	ADJ
iajs-2434	64	5	,	,	PUNCT
iajs-2434	64	6	(	(	PUNCT
iajs-2434	64	7	22	22	NUM
iajs-2434	64	8	)	)	PUNCT
iajs-2434	64	9	if	if	SCONJ
iajs-2434	64	10	k	k	PROPN
iajs-2434	64	11	is	be	AUX
iajs-2434	64	12	positive	positive	ADJ
iajs-2434	64	13	integer	integer	NOUN
iajs-2434	64	14	,	,	PUNCT
iajs-2434	64	15	it	it	PRON
iajs-2434	64	16	is	be	AUX
iajs-2434	64	17	well	well	ADV
iajs-2434	64	18	known	know	VERB
iajs-2434	64	19	that	that	SCONJ
iajs-2434	64	20	𝐸	𝐸	PROPN
iajs-2434	64	21	𝜃	𝜃	NUM
iajs-2434	64	22	|𝑡	|𝑡	X
iajs-2434	64	23	𝜃	𝜃	X
iajs-2434	64	24	ℎ	ℎ	PROPN
iajs-2434	64	25	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	64	26	𝑑𝜃	𝑑𝜃	PROPN
iajs-2434	64	27	(	(	PUNCT
iajs-2434	64	28	23	23	NUM
iajs-2434	64	29	)	)	PUNCT
iajs-2434	64	30	on	on	ADP
iajs-2434	64	31	the	the	DET
iajs-2434	64	32	basis	basis	NOUN
iajs-2434	64	33	of	of	ADP
iajs-2434	64	34	jeffrey	jeffrey	PROPN
iajs-2434	64	35	's	's	PART
iajs-2434	64	36	prior	prior	ADJ
iajs-2434	64	37	information	information	NOUN
iajs-2434	64	38	and	and	CCONJ
iajs-2434	64	39	by	by	ADP
iajs-2434	64	40	substituting	substitute	VERB
iajs-2434	64	41	ℎ	ℎ	NOUN
iajs-2434	64	42	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	64	43	by	by	ADP
iajs-2434	64	44	ℎ	ℎ	PROPN
iajs-2434	64	45	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	64	46	given	give	VERB
iajs-2434	64	47	in	in	ADP
iajs-2434	64	48	equation	equation	NOUN
iajs-2434	64	49	(	(	PUNCT
iajs-2434	64	50	10	10	NUM
iajs-2434	64	51	)	)	PUNCT
iajs-2434	64	52	,	,	PUNCT
iajs-2434	64	53	then	then	ADV
iajs-2434	64	54	evaluating	evaluate	VERB
iajs-2434	64	55	the	the	DET
iajs-2434	64	56	integral	integral	ADJ
iajs-2434	64	57	in	in	ADP
iajs-2434	64	58	(	(	PUNCT
iajs-2434	64	59	23	23	NUM
iajs-2434	64	60	)	)	PUNCT
iajs-2434	64	61	;	;	PUNCT
iajs-2434	64	62	it	it	PRON
iajs-2434	64	63	can	can	AUX
iajs-2434	64	64	easily	easily	ADV
iajs-2434	64	65	be	be	AUX
iajs-2434	64	66	shown	show	VERB
iajs-2434	64	67	𝐸	𝐸	PROPN
iajs-2434	64	68	𝜃	𝜃	DET
iajs-2434	64	69	|𝑡	|𝑡	X
iajs-2434	64	70	(	(	PUNCT
iajs-2434	64	71	24	24	NUM
iajs-2434	64	72	)	)	PUNCT
iajs-2434	64	73	  	  	SPACE
iajs-2434	64	74	133	133	NUM
iajs-2434	64	75	  	  	SPACE
iajs-2434	64	76	ibn	ibn	PROPN
iajs-2434	64	77	al	al	PROPN
iajs-2434	64	78	-	-	PUNCT
iajs-2434	64	79	haitham	haitham	PROPN
iajs-2434	64	80	jour	jour	X
iajs-2434	64	81	.	.	PROPN
iajs-2434	65	1	for	for	ADP
iajs-2434	65	2	pure	pure	ADJ
iajs-2434	65	3	&	&	CCONJ
iajs-2434	65	4	appl	appl	PROPN
iajs-2434	65	5	.	.	PUNCT
iajs-2434	66	1	sci	sci	PROPN
iajs-2434	66	2	.	.	PROPN
iajs-2434	67	1	33	33	NUM
iajs-2434	67	2	(	(	PUNCT
iajs-2434	67	3	1	1	NUM
iajs-2434	67	4	)	)	PUNCT
iajs-2434	67	5	2020	2020	NUM
iajs-2434	67	6	therefore	therefore	ADV
iajs-2434	67	7	,	,	PUNCT
iajs-2434	67	8	the	the	DET
iajs-2434	67	9	bayes	bayes	PROPN
iajs-2434	67	10	estimator	estimator	NOUN
iajs-2434	67	11	given	give	VERB
iajs-2434	67	12	in	in	ADP
iajs-2434	67	13	equation	equation	NOUN
iajs-2434	67	14	(	(	PUNCT
iajs-2434	67	15	22	22	NUM
iajs-2434	67	16	)	)	PUNCT
iajs-2434	67	17	can	can	AUX
iajs-2434	67	18	be	be	AUX
iajs-2434	67	19	simplified	simplify	VERB
iajs-2434	67	20	to	to	PART
iajs-2434	67	21	be	be	AUX
iajs-2434	67	22	:	:	PUNCT
iajs-2434	67	23	𝜃	𝜃	X
iajs-2434	67	24	(	(	PUNCT
iajs-2434	67	25	25	25	NUM
iajs-2434	67	26	)	)	PUNCT
iajs-2434	67	27	if	if	SCONJ
iajs-2434	67	28	r=1	r=1	NOUN
iajs-2434	67	29	we	we	PRON
iajs-2434	67	30	get	get	VERB
iajs-2434	67	31	𝜃	𝜃	X
iajs-2434	67	32	(	(	PUNCT
iajs-2434	67	33	26	26	NUM
iajs-2434	67	34	)	)	PUNCT
iajs-2434	67	35	if	if	SCONJ
iajs-2434	67	36	r=2	r=2	PRON
iajs-2434	67	37	we	we	PRON
iajs-2434	67	38	get	get	VERB
iajs-2434	67	39	𝜃	𝜃	X
iajs-2434	67	40	(	(	PUNCT
iajs-2434	67	41	27	27	NUM
iajs-2434	67	42	)	)	PUNCT
iajs-2434	67	43	if	if	SCONJ
iajs-2434	67	44	r=3	r=3	PROPN
iajs-2434	67	45	then	then	ADV
iajs-2434	67	46	we	we	PRON
iajs-2434	67	47	obtain	obtain	VERB
iajs-2434	67	48	,	,	PUNCT
iajs-2434	67	49	𝜃	𝜃	X
iajs-2434	67	50	(	(	PUNCT
iajs-2434	67	51	28	28	NUM
iajs-2434	67	52	)	)	PUNCT
iajs-2434	67	53	on	on	ADP
iajs-2434	67	54	the	the	DET
iajs-2434	67	55	basis	basis	NOUN
iajs-2434	67	56	of	of	ADP
iajs-2434	67	57	exponential	exponential	ADJ
iajs-2434	67	58	prior	prior	ADJ
iajs-2434	67	59	distribution	distribution	NOUN
iajs-2434	67	60	and	and	CCONJ
iajs-2434	67	61	by	by	ADP
iajs-2434	67	62	replacing	replace	VERB
iajs-2434	67	63	ℎ	ℎ	ADP
iajs-2434	67	64	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	67	65	in	in	ADP
iajs-2434	67	66	equation	equation	NOUN
iajs-2434	67	67	(	(	PUNCT
iajs-2434	67	68	23	23	NUM
iajs-2434	67	69	)	)	PUNCT
iajs-2434	67	70	by	by	ADP
iajs-2434	67	71	ℎ	ℎ	X
iajs-2434	67	72	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	67	73	given	give	VERB
iajs-2434	67	74	in	in	ADP
iajs-2434	67	75	equation	equation	NOUN
iajs-2434	67	76	(	(	PUNCT
iajs-2434	67	77	13	13	NUM
iajs-2434	67	78	)	)	PUNCT
iajs-2434	67	79	,	,	PUNCT
iajs-2434	67	80	we	we	PRON
iajs-2434	67	81	get	get	VERB
iajs-2434	67	82	:	:	PUNCT
iajs-2434	67	83	𝐸	𝐸	PROPN
iajs-2434	67	84	𝜃	𝜃	PRON
iajs-2434	67	85	|𝑡	|𝑡	X
iajs-2434	67	86	,	,	PUNCT
iajs-2434	67	87	k=1,2	k=1,2	PROPN
iajs-2434	67	88	(	(	PUNCT
iajs-2434	67	89	29	29	NUM
iajs-2434	67	90	)	)	PUNCT
iajs-2434	67	91	where	where	SCONJ
iajs-2434	67	92	𝑝	𝑝	X
iajs-2434	67	93	𝑇	𝑇	PROPN
iajs-2434	67	94	𝜆	𝜆	X
iajs-2434	67	95	therefore	therefore	ADV
iajs-2434	67	96	,	,	PUNCT
iajs-2434	67	97	the	the	DET
iajs-2434	67	98	bayes	bayes	PROPN
iajs-2434	67	99	estimator	estimator	NOUN
iajs-2434	67	100	given	give	VERB
iajs-2434	67	101	in	in	ADP
iajs-2434	67	102	equation	equation	NOUN
iajs-2434	67	103	(	(	PUNCT
iajs-2434	67	104	22	22	NUM
iajs-2434	67	105	)	)	PUNCT
iajs-2434	67	106	can	can	AUX
iajs-2434	67	107	be	be	AUX
iajs-2434	67	108	simplified	simplify	VERB
iajs-2434	67	109	to	to	PART
iajs-2434	67	110	be	be	AUX
iajs-2434	67	111	:	:	PUNCT
iajs-2434	67	112	𝜃	𝜃	X
iajs-2434	67	113	(	(	PUNCT
iajs-2434	67	114	30	30	NUM
iajs-2434	67	115	)	)	PUNCT
iajs-2434	67	116	for	for	ADP
iajs-2434	67	117	r=1	r=1	NOUN
iajs-2434	67	118	we	we	PRON
iajs-2434	67	119	get	get	VERB
iajs-2434	67	120	:	:	PUNCT
iajs-2434	67	121	𝜃	𝜃	X
iajs-2434	67	122	(	(	PUNCT
iajs-2434	67	123	31	31	NUM
iajs-2434	67	124	)	)	PUNCT
iajs-2434	67	125	for	for	ADP
iajs-2434	67	126	r=2	r=2	PRON
iajs-2434	67	127	we	we	PRON
iajs-2434	67	128	get	get	VERB
iajs-2434	67	129	:	:	PUNCT
iajs-2434	67	130	𝜃	𝜃	X
iajs-2434	67	131	(	(	PUNCT
iajs-2434	67	132	32	32	NUM
iajs-2434	67	133	)	)	PUNCT
iajs-2434	67	134	for	for	ADP
iajs-2434	67	135	r=3	r=3	ADV
iajs-2434	68	1	we	we	PRON
iajs-2434	68	2	get	get	VERB
iajs-2434	68	3	:	:	PUNCT
iajs-2434	68	4	𝜃	𝜃	X
iajs-2434	68	5	(	(	PUNCT
iajs-2434	68	6	33	33	NUM
iajs-2434	68	7	)	)	PUNCT
iajs-2434	68	8	10	10	NUM
iajs-2434	68	9	.	.	PUNCT
iajs-2434	69	1	bayes	bayes	PROPN
iajs-2434	69	2	estimator	estimator	NOUN
iajs-2434	69	3	of	of	ADP
iajs-2434	69	4	the	the	DET
iajs-2434	69	5	inverse	inverse	NOUN
iajs-2434	69	6	rayleigh	rayleigh	PROPN
iajs-2434	69	7	parameter	parameter	NOUN
iajs-2434	70	1	𝜽	𝜽	INTJ
iajs-2434	70	2	under	under	ADP
iajs-2434	70	3	precautionary	precautionary	ADJ
iajs-2434	70	4	loss	loss	NOUN
iajs-2434	70	5	function	function	NOUN
iajs-2434	70	6	by	by	ADP
iajs-2434	70	7	substituting	substitute	VERB
iajs-2434	70	8	𝐿	𝐿	PROPN
iajs-2434	70	9	𝜃	𝜃	PROPN
iajs-2434	70	10	,	,	PUNCT
iajs-2434	70	11	𝜃	𝜃	PRON
iajs-2434	70	12	presented	present	VERB
iajs-2434	70	13	in	in	ADP
iajs-2434	70	14	equation	equation	NOUN
iajs-2434	70	15	(	(	PUNCT
iajs-2434	70	16	17	17	NUM
iajs-2434	70	17	)	)	PUNCT
iajs-2434	70	18	into	into	ADP
iajs-2434	70	19	equation	equation	NOUN
iajs-2434	70	20	(	(	PUNCT
iajs-2434	70	21	18	18	NUM
iajs-2434	70	22	)	)	PUNCT
iajs-2434	70	23	,	,	PUNCT
iajs-2434	70	24	we	we	PRON
iajs-2434	70	25	get	get	VERB
iajs-2434	70	26	:	:	PUNCT
iajs-2434	70	27	𝑅	𝑅	PROPN
iajs-2434	70	28	𝜃	𝜃	PROPN
iajs-2434	70	29	,	,	PUNCT
iajs-2434	70	30	𝜃	𝜃	NUM
iajs-2434	70	31	ℎ	ℎ	NOUN
iajs-2434	70	32	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	70	33	𝑑𝜃	𝑑𝜃	NOUN
iajs-2434	70	34	by	by	ADP
iajs-2434	70	35	evaluating	evaluate	VERB
iajs-2434	70	36	the	the	DET
iajs-2434	70	37	integral	integral	ADJ
iajs-2434	70	38	,	,	PUNCT
iajs-2434	70	39	we	we	PRON
iajs-2434	70	40	get	get	VERB
iajs-2434	70	41	:	:	PUNCT
iajs-2434	70	42	  	  	SPACE
iajs-2434	70	43	134	134	NUM
iajs-2434	70	44	  	  	SPACE
iajs-2434	70	45	ibn	ibn	PROPN
iajs-2434	70	46	al	al	PROPN
iajs-2434	70	47	-	-	PUNCT
iajs-2434	70	48	haitham	haitham	PROPN
iajs-2434	70	49	jour	jour	X
iajs-2434	70	50	.	.	PROPN
iajs-2434	71	1	for	for	ADP
iajs-2434	71	2	pure	pure	ADJ
iajs-2434	71	3	&	&	CCONJ
iajs-2434	71	4	appl	appl	PROPN
iajs-2434	71	5	.	.	PUNCT
iajs-2434	72	1	sci	sci	PROPN
iajs-2434	72	2	.	.	PROPN
iajs-2434	73	1	33	33	NUM
iajs-2434	73	2	(	(	PUNCT
iajs-2434	73	3	1	1	NUM
iajs-2434	73	4	)	)	PUNCT
iajs-2434	73	5	2020	2020	NUM
iajs-2434	73	6	𝑅	𝑅	PROPN
iajs-2434	73	7	𝜃	𝜃	PROPN
iajs-2434	73	8	,	,	PUNCT
iajs-2434	73	9	𝜃	𝜃	X
iajs-2434	73	10	=	=	SYM
iajs-2434	73	11	𝐸	𝐸	PROPN
iajs-2434	73	12	𝜃	𝜃	NUM
iajs-2434	73	13	|𝑡	|𝑡	NOUN
iajs-2434	73	14	2𝐸	2𝐸	ADJ
iajs-2434	73	15	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	73	16	𝜃	𝜃	AUX
iajs-2434	73	17	differentiating	differentiate	VERB
iajs-2434	73	18	𝑅	𝑅	PROPN
iajs-2434	73	19	𝜃	𝜃	PROPN
iajs-2434	73	20	,	,	PUNCT
iajs-2434	73	21	𝜃	𝜃	NOUN
iajs-2434	73	22	with	with	ADP
iajs-2434	73	23	respect	respect	NOUN
iajs-2434	73	24	to	to	ADP
iajs-2434	73	25	𝜃	𝜃	NOUN
iajs-2434	73	26	and	and	CCONJ
iajs-2434	73	27	setting	set	VERB
iajs-2434	73	28	the	the	DET
iajs-2434	73	29	derivative	derivative	ADJ
iajs-2434	73	30	equal	equal	ADJ
iajs-2434	73	31	to	to	ADP
iajs-2434	73	32	zero	zero	NUM
iajs-2434	73	33	then	then	ADV
iajs-2434	73	34	solving	solve	VERB
iajs-2434	73	35	for	for	ADP
iajs-2434	73	36	𝜃	𝜃	PROPN
iajs-2434	73	37	,	,	PUNCT
iajs-2434	73	38	we	we	PRON
iajs-2434	73	39	get	get	VERB
iajs-2434	73	40	the	the	DET
iajs-2434	73	41	bayes	bayes	PROPN
iajs-2434	73	42	estimator	estimator	NOUN
iajs-2434	73	43	of	of	ADP
iajs-2434	73	44	𝜃	𝜃	NUM
iajs-2434	73	45	under	under	ADP
iajs-2434	73	46	precautionary	precautionary	ADJ
iajs-2434	73	47	loss	loss	NOUN
iajs-2434	73	48	function	function	NOUN
iajs-2434	73	49	denoted	denote	VERB
iajs-2434	73	50	as	as	ADP
iajs-2434	73	51	𝜃	𝜃	PROPN
iajs-2434	73	52	,	,	PUNCT
iajs-2434	73	53	that	that	PRON
iajs-2434	73	54	is	be	AUX
iajs-2434	73	55	:	:	PUNCT
iajs-2434	73	56	𝜃	𝜃	X
iajs-2434	73	57	𝐸	𝐸	PROPN
iajs-2434	73	58	𝜃	𝜃	PRON
iajs-2434	73	59	|𝑡	|𝑡	X
iajs-2434	73	60	(	(	PUNCT
iajs-2434	73	61	34	34	NUM
iajs-2434	73	62	)	)	PUNCT
iajs-2434	73	63	on	on	ADP
iajs-2434	73	64	the	the	DET
iajs-2434	73	65	basis	basis	NOUN
iajs-2434	73	66	of	of	ADP
iajs-2434	73	67	jeffrey	jeffrey	PROPN
iajs-2434	73	68	's	's	PART
iajs-2434	73	69	prior	prior	ADJ
iajs-2434	73	70	information	information	NOUN
iajs-2434	73	71	,	,	PUNCT
iajs-2434	73	72	the	the	DET
iajs-2434	73	73	bayes	bayes	PROPN
iajs-2434	73	74	estimator	estimator	NOUN
iajs-2434	73	75	of	of	ADP
iajs-2434	73	76	the	the	DET
iajs-2434	73	77	inverse	inverse	NOUN
iajs-2434	73	78	rayleigh	rayleigh	PROPN
iajs-2434	73	79	parameter	parameter	PROPN
iajs-2434	73	80	𝜃	𝜃	PRON
iajs-2434	73	81	can	can	AUX
iajs-2434	73	82	be	be	AUX
iajs-2434	73	83	obtained	obtain	VERB
iajs-2434	73	84	by	by	ADP
iajs-2434	73	85	assuming	assume	VERB
iajs-2434	73	86	that	that	SCONJ
iajs-2434	73	87	k=2	k=2	PROPN
iajs-2434	73	88	in	in	ADP
iajs-2434	73	89	equation	equation	NOUN
iajs-2434	73	90	(	(	PUNCT
iajs-2434	73	91	24	24	NUM
iajs-2434	73	92	)	)	PUNCT
iajs-2434	73	93	to	to	PART
iajs-2434	73	94	get	get	VERB
iajs-2434	73	95	𝐸	𝐸	PROPN
iajs-2434	73	96	𝜃	𝜃	PRON
iajs-2434	73	97	|𝑡	|𝑡	NOUN
iajs-2434	73	98	,	,	PUNCT
iajs-2434	73	99	then	then	ADV
iajs-2434	73	100	substituting	substitute	VERB
iajs-2434	73	101	it	it	PRON
iajs-2434	73	102	into	into	ADP
iajs-2434	73	103	equation	equation	NOUN
iajs-2434	73	104	(	(	PUNCT
iajs-2434	73	105	34	34	NUM
iajs-2434	73	106	)	)	PUNCT
iajs-2434	73	107	,	,	PUNCT
iajs-2434	73	108	so	so	ADV
iajs-2434	73	109	we	we	PRON
iajs-2434	73	110	obtain	obtain	VERB
iajs-2434	73	111	,	,	PUNCT
iajs-2434	73	112	𝜃	𝜃	X
iajs-2434	73	113	(	(	PUNCT
iajs-2434	73	114	35	35	NUM
iajs-2434	73	115	)	)	PUNCT
iajs-2434	73	116	on	on	ADP
iajs-2434	73	117	the	the	DET
iajs-2434	73	118	same	same	ADJ
iajs-2434	73	119	manner	manner	NOUN
iajs-2434	73	120	,	,	PUNCT
iajs-2434	73	121	by	by	ADP
iajs-2434	73	122	putting	put	VERB
iajs-2434	73	123	k=2	k=2	PROPN
iajs-2434	73	124	in	in	ADP
iajs-2434	73	125	equation	equation	NOUN
iajs-2434	73	126	(	(	PUNCT
iajs-2434	73	127	29	29	NUM
iajs-2434	73	128	)	)	PUNCT
iajs-2434	73	129	,	,	PUNCT
iajs-2434	73	130	then	then	ADV
iajs-2434	73	131	substituting	substitute	VERB
iajs-2434	73	132	)	)	PUNCT
iajs-2434	73	133	it	it	PRON
iajs-2434	73	134	into	into	ADP
iajs-2434	73	135	equation	equation	NOUN
iajs-2434	73	136	(	(	PUNCT
iajs-2434	73	137	34	34	NUM
iajs-2434	73	138	)	)	PUNCT
iajs-2434	73	139	,	,	PUNCT
iajs-2434	73	140	we	we	PRON
iajs-2434	73	141	get	get	VERB
iajs-2434	73	142	the	the	DET
iajs-2434	73	143	bayes	bayes	PROPN
iajs-2434	73	144	estimator	estimator	NOUN
iajs-2434	73	145	of	of	ADP
iajs-2434	73	146	inverse	inverse	PROPN
iajs-2434	73	147	rayleigh	rayleigh	PROPN
iajs-2434	73	148	parameter	parameter	PROPN
iajs-2434	73	149	𝜃	𝜃	X
iajs-2434	73	150	under	under	ADP
iajs-2434	73	151	precautionary	precautionary	ADJ
iajs-2434	73	152	loss	loss	NOUN
iajs-2434	73	153	function	function	NOUN
iajs-2434	73	154	and	and	CCONJ
iajs-2434	73	155	exponential	exponential	ADJ
iajs-2434	73	156	prior	prior	ADJ
iajs-2434	73	157	distribution	distribution	NOUN
iajs-2434	73	158	,	,	PUNCT
iajs-2434	73	159	denoted	denote	VERB
iajs-2434	73	160	as	as	ADP
iajs-2434	73	161	𝜃	𝜃	NUM
iajs-2434	73	162	and	and	CCONJ
iajs-2434	73	163	given	give	VERB
iajs-2434	73	164	by	by	ADP
iajs-2434	73	165	:	:	PUNCT
iajs-2434	73	166	𝜃	𝜃	X
iajs-2434	73	167	(	(	PUNCT
iajs-2434	73	168	36	36	NUM
iajs-2434	73	169	)	)	PUNCT
iajs-2434	73	170	11	11	NUM
iajs-2434	73	171	.	.	PUNCT
iajs-2434	74	1	bayes	bayes	PROPN
iajs-2434	74	2	estimator	estimator	NOUN
iajs-2434	74	3	of	of	ADP
iajs-2434	74	4	the	the	DET
iajs-2434	74	5	reliability	reliability	NOUN
iajs-2434	74	6	function	function	NOUN
iajs-2434	74	7	r(t	r(t	NOUN
iajs-2434	74	8	)	)	PUNCT
iajs-2434	74	9	of	of	ADP
iajs-2434	74	10	ird	ird	PROPN
iajs-2434	74	11	under	under	ADP
iajs-2434	74	12	self	self	NOUN
iajs-2434	74	13	let	let	VERB
iajs-2434	74	14	us	we	PRON
iajs-2434	74	15	assume	assume	VERB
iajs-2434	74	16	that	that	SCONJ
iajs-2434	74	17	k	k	PROPN
iajs-2434	74	18	is	be	AUX
iajs-2434	74	19	any	any	DET
iajs-2434	74	20	positive	positive	ADJ
iajs-2434	74	21	integer	integer	NOUN
iajs-2434	74	22	,	,	PUNCT
iajs-2434	74	23	then	then	ADV
iajs-2434	74	24	,	,	PUNCT
iajs-2434	74	25	𝐸	𝐸	PROPN
iajs-2434	74	26	𝑅	𝑅	PROPN
iajs-2434	74	27	𝑡	𝑡	PROPN
iajs-2434	74	28	|𝑡	|𝑡	X
iajs-2434	74	29	=	=	SYM
iajs-2434	74	30	𝑅	𝑅	PROPN
iajs-2434	74	31	𝑡	𝑡	NOUN
iajs-2434	74	32	ℎ	ℎ	NOUN
iajs-2434	74	33	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	74	34	𝑑𝜃	𝑑𝜃	PROPN
iajs-2434	74	35	for	for	ADP
iajs-2434	74	36	ird	ird	PROPN
iajs-2434	74	37	and	and	CCONJ
iajs-2434	74	38	according	accord	VERB
iajs-2434	74	39	to	to	ADP
iajs-2434	74	40	equation	equation	NOUN
iajs-2434	74	41	(	(	PUNCT
iajs-2434	74	42	3	3	NUM
iajs-2434	74	43	)	)	PUNCT
iajs-2434	74	44	,	,	PUNCT
iajs-2434	74	45	we	we	PRON
iajs-2434	74	46	have	have	VERB
iajs-2434	74	47	,	,	PUNCT
iajs-2434	74	48	𝐸	𝐸	PROPN
iajs-2434	74	49	𝑅	𝑅	PROPN
iajs-2434	74	50	𝑡	𝑡	X
iajs-2434	74	51	|𝑡	|𝑡	X
iajs-2434	74	52	=	=	SYM
iajs-2434	74	53	1	1	NUM
iajs-2434	74	54	𝑒	𝑒	PROPN
iajs-2434	74	55	ℎ	ℎ	PROPN
iajs-2434	74	56	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	74	57	𝑑𝜃	𝑑𝜃	PROPN
iajs-2434	74	58	(	(	PUNCT
iajs-2434	74	59	37	37	NUM
iajs-2434	74	60	)	)	PUNCT
iajs-2434	74	61	for	for	ADP
iajs-2434	74	62	jeffrey	jeffrey	PROPN
iajs-2434	74	63	's	's	PART
iajs-2434	74	64	prior	prior	ADJ
iajs-2434	74	65	information	information	NOUN
iajs-2434	74	66	,	,	PUNCT
iajs-2434	74	67	we	we	PRON
iajs-2434	74	68	substitute	substitute	VERB
iajs-2434	74	69	from	from	ADP
iajs-2434	74	70	ℎ	ℎ	PROPN
iajs-2434	74	71	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	74	72	in	in	ADP
iajs-2434	74	73	equation	equation	NOUN
iajs-2434	74	74	(	(	PUNCT
iajs-2434	74	75	37	37	NUM
iajs-2434	74	76	)	)	PUNCT
iajs-2434	74	77	by	by	ADP
iajs-2434	74	78	ℎ	ℎ	X
iajs-2434	74	79	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	74	80	given	give	VERB
iajs-2434	74	81	in	in	ADP
iajs-2434	74	82	equation	equation	NOUN
iajs-2434	74	83	(	(	PUNCT
iajs-2434	74	84	10	10	NUM
iajs-2434	74	85	)	)	PUNCT
iajs-2434	74	86	,	,	PUNCT
iajs-2434	74	87	then	then	ADV
iajs-2434	74	88	in	in	ADP
iajs-2434	74	89	order	order	NOUN
iajs-2434	74	90	to	to	PART
iajs-2434	74	91	evaluate	evaluate	VERB
iajs-2434	74	92	the	the	DET
iajs-2434	74	93	integral	integral	ADJ
iajs-2434	74	94	in	in	ADP
iajs-2434	74	95	equation	equation	NOUN
iajs-2434	74	96	(	(	PUNCT
iajs-2434	74	97	37	37	NUM
iajs-2434	74	98	)	)	PUNCT
iajs-2434	74	99	,	,	PUNCT
iajs-2434	74	100	we	we	PRON
iajs-2434	74	101	develop	develop	VERB
iajs-2434	74	102	the	the	DET
iajs-2434	74	103	following	follow	VERB
iajs-2434	74	104	formula	formula	NOUN
iajs-2434	74	105	:	:	PUNCT
iajs-2434	74	106	1	1	NUM
iajs-2434	74	107	𝑒	𝑒	ADP
iajs-2434	74	108	∑	∑	PROPN
iajs-2434	74	109	1	1	NUM
iajs-2434	74	110	𝑒	𝑒	PROPN
iajs-2434	74	111	(	(	PUNCT
iajs-2434	74	112	38	38	NUM
iajs-2434	74	113	)	)	PUNCT
iajs-2434	74	114	the	the	DET
iajs-2434	74	115	integral	integral	ADJ
iajs-2434	74	116	in	in	ADP
iajs-2434	74	117	equation	equation	NOUN
iajs-2434	74	118	(	(	PUNCT
iajs-2434	74	119	37	37	NUM
iajs-2434	74	120	)	)	PUNCT
iajs-2434	74	121	should	should	AUX
iajs-2434	74	122	be	be	AUX
iajs-2434	74	123	reduced	reduce	VERB
iajs-2434	74	124	to	to	ADP
iajs-2434	74	125	:	:	PUNCT
iajs-2434	74	126	𝐸	𝐸	PROPN
iajs-2434	74	127	𝑅	𝑅	PROPN
iajs-2434	74	128	𝑡	𝑡	PROPN
iajs-2434	74	129	|𝑡	|𝑡	ADP
iajs-2434	74	130	∑	∑	PROPN
iajs-2434	74	131	1	1	NUM
iajs-2434	74	132	𝑒	𝑒	PROPN
iajs-2434	74	133	ℎ	ℎ	PROPN
iajs-2434	74	134	(	(	PUNCT
iajs-2434	74	135	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	74	136	𝑑𝜃	𝑑𝜃	ADP
iajs-2434	74	137	this	this	PRON
iajs-2434	74	138	implies	imply	VERB
iajs-2434	74	139	that	that	SCONJ
iajs-2434	74	140	:	:	PUNCT
iajs-2434	74	141	𝐸	𝐸	PROPN
iajs-2434	74	142	𝑅	𝑅	PROPN
iajs-2434	74	143	𝑡	𝑡	PROPN
iajs-2434	74	144	|𝑡	|𝑡	ADP
iajs-2434	74	145	∑	∑	PROPN
iajs-2434	74	146	1	1	NUM
iajs-2434	74	147	(	(	PUNCT
iajs-2434	74	148	39	39	NUM
iajs-2434	74	149	)	)	PUNCT
iajs-2434	74	150	where	where	SCONJ
iajs-2434	74	151	t=∑	t=∑	NOUN
iajs-2434	74	152	for	for	ADP
iajs-2434	74	153	exponential	exponential	ADJ
iajs-2434	74	154	prior	prior	ADJ
iajs-2434	74	155	distribution	distribution	NOUN
iajs-2434	74	156	,	,	PUNCT
iajs-2434	74	157	it	it	PRON
iajs-2434	74	158	can	can	AUX
iajs-2434	74	159	be	be	AUX
iajs-2434	74	160	shown	show	VERB
iajs-2434	74	161	in	in	ADP
iajs-2434	74	162	the	the	DET
iajs-2434	74	163	same	same	ADJ
iajs-2434	74	164	manner	manner	NOUN
iajs-2434	74	165	that	that	PRON
iajs-2434	74	166	:	:	PUNCT
iajs-2434	74	167	  	  	SPACE
iajs-2434	74	168	135	135	NUM
iajs-2434	74	169	  	  	SPACE
iajs-2434	74	170	ibn	ibn	PROPN
iajs-2434	74	171	al	al	PROPN
iajs-2434	74	172	-	-	PUNCT
iajs-2434	74	173	haitham	haitham	PROPN
iajs-2434	74	174	jour	jour	X
iajs-2434	74	175	.	.	PROPN
iajs-2434	75	1	for	for	ADP
iajs-2434	75	2	pure	pure	ADJ
iajs-2434	75	3	&	&	CCONJ
iajs-2434	75	4	appl	appl	PROPN
iajs-2434	75	5	.	.	PUNCT
iajs-2434	76	1	sci	sci	PROPN
iajs-2434	76	2	.	.	PROPN
iajs-2434	77	1	33	33	NUM
iajs-2434	77	2	(	(	PUNCT
iajs-2434	77	3	1	1	NUM
iajs-2434	77	4	)	)	PUNCT
iajs-2434	77	5	2020	2020	NUM
iajs-2434	77	6	𝐸	𝐸	PROPN
iajs-2434	77	7	𝑅	𝑅	PROPN
iajs-2434	77	8	𝑡	𝑡	PROPN
iajs-2434	77	9	|𝑡	|𝑡	ADP
iajs-2434	77	10	∑	∑	PROPN
iajs-2434	77	11	1	1	NUM
iajs-2434	77	12	𝑒	𝑒	PROPN
iajs-2434	77	13	ℎ	ℎ	PROPN
iajs-2434	77	14	(	(	PUNCT
iajs-2434	77	15	𝜃|𝑡	𝜃|𝑡	NOUN
iajs-2434	77	16	𝑑𝜃	𝑑𝜃	PROPN
iajs-2434	77	17	,	,	PUNCT
iajs-2434	77	18	which	which	PRON
iajs-2434	77	19	implies	imply	VERB
iajs-2434	77	20	that	that	SCONJ
iajs-2434	77	21	:	:	PUNCT
iajs-2434	77	22	𝐸	𝐸	PROPN
iajs-2434	77	23	𝑅	𝑅	PROPN
iajs-2434	77	24	𝑡	𝑡	PROPN
iajs-2434	77	25	|𝑡	|𝑡	ADP
iajs-2434	77	26	∑	∑	PROPN
iajs-2434	77	27	1	1	NUM
iajs-2434	77	28	(	(	PUNCT
iajs-2434	77	29	40	40	NUM
iajs-2434	77	30	)	)	PUNCT
iajs-2434	78	1	where	where	SCONJ
iajs-2434	78	2	p	p	X
iajs-2434	78	3	=	=	NOUN
iajs-2434	78	4	t+λ	t+λ	NUM
iajs-2434	78	5	under	under	ADP
iajs-2434	78	6	self	self	NOUN
iajs-2434	78	7	and	and	CCONJ
iajs-2434	78	8	according	accord	VERB
iajs-2434	78	9	to	to	ADP
iajs-2434	78	10	equation	equation	NOUN
iajs-2434	78	11	(	(	PUNCT
iajs-2434	78	12	19	19	NUM
iajs-2434	78	13	)	)	PUNCT
iajs-2434	78	14	,	,	PUNCT
iajs-2434	78	15	we	we	PRON
iajs-2434	78	16	conclude	conclude	VERB
iajs-2434	78	17	that	that	SCONJ
iajs-2434	78	18	:	:	PUNCT
iajs-2434	78	19	𝑅	𝑅	PROPN
iajs-2434	78	20	𝑡	𝑡	PROPN
iajs-2434	78	21	𝐸	𝐸	PROPN
iajs-2434	78	22	𝑅	𝑅	PROPN
iajs-2434	78	23	𝑡	𝑡	PROPN
iajs-2434	78	24	|𝑡	|𝑡	X
iajs-2434	78	25	for	for	ADP
iajs-2434	78	26	jeffrey	jeffrey	PROPN
iajs-2434	78	27	's	's	PART
iajs-2434	78	28	prior	prior	ADJ
iajs-2434	78	29	information	information	NOUN
iajs-2434	78	30	,	,	PUNCT
iajs-2434	78	31	putting	put	VERB
iajs-2434	78	32	k=1	k=1	X
iajs-2434	78	33	in	in	ADP
iajs-2434	78	34	equation	equation	NOUN
iajs-2434	78	35	(	(	PUNCT
iajs-2434	78	36	39	39	NUM
iajs-2434	78	37	)	)	PUNCT
iajs-2434	78	38	,	,	PUNCT
iajs-2434	78	39	we	we	PRON
iajs-2434	78	40	get	get	VERB
iajs-2434	78	41	:	:	PUNCT
iajs-2434	78	42	𝑅	𝑅	PROPN
iajs-2434	78	43	𝑡	𝑡	NOUN
iajs-2434	78	44	1	1	NUM
iajs-2434	78	45	(	(	PUNCT
iajs-2434	78	46	41	41	NUM
iajs-2434	78	47	)	)	PUNCT
iajs-2434	78	48	for	for	ADP
iajs-2434	78	49	exponential	exponential	ADJ
iajs-2434	78	50	prior	prior	ADJ
iajs-2434	78	51	distribution	distribution	NOUN
iajs-2434	78	52	,	,	PUNCT
iajs-2434	78	53	putting	put	VERB
iajs-2434	78	54	k=1	k=1	X
iajs-2434	78	55	in	in	ADP
iajs-2434	78	56	equation	equation	NOUN
iajs-2434	78	57	(	(	PUNCT
iajs-2434	78	58	40	40	NUM
iajs-2434	78	59	)	)	PUNCT
iajs-2434	78	60	,	,	PUNCT
iajs-2434	78	61	we	we	PRON
iajs-2434	78	62	get	get	VERB
iajs-2434	78	63	:	:	PUNCT
iajs-2434	78	64	𝑅	𝑅	PROPN
iajs-2434	78	65	𝑡	𝑡	NOUN
iajs-2434	78	66	1	1	NUM
iajs-2434	78	67	(	(	PUNCT
iajs-2434	78	68	42	42	NUM
iajs-2434	78	69	)	)	PUNCT
iajs-2434	78	70	12	12	NUM
iajs-2434	78	71	.	.	PUNCT
iajs-2434	79	1	bayes	bayes	PROPN
iajs-2434	79	2	estimator	estimator	NOUN
iajs-2434	79	3	of	of	ADP
iajs-2434	79	4	the	the	DET
iajs-2434	79	5	reliability	reliability	NOUN
iajs-2434	79	6	function	function	NOUN
iajs-2434	79	7	r(t	r(t	NOUN
iajs-2434	79	8	)	)	PUNCT
iajs-2434	79	9	of	of	ADP
iajs-2434	79	10	ird	ird	PROPN
iajs-2434	79	11	under	under	ADP
iajs-2434	79	12	mself	mself	PRON
iajs-2434	79	13	from	from	ADP
iajs-2434	79	14	equation	equation	NOUN
iajs-2434	79	15	(	(	PUNCT
iajs-2434	79	16	22	22	NUM
iajs-2434	79	17	)	)	PUNCT
iajs-2434	79	18	it	it	PRON
iajs-2434	79	19	is	be	AUX
iajs-2434	79	20	clear	clear	ADJ
iajs-2434	79	21	that	that	SCONJ
iajs-2434	79	22	the	the	DET
iajs-2434	79	23	estimator	estimator	NOUN
iajs-2434	79	24	of	of	ADP
iajs-2434	79	25	the	the	DET
iajs-2434	79	26	reliability	reliability	NOUN
iajs-2434	79	27	function	function	NOUN
iajs-2434	79	28	r(t	r(t	NOUN
iajs-2434	79	29	)	)	PUNCT
iajs-2434	79	30	under	under	ADP
iajs-2434	79	31	mself	mself	PRON
iajs-2434	79	32	is	be	AUX
iajs-2434	79	33	given	give	VERB
iajs-2434	79	34	by	by	ADP
iajs-2434	79	35	:	:	PUNCT
iajs-2434	79	36	𝑅	𝑅	PROPN
iajs-2434	79	37	𝑡	𝑡	PROPN
iajs-2434	79	38	|	|	ADV
iajs-2434	79	39	|	|	ADV
iajs-2434	79	40	,	,	PUNCT
iajs-2434	79	41	r=1,2	r=1,2	ADJ
iajs-2434	79	42	,	,	PUNCT
iajs-2434	79	43	…	…	PUNCT
iajs-2434	79	44	for	for	ADP
iajs-2434	79	45	ird	ird	PROPN
iajs-2434	79	46	,	,	PUNCT
iajs-2434	79	47	with	with	ADP
iajs-2434	79	48	jeffry	jeffry	PROPN
iajs-2434	79	49	's	's	PART
iajs-2434	79	50	prior	prior	ADJ
iajs-2434	79	51	information	information	NOUN
iajs-2434	79	52	and	and	CCONJ
iajs-2434	79	53	r=1	r=1	NOUN
iajs-2434	79	54	then	then	ADV
iajs-2434	79	55	,	,	PUNCT
iajs-2434	79	56	𝑅	𝑅	PROPN
iajs-2434	79	57	𝑡	𝑡	PROPN
iajs-2434	79	58	|	|	ADV
iajs-2434	79	59	|	|	ADV
iajs-2434	79	60	.	.	PUNCT
iajs-2434	80	1	by	by	ADP
iajs-2434	80	2	putting	put	VERB
iajs-2434	80	3	k=2	k=2	PROPN
iajs-2434	80	4	,	,	PUNCT
iajs-2434	80	5	k=1	k=1	X
iajs-2434	80	6	in	in	ADP
iajs-2434	80	7	equation	equation	NOUN
iajs-2434	80	8	(	(	PUNCT
iajs-2434	80	9	39	39	NUM
iajs-2434	80	10	)	)	PUNCT
iajs-2434	80	11	we	we	PRON
iajs-2434	80	12	obtain	obtain	VERB
iajs-2434	80	13	𝐸	𝐸	PROPN
iajs-2434	80	14	𝑅	𝑅	PROPN
iajs-2434	80	15	𝑡	𝑡	PROPN
iajs-2434	80	16	|𝑡	|𝑡	X
iajs-2434	80	17	,	,	PUNCT
iajs-2434	80	18	𝐸	𝐸	PROPN
iajs-2434	80	19	𝑅	𝑅	PROPN
iajs-2434	80	20	𝑡	𝑡	PROPN
iajs-2434	80	21	|𝑡	|𝑡	NOUN
iajs-2434	80	22	respectively	respectively	ADV
iajs-2434	80	23	.	.	PUNCT
iajs-2434	81	1	this	this	PRON
iajs-2434	81	2	implies	imply	VERB
iajs-2434	81	3	that	that	SCONJ
iajs-2434	81	4	:	:	PUNCT
iajs-2434	81	5	𝑅	𝑅	PROPN
iajs-2434	81	6	𝑡	𝑡	PROPN
iajs-2434	81	7	(	(	PUNCT
iajs-2434	81	8	43	43	NUM
iajs-2434	81	9	)	)	PUNCT
iajs-2434	81	10	for	for	ADP
iajs-2434	81	11	r=2	r=2	PROPN
iajs-2434	81	12	,	,	PUNCT
iajs-2434	81	13	it	it	PRON
iajs-2434	81	14	follows	follow	VERB
iajs-2434	81	15	that	that	SCONJ
iajs-2434	81	16	:	:	PUNCT
iajs-2434	81	17	𝑅	𝑅	PROPN
iajs-2434	81	18	𝑡	𝑡	PROPN
iajs-2434	81	19	|	|	ADV
iajs-2434	81	20	|	|	ADV
iajs-2434	81	21	,	,	PUNCT
iajs-2434	81	22	putting	put	VERB
iajs-2434	81	23	k=3	k=3	NOUN
iajs-2434	81	24	in	in	ADP
iajs-2434	81	25	equation	equation	NOUN
iajs-2434	81	26	(	(	PUNCT
iajs-2434	81	27	39	39	NUM
iajs-2434	81	28	)	)	PUNCT
iajs-2434	81	29	we	we	PRON
iajs-2434	81	30	obtain	obtain	VERB
iajs-2434	81	31	𝐸	𝐸	PROPN
iajs-2434	81	32	𝑅	𝑅	PROPN
iajs-2434	81	33	𝑡	𝑡	PROPN
iajs-2434	81	34	|𝑡	|𝑡	X
iajs-2434	81	35	.	.	PUNCT
iajs-2434	82	1	hence	hence	ADV
iajs-2434	82	2	,	,	PUNCT
iajs-2434	82	3	𝑅	𝑅	PROPN
iajs-2434	82	4	𝑡	𝑡	PROPN
iajs-2434	82	5	(	(	PUNCT
iajs-2434	82	6	44	44	NUM
iajs-2434	82	7	)	)	PUNCT
iajs-2434	82	8	for	for	ADP
iajs-2434	82	9	r=3	r=3	PUNCT
iajs-2434	82	10	it	it	PRON
iajs-2434	82	11	follows	follow	VERB
iajs-2434	82	12	that	that	SCONJ
iajs-2434	82	13	:	:	PUNCT
iajs-2434	82	14	  	  	SPACE
iajs-2434	82	15	136	136	NUM
iajs-2434	82	16	  	  	SPACE
iajs-2434	82	17	ibn	ibn	PROPN
iajs-2434	82	18	al	al	PROPN
iajs-2434	82	19	-	-	PUNCT
iajs-2434	82	20	haitham	haitham	PROPN
iajs-2434	82	21	jour	jour	X
iajs-2434	82	22	.	.	PROPN
iajs-2434	83	1	for	for	ADP
iajs-2434	83	2	pure	pure	ADJ
iajs-2434	83	3	&	&	CCONJ
iajs-2434	83	4	appl	appl	PROPN
iajs-2434	83	5	.	.	PUNCT
iajs-2434	84	1	sci	sci	PROPN
iajs-2434	84	2	.	.	PROPN
iajs-2434	85	1	33	33	NUM
iajs-2434	85	2	(	(	PUNCT
iajs-2434	85	3	1	1	NUM
iajs-2434	85	4	)	)	PUNCT
iajs-2434	85	5	2020	2020	NUM
iajs-2434	85	6	𝑅	𝑅	PROPN
iajs-2434	85	7	𝑡	𝑡	PROPN
iajs-2434	85	8	|	|	ADV
iajs-2434	85	9	|	|	ADV
iajs-2434	85	10	,	,	PUNCT
iajs-2434	85	11	putting	put	VERB
iajs-2434	85	12	k=4	k=4	PROPN
iajs-2434	85	13	in	in	ADP
iajs-2434	85	14	equation	equation	NOUN
iajs-2434	85	15	(	(	PUNCT
iajs-2434	85	16	39	39	NUM
iajs-2434	85	17	)	)	PUNCT
iajs-2434	85	18	,	,	PUNCT
iajs-2434	85	19	we	we	PRON
iajs-2434	85	20	get	get	VERB
iajs-2434	85	21	𝐸	𝐸	PROPN
iajs-2434	85	22	𝑅	𝑅	PROPN
iajs-2434	85	23	𝑡	𝑡	NOUN
iajs-2434	85	24	|𝑡	|𝑡	NOUN
iajs-2434	85	25	,	,	PUNCT
iajs-2434	85	26	and	and	CCONJ
iajs-2434	85	27	hence	hence	ADV
iajs-2434	85	28	𝑅	𝑅	PROPN
iajs-2434	85	29	𝑡	𝑡	PROPN
iajs-2434	85	30	(	(	PUNCT
iajs-2434	85	31	45	45	NUM
iajs-2434	85	32	)	)	PUNCT
iajs-2434	85	33	similarly	similarly	ADV
iajs-2434	85	34	,	,	PUNCT
iajs-2434	85	35	for	for	ADP
iajs-2434	85	36	exponential	exponential	ADJ
iajs-2434	85	37	prior	prior	ADJ
iajs-2434	85	38	distribution	distribution	NOUN
iajs-2434	85	39	and	and	CCONJ
iajs-2434	85	40	according	accord	VERB
iajs-2434	85	41	to	to	ADP
iajs-2434	85	42	equations	equation	NOUN
iajs-2434	85	43	(	(	PUNCT
iajs-2434	85	44	22	22	NUM
iajs-2434	85	45	)	)	PUNCT
iajs-2434	85	46	and	and	CCONJ
iajs-2434	85	47	(	(	PUNCT
iajs-2434	85	48	40	40	NUM
iajs-2434	85	49	)	)	PUNCT
iajs-2434	85	50	,	,	PUNCT
iajs-2434	85	51	it	it	PRON
iajs-2434	85	52	can	can	AUX
iajs-2434	85	53	be	be	AUX
iajs-2434	85	54	shown	show	VERB
iajs-2434	85	55	that	that	SCONJ
iajs-2434	85	56	the	the	DET
iajs-2434	85	57	bayes	bayes	NOUN
iajs-2434	85	58	estimators	estimator	NOUN
iajs-2434	85	59	of	of	ADP
iajs-2434	85	60	the	the	DET
iajs-2434	85	61	reliability	reliability	NOUN
iajs-2434	85	62	function	function	NOUN
iajs-2434	85	63	r(t	r(t	NOUN
iajs-2434	85	64	)	)	PUNCT
iajs-2434	85	65	under	under	ADP
iajs-2434	85	66	mself	mself	PRON
iajs-2434	85	67	for	for	ADP
iajs-2434	85	68	r=1,2,3	r=1,2,3	NUM
iajs-2434	85	69	are	be	AUX
iajs-2434	85	70	given	give	VERB
iajs-2434	85	71	in	in	ADP
iajs-2434	85	72	respective	respective	ADJ
iajs-2434	85	73	𝑅	𝑅	PROPN
iajs-2434	85	74	𝑡	𝑡	PROPN
iajs-2434	85	75	(	(	PUNCT
iajs-2434	85	76	46	46	NUM
iajs-2434	85	77	)	)	PUNCT
iajs-2434	85	78	𝑅	𝑅	PROPN
iajs-2434	85	79	𝑡	𝑡	PROPN
iajs-2434	85	80	(	(	PUNCT
iajs-2434	85	81	47	47	NUM
iajs-2434	85	82	)	)	PUNCT
iajs-2434	85	83	𝑅	𝑅	PROPN
iajs-2434	85	84	𝑡	𝑡	PROPN
iajs-2434	85	85	(	(	PUNCT
iajs-2434	85	86	48	48	NUM
iajs-2434	85	87	)	)	PUNCT
iajs-2434	85	88	13	13	NUM
iajs-2434	85	89	.	.	PUNCT
iajs-2434	85	90	bayes	bayes	PROPN
iajs-2434	85	91	estimator	estimator	NOUN
iajs-2434	85	92	of	of	ADP
iajs-2434	85	93	the	the	DET
iajs-2434	85	94	reliability	reliability	NOUN
iajs-2434	85	95	function	function	NOUN
iajs-2434	85	96	r(t	r(t	NOUN
iajs-2434	85	97	)	)	PUNCT
iajs-2434	85	98	of	of	ADP
iajs-2434	85	99	ird	ird	PROPN
iajs-2434	85	100	under	under	ADP
iajs-2434	85	101	precautionary	precautionary	ADJ
iajs-2434	85	102	loss	loss	NOUN
iajs-2434	85	103	function	function	NOUN
iajs-2434	85	104	from	from	ADP
iajs-2434	85	105	equation	equation	NOUN
iajs-2434	85	106	(	(	PUNCT
iajs-2434	85	107	34	34	NUM
iajs-2434	85	108	)	)	PUNCT
iajs-2434	85	109	,	,	PUNCT
iajs-2434	85	110	it	it	PRON
iajs-2434	85	111	is	be	AUX
iajs-2434	85	112	clear	clear	ADJ
iajs-2434	85	113	that	that	SCONJ
iajs-2434	85	114	the	the	DET
iajs-2434	85	115	estimator	estimator	NOUN
iajs-2434	85	116	of	of	ADP
iajs-2434	85	117	the	the	DET
iajs-2434	85	118	reliability	reliability	NOUN
iajs-2434	85	119	function	function	NOUN
iajs-2434	85	120	r(t	r(t	NOUN
iajs-2434	85	121	)	)	PUNCT
iajs-2434	85	122	under	under	ADP
iajs-2434	85	123	precautionary	precautionary	ADJ
iajs-2434	85	124	loss	loss	NOUN
iajs-2434	85	125	function	function	NOUN
iajs-2434	85	126	is	be	AUX
iajs-2434	85	127	given	give	VERB
iajs-2434	85	128	by	by	ADP
iajs-2434	85	129	:	:	PUNCT
iajs-2434	85	130	𝑅	𝑅	PROPN
iajs-2434	85	131	𝑡	𝑡	PROPN
iajs-2434	85	132	𝐸	𝐸	PROPN
iajs-2434	85	133	𝑅	𝑅	PROPN
iajs-2434	85	134	𝑡	𝑡	PROPN
iajs-2434	85	135	|𝑡	|𝑡	X
iajs-2434	85	136	for	for	ADP
iajs-2434	85	137	jeffrey	jeffrey	PROPN
iajs-2434	85	138	's	's	PART
iajs-2434	85	139	prior	prior	ADJ
iajs-2434	85	140	information	information	NOUN
iajs-2434	85	141	,	,	PUNCT
iajs-2434	85	142	putting	put	VERB
iajs-2434	85	143	k=2	k=2	PROPN
iajs-2434	85	144	in	in	ADP
iajs-2434	85	145	equation	equation	NOUN
iajs-2434	85	146	(	(	PUNCT
iajs-2434	85	147	39	39	NUM
iajs-2434	85	148	)	)	PUNCT
iajs-2434	85	149	,	,	PUNCT
iajs-2434	85	150	we	we	PRON
iajs-2434	85	151	get	get	VERB
iajs-2434	85	152	:	:	PUNCT
iajs-2434	85	153	𝑅	𝑅	NOUN
iajs-2434	85	154	𝑡	𝑡	NOUN
iajs-2434	85	155	1	1	NUM
iajs-2434	85	156	2	2	NUM
iajs-2434	85	157	(	(	PUNCT
iajs-2434	85	158	49	49	NUM
iajs-2434	85	159	)	)	PUNCT
iajs-2434	85	160	on	on	ADP
iajs-2434	85	161	the	the	DET
iajs-2434	85	162	basis	basis	NOUN
iajs-2434	85	163	of	of	ADP
iajs-2434	85	164	exponential	exponential	ADJ
iajs-2434	85	165	prior	prior	ADJ
iajs-2434	85	166	distribution	distribution	NOUN
iajs-2434	85	167	,	,	PUNCT
iajs-2434	85	168	putting	put	VERB
iajs-2434	85	169	k=2	k=2	PROPN
iajs-2434	85	170	in	in	ADP
iajs-2434	85	171	equation	equation	NOUN
iajs-2434	85	172	(	(	PUNCT
iajs-2434	85	173	40	40	NUM
iajs-2434	85	174	)	)	PUNCT
iajs-2434	85	175	,	,	PUNCT
iajs-2434	85	176	we	we	PRON
iajs-2434	85	177	get	get	VERB
iajs-2434	85	178	:	:	PUNCT
iajs-2434	85	179	𝑅	𝑅	NOUN
iajs-2434	85	180	𝑡	𝑡	NOUN
iajs-2434	85	181	1	1	NUM
iajs-2434	85	182	2	2	NUM
iajs-2434	85	183	(	(	PUNCT
iajs-2434	85	184	50	50	NUM
iajs-2434	85	185	)	)	PUNCT
iajs-2434	85	186	14	14	NUM
iajs-2434	85	187	.	.	PUNCT
iajs-2434	86	1	simulation	simulation	NOUN
iajs-2434	86	2	study	study	NOUN
iajs-2434	86	3	in	in	ADP
iajs-2434	86	4	our	our	PRON
iajs-2434	86	5	simulation	simulation	NOUN
iajs-2434	86	6	study	study	NOUN
iajs-2434	86	7	,	,	PUNCT
iajs-2434	86	8	l=2000	l=2000	PROPN
iajs-2434	86	9	sample	sample	NOUN
iajs-2434	86	10	of	of	ADP
iajs-2434	86	11	size	size	NOUN
iajs-2434	86	12	n=10	n=10	PROPN
iajs-2434	86	13	,	,	PUNCT
iajs-2434	86	14	50	50	NUM
iajs-2434	86	15	,	,	PUNCT
iajs-2434	86	16	100	100	NUM
iajs-2434	86	17	and	and	CCONJ
iajs-2434	86	18	200	200	NUM
iajs-2434	86	19	were	be	AUX
iajs-2434	86	20	generated	generate	VERB
iajs-2434	86	21	in	in	ADP
iajs-2434	86	22	order	order	NOUN
iajs-2434	86	23	to	to	PART
iajs-2434	86	24	represent	represent	VERB
iajs-2434	86	25	,	,	PUNCT
iajs-2434	86	26	small	small	ADJ
iajs-2434	86	27	,	,	PUNCT
iajs-2434	86	28	moderate	moderate	ADJ
iajs-2434	86	29	,	,	PUNCT
iajs-2434	86	30	large	large	ADJ
iajs-2434	86	31	and	and	CCONJ
iajs-2434	86	32	very	very	ADV
iajs-2434	86	33	large	large	ADJ
iajs-2434	86	34	sample	sample	NOUN
iajs-2434	86	35	sizes	size	NOUN
iajs-2434	86	36	from	from	ADP
iajs-2434	86	37	inverse	inverse	ADJ
iajs-2434	86	38	rayleigh	rayleigh	NOUN
iajs-2434	86	39	distribution	distribution	NOUN
iajs-2434	86	40	with	with	ADP
iajs-2434	86	41	two	two	NUM
iajs-2434	86	42	values	value	NOUN
iajs-2434	86	43	of	of	ADP
iajs-2434	86	44	the	the	DET
iajs-2434	86	45	scale	scale	NOUN
iajs-2434	86	46	parameter	parameter	NOUN
iajs-2434	86	47	(	(	PUNCT
iajs-2434	86	48	𝛳	𝛳	PROPN
iajs-2434	86	49	0.5	0.5	NUM
iajs-2434	86	50	,	,	PUNCT
iajs-2434	86	51	𝛳	𝛳	PROPN
iajs-2434	86	52	1.5	1.5	NUM
iajs-2434	86	53	(	(	PUNCT
iajs-2434	86	54	.the	.the	NOUN
iajs-2434	86	55	)	)	PUNCT
iajs-2434	86	56	scale	scale	NOUN
iajs-2434	86	57	parameter	parameter	NOUN
iajs-2434	86	58	λ	λ	PROPN
iajs-2434	86	59	of	of	ADP
iajs-2434	86	60	exponential	exponential	NOUN
iajs-2434	86	61	prior	prior	ADV
iajs-2434	86	62	was	be	AUX
iajs-2434	86	63	chosen	choose	VERB
iajs-2434	86	64	to	to	PART
iajs-2434	86	65	be	be	AUX
iajs-2434	86	66	(	(	PUNCT
iajs-2434	86	67	λ=0.5	λ=0.5	NOUN
iajs-2434	86	68	,	,	PUNCT
iajs-2434	86	69	λ=1	λ=1	PRON
iajs-2434	86	70	)	)	PUNCT
iajs-2434	86	71	and	and	CCONJ
iajs-2434	86	72	assumed	assume	VERB
iajs-2434	86	73	the	the	DET
iajs-2434	86	74	values	value	NOUN
iajs-2434	86	75	of	of	ADP
iajs-2434	86	76	r	r	NOUN
iajs-2434	86	77	in	in	ADP
iajs-2434	86	78	modified	modify	VERB
iajs-2434	86	79	square	square	ADJ
iajs-2434	86	80	error	error	NOUN
iajs-2434	86	81	loss	loss	NOUN
iajs-2434	86	82	function	function	NOUN
iajs-2434	86	83	to	to	PART
iajs-2434	86	84	be	be	AUX
iajs-2434	86	85	r=1	r=1	NOUN
iajs-2434	86	86	,	,	PUNCT
iajs-2434	86	87	r=2	r=2	X
iajs-2434	86	88	and	and	CCONJ
iajs-2434	86	89	r=3	r=3	PROPN
iajs-2434	86	90	(	(	PUNCT
iajs-2434	86	91	.	.	PUNCT
iajs-2434	87	1	the	the	DET
iajs-2434	87	2	)	)	PUNCT
iajs-2434	87	3	criterion	criterion	NOUN
iajs-2434	87	4	mean	mean	VERB
iajs-2434	87	5	square	square	ADJ
iajs-2434	87	6	error	error	NOUN
iajs-2434	87	7	(	(	PUNCT
iajs-2434	87	8	mse	mse	NOUN
iajs-2434	87	9	)	)	PUNCT
iajs-2434	87	10	was	be	AUX
iajs-2434	87	11	employed	employ	VERB
iajs-2434	87	12	to	to	PART
iajs-2434	87	13	compare	compare	VERB
iajs-2434	87	14	the	the	DET
iajs-2434	87	15	performance	performance	NOUN
iajs-2434	87	16	of	of	ADP
iajs-2434	87	17	different	different	ADJ
iajs-2434	87	18	methods	method	NOUN
iajs-2434	87	19	of	of	ADP
iajs-2434	87	20	estimation	estimation	NOUN
iajs-2434	87	21	of	of	ADP
iajs-2434	87	22	the	the	DET
iajs-2434	87	23	scale	scale	NOUN
iajs-2434	87	24	parameter	parameter	NOUN
iajs-2434	87	25	and	and	CCONJ
iajs-2434	87	26	reliability	reliability	NOUN
iajs-2434	87	27	function	function	NOUN
iajs-2434	87	28	of	of	ADP
iajs-2434	87	29	ird	ird	PROPN
iajs-2434	87	30	where	where	SCONJ
iajs-2434	87	31	𝑀𝑆𝐸	𝑀𝑆𝐸	PROPN
iajs-2434	87	32	𝜃	𝜃	NOUN
iajs-2434	87	33	∑	∑	ADP
iajs-2434	87	34	𝜃	𝜃	X
iajs-2434	87	35	𝜃	𝜃	X
iajs-2434	87	36	(	(	PUNCT
iajs-2434	87	37	51	51	NUM
iajs-2434	87	38	)	)	PUNCT
iajs-2434	87	39	  	  	SPACE
iajs-2434	87	40	137	137	NUM
iajs-2434	87	41	  	  	SPACE
iajs-2434	87	42	ibn	ibn	PROPN
iajs-2434	87	43	al	al	PROPN
iajs-2434	87	44	-	-	PUNCT
iajs-2434	87	45	haitham	haitham	PROPN
iajs-2434	87	46	jour	jour	X
iajs-2434	87	47	.	.	PROPN
iajs-2434	88	1	for	for	ADP
iajs-2434	88	2	pure	pure	ADJ
iajs-2434	88	3	&	&	CCONJ
iajs-2434	88	4	appl	appl	PROPN
iajs-2434	88	5	.	.	PUNCT
iajs-2434	89	1	sci	sci	PROPN
iajs-2434	89	2	.	.	PROPN
iajs-2434	90	1	33	33	NUM
iajs-2434	90	2	(	(	PUNCT
iajs-2434	90	3	1	1	NUM
iajs-2434	90	4	)	)	PUNCT
iajs-2434	90	5	2020	2020	NUM
iajs-2434	90	6	𝑀𝑆𝐸	𝑀𝑆𝐸	PROPN
iajs-2434	90	7	𝑅	𝑅	PROPN
iajs-2434	90	8	𝑡	𝑡	PROPN
iajs-2434	90	9	∑	∑	PROPN
iajs-2434	90	10	𝑅	𝑅	PROPN
iajs-2434	90	11	𝑡	𝑡	PROPN
iajs-2434	90	12	𝑅	𝑅	PROPN
iajs-2434	90	13	𝑡	𝑡	PROPN
iajs-2434	90	14	(	(	PUNCT
iajs-2434	90	15	52	52	NUM
iajs-2434	90	16	)	)	PUNCT
iajs-2434	90	17	the	the	DET
iajs-2434	90	18	results	result	NOUN
iajs-2434	90	19	are	be	AUX
iajs-2434	90	20	presented	present	VERB
iajs-2434	90	21	in	in	ADP
iajs-2434	90	22	the	the	DET
iajs-2434	90	23	following	follow	VERB
iajs-2434	90	24	tables	table	NOUN
iajs-2434	90	25	.	.	PUNCT
iajs-2434	91	1	table1	table1	PROPN
iajs-2434	91	2	.	.	PUNCT
iajs-2434	92	1	(	(	PUNCT
iajs-2434	92	2	mse	mse	PROPN
iajs-2434	92	3	)	)	PUNCT
iajs-2434	92	4	for	for	ADP
iajs-2434	92	5	parameter	parameter	NOUN
iajs-2434	92	6	𝜃	𝜃	NUM
iajs-2434	92	7	by	by	ADP
iajs-2434	92	8	using	use	VERB
iajs-2434	92	9	jeffrey	jeffrey	PROPN
iajs-2434	92	10	's	's	PART
iajs-2434	92	11	prior	prior	ADJ
iajs-2434	92	12	information	information	NOUN
iajs-2434	92	13	at	at	ADP
iajs-2434	92	14	𝜃	𝜃	SYM
iajs-2434	92	15	0.5	0.5	NUM
iajs-2434	92	16	.	.	PUNCT
iajs-2434	93	1	n	n	PROPN
iajs-2434	93	2	estimator	estimator	NOUN
iajs-2434	93	3	10	10	NUM
iajs-2434	93	4	50	50	NUM
iajs-2434	93	5	100	100	NUM
iajs-2434	93	6	200	200	NUM
iajs-2434	93	7	sq	sq	NUM
iajs-2434	93	8	0.0043	0.0043	NUM
iajs-2434	93	9	0.0001081	0.0001081	NUM
iajs-2434	93	10	0.000026174	0.000026174	NUM
iajs-2434	93	11	0.000006512	0.000006512	NUM
iajs-2434	93	12	ms	ms	NOUN
iajs-2434	93	13	r=1	r=1	NOUN
iajs-2434	93	14	0.0061	0.0061	NUM
iajs-2434	93	15	0.0001186	0.0001186	NUM
iajs-2434	93	16	0.000027468	0.000027468	NUM
iajs-2434	93	17	0.000006676	0.000006676	NUM
iajs-2434	93	18	ms	ms	PROPN
iajs-2434	93	19	r=2	r=2	PROPN
iajs-2434	93	20	0.0086	0.0086	NUM
iajs-2434	93	21	0.0001334	0.0001334	NUM
iajs-2434	93	22	0.000029277	0.000029277	NUM
iajs-2434	93	23	0.000006903	0.000006903	NUM
iajs-2434	93	24	ms	ms	NOUN
iajs-2434	93	25	r=3	r=3	PROPN
iajs-2434	93	26	0.0119	0.0119	NUM
iajs-2434	93	27	0.0001524	0.0001524	NUM
iajs-2434	93	28	0.000031602	0.000031602	NUM
iajs-2434	93	29	0.000007193	0.000007193	NUM
iajs-2434	93	30	pr	pr	NOUN
iajs-2434	93	31	0.0215	0.0215	NUM
iajs-2434	93	32	0.0049	0.0049	NUM
iajs-2434	93	33	0.0025	0.0025	NUM
iajs-2434	93	34	0.0012	0.0012	NUM
iajs-2434	93	35	best	good	ADJ
iajs-2434	93	36	sq	sq	ADJ
iajs-2434	93	37	sq	sq	INTJ
iajs-2434	93	38	sq	sq	ADJ
iajs-2434	93	39	sq	sq	PROPN
iajs-2434	93	40	table	table	NOUN
iajs-2434	93	41	2	2	NUM
iajs-2434	93	42	.	.	PUNCT
iajs-2434	94	1	(	(	PUNCT
iajs-2434	94	2	mse	mse	NOUN
iajs-2434	94	3	)	)	PUNCT
iajs-2434	94	4	values	value	NOUN
iajs-2434	94	5	of	of	ADP
iajs-2434	94	6	the	the	DET
iajs-2434	94	7	reliability	reliability	NOUN
iajs-2434	94	8	function	function	NOUN
iajs-2434	94	9	estimators	estimator	NOUN
iajs-2434	94	10	by	by	ADP
iajs-2434	94	11	using	use	VERB
iajs-2434	94	12	jeffrey	jeffrey	PROPN
iajs-2434	94	13	's	's	PART
iajs-2434	94	14	prior	prior	ADJ
iajs-2434	94	15	information	information	NOUN
iajs-2434	94	16	at	at	ADP
iajs-2434	94	17	𝜃	𝜃	SYM
iajs-2434	94	18	0.5	0.5	NUM
iajs-2434	94	19	.	.	PUNCT
iajs-2434	95	1	n	n	PROPN
iajs-2434	95	2	estimator	estimator	NOUN
iajs-2434	95	3	10	10	NUM
iajs-2434	95	4	50	50	NUM
iajs-2434	95	5	100	100	NUM
iajs-2434	95	6	200	200	NUM
iajs-2434	95	7	sq	sq	NOUN
iajs-2434	95	8	0.000295	0.000295	NUM
iajs-2434	95	9	0.0000099	0.0000099	NUM
iajs-2434	95	10	0.0000024714	0.0000024714	NUM
iajs-2434	95	11	0.0000006220	0.0000006220	NUM
iajs-2434	95	12	ms	ms	NOUN
iajs-2434	95	13	r=1	r=1	NOUN
iajs-2434	95	14	0.000353	0.000353	NUM
iajs-2434	95	15	0.0000103	0.0000103	NUM
iajs-2434	95	16	0.0000025315	0.0000025315	NUM
iajs-2434	95	17	0.0000006297	0.0000006297	NUM
iajs-2434	95	18	ms	ms	PROPN
iajs-2434	95	19	r=2	r=2	PROPN
iajs-2434	95	20	0.000436	0.000436	NUM
iajs-2434	95	21	0.0000111	0.0000111	NUM
iajs-2434	95	22	0.0000026240	0.0000026240	NUM
iajs-2434	95	23	0.0000006416	0.0000006416	NUM
iajs-2434	95	24	ms	ms	PROPN
iajs-2434	95	25	r=3	r=3	PROPN
iajs-2434	95	26	0.000541	0.000541	NUM
iajs-2434	96	1	0.0000120	0.0000120	NUM
iajs-2434	96	2	0.0000027483	0.0000027483	NUM
iajs-2434	96	3	0.0000006575	0.0000006575	NUM
iajs-2434	96	4	pr	pr	VERB
iajs-2434	96	5	0.000319	0.000319	NUM
iajs-2434	96	6	0.0000101	0.0000101	NUM
iajs-2434	96	7	0.0000024973	0.0000024973	NUM
iajs-2434	96	8	0.0000006253	0.0000006253	NUM
iajs-2434	96	9	best	good	ADJ
iajs-2434	96	10	sq	sq	INTJ
iajs-2434	96	11	sq	sq	INTJ
iajs-2434	96	12	sq	sq	ADJ
iajs-2434	96	13	sq	sq	PROPN
iajs-2434	96	14	table	table	NOUN
iajs-2434	96	15	3	3	NUM
iajs-2434	96	16	.	.	PUNCT
iajs-2434	96	17	(	(	PUNCT
iajs-2434	96	18	mse	mse	PROPN
iajs-2434	96	19	)	)	PUNCT
iajs-2434	96	20	for	for	ADP
iajs-2434	96	21	parameter	parameter	NOUN
iajs-2434	96	22	𝜃	𝜃	NUM
iajs-2434	96	23	by	by	ADP
iajs-2434	96	24	using	use	VERB
iajs-2434	96	25	exponential	exponential	ADJ
iajs-2434	96	26	prior	prior	ADJ
iajs-2434	96	27	information	information	NOUN
iajs-2434	96	28	at	at	ADP
iajs-2434	96	29	𝜃	𝜃	SYM
iajs-2434	96	30	0.5	0.5	NUM
iajs-2434	96	31	.	.	PUNCT
iajs-2434	97	1	n	n	PROPN
iajs-2434	97	2	estimator	estimator	NOUN
iajs-2434	97	3	10	10	NUM
iajs-2434	97	4	50	50	NUM
iajs-2434	97	5	100	100	NUM
iajs-2434	97	6	200	200	NUM
iajs-2434	97	7	sq	sq	ADJ
iajs-2434	97	8	λ	λ	PROPN
iajs-2434	97	9	0.5	0.5	NUM
iajs-2434	97	10	0.0051	0.0051	NUM
iajs-2434	97	11	0.0001143	0.0001143	NUM
iajs-2434	97	12	0.000026952	0.000026952	NUM
iajs-2434	97	13	0.000006612	0.000006612	NUM
iajs-2434	97	14	λ	λ	NOUN
iajs-2434	97	15	1	1	NUM
iajs-2434	97	16	0.0043	0.0043	NUM
iajs-2434	97	17	0.0001103	0.0001103	NUM
iajs-2434	97	18	0.000026474	0.000026474	NUM
iajs-2434	97	19	0.000006552	0.000006552	NUM
iajs-2434	97	20	ms	ms	NOUN
iajs-2434	97	21	r=1	r=1	PROPN
iajs-2434	97	22	λ	λ	PROPN
iajs-2434	97	23	0.5	0.5	NUM
iajs-2434	97	24	0.0073	0.0073	NUM
iajs-2434	97	25	0.0001278	0.0001278	NUM
iajs-2434	97	26	0.000028621	0.000028621	NUM
iajs-2434	97	27	0.000006822	0.000006822	NUM
iajs-2434	97	28	λ	λ	NOUN
iajs-2434	97	29	1	1	NUM
iajs-2434	97	30	0.0061	0.0061	NUM
iajs-2434	97	31	0.0001226	0.0001226	NUM
iajs-2434	97	32	0.000028004	0.000028004	NUM
iajs-2434	97	33	0.000006746	0.000006746	NUM
iajs-2434	97	34	jms	jms	PROPN
iajs-2434	97	35	r=2	r=2	PROPN
iajs-2434	97	36	λ	λ	PROPN
iajs-2434	97	37	0.5	0.5	NUM
iajs-2434	97	38	0.0100	0.0100	NUM
iajs-2434	97	39	0.0001455	0.0001455	NUM
iajs-2434	97	40	0.000030803	0.000030803	NUM
iajs-2434	97	41	0.000007096	0.000007096	NUM
iajs-2434	97	42	λ	λ	NOUN
iajs-2434	97	43	1	1	NUM
iajs-2434	97	44	0.0085	0.0085	NUM
iajs-2434	97	45	0.0001391	0.0001391	NUM
iajs-2434	97	46	0.000030045	0.000030045	NUM
iajs-2434	97	47	0.000007003	0.000007003	NUM
iajs-2434	97	48	ms	ms	NOUN
iajs-2434	97	49	r=3	r=3	PROPN
iajs-2434	97	50	λ	λ	PROPN
iajs-2434	97	51	0.5	0.5	NUM
iajs-2434	97	52	0.0135	0.0135	NUM
iajs-2434	97	53	0.0001674	0.0001674	NUM
iajs-2434	97	54	0.000033498	0.000033498	NUM
iajs-2434	97	55	0.000007433	0.000007433	NUM
iajs-2434	97	56	λ	λ	NOUN
iajs-2434	97	57	1	1	NUM
iajs-2434	97	58	0.0115	0.0115	NUM
iajs-2434	97	59	0.0001597	0.0001597	NUM
iajs-2434	97	60	0.000032596	0.000032596	NUM
iajs-2434	97	61	0.000007323	0.000007323	NUM
iajs-2434	97	62	pr	pr	NOUN
iajs-2434	97	63	λ	λ	PROPN
iajs-2434	97	64	0.5	0.5	NUM
iajs-2434	97	65	0.0061	0.0061	NUM
iajs-2434	97	66	0.0001205	0.0001205	NUM
iajs-2434	97	67	0.00002772	0.00002772	NUM
iajs-2434	97	68	0.000006709	0.000006709	NUM
iajs-2434	97	69	λ	λ	NOUN
iajs-2434	97	70	1	1	NUM
iajs-2434	97	71	0.0051	0.0051	NUM
iajs-2434	97	72	0.0001159	0.0001159	NUM
iajs-2434	97	73	0.000027173	0.000027173	NUM
iajs-2434	97	74	0.000006641	0.000006641	NUM
iajs-2434	97	75	best	good	ADJ
iajs-2434	97	76	sq	sq	ADJ
iajs-2434	97	77	sq	sq	INTJ
iajs-2434	97	78	sq	sq	INTJ
iajs-2434	97	79	sq	sq	PROPN
iajs-2434	97	80	  	  	SPACE
iajs-2434	97	81	138	138	NUM
iajs-2434	97	82	  	  	SPACE
iajs-2434	97	83	ibn	ibn	PROPN
iajs-2434	97	84	al	al	PROPN
iajs-2434	97	85	-	-	PUNCT
iajs-2434	97	86	haitham	haitham	PROPN
iajs-2434	97	87	jour	jour	X
iajs-2434	97	88	.	.	PROPN
iajs-2434	98	1	for	for	ADP
iajs-2434	98	2	pure	pure	ADJ
iajs-2434	98	3	&	&	CCONJ
iajs-2434	98	4	appl	appl	PROPN
iajs-2434	98	5	.	.	PUNCT
iajs-2434	99	1	sci	sci	PROPN
iajs-2434	99	2	.	.	PROPN
iajs-2434	100	1	33	33	NUM
iajs-2434	100	2	(	(	PUNCT
iajs-2434	100	3	1	1	NUM
iajs-2434	100	4	)	)	PUNCT
iajs-2434	100	5	2020	2020	NUM
iajs-2434	100	6	table	table	NOUN
iajs-2434	100	7	4	4	NUM
iajs-2434	100	8	.	.	PUNCT
iajs-2434	101	1	(	(	PUNCT
iajs-2434	101	2	mse	mse	NOUN
iajs-2434	101	3	)	)	PUNCT
iajs-2434	101	4	values	value	NOUN
iajs-2434	101	5	of	of	ADP
iajs-2434	101	6	the	the	DET
iajs-2434	101	7	reliability	reliability	NOUN
iajs-2434	101	8	function	function	NOUN
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iajs-2434	101	10	by	by	ADP
iajs-2434	101	11	using	use	VERB
iajs-2434	101	12	exponential	exponential	ADJ
iajs-2434	101	13	prior	prior	ADJ
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iajs-2434	101	15	at	at	ADP
iajs-2434	101	16	𝜃	𝜃	SYM
iajs-2434	101	17	0.5	0.5	NUM
iajs-2434	101	18	.	.	PUNCT
iajs-2434	102	1	n	n	PROPN
iajs-2434	102	2	estimator	estimator	NOUN
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iajs-2434	102	4	50	50	NUM
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iajs-2434	102	7	sq	sq	ADJ
iajs-2434	102	8	λ	λ	PROPN
iajs-2434	102	9	0.5	0.5	NUM
iajs-2434	102	10	0.000332	0.000332	NUM
iajs-2434	102	11	0.0000102	0.0000102	NUM
iajs-2434	102	12	0.0000025179	0.0000025179	NUM
iajs-2434	102	13	0.0000006281	0.0000006281	NUM
iajs-2434	102	14	λ	λ	NOUN
iajs-2434	102	15	1	1	NUM
iajs-2434	102	16	0.000290	0.000290	NUM
iajs-2434	102	17	0.0000099	0.0000099	NUM
iajs-2434	102	18	0.0000024824	0.0000024824	NUM
iajs-2434	102	19	0.0000006235	0.0000006235	NUM
iajs-2434	102	20	ms	ms	NOUN
iajs-2434	102	21	r=1	r=1	PROPN
iajs-2434	102	22	λ	λ	PROPN
iajs-2434	102	23	0.5	0.5	NUM
iajs-2434	102	24	0.0031	0.0031	NUM
iajs-2434	102	25	0.0000364	0.0000364	NUM
iajs-2434	102	26	0.0000058603	0.0000058603	NUM
iajs-2434	103	1	0.000001052	0.000001052	NUM
iajs-2434	103	2	λ	λ	PROPN
iajs-2434	103	3	1	1	NUM
iajs-2434	103	4	0.0030	0.0030	NUM
iajs-2434	103	5	0.0000354	0.0000354	NUM
iajs-2434	103	6	0.0000057318	0.0000057318	NUM
iajs-2434	103	7	0.000001035	0.000001035	NUM
iajs-2434	103	8	ms	ms	PROPN
iajs-2434	103	9	r=2	r=2	PROPN
iajs-2434	103	10	λ	λ	PROPN
iajs-2434	103	11	0.5	0.5	NUM
iajs-2434	103	12	0.000508	0.000508	NUM
iajs-2434	103	13	0.0000119	0.0000119	NUM
iajs-2434	103	14	0.0000027277	0.0000027277	NUM
iajs-2434	103	15	0.0000006549	0.0000006549	NUM
iajs-2434	103	16	λ	λ	NOUN
iajs-2434	103	17	1	1	NUM
iajs-2434	103	18	0.000443	0.000443	NUM
iajs-2434	103	19	0.0000114	0.0000114	NUM
iajs-2434	103	20	0.0000026716	0.0000026716	NUM
iajs-2434	103	21	0.0000006479	0.0000006479	NUM
iajs-2434	103	22	ms	ms	NOUN
iajs-2434	103	23	r=3	r=3	PROPN
iajs-2434	103	24	λ	λ	PROPN
iajs-2434	103	25	0.5	0.5	NUM
iajs-2434	103	26	0.000625	0.000625	NUM
iajs-2434	103	27	0.0000130	0.0000130	NUM
iajs-2434	103	28	0.0000028797	0.0000028797	NUM
iajs-2434	103	29	0.0000006745	0.0000006745	NUM
iajs-2434	103	30	λ	λ	NOUN
iajs-2434	103	31	1	1	NUM
iajs-2434	103	32	0.000548	0.000548	NUM
iajs-2434	103	33	0.0000125	0.0000125	NUM
iajs-2434	103	34	0.0000028134	0.0000028134	NUM
iajs-2434	103	35	0.0000006661	0.0000006661	NUM
iajs-2434	103	36	pr	pr	NOUN
iajs-2434	103	37	λ	λ	PROPN
iajs-2434	103	38	0.5	0.5	NUM
iajs-2434	103	39	0.2320	0.2320	NUM
iajs-2434	103	40	0.0470	0.0470	NUM
iajs-2434	103	41	0.0235	0.0235	NUM
iajs-2434	103	42	0.0118	0.0118	NUM
iajs-2434	103	43	λ	λ	NOUN
iajs-2434	103	44	1	1	NUM
iajs-2434	103	45	0.2328	0.2328	NUM
iajs-2434	103	46	0.0470	0.0470	NUM
iajs-2434	103	47	0.0235	0.0235	NUM
iajs-2434	103	48	0.0118	0.0118	NUM
iajs-2434	103	49	best	good	ADJ
iajs-2434	103	50	sq	sq	ADJ
iajs-2434	103	51	sq	sq	INTJ
iajs-2434	103	52	sq	sq	ADJ
iajs-2434	103	53	sq	sq	PROPN
iajs-2434	103	54	table	table	NOUN
iajs-2434	103	55	5	5	NUM
iajs-2434	103	56	.	.	PUNCT
iajs-2434	103	57	(	(	PUNCT
iajs-2434	103	58	mse	mse	PROPN
iajs-2434	103	59	)	)	PUNCT
iajs-2434	103	60	for	for	ADP
iajs-2434	103	61	parameter	parameter	NOUN
iajs-2434	103	62	𝜃	𝜃	NUM
iajs-2434	103	63	by	by	ADP
iajs-2434	103	64	using	use	VERB
iajs-2434	103	65	jeffrey	jeffrey	PROPN
iajs-2434	103	66	's	's	PART
iajs-2434	103	67	prior	prior	ADJ
iajs-2434	103	68	information	information	NOUN
iajs-2434	103	69	at	at	ADP
iajs-2434	103	70	𝜃	𝜃	NUM
iajs-2434	103	71	1.5	1.5	NUM
iajs-2434	103	72	.	.	PUNCT
iajs-2434	104	1	n	n	PRON
iajs-2434	104	2	estimator	estimator	NOUN
iajs-2434	104	3	10	10	NUM
iajs-2434	104	4	50	50	NUM
iajs-2434	104	5	100	100	NUM
iajs-2434	104	6	200	200	NUM
iajs-2434	104	7	sq	sq	NUM
iajs-2434	104	8	0.0391	0.0391	NUM
iajs-2434	104	9	0.00097346	0.00097346	NUM
iajs-2434	104	10	0.00023555	0.00023555	NUM
iajs-2434	104	11	0.00005861	0.00005861	NUM
iajs-2434	104	12	ms	ms	NOUN
iajs-2434	104	13	r=1	r=1	NOUN
iajs-2434	104	14	0.0553	0.0553	NUM
iajs-2434	104	15	0.0011	0.0011	NUM
iajs-2434	104	16	0.00024721	0.00024721	NUM
iajs-2434	104	17	0.000060085	0.000060085	NUM
iajs-2434	104	18	ms	ms	PROPN
iajs-2434	104	19	r=2	r=2	PROPN
iajs-2434	104	20	0.778	0.778	NUM
iajs-2434	104	21	0.0012	0.0012	NUM
iajs-2434	104	22	0.00026350	0.00026350	NUM
iajs-2434	104	23	0.000062128	0.000062128	NUM
iajs-2434	104	24	ms	ms	PROPN
iajs-2434	104	25	r=3	r=3	PROPN
iajs-2434	104	26	0.1067	0.1067	NUM
iajs-2434	104	27	0.0014	0.0014	NUM
iajs-2434	104	28	0.00028442	0.00028442	NUM
iajs-2434	104	29	0.000064741	0.000064741	NUM
iajs-2434	104	30	pr	pr	VERB
iajs-2434	104	31	0.1444	0.1444	NUM
iajs-2434	104	32	0.0422	0.0422	NUM
iajs-2434	104	33	0.0218	0.0218	NUM
iajs-2434	104	34	0.0111	0.0111	NUM
iajs-2434	104	35	best	good	ADJ
iajs-2434	104	36	sq	sq	ADJ
iajs-2434	104	37	sq	sq	INTJ
iajs-2434	104	38	sq	sq	ADJ
iajs-2434	104	39	sq	sq	PROPN
iajs-2434	104	40	table	table	NOUN
iajs-2434	104	41	6	6	NUM
iajs-2434	104	42	.	.	PUNCT
iajs-2434	105	1	(	(	PUNCT
iajs-2434	105	2	mse	mse	NOUN
iajs-2434	105	3	)	)	PUNCT
iajs-2434	105	4	values	value	NOUN
iajs-2434	105	5	of	of	ADP
iajs-2434	105	6	the	the	DET
iajs-2434	105	7	reliability	reliability	NOUN
iajs-2434	105	8	function	function	NOUN
iajs-2434	105	9	estimators	estimator	NOUN
iajs-2434	105	10	by	by	ADP
iajs-2434	105	11	using	use	VERB
iajs-2434	105	12	prior	prior	ADJ
iajs-2434	105	13	information	information	NOUN
iajs-2434	105	14	at	at	ADP
iajs-2434	105	15	𝜃	𝜃	NUM
iajs-2434	105	16	1.5	1.5	NUM
iajs-2434	105	17	.	.	PUNCT
iajs-2434	106	1	n	n	PRON
iajs-2434	106	2	estimator	estimator	NOUN
iajs-2434	106	3	10	10	NUM
iajs-2434	106	4	50	50	NUM
iajs-2434	106	5	100	100	NUM
iajs-2434	106	6	200	200	NUM
iajs-2434	106	7	sq	sq	NUM
iajs-2434	106	8	0.000640	0.000640	NUM
iajs-2434	106	9	0.000024186	0.000024186	NUM
iajs-2434	106	10	0.000006000951	0.000006000951	NUM
iajs-2434	106	11	0.0000015384	0.0000015384	NUM
iajs-2434	106	12	ms	ms	NOUN
iajs-2434	106	13	r=1	r=1	NOUN
iajs-2434	106	14	0.000699	0.000699	NUM
iajs-2434	106	15	0.000024643	0.000024643	NUM
iajs-2434	106	16	0.0000061533	0.0000061533	NUM
iajs-2434	106	17	0.0000015461	0.0000015461	NUM
iajs-2434	106	18	ms	ms	PROPN
iajs-2434	106	19	r=2	r=2	PROPN
iajs-2434	106	20	0.000804	0.000804	NUM
iajs-2434	106	21	0.000025556	0.000025556	NUM
iajs-2434	106	22	0.0000062697	0.0000062697	NUM
iajs-2434	106	23	0.0000015611	0.0000015611	NUM
iajs-2434	106	24	ms	ms	NOUN
iajs-2434	106	25	r=3	r=3	PROPN
iajs-2434	106	26	0.000945	0.000945	NUM
iajs-2434	106	27	0.0000120	0.0000120	NUM
iajs-2434	106	28	0.0000064431	0.0000064431	NUM
iajs-2434	106	29	0.0000015834	0.0000015834	NUM
iajs-2434	106	30	pr	pr	NOUN
iajs-2434	106	31	0.000662	0.000662	NUM
iajs-2434	106	32	0.000024355	0.000024355	NUM
iajs-2434	106	33	0.0000061167	0.0000061167	NUM
iajs-2434	106	34	0.0000015413	0.0000015413	NUM
iajs-2434	106	35	best	good	ADJ
iajs-2434	106	36	sq	sq	ADJ
iajs-2434	106	37	sq	sq	INTJ
iajs-2434	106	38	sq	sq	ADJ
iajs-2434	106	39	sq	sq	PROPN
iajs-2434	106	40	table	table	NOUN
iajs-2434	106	41	7	7	NUM
iajs-2434	106	42	.	.	PUNCT
iajs-2434	106	43	(	(	PUNCT
iajs-2434	106	44	mse	mse	NOUN
iajs-2434	106	45	)	)	PUNCT
iajs-2434	106	46	for	for	ADP
iajs-2434	106	47	parameter	parameter	NOUN
iajs-2434	106	48	𝜃	𝜃	NUM
iajs-2434	106	49	by	by	ADP
iajs-2434	106	50	using	use	VERB
iajs-2434	106	51	exponential	exponential	ADJ
iajs-2434	106	52	prior	prior	ADJ
iajs-2434	106	53	information	information	NOUN
iajs-2434	106	54	at	at	ADP
iajs-2434	106	55	𝜃	𝜃	NUM
iajs-2434	106	56	1.5	1.5	NUM
iajs-2434	106	57	.	.	PUNCT
iajs-2434	107	1	n	n	PRON
iajs-2434	107	2	estimator	estimator	NOUN
iajs-2434	107	3	10	10	NUM
iajs-2434	107	4	50	50	NUM
iajs-2434	107	5	100	100	NUM
iajs-2434	107	6	200	200	NUM
iajs-2434	107	7	sq	sq	ADJ
iajs-2434	107	8	λ	λ	PROPN
iajs-2434	107	9	0.5	0.5	NUM
iajs-2434	107	10	0.0328	0.0328	NUM
iajs-2434	107	11	0.00096071	0.00096071	NUM
iajs-2434	107	12	0.0002343	0.0002343	NUM
iajs-2434	107	13	0.00005847	0.00005847	NUM
iajs-2434	107	14	λ	λ	NOUN
iajs-2434	107	15	1	1	NUM
iajs-2434	107	16	0.0211	0.0211	NUM
iajs-2434	107	17	0.0008813	0.0008813	NUM
iajs-2434	107	18	0.00022438	0.00022438	NUM
iajs-2434	107	19	0.00005720	0.00005720	NUM
iajs-2434	107	20	ms	ms	NOUN
iajs-2434	107	21	r=1	r=1	PROPN
iajs-2434	107	22	λ	λ	PROPN
iajs-2434	107	23	0.5	0.5	NUM
iajs-2434	107	24	0.0463	0.0463	NUM
iajs-2434	107	25	0.0011	0.0011	NUM
iajs-2434	107	26	0.00024684	0.00024684	NUM
iajs-2434	107	27	0.00006007	0.00006007	NUM
iajs-2434	107	28	λ	λ	NOUN
iajs-2434	107	29	1	1	NUM
iajs-2434	107	30	0.0285	0.0285	NUM
iajs-2434	107	31	0.0009501	0.0009501	NUM
iajs-2434	107	32	0.00023329	0.00023329	NUM
iajs-2434	107	33	0.00005836	0.00005836	NUM
iajs-2434	107	34	ms	ms	PROPN
iajs-2434	107	35	r=2	r=2	PROPN
iajs-2434	107	36	λ	λ	PROPN
iajs-2434	107	37	0.5	0.5	NUM
iajs-2434	107	38	0.0650	0.0650	NUM
iajs-2434	107	39	0.0012	0.0012	NUM
iajs-2434	107	40	0.00026395	0.00026395	NUM
iajs-2434	107	41	0.00006223	0.00006223	NUM
iajs-2434	107	42	λ	λ	NOUN
iajs-2434	107	43	1	1	NUM
iajs-2434	107	44	0.0403	0.0403	NUM
iajs-2434	107	45	0.0011	0.0011	NUM
iajs-2434	107	46	0.0002467	0.0002467	NUM
iajs-2434	107	47	0.00006008	0.00006008	NUM
iajs-2434	107	48	ms	ms	NOUN
iajs-2434	107	49	r=3	r=3	PROPN
iajs-2434	107	50	λ	λ	PROPN
iajs-2434	107	51	0.5	0.5	NUM
iajs-2434	107	52	0.0889	0.0889	NUM
iajs-2434	107	53	0,0014	0,0014	NUM
iajs-2434	107	54	0.0002856	0.0002856	NUM
iajs-2434	107	55	0.00006496	0.00006496	NUM
iajs-2434	107	56	λ	λ	NOUN
iajs-2434	107	57	1	1	NUM
iajs-2434	107	58	0.0564	0.0564	NUM
iajs-2434	107	59	0.0012	0.0012	NUM
iajs-2434	107	60	0.0002646	0.0002646	NUM
iajs-2434	107	61	0.00006237	0.00006237	NUM
iajs-2434	107	62	pr	pr	NOUN
iajs-2434	107	63	λ	λ	PROPN
iajs-2434	107	64	0.5	0.5	NUM
iajs-2434	107	65	0.388	0.388	NUM
iajs-2434	107	66	0.0010	0.0010	NUM
iajs-2434	107	67	0.00023998	0.00023998	NUM
iajs-2434	107	68	0.00005920	0.00005920	NUM
iajs-2434	107	69	λ	λ	NOUN
iajs-2434	107	70	1	1	NUM
iajs-2434	107	71	0.0242	0.0242	NUM
iajs-2434	107	72	0.0009110	0.0009110	NUM
iajs-2434	107	73	0.00022826	0.00022826	NUM
iajs-2434	107	74	0.00005771	0.00005771	NUM
iajs-2434	107	75	best	good	ADJ
iajs-2434	107	76	sq	sq	INTJ
iajs-2434	107	77	sq	sq	INTJ
iajs-2434	107	78	sq	sq	INTJ
iajs-2434	107	79	sq	sq	PROPN
iajs-2434	107	80	  	  	SPACE
iajs-2434	107	81	139	139	NUM
iajs-2434	107	82	  	  	SPACE
iajs-2434	107	83	ibn	ibn	PROPN
iajs-2434	107	84	al	al	PROPN
iajs-2434	107	85	-	-	PUNCT
iajs-2434	107	86	haitham	haitham	PROPN
iajs-2434	107	87	jour	jour	X
iajs-2434	107	88	.	.	PROPN
iajs-2434	108	1	for	for	ADP
iajs-2434	108	2	pure	pure	ADJ
iajs-2434	108	3	&	&	CCONJ
iajs-2434	108	4	appl	appl	PROPN
iajs-2434	108	5	.	.	PUNCT
iajs-2434	109	1	sci	sci	PROPN
iajs-2434	109	2	.	.	PROPN
iajs-2434	110	1	33	33	NUM
iajs-2434	110	2	(	(	PUNCT
iajs-2434	110	3	1	1	NUM
iajs-2434	110	4	)	)	PUNCT
iajs-2434	110	5	2020	2020	NUM
iajs-2434	110	6	table	table	NOUN
iajs-2434	110	7	8	8	NUM
iajs-2434	110	8	.	.	PUNCT
iajs-2434	111	1	(	(	PUNCT
iajs-2434	111	2	mse	mse	NOUN
iajs-2434	111	3	)	)	PUNCT
iajs-2434	111	4	values	value	NOUN
iajs-2434	111	5	of	of	ADP
iajs-2434	111	6	the	the	DET
iajs-2434	111	7	reliability	reliability	NOUN
iajs-2434	111	8	function	function	NOUN
iajs-2434	111	9	estimators	estimator	NOUN
iajs-2434	111	10	by	by	ADP
iajs-2434	111	11	using	use	VERB
iajs-2434	111	12	exponential	exponential	ADJ
iajs-2434	111	13	prior	prior	ADJ
iajs-2434	111	14	information	information	NOUN
iajs-2434	111	15	at	at	ADP
iajs-2434	111	16	𝜃	𝜃	NUM
iajs-2434	111	17	1.5	1.5	NUM
iajs-2434	111	18	.	.	PUNCT
iajs-2434	112	1	n	n	PRON
iajs-2434	112	2	estimator	estimator	NOUN
iajs-2434	112	3	10	10	NUM
iajs-2434	112	4	50	50	NUM
iajs-2434	112	5	100	100	NUM
iajs-2434	112	6	200	200	NUM
iajs-2434	112	7	sq	sq	ADJ
iajs-2434	112	8	λ	λ	PROPN
iajs-2434	112	9	0.5	0.5	NUM
iajs-2434	112	10	0.000553	0.000553	NUM
iajs-2434	112	11	0.000023591	0.000023591	NUM
iajs-2434	112	12	0.0000060208	0.0000060208	NUM
iajs-2434	112	13	0.000001529	0.000001529	NUM
iajs-2434	112	14	λ	λ	NOUN
iajs-2434	112	15	1	1	NUM
iajs-2434	112	16	0.000456	0.000456	NUM
iajs-2434	112	17	0.00002269	0.00002269	NUM
iajs-2434	112	18	0.0000059033	0.0000059033	NUM
iajs-2434	112	19	0.000001513	0.000001513	NUM
iajs-2434	112	20	ms	ms	NOUN
iajs-2434	112	21	r=1	r=1	PROPN
iajs-2434	112	22	λ	λ	PROPN
iajs-2434	112	23	0.5	0.5	NUM
iajs-2434	112	24	0.0022	0.0022	NUM
iajs-2434	112	25	0.00003918	0.00003918	NUM
iajs-2434	112	26	0.0000080152	0.0000080152	NUM
iajs-2434	112	27	0.000001783	0.000001783	NUM
iajs-2434	112	28	λ	λ	NOUN
iajs-2434	112	29	1	1	NUM
iajs-2434	112	30	0.0019	0.0019	NUM
iajs-2434	112	31	0.00003548	0.00003548	NUM
iajs-2434	112	32	0.0000075334	0.0000075334	NUM
iajs-2434	112	33	0.000001721	0.000001721	NUM
iajs-2434	112	34	ms	ms	PROPN
iajs-2434	112	35	r=2	r=2	PROPN
iajs-2434	112	36	λ	λ	PROPN
iajs-2434	112	37	0.5	0.5	NUM
iajs-2434	112	38	0.000717	0.000717	NUM
iajs-2434	112	39	0.000025211	0.000025211	NUM
iajs-2434	112	40	0.0000062315	0.0000062315	NUM
iajs-2434	112	41	0.000001556	0.000001556	NUM
iajs-2434	112	42	λ	λ	NOUN
iajs-2434	112	43	1	1	NUM
iajs-2434	112	44	0.000516	0.000516	NUM
iajs-2434	112	45	0.00002336	0.00002336	NUM
iajs-2434	112	46	0.0000059928	0.0000059928	NUM
iajs-2434	112	47	0.000001525	0.000001525	NUM
iajs-2434	112	48	ms	ms	NOUN
iajs-2434	112	49	r=3	r=3	PROPN
iajs-2434	112	50	λ	λ	PROPN
iajs-2434	112	51	0.5	0.5	NUM
iajs-2434	112	52	0.000849	0.000849	NUM
iajs-2434	112	53	0.000036657	0.000036657	NUM
iajs-2434	112	54	0.0000064211	0.0000064211	NUM
iajs-2434	112	55	0.000001581	0.000001581	NUM
iajs-2434	112	56	λ	λ	NOUN
iajs-2434	112	57	1	1	NUM
iajs-2434	112	58	0.000601	0.000601	NUM
iajs-2434	112	59	0.00002433	0.00002433	NUM
iajs-2434	112	60	0.0000061224	0.0000061224	NUM
iajs-2434	112	61	0.000001542	0.000001542	NUM
iajs-2434	112	62	pr	pr	NOUN
iajs-2434	112	63	λ	λ	PROPN
iajs-2434	112	64	0.5	0.5	NUM
iajs-2434	112	65	0.15170	0.15170	NUM
iajs-2434	112	66	0.0306	0.0306	NUM
iajs-2434	113	1	0.0153	0.0153	NUM
iajs-2434	113	2	0.0077	0.0077	NUM
iajs-2434	113	3	λ	λ	PROPN
iajs-2434	113	4	1	1	NUM
iajs-2434	113	5	0.15430	0.15430	NUM
iajs-2434	113	6	0.0307	0.0307	NUM
iajs-2434	113	7	0.0153	0.0153	NUM
iajs-2434	113	8	0.0077	0.0077	NUM
iajs-2434	113	9	best	good	ADJ
iajs-2434	113	10	sq	sq	INTJ
iajs-2434	113	11	sq	sq	INTJ
iajs-2434	113	12	sq	sq	INTJ
iajs-2434	113	13	sq	sq	INTJ
iajs-2434	113	14	15	15	NUM
iajs-2434	113	15	.	.	PUNCT
iajs-2434	114	1	simulation	simulation	NOUN
iajs-2434	114	2	results	result	NOUN
iajs-2434	114	3	and	and	CCONJ
iajs-2434	114	4	conclusions	conclusion	NOUN
iajs-2434	114	5	from	from	ADP
iajs-2434	114	6	our	our	PRON
iajs-2434	114	7	simulation	simulation	NOUN
iajs-2434	114	8	study	study	NOUN
iajs-2434	114	9	,	,	PUNCT
iajs-2434	114	10	we	we	PRON
iajs-2434	114	11	conclude	conclude	VERB
iajs-2434	114	12	that	that	SCONJ
iajs-2434	114	13	the	the	DET
iajs-2434	114	14	performance	performance	NOUN
iajs-2434	114	15	of	of	ADP
iajs-2434	114	16	the	the	DET
iajs-2434	114	17	bayes	bayes	NOUN
iajs-2434	114	18	estimators	estimator	NOUN
iajs-2434	114	19	under	under	ADP
iajs-2434	114	20	square	square	ADJ
iajs-2434	114	21	error	error	NOUN
iajs-2434	114	22	loss	loss	NOUN
iajs-2434	114	23	function	function	NOUN
iajs-2434	114	24	are	be	AUX
iajs-2434	114	25	the	the	DET
iajs-2434	114	26	best	good	ADJ
iajs-2434	114	27	compared	compare	VERB
iajs-2434	114	28	to	to	ADP
iajs-2434	114	29	other	other	ADJ
iajs-2434	114	30	estimators	estimator	NOUN
iajs-2434	114	31	in	in	ADP
iajs-2434	114	32	all	all	DET
iajs-2434	114	33	cases	case	NOUN
iajs-2434	114	34	that	that	PRON
iajs-2434	114	35	are	be	AUX
iajs-2434	114	36	included	include	VERB
iajs-2434	114	37	in	in	ADP
iajs-2434	114	38	our	our	PRON
iajs-2434	114	39	study	study	NOUN
iajs-2434	114	40	,	,	PUNCT
iajs-2434	114	41	followed	follow	VERB
iajs-2434	114	42	by	by	ADP
iajs-2434	114	43	the	the	DET
iajs-2434	114	44	estimators	estimator	NOUN
iajs-2434	114	45	under	under	ADP
iajs-2434	114	46	precautionary	precautionary	ADJ
iajs-2434	114	47	loss	loss	NOUN
iajs-2434	114	48	function	function	NOUN
iajs-2434	114	49	in	in	ADP
iajs-2434	114	50	the	the	PRON
iajs-2434	114	51	in	in	ADP
iajs-2434	114	52	the	the	DET
iajs-2434	114	53	cases	case	NOUN
iajs-2434	114	54	presented	present	VERB
iajs-2434	114	55	in	in	ADP
iajs-2434	114	56	table	table	NOUN
iajs-2434	114	57	2	2	NUM
iajs-2434	114	58	,	,	PUNCT
iajs-2434	114	59	3,6	3,6	NUM
iajs-2434	114	60	.	.	PUNCT
iajs-2434	115	1	the	the	DET
iajs-2434	115	2	estimators	estimator	NOUN
iajs-2434	115	3	under	under	ADP
iajs-2434	115	4	modified	modified	ADJ
iajs-2434	115	5	square	square	ADJ
iajs-2434	115	6	error	error	NOUN
iajs-2434	115	7	loss	loss	NOUN
iajs-2434	115	8	function	function	NOUN
iajs-2434	115	9	when	when	SCONJ
iajs-2434	115	10	(	(	PUNCT
iajs-2434	115	11	r=1	r=1	NOUN
iajs-2434	115	12	)	)	PUNCT
iajs-2434	115	13	presented	present	VERB
iajs-2434	115	14	in	in	ADP
iajs-2434	115	15	table	table	NOUN
iajs-2434	115	16	1	1	NUM
iajs-2434	115	17	,	,	PUNCT
iajs-2434	115	18	5	5	NUM
iajs-2434	115	19	,	,	PUNCT
iajs-2434	115	20	7	7	NUM
iajs-2434	115	21	.	.	NUM
iajs-2434	115	22	references	reference	NOUN
iajs-2434	115	23	1	1	NUM
iajs-2434	115	24	.	.	PUNCT
iajs-2434	116	1	mukherjee	mukherjee	PROPN
iajs-2434	116	2	,	,	PUNCT
iajs-2434	116	3	s.p	s.p	PROPN
iajs-2434	116	4	.	.	PROPN
iajs-2434	116	5	;	;	PUNCT
iajs-2434	117	1	saran	saran	PROPN
iajs-2434	117	2	,	,	PUNCT
iajs-2434	117	3	i.k	i.k	PROPN
iajs-2434	117	4	.	.	PROPN
iajs-2434	117	5	bivariate	bivariate	ADJ
iajs-2434	117	6	inverse	inverse	ADJ
iajs-2434	117	7	rayleigh	rayleigh	NOUN
iajs-2434	117	8	distribution	distribution	NOUN
iajs-2434	117	9	in	in	ADP
iajs-2434	117	10	reliability	reliability	NOUN
iajs-2434	117	11	studies	study	NOUN
iajs-2434	117	12	jour	jour	X
iajs-2434	117	13	.	.	PUNCT
iajs-2434	117	14	ind	ind	NOUN
iajs-2434	117	15	.	.	PUNCT
iajs-2434	118	1	statistical	statistical	ADJ
iajs-2434	118	2	assoc.2.1984	assoc.2.1984	SYM
iajs-2434	118	3	,	,	PUNCT
iajs-2434	118	4	23	23	NUM
iajs-2434	118	5	-	-	SYM
iajs-2434	118	6	31	31	NUM
iajs-2434	118	7	.	.	PUNCT
iajs-2434	119	1	2	2	X
iajs-2434	119	2	.	.	X
iajs-2434	119	3	gharrabh	gharrabh	PROPN
iajs-2434	119	4	,	,	PUNCT
iajs-2434	119	5	m.k	m.k	PROPN
iajs-2434	119	6	.	.	PROPN
iajs-2434	119	7	comparison	comparison	NOUN
iajs-2434	119	8	of	of	ADP
iajs-2434	119	9	estimators	estimator	NOUN
iajs-2434	119	10	of	of	ADP
iajs-2434	119	11	location	location	NOUN
iajs-2434	119	12	measures	measure	NOUN
iajs-2434	119	13	of	of	ADP
iajs-2434	119	14	an	an	DET
iajs-2434	119	15	inverse	inverse	ADJ
iajs-2434	119	16	rayleigh	rayleigh	NOUN
iajs-2434	119	17	distribution	distribution	NOUN
iajs-2434	119	18	the	the	DET
iajs-2434	119	19	egyptian	egyptian	ADJ
iajs-2434	119	20	statistical	statistical	ADJ
iajs-2434	119	21	journal.1993	journal.1993	PROPN
iajs-2434	119	22	,	,	PUNCT
iajs-2434	119	23	37	37	NUM
iajs-2434	119	24	,	,	PUNCT
iajs-2434	119	25	2	2	NUM
iajs-2434	119	26	,	,	PUNCT
iajs-2434	119	27	295	295	NUM
iajs-2434	119	28	-	-	SYM
iajs-2434	119	29	309	309	NUM
iajs-2434	119	30	.	.	PUNCT
iajs-2434	120	1	3	3	X
iajs-2434	120	2	.	.	X
iajs-2434	120	3	mukherjee	mukherjee	PROPN
iajs-2434	120	4	,	,	PUNCT
iajs-2434	120	5	s.p	s.p	PROPN
iajs-2434	120	6	.	.	PROPN
iajs-2434	120	7	;	;	PUNCT
iajs-2434	120	8	maiti	maiti	PROPN
iajs-2434	120	9	,	,	PUNCT
iajs-2434	120	10	s.s	s.s	PROPN
iajs-2434	120	11	.	.	PROPN
iajs-2434	121	1	a	a	DET
iajs-2434	121	2	percentile	percentile	ADJ
iajs-2434	121	3	estimator	estimator	NOUN
iajs-2434	121	4	of	of	ADP
iajs-2434	121	5	the	the	DET
iajs-2434	121	6	inverse	inverse	NOUN
iajs-2434	121	7	rayleigh	rayleigh	PROPN
iajs-2434	121	8	parameter	parameter	PROPN
iajs-2434	121	9	iapqr	iapqr	PROPN
iajs-2434	121	10	.	.	PUNCT
iajs-2434	122	1	trans.1996	trans.1996	PROPN
iajs-2434	122	2	,	,	PUNCT
iajs-2434	122	3	21	21	NUM
iajs-2434	122	4	,	,	PUNCT
iajs-2434	122	5	63	63	NUM
iajs-2434	122	6	-	-	SYM
iajs-2434	122	7	65	65	NUM
iajs-2434	122	8	.	.	NOUN
iajs-2434	123	1	4	4	X
iajs-2434	123	2	.	.	X
iajs-2434	123	3	abdel	abdel	PROPN
iajs-2434	123	4	-	-	PUNCT
iajs-2434	123	5	menem	menem	PROPN
iajs-2434	123	6	,	,	PUNCT
iajs-2434	123	7	a.a	a.a	PROPN
iajs-2434	123	8	.	.	PROPN
iajs-2434	123	9	estimation	estimation	NOUN
iajs-2434	123	10	and	and	CCONJ
iajs-2434	123	11	prediction	prediction	NOUN
iajs-2434	123	12	for	for	ADP
iajs-2434	123	13	inverse	inverse	NOUN
iajs-2434	123	14	rayleigh	rayleigh	NOUN
iajs-2434	123	15	life	life	PROPN
iajs-2434	123	16	distribution	distribution	NOUN
iajs-2434	123	17	m.sc	m.sc	PROPN
iajs-2434	123	18	.	.	PUNCT
iajs-2434	124	1	thesis	thesis	NOUN
iajs-2434	124	2	faculty	faculty	NOUN
iajs-2434	124	3	of	of	ADP
iajs-2434	124	4	education	education	NOUN
iajs-2434	124	5	,	,	PUNCT
iajs-2434	124	6	ain	ain	PROPN
iajs-2434	124	7	shames	shame	VERB
iajs-2434	124	8	university	university	NOUN
iajs-2434	124	9	,	,	PUNCT
iajs-2434	124	10	2003	2003	NUM
iajs-2434	124	11	.	.	PUNCT
iajs-2434	125	1	5	5	NUM
iajs-2434	125	2	.	.	X
iajs-2434	125	3	el	el	NOUN
iajs-2434	125	4	-	-	PUNCT
iajs-2434	125	5	halbawy	halbawy	PROPN
iajs-2434	125	6	,	,	PUNCT
iajs-2434	125	7	a.a	a.a	PROPN
iajs-2434	125	8	.	.	PROPN
iajs-2434	125	9	;	;	PUNCT
iajs-2434	125	10	abd	abd	PROPN
iajs-2434	125	11	-	-	PUNCT
iajs-2434	125	12	el	el	PROPN
iajs-2434	125	13	-	-	PUNCT
iajs-2434	125	14	monem	monem	ADJ
iajs-2434	125	15	,	,	PUNCT
iajs-2434	125	16	bayesian	bayesian	NOUN
iajs-2434	125	17	estimation	estimation	NOUN
iajs-2434	125	18	and	and	CCONJ
iajs-2434	125	19	prediction	prediction	NOUN
iajs-2434	125	20	for	for	ADP
iajs-2434	125	21	the	the	DET
iajs-2434	125	22	inverse	inverse	NOUN
iajs-2434	125	23	rayleigh	rayleigh	NOUN
iajs-2434	125	24	lifetime	lifetime	NOUN
iajs-2434	125	25	distribution	distribution	NOUN
iajs-2434	125	26	proceeding	proceeding	NOUN
iajs-2434	125	27	of	of	ADP
iajs-2434	125	28	the	the	DET
iajs-2434	125	29	lost	lose	VERB
iajs-2434	125	30	annual	annual	ADJ
iajs-2434	125	31	conference	conference	NOUN
iajs-2434	125	32	of	of	ADP
iajs-2434	125	33	statistics	statistic	NOUN
iajs-2434	125	34	,	,	PUNCT
iajs-2434	125	35	computer	computer	NOUN
iajs-2434	125	36	sciences	science	NOUN
iajs-2434	125	37	and	and	CCONJ
iajs-2434	125	38	operation	operation	NOUN
iajs-2434	125	39	research	research	NOUN
iajs-2434	125	40	,	,	PUNCT
iajs-2434	125	41	issr	issr	PROPN
iajs-2434	125	42	–	–	PUNCT
iajs-2434	125	43	cairo	cairo	PROPN
iajs-2434	125	44	university.2005	university.2005	PROPN
iajs-2434	125	45	,	,	PUNCT
iajs-2434	125	46	45	45	NUM
iajs-2434	125	47	-	-	SYM
iajs-2434	125	48	59	59	NUM
iajs-2434	125	49	.	.	NOUN
iajs-2434	126	1	6	6	NUM
iajs-2434	126	2	.	.	X
iajs-2434	126	3	soliman	soliman	PROPN
iajs-2434	126	4	,	,	PUNCT
iajs-2434	126	5	a.	a.	PROPN
iajs-2434	126	6	;	;	PUNCT
iajs-2434	126	7	essam	essam	PROPN
iajs-2434	126	8	,	,	PUNCT
iajs-2434	126	9	a.	a.	PROPN
iajs-2434	126	10	;	;	PUNCT
iajs-2434	126	11	amin	amin	PROPN
iajs-2434	126	12	,	,	PUNCT
iajs-2434	126	13	e.a	e.a	PROPN
iajs-2434	126	14	.	.	PROPN
iajs-2434	126	15	;	;	PUNCT
iajs-2434	126	16	abd	abd	PROPN
iajs-2434	126	17	-	-	PUNCT
iajs-2434	126	18	elaziz	elaziz	PROPN
iajs-2434	126	19	,	,	PUNCT
iajs-2434	126	20	a.a	a.a	PROPN
iajs-2434	126	21	.	.	PROPN
iajs-2434	126	22	estimation	estimation	NOUN
iajs-2434	126	23	and	and	CCONJ
iajs-2434	126	24	prediction	prediction	NOUN
iajs-2434	126	25	from	from	ADP
iajs-2434	126	26	inverse	inverse	ADJ
iajs-2434	126	27	rayleigh	rayleigh	NOUN
iajs-2434	126	28	distribution	distribution	NOUN
iajs-2434	126	29	based	base	VERB
iajs-2434	126	30	on	on	ADP
iajs-2434	126	31	lower	low	ADJ
iajs-2434	126	32	record	record	NOUN
iajs-2434	126	33	values	value	NOUN
iajs-2434	126	34	applied	apply	VERB
iajs-2434	126	35	mathematical	mathematical	ADJ
iajs-2434	126	36	science.2010	science.2010	PROPN
iajs-2434	126	37	,	,	PUNCT
iajs-2434	126	38	4	4	NUM
iajs-2434	126	39	,	,	PUNCT
iajs-2434	126	40	62	62	NUM
iajs-2434	126	41	,	,	PUNCT
iajs-2434	126	42	3057	3057	NUM
iajs-2434	126	43	-	-	SYM
iajs-2434	126	44	3066	3066	NUM
iajs-2434	126	45	.	.	PUNCT
iajs-2434	127	1	7	7	X
iajs-2434	127	2	.	.	X
iajs-2434	127	3	dey	dey	PROPN
iajs-2434	127	4	,	,	PUNCT
iajs-2434	127	5	s.	s.	PROPN
iajs-2434	127	6	bayesian	bayesian	NOUN
iajs-2434	127	7	estimation	estimation	NOUN
iajs-2434	127	8	of	of	ADP
iajs-2434	127	9	the	the	DET
iajs-2434	127	10	parameter	parameter	NOUN
iajs-2434	127	11	and	and	CCONJ
iajs-2434	127	12	reliability	reliability	NOUN
iajs-2434	127	13	function	function	NOUN
iajs-2434	127	14	of	of	ADP
iajs-2434	127	15	an	an	DET
iajs-2434	127	16	inverse	inverse	ADJ
iajs-2434	127	17	rayleigh	rayleigh	NOUN
iajs-2434	127	18	distribution	distribution	PROPN
iajs-2434	127	19	malaysian	malaysian	PROPN
iajs-2434	127	20	journal	journal	PROPN
iajs-2434	127	21	of	of	ADP
iajs-2434	127	22	mathematical	mathematical	ADJ
iajs-2434	127	23	sciences.2012	sciences.2012	PROPN
iajs-2434	127	24	,	,	PUNCT
iajs-2434	127	25	6	6	NUM
iajs-2434	127	26	,	,	PUNCT
iajs-2434	127	27	1	1	NUM
iajs-2434	127	28	,	,	PUNCT
iajs-2434	127	29	113124	113124	NUM
iajs-2434	127	30	.	.	PUNCT
iajs-2434	128	1	8	8	NUM
iajs-2434	128	2	.	.	X
iajs-2434	128	3	ali	ali	PROPN
iajs-2434	128	4	,	,	PUNCT
iajs-2434	128	5	m.j	m.j	PROPN
iajs-2434	128	6	.	.	PROPN
iajs-2434	128	7	;	;	PUNCT
iajs-2434	128	8	gorgeees	gorgeees	PROPN
iajs-2434	128	9	,	,	PUNCT
iajs-2434	128	10	h.m	h.m	PROPN
iajs-2434	128	11	.	.	PROPN
iajs-2434	128	12	;	;	PUNCT
iajs-2434	128	13	hussian	hussian	PROPN
iajs-2434	128	14	,	,	PUNCT
iajs-2434	128	15	a.a	a.a	PROPN
iajs-2434	128	16	.	.	PROPN
iajs-2434	129	1	the	the	DET
iajs-2434	129	2	comparison	comparison	NOUN
iajs-2434	129	3	between	between	ADP
iajs-2434	129	4	standard	standard	ADJ
iajs-2434	129	5	bayes	bayes	NOUN
iajs-2434	129	6	estimators	estimator	NOUN
iajs-2434	129	7	of	of	ADP
iajs-2434	129	8	the	the	DET
iajs-2434	129	9	reliability	reliability	NOUN
iajs-2434	129	10	function	function	NOUN
iajs-2434	129	11	of	of	ADP
iajs-2434	129	12	exponential	exponential	ADJ
iajs-2434	129	13	distribution	distribution	NOUN
iajs-2434	129	14	ibn	ibn	PROPN
iajs-2434	129	15	al	al	PROPN
iajs-2434	129	16	-	-	PUNCT
iajs-2434	129	17	haitham	haitham	PROPN
iajs-2434	129	18	jour	jour	X
iajs-2434	129	19	.	.	PROPN
iajs-2434	129	20	for	for	ADP
iajs-2434	129	21	pure	pure	ADJ
iajs-2434	129	22	&	&	CCONJ
iajs-2434	129	23	appl	appl	PROPN
iajs-2434	129	24	.	.	PUNCT
iajs-2434	130	1	sci.2018	sci.2018	PROPN
iajs-2434	130	2	,	,	PUNCT
iajs-2434	130	3	31	31	NUM
iajs-2434	130	4	,	,	PUNCT
iajs-2434	130	5	3	3	NUM
iajs-2434	130	6	,	,	PUNCT
iajs-2434	130	7	135	135	NUM
iajs-2434	130	8	-	-	SYM
iajs-2434	130	9	142	142	NUM
iajs-2434	130	10	.	.	PUNCT