Goodness-of-fit testing for the inverse Gaussian distribution based on new entropy estimation using ranked set sampling and double ranked set sampling

Al-Omari, Amer Ibrahim; Haq, Abdul

doi:10.1186/2193-2697-1-8

Environmental Systems Research

Table 2 Monte Carlo RMSEs and bias values of the entropy estimators VE_{(
m,n
)} and AE_{(
m,n
)} for the exponential distribution, H(f) = 1

From: Goodness-of-fit testing for the inverse Gaussian distribution based on new entropy estimation using ranked set sampling and double ranked set sampling

n	m	SRS				RSS
		VE _(m,n)		AE _(m,n)		VE _(m,n)		AE _(m,n)
		Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
10	1	−0.552032	0.677001	−0.495449	0.631471	−0.430553	0.505229	−0.376361	0.461201
	2	−0.442683	0.571820	−0.323532	0.483573	−0.337494	0.404667	−0.220406	0.315220
	3	−0.435444	0.561640	−0.265713	0.443276	−0.332760	0.401125	−0.159787	0.276197
	4	−0.451545	0.575390	−0.221689	0.424404	−0.348029	0.420617	−0.121584	0.266664
	5	−0.469437	0.597761	−0.179844	0.413541	−0.366628	0.445977	−0.080667	0.266812
20	1	−0.414064	0.490107	−0.384516	0.464796	−0.357765	0.398661	−0.333540	0.376843
	2	−0.285717	0.376086	−0.232518	0.338830	−0.234959	0.280262	−0.176512	0.232710
	3	−0.260773	0.351341	−0.175461	0.298406	−0.213397	0.261261	−0.125059	0.194705
	4	−0.256116	0.352810	0.141143	0.279706	−0.210620	0.259248	−0.098056	0.179990
	5	−0.262412	0.358638	0.118697	0.271887	−0.214122	0.265246	−0.072456	0.172661
	6	−0.265650	0.360325	0.090043	0.263318	−0.218028	0.272315	−0.048075	0.168086
	7	−0.266934	0.365008	−0.067175	0.260090	−0.224596	0.282196	−0.023128	0.173677
	8	−0.273952	0.377519	−0.041928	0.258647	−0.232629	0.293062	−0.000531	0.176806
	9	−0.280123	0.381968	−0.021108	0.262708	−0.236125	0.302083	0.027269	0.190739
	10	−0.285183	0.391290	0.004497	0.267634	−0.238413	0.310922	0.044912	0.203657
30	1	−0.367058	0.423423	−0.346283	0.406311	−0.332526	0.361491	−0.313657	0.343784
	2	−0.233677	0.306086	−0.198867	0.280012	−0.203455	0.236001	−0.163180	0.203230
	3	−0.202277	0.281503	−0.145618	0.241162	−0.170859	0.207468	−0.111717	0.161754
	4	−0.194424	0.275072	−0.115163	0.224526	−0.160246	0.199410	−0.084854	0.145930
	5	−0.191705	0.272356	−0.095073	0.217468	−0.159714	0.200465	−0.059819	0.134539
	6	−0.186870	0.272196	−0.070590	0.208597	−0.158702	0.202869	−0.043778	0.132887
	7	−0.191094	0.275374	−0.058550	0.205261	−0.161705	0.206226	−0.027194	0.130283
	8	−0.195662	0.280589	−0.036080	0.200329	−0.164468	0.212265	−0.010631	0.136358
	9	−0.196983	0.282040	−0.021144	0.202056	−0.165511	0.217222	−0.006685	0.138626
	10	−0.197171	0.283394	−0.005890	0.204787	−0.167152	0.220237	0.024904	0.145306
	11	−0.198853	0.286241	0.008492	0.207709	−0.173076	0.229318	0.039837	0.154215
	12	−0.204089	0.293653	0.022622	0.213445	−0.171555	0.232740	0.055108	0.163320
	13	−0.202908	0.298108	0.049154	0.220522	−0.176996	0.240454	0.070977	0.176787
	14	−0.205700	0.300842	0.061987	0.226574	−0.176922	0.244541	0.093001	0.193377
	15	−0.210699	0.305809	0.081431	0.238902	−0.177959	0.248760	0.109754	0.205539

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