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 4 Monte Carlo RMSEs and bias values of the entropy estimators VE_{(
m,n
)} and AE_{(
m,n
)} for the uniform distribution with H(f) = 0 and exponential distribution with H(f) = 1 using DRSS

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	Uniform distribution and $H (f) = 0$				Exponential distribution and $H (f) = 1$
		VE _(m,n)		AE _(m,n)		VE _(m,n)		AE _(m,n)
		Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
10	1	−0.327408	0.369593	−0.267924	0.318205	−0.365854	0.425279	−0.305667	0.379121
	2	−0.260621	0.278731	−0.145388	0.176159	−0.288898	0.340618	−0.173991	0.251460
	3	−0.296104	0.306116	−0.122180	0.144286	−0.300393	0.351750	−0.128545	0.223802
	4	−0.346305	0.352712	−0.115995	0.134276	−0.322839	0.377437	−0.089495	0.215854
	5	−0.404121	0.409902	−0.116805	0.135411	−0.335248	0.399189	−0.047170	0.219634
20	1	−0.308453	0.329353	−0.279902	0.302719	−0.329105	0.363241	−0.298237	0.335475
	2	−0.189231	0.202666	−0.132076	0.151177	−0.204908	0.240316	−0.150759	0.196279
	3	−0.182095	0.191163	−0.095961	0.112229	−0.191216	0.228320	−0.104346	0.163293
	4	−0.197693	0.204342	−0.082268	0.096978	−0.190904	0.229986	−0.075338	0.179771
	5	−0.220876	0.225845	−0.077708	0.091093	−0.197900	0.239789	−0.052175	0.145269
	6	−0.247733	0.251580	−0.075071	0.086966	−0.207032	0.251002	−0.026183	0.146832
	7	−0.275808	0.278919	−0.074331	0.085055	−0.209883	0.258152	−0.012044	0.152682
	8	−0.303823	0.306608	−0.073793	0.084202	−0.218701	0.271560	0.014201	0.161180
	9	−0.333903	0.336495	−0.075306	0.086127	−0.223692	0.278728	0.035069	0.173654
	10	−0.363272	0.365731	−0.075514	0.086480	−0.228126	0.290431	0.061574	0.189857
30	1	−0.298092	0.312767	−0.278830	0.293698	−0.308011	0.331033	−0.289677	0.314515
	2	−0.170745	0.180210	−0.133715	0.146379	−0.182416	0.207785	−0.143418	0.174632
	3	−0.146113	0.153646	−0.088998	0.100564	−0.152039	0.180708	−0.094799	0.136371
	4	−0.149143	0.154886	−0.072297	0.083848	−0.145325	0.176699	−0.071094	0.123270
	5	−0.159888	0.164564	−0.063874	0.074562	−0.146632	0.179028	−0.049250	0.114227
	6	−0.174419	0.178204	−0.060394	0.070784	−0.149443	0.184598	−0.030887	0.113500
	7	−0.191854	0.194940	−0.058041	0.067650	−0.150245	0.188158	−0.046556	0.115023
	8	−0.209886	0.212509	−0.056421	0.065369	−0.153441	0.194332	−0.001239	0.120306
	9	−0.229010	0.231261	−0.056053	0.064628	−0.157250	0.199936	0.012716	0.124585
	10	−0.248006	0.249993	−0.056843	0.064868	−0.162854	0.208891	0.029477	0.133242
	11	−0.267506	0.269188	−0.056931	0.064430	−0.163540	0.213175	0.045951	0.145582
	12	−0.287408	0.289018	−0.056982	0.064673	−0.167660	0.221482	0.063602	0.155340
	13	−0.307160	0.308699	−0.058363	0.066130	−0.171024	0.225764	0.079779	0.169499
	14	−0.327370	0.328890	−0.058038	0.065797	−0.170880	0.232977	0.096359	0.182124
	15	−0.346997	0.348439	−0.059523	0.067623	−0.169873	0.235173	0.115563	0.198755

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