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

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	−0.519826	0.569537	−0.046482	0.521035	−0.396308	0.443439	−0.343522	0.396739
	2	−0.415135	0.452358	−0.298609	0.350332	−0.304078	0.329233	−0.189664	0.228762
	3	−0.422613	0.453818	−0.249056	0.298944	−0.327681	0.343991	−0.154894	0.186380
	4	−0.458940	0.487054	−0.229082	0.281422	−0.371538	0.383103	−0.143218	0.171767
	5	−0.502063	0.527918	−0.215077	0.270468	−0.425903	0.436521	−0.137821	0.168029
20	1	−0.393900	0.418346	−0.366867	0.392622	−0.343340	0.365754	−0.314244	0.338695
	2	−0.271880	0.290818	−0.212993	0.236696	−0.217937	0.233026	−0.162729	0.183187
	3	−0.253931	0.270200	−0.168961	0.192998	−0.205321	0.216879	−0.117939	0.136570
	4	−0.260596	0.274678	−0.144016	0.167779	−0.214042	0.222524	−0.100304	0.118284
	5	−0.276800	0.288985	−0.133179	0.157805	−0.235141	0.242179	−0.091608	0.108584
	6	−0.299321	0.310256	−0.125960	0.150733	−0.258899	0.264554	−0.085981	0.101365
	7	−0.322084	0.332301	−0.121244	0.146386	−0.285310	0.290156	−0.084733	0.099613
	8	−0.348254	0.357901	−0.118562	0.144786	−0.314138	0.318471	−0.083482	0.098588
	9	−0.374620	0.383864	−0.116399	0.143986	−0.343410	0.347711	−0.083926	0.099430
	10	−0.402840	0.411741	−0.117057	0.145063	−0.371780	0.375737	−0.848235	0.101014
30	1	−0.352853	0.368369	−0.334631	0.351096	−0.319230	0.333509	−0.300423	0.316118
	2	−0.223356	0.235685	−0.184969	0.199765	−0.190866	0.201625	−0.152577	0.165665
	3	−0.197719	0.208362	−0.141411	0.156683	−0.165182	0.173360	−0.106329	0.119047
	4	−0.196240	0.205882	−0.118803	0.133958	−0.162899	0.169841	−0.087046	0.099566
	5	−0.202003	0.210395	−0.105711	0.120861	−0.172441	0.178293	−0.078599	0.088072
	6	−0.213804	0.221385	−0.097719	0.113216	−0.185622	0.190458	−0.069898	0.081972
	7	−0.226688	0.233521	−0.092957	0.109089	−0.200036	0.204048	−0.066053	0.077716
	8	−0.242599	0.248992	−0.089259	0.105818	−0.217704	0.221309	−0.064713	0.076188
	9	−0.259471	0.265356	−0.087074	0.103535	−0.235661	0.238850	−0.062931	0.073734
	10	−0.276934	0.282548	−0.085151	0.102071	−0.254437	0.257257	−0.062044	0.072402
	11	−0.295302	0.300725	−0.841357	0.101314	−0.273700	0.276336	−0.062243	0.072977
	12	−0.313803	0.319255	−0.083206	0.102002	−0.293398	0.295911	−0.062262	0.072981
	13	−0.332279	0.337432	−0.082858	0.101944	−0.311978	0.341101	−0.063754	0.074987
	14	−0.351090	0.356205	−0.082540	0.101854	−0.332096	0.334518	−0.063579	0.075100
	15	−0.370555	0.375518	−0.082665	0.102618	−0.352077	0.354327	−0.064127	0.075825

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