Estimates of Inequality Indices Based on Simple Random, Ranked Set, and Systematic Sampling

Table 7

Relative efficiency of Gini index for exponential distribution.

𝑟	𝑚	MSE (RSS)	MSE (SRS)	MSE (SYS)	𝐸(1)	𝐸(2)	𝐸(3)
2	3	0.02498093	0.04457217	0.00910646	1.784248	4.894566	2.743210
	4	0.01530442	0.03360818	0.004001166	2.195979	8.399597	3.824990
	5	0.01046073	0.02692506	0.002174010	2.573918	12.384975	4.811721
	6	0.007608975	0.02218654	0.001295014	2.915837	17.132278	5.875593
5	3	0.01002222	0.01747601	0.003524347	1.743726	4.958652	2.843710
	4	0.00611229	0.01333912	0.001584625	2.182345	8.417840	3.857247
	5	0.004159828	0.01100573	0.0008643665	2.645717	12.732712	4.812574
	6	0.003042587	0.00911744	0.0005193771	2.996608	17.554567	5.858146
20	3	0.002467123	0.00450777	0.0009057722	1.827136	4.976715	2.723779
	4	0.001525546	0.003313244	0.0004123536	2.171842	8.034958	3.699606
	5	0.001024757	0.002690909	0.0002184094	2.625900	12.320482	4.691909
	6	0.0007222134	0.002298709	0.0001300434	3.182866	17.676476	5.553634
100	3	0.0005033155	0.0008831595	0.0001777265	1.754684	4.969205	2.831967
	4	0.0003078470	0.0006709811	8.14811𝑒−05	2.179593	8.234807	3.778140
	5	0.0002099437	0.0005397776	4.331869𝑒−05	2.571059	12.460617	4.846492
	6	0.0001524544	0.0004400118	2.622736𝑒−05	2.886186	16.776824	5.812800
200	3	0.0002471209	0.0004459992	8.781071𝑒−05	1.804781	5.079098	2.814246
	4	0.000153431	0.0003294056	4.053465𝑒−05	2.14693	8.126519	3.785181
	5	0.0001031339	0.0002670593	2.214463𝑒−05	2.589443	12.059777	4.657287
	6	7.600503𝑒−05	0.0002178877	1.308801𝑒−05	2.866754	16.647886	5.807226
500	3	0.0001002982	0.0001764347	3.693063𝑒−05	1.759102	4.777463	2.715854
	4	5.943145𝑒−05	0.0001320398	1.595697𝑒−05	2.221716	8.274741	3.724482
	5	4.208938𝑒−05	0.0001076813	8.8025𝑒−06	2.558395	12.233036	4.781526
	6	3.117683𝑒−05	9.065143𝑒−05	5.230148𝑒−06	2.907654	17.332479	5.960984