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

Table 9

Relative efficiency of Gini index for power (𝛼=3) distribution.

𝑟	𝑚	MSE (RSS)	MSE (SRS)	MSE (SYS)	𝐸(1)	𝐸(2)	𝐸(3)
2	3	0.03002883	0.05904002	0.006465061	1.966111	9.132168	4.644787
	4	0.01837878	0.04518542	0.002769992	2.458565	16.312473	6.634958
	5	0.01202134	0.03688425	0.001390412	3.068232	26.527569	8.645883
	6	0.008600471	0.02950916	0.000838656	3.431109	35.186250	10.255064
5	3	0.01183113	0.02385245	0.00263158	2.016075	9.063927	4.495828
	4	0.007109205	0.01767874	0.001112017	2.486739	15.897904	6.393072
	5	0.004782672	0.01397249	0.0005790662	2.921482	24.129348	8.259284
	6	0.003415356	0.01160659	0.0003343554	3.398354	34.713332	10.214748
20	3	0.003007737	0.005933085	0.0006660064	1.972607	8.908450	4.516078
	4	0.001856484	0.004438954	0.0002774993	2.391054	15.996271	6.690049
	5	0.001176903	0.003597289	0.0001420534	3.056573	25.323498	8.284934
	6	0.0008649264	0.00293501	8.396861𝑒−05	3.393364	34.953657	10.300592
100	3	0.0006040928	0.001167984	0.0001285668	1.933451	9.084647	4.698669
	4	0.0003599259	0.0008980578	5.426289𝑒−05	2.495118	16.550128	6.633003
	5	0.0002358945	0.0007081798	2.842227𝑒−05	3.002103	24.916370	8.299636
	6	0.000173568	0.0005906876	1.640179𝑒−05	3.403206	36.013606	10.582260
200	3	0.0002970297	0.0005835807	6.760029𝑒−05	1.964722	8.632814	4.393912
	4	0.0001840207	0.0004393907	2.766382𝑒−05	2.387724	15.883226	6.652035
	5	0.0001199216	0.0003552514	1.421686𝑒−05	2.962364	24.988035	8.435168
	6	8.84773𝑒−05	0.0002953183	8.21482𝑒−06	3.337786	35.949455	10.770449
500	3	0.0001217598	0.0002407522	2.666487𝑒−05	1.977272	9.028816	4.566300
	4	7.261201𝑒−05	0.0001784493	1.124082𝑒−05	2.457572	15.875114	6.459672
	5	4.8425𝑒−05	0.0001436364	5.589331𝑒−06	2.966163	25.698317	8.663828
	6	3.399731𝑒−05	0.0001184066	3.256773𝑒−06	3.482823	36.357032	10.438956