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

Table 10

Relative efficiency of Bonferroni index for rectangular (𝜃=3) distribution.

𝑟	𝑚	MSE (RSS)	MSE (SRS)	MSE (SYS)	𝐸(1)	𝐸(2)	𝐸(3)
2	3	0.06202481	0.1235527	0.01377850	1.991989	8.967065	4.501565
	4	0.0381469	0.09533465	0.005916627	2.499146	16.113007	6.447407
	5	0.02535770	0.07558111	0.002995199	2.980598	25.234086	8.466115
	6	0.01791203	0.06181676	0.001748279	3.451131	35.358636	10.245521
5	3	0.02490822	0.05036193	0.005549141	2.0219	9.075626	4.488662
	4	0.01489808	0.03685433	0.002358322	2.473765	15.627353	6.317237
	5	0.00982462	0.03053955	0.001206127	3.108471	25.320344	8.145593
	6	0.007220886	0.02487922	0.0006952421	3.445452	35.784973	10.386146
20	3	0.006252341	0.01245597	0.001364699	1.992209	9.127265	4.581480
	4	0.003685856	0.009230949	0.0005877362	2.504425	15.705939	6.271276
	5	0.002550649	0.007501943	0.0002866664	2.941190	26.169593	8.897621
	6	0.001808095	0.00619635	0.0001755058	3.427005	35.305671	10.302195
100	3	0.001249233	0.002446855	0.0002789078	1.958686	8.772989	4.479018
	4	0.0007403018	0.001914464	0.0001151496	2.586059	16.625885	6.429044
	5	0.000504336	0.001465721	6.01177𝑒−05	2.906238	24.380856	8.389143
	6	0.0003529966	0.001248915	3.414360𝑒−05	3.538037	36.578305	10.338588
200	3	0.0006307183	0.001248089	0.0001376957	1.978838	9.064110	4.580523
	4	0.0003722346	0.0009302265	5.962156𝑒−05	2.499033	15.602183	6.243289
	5	0.0002493340	0.0007560325	2.945604𝑒−05	3.032207	25.666468	8.464614
	6	0.0001767726	0.000618749	1.745216𝑒−05	3.500253	35.454007	10.128981
500	3	0.0002467436	0.0005050265	5.529099𝑒−05	2.046767	9.133975	4.462637
	4	0.0001511701	0.0003785248	2.356102𝑒−05	2.503966	16.065722	6.416110
	5	9.98555𝑒−05	0.0002998347	1.208355𝑒−05	3.002686	24.813461	8.263755
	6	7.085566𝑒−05	0.000252477	6.991167𝑒−06	3.563258	36.113713	10.135026