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

Table 13

Relative efficiency of absolute Lorenz index for pareto (𝛼=3, 𝑥₀=200) distribution.

𝑟	𝑚	MSE (RSS)	MSE (SRS)	MSE (SYS)	𝐸(1)	𝐸(2)	𝐸(3)
2	3	20.70694	28.60494	10.57485	1.381418	2.704997	1.958131
	4	13.5872	21.77554	5.390407	1.602651	4.039684	2.520626
	5	9.815137	17.37329	3.06463	1.770051	5.668968	3.202715
	6	7.333079	14.3627	1.935963	1.958618	7.418892	3.787820
5	3	8.490195	11.32587	4.191259	1.333994	2.702260	2.025691
	4	5.523156	8.495127	2.138295	1.538093	3.972851	2.582972
	5	3.839579	6.901874	1.21959	1.79756	5.659176	3.148254
	6	2.848677	5.687296	0.7867597	1.996469	7.228759	3.620771
20	3	2.050789	2.857925	1.037954	1.393574	2.753422	1.975800
	4	1.377661	2.149993	0.521389	1.560612	4.123587	2.642290
	5	0.9706388	1.714577	0.301321	1.766442	5.690201	3.221278
	6	0.7303821	1.413525	0.1940954	1.935322	7.282630	3.763006
100	3	0.4120384	0.5679051	0.2109544	1.378282	2.692075	1.953211
	4	0.270179	0.4210431	0.1080168	1.558386	3.897941	2.501268
	5	0.1956007	0.3382184	0.06211348	1.729127	5.445169	3.149086
	6	0.1465505	0.2881033	0.03872126	1.965897	7.440442	3.784755
200	3	0.2098861	0.2912766	0.1067612	1.387785	2.728300	1.965940
	4	0.1389657	0.2102593	0.05198104	1.513031	4.044923	2.673392
	5	0.1003489	0.1699745	0.03067446	1.693835	5.541239	3.271415
	6	0.07082068	0.1436694	0.01940810	2.028637	7.402548	3.649027
500	3	0.08326179	0.1144187	0.04192018	1.374205	2.729442	1.986198
	4	0.0548825	0.08290751	0.02124204	1.510636	3.902992	2.583674
	5	0.03854217	0.0686116	0.01242014	1.780170	5.524221	3.103199
	6	0.02853415	0.05816632	0.007684862	2.038481	7.568948	3.713033