Table 3 Comparison of percent relative efficiency (PRE) between the proposed estimator \(\hat{\pi }\) and \(\hat{\pi }_{ST}\) (Singh) estimator.

From: A two-stage randomized response technique for simultaneous estimation of sensitivity and truthfulness

		\(p=.2\)				\(\pi\)
\(p_o\)	T	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8
0.6	0.2	344.55	335.26	328.94	325.23	324.00	325.26	329.22	336.28
	0.4	344.84	335.58	329.15	325.30	324.00	325.38	329.81	337.96
	0.6	345.15	335.92	329.38	325.38	324.00	325.52	330.54	340.17
	0.8	345.46	336.28	329.63	325.47	324.00	325.69	331.48	343.22
0.7	0.2	798.44	739.93	703.14	682.64	676.00	682.83	704.74	746.07
	0.4	800.39	741.85	704.32	683.03	676.00	683.46	708.05	756.35
	0.6	802.41	743.89	705.61	683.46	676.00	684.21	712.22	770.16
	0.8	804.50	746.07	707.03	683.94	676.00	685.14	717.65	789.72
0.8	0.2	1608.08	1373.57	1244.02	1177.00	1156.00	1177.59	1249.41	1396.43
	0.4	1616.61	1380.69	1248.00	1178.22	1156.00	1179.59	1260.61	1435.59
	0.6	1625.47	1388.30	1252.36	1179.59	1156.00	1182.00	1274.88	1489.98
	0.8	1634.67	1396.43	1257.15	1181.15	1156.00	1184.97	1293.64	1570.65
		\(p=.3\)
0.6	0.2	231.71	224.06	218.99	216.07	215.11	216.11	219.30	225.19
	0.4	232.04	224.41	219.22	216.15	215.11	216.24	219.97	227.24
	0.6	232.38	224.78	219.47	216.24	215.11	216.40	220.90	230.33
	0.8	232.74	225.19	219.76	216.34	215.11	216.62	222.26	235.54
0.7	0.2	450.54	413.00	390.23	377.78	373.78	377.94	391.56	418.31
	0.4	452.25	414.63	391.21	378.10	373.78	378.47	394.50	428.12
	0.6	454.05	416.39	392.31	378.47	373.78	379.16	398.61	443.48
	0.8	455.93	418.31	393.57	378.91	373.78	380.09	404.75	470.92
0.8	0.2	818.43	689.92	621.56	586.82	576.00	587.24	625.39	706.83
	0.4	824.85	695.05	624.37	587.68	576.00	588.69	633.90	739.12
	0.6	831.62	700.66	627.55	588.69	576.00	590.58	645.97	792.57
	0.8	838.76	706.83	631.18	589.89	576.00	593.13	664.39	898.12
		\(p=.4\)
0.6	0.2	183.78	176.77	172.32	169.82	169.00	169.85	172.63	177.97
	0.4	184.14	177.13	172.55	169.89	169.00	169.98	173.34	180.28
	0.6	184.52	177.53	172.81	169.98	169.00	170.16	174.39	184.20
	0.8	184.92	177.97	173.11	170.09	169.00	170.41	176.12	192.30
0.7	0.2	312.90	284.25	267.66	258.82	256.00	258.94	268.78	288.91
	0.4	314.47	285.65	268.48	259.08	256.00	259.39	271.36	298.18
	0.6	316.12	287.20	269.42	259.39	256.00	260.01	275.24	314.72
	0.8	317.86	288.91	270.52	259.78	256.00	260.89	281.76	352.59
0.8	0.2	518.87	433.01	389.38	367.70	361.00	368.00	392.20	446.00
	0.4	523.99	436.88	391.44	368.32	361.00	369.08	398.76	472.93
	0.6	529.46	441.18	393.83	369.08	361.00	370.55	408.82	524.83
	0.8	535.30	446.00	396.62	370.00	361.00	372.68	426.19	666.47

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Table 3 Comparison of percent relative efficiency (PRE) between the proposed estimator \(\hat{\pi }\) and \(\hat{\pi }_{ST}\) (Singh) estimator.

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