Table 1 Comparison of percent relative efficiency (PRE) between the proposed estimator \(\hat{\pi }\) and \(\hat{\pi }_{H}\) (Huang) estimator.

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

p_o	T	\(p=.6\)				\(\pi\)
p_o	T	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8
0.2	0.2	344.69	335.42	329.04	325.26	324.00	325.32	329.50	337.07
	0.4	345.15	335.92	329.38	325.38	324.00	325.52	330.54	340.17
	0.6	345.62	336.47	329.76	325.52	324.00	325.79	332.06	345.22
	0.8	346.11	337.07	330.20	325.69	324.00	326.17	334.52	354.83
0.5	0.2	1145.63	1024.62	952.08	912.68	900.00	913.24	957.03	1044.64
	0.4	1152.08	1030.65	955.71	913.85	900.00	915.25	968.41	1084.09
	0.6	1158.88	1037.29	959.88	915.25	900.00	918.00	985.46	1153.13
	0.8	1166.05	1044.64	964.72	916.98	900.00	921.95	1013.83	1305.00
0.8	0.2	2256.96	1814.81	1590.13	1478.50	1444.00	1480.04	1604.64	1881.72
	0.4	2283.33	1834.72	1600.75	1481.72	1444.00	1485.60	1638.44	2020.38
	0.6	2311.47	1856.88	1613.04	1485.60	1444.00	1493.19	1690.26	2287.64
	0.8	2341.55	1881.72	1627.42	1490.37	1444.00	1504.17	1779.71	3017.00
		p=.7
0.2	0.2	183.74	176.73	172.29	169.81	169.00	169.84	172.56	177.74
	0.4	184.05	177.04	172.49	169.87	169.00	169.95	173.14	179.60
	0.6	184.38	177.38	172.71	169.95	169.00	170.09	173.94	182.45
	0.8	184.72	177.74	172.95	170.04	169.00	170.27	175.14	187.40
0.5	0.2	402.85	352.30	324.81	310.68	306.25	310.85	326.36	359.04
	0.4	405.33	354.35	325.95	311.03	306.25	311.44	329.81	371.83
	0.6	407.95	356.59	327.24	311.44	306.25	312.21	334.68	392.79
	0.8	410.71	359.04	328.71	311.93	306.25	313.25	342.09	433.46
0.8	0.2	874.33	639.69	541.62	497.19	484.00	497.70	546.73	666.43
	0.4	888.25	647.69	545.37	498.25	484.00	499.50	558.24	720.63
	0.6	903.21	656.55	549.64	499.50	484.00	501.84	574.92	820.63
	0.8	919.32	666.43	554.54	500.99	484.00	505.02	601.28	1067.03
		p=.8
0.2	0.2	140.62	134.31	130.82	129.01	128.44	129.03	130.96	134.92
	0.4	140.85	134.50	130.92	129.04	128.44	129.08	131.26	135.98
	0.6	141.09	134.70	131.04	129.08	128.44	129.14	131.65	137.44
	0.8	141.34	134.92	131.17	129.12	128.44	129.22	132.15	139.61
0.5	0.2	232.93	201.86	187.05	179.93	177.78	180.00	187.63	204.64
	0.4	234.18	202.72	187.48	180.06	177.78	180.20	188.86	209.51
	0.6	235.49	203.64	187.96	180.20	177.78	180.45	190.44	216.53
	0.8	236.86	204.64	188.48	180.37	177.78	180.76	192.55	227.56
0.8	0.2	399.40	296.59	257.26	240.11	235.11	240.25	258.72	304.55
	0.4	404.25	299.03	258.34	240.41	235.11	240.74	261.81	319.04
	0.6	409.41	301.67	259.53	240.74	235.11	241.33	265.82	341.19
	0.8	414.89	304.55	260.85	241.12	235.11	242.05	271.26	379.21

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Table 1 Comparison of percent relative efficiency (PRE) between the proposed estimator \(\hat{\pi }\) and \(\hat{\pi }_{H}\) (Huang) estimator.

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