Table 6 PRE of the proposed estimator \(\hat{\pi }_{S}\) with \(\hat{\pi }_{TS}\)¹⁴ estimator in stratified random sampling using an optimal allocation.

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

\(\pi _{S}\)	\(\pi _{S1}\)	\(\pi _{S2}\)	\(w_{1}\)	\(w_{2}\)	\(p_1\)	0.6	0.7	0.8	0.6	0.7	0.8	0.6	0.7	0.8
					\(p_2\)	0.65	0.75	0.85	0.65	0.75	0.85	0.65	0.75	0.85
					T
0.24	0.3	0.2	0.4	0.6	0.3	604.00	275.94	179.04	910.34	355.99	204.08	1297.64	445.88	230.14
0.32	0.5	0.2	0.4	0.6		591.27	270.69	175.66	882.60	346.04	198.94	1241.77	428.85	222.83
0.40	0.7	0.2	0.4	0.6		599.90	277.00	179.53	906.35	357.59	204.61	1293.17	447.81	230.65
0.39	0.3	0.45	0.4	0.6	0.5	599.98	263.57	167.62	861.44	325.34	185.64	1150.79	387.62	203.23
0.47	0.5	0.45	0.4	0.6		584.10	258.44	164.85	829.52	316.11	181.61	1092.81	372.91	197.76
0.55	0.7	0.45	0.4	0.6		591.61	264.27	167.68	848.50	325.26	185.36	1127.17	385.73	202.48
0.60	0.3	0.8	0.4	0.6	0.7	671.96	368.39	203.08	1506.36	480.58	231.13	2193.57	600.01	259.49
0.68	0.5	0.8	0.4	0.6		656.98	363.98	198.35	1484.53	466.76	223.55	2094.97	570.30	248.41
0.76	0.7	0.8	0.4	0.6		671.97	401.03	208.47	1771.85	526.79	237.10	2628.54	656.38	265.65
0.26	0.3	0.2	0.6	0.4	0.3	774.70	309.36	190.95	1155.14	396.38	217.46	1626.21	493.03	245.10
0.38	0.5	0.2	0.6	0.4		749.84	297.90	183.57	1095.12	374.63	206.41	1500.55	456.20	229.58
0.50	0.7	0.2	0.6	0.4		789.01	315.71	192.98	1181.21	404.78	219.69	1663.49	502.85	247.41
0.36	0.3	0.45	0.6	0.4	0.5	785.73	306.44	186.04	1148.95	385.25	209.13	1572.51	468.53	232.49
0.48	0.5	0.45	0.6	0.4		762.75	295.97	179.34	1089.70	364.69	199.14	1446.53	433.70	218.59
0.60	0.7	0.45	0.6	0.4		818.43	317.93	188.85	1199.84	398.47	211.77	1630.11	481.10	234.64
0.50	0.3	0.8	0.6	0.4	0.7	947.50	352.94	202.89	1433.73	453.18	230.83	2021.01	561.37	259.56
0.62	0.5	0.8	0.6	0.4		948.63	344.70	194.75	1393.34	430.44	217.92	1875.07	515.78	240.77
0.74	0.7	0.8	0.6	0.4		1155.08	404.22	213.24	1807.78	521.09	242.26	2556.02	640.53	271.46

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Table 6 PRE of the proposed estimator \(\hat{\pi }_{S}\) with \(\hat{\pi }_{TS}\)¹⁴ estimator in stratified random sampling using an optimal allocation.

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