Table 4 Percent Relative Error (PRE) of proposed estimator \(\hat{T}\) relative to \(\hat{T}_{ST}\) (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

289.53

251.10

226.36

209.09

196.36

186.59

178.85

172.57

 

0.4

312.27

280.91

257.83

240.14

226.15

214.80

205.41

197.52

 

0.6

321.25

293.66

271.90

254.29

239.75

227.54

217.14

208.18

 

0.8

326.14

300.75

279.71

261.97

246.83

233.75

222.33

212.28

0.7

0.2

525.78

395.40

328.34

287.49

260.00

240.23

225.33

213.70

 

0.4

628.77

499.27

421.84

370.33

333.59

306.07

284.68

267.58

 

0.6

676.00

552.68

472.35

415.88

374.00

341.71

316.06

295.18

 

0.8

703.66

585.49

503.71

443.75

397.92

361.73

332.45

308.26

0.8

0.2

770.67

511.94

401.06

339.46

300.26

273.12

253.22

238.00

 

0.4

1038.94

721.70

567.32

476.00

415.66

372.82

340.83

316.03

 

0.6

1186.49

850.31

672.66

562.79

488.13

434.09

393.16

361.10

 

0.8

1281.99

938.40

745.29

621.57

535.53

472.23

423.71

385.33

  

\(p=.3\)

0.6

0.2

193.38

169.80

155.98

146.90

140.48

135.70

132.01

129.06

 

0.4

210.46

189.92

175.70

165.27

157.29

150.99

145.90

141.69

 

0.6

217.84

199.66

185.80

174.89

166.07

158.80

152.71

147.52

 

0.8

222.09

205.54

191.97

180.66

171.08

162.86

155.74

149.50

0.7

0.2

296.71

230.44

198.27

179.27

166.72

157.82

151.18

146.03

 

0.4

357.97

287.45

247.08

220.94

202.62

189.08

178.66

170.39

 

0.6

388.78

320.15

276.53

246.35

224.24

207.33

193.99

183.19

 

0.8

407.96

341.92

296.44

263.21

237.88

217.91

201.78

188.48

0.8

0.2

399.44

278.87

228.73

201.25

183.91

171.96

163.23

156.58

 

0.4

540.21

383.22

308.80

265.37

236.91

216.82

201.88

190.33

 

0.6

624.82

453.41

364.14

309.38

272.36

245.66

225.50

209.73

 

0.8

683.34

505.37

405.32

341.21

296.62

263.82

238.67

218.78

  

\(p=.4\)

0.6

0.2

153.31

137.09

128.43

123.03

119.35

116.68

114.65

113.06

 

0.4

167.38

151.85

141.79

134.76

129.55

125.55

122.38

119.80

 

0.6

174.14

160.06

149.76

141.90

135.70

130.69

126.56

123.09

 

0.8

178.29

165.51

155.21

146.74

139.64

133.61

128.43

123.92

0.7

0.2

208.27

168.11

149.69

139.12

132.27

127.46

123.90

121.16

 

0.4

251.15

204.63

179.27

163.30

152.33

144.32

138.22

133.42

 

0.6

275.12

228.30

199.44

179.87

165.72

155.02

146.64

139.91

 

0.8

291.13

245.64

214.60

192.08

174.98

161.57

150.76

141.86

0.8

0.2

261.48

193.01

165.39

150.45

141.10

134.69

130.03

126.48

 

0.4

350.83

255.26

211.30

186.03

169.61

158.10

149.57

143.01

 

0.6

410.16

301.74

246.37

212.76

190.19

173.99

161.80

152.29

 

0.8

454.47

339.52

275.11

233.92

205.32

184.29

168.18

155.44

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