Table 12 Percentage relative efficiency using Population 4, 5, 6 when \(\{ x=\overline{{\mathcal{X}}},y=\overline{{\mathcal{Y}}}\}\).
From: Construction of improved comprehensive classes of estimators for population distribution function
Estimators | Population 4 | Population 5 | Population 6 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | |||
\({\widehat{\mathcal{F}}}_{GK}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(1)}(\mathcal{Y})\) | 303.27 | 323.67 | 330.99 | 111.54 | 121.05 | 118.69 | 189.48 | 203.23 | 191.16 |
\({\widehat{\mathcal{F}}}_{GK}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(2)}(\mathcal{Y})\) | 301.67 | 321.31 | 329.60 | 111.37 | 120.67 | 118.33 | 189.46 | 203.17 | 191.10 |
\({\widehat{\mathcal{F}}}_{GK}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(3)}(\mathcal{Y})\) | 303.87 | 325.16 | 331.53 | 111.62 | 121.22 | 118.87 | 189.51 | 203.30 | 191.22 |
\({\widehat{\mathcal{F}}}_{GK}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(4)}(\mathcal{Y})\) | 301.58 | 321.13 | 329.42 | 111.29 | 120.49 | 118.15 | 189.45 | 203.17 | 191.10 |
\({\widehat{\mathcal{F}}}_{GK}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(5)}(\mathcal{Y})\) | 303.06 | 323.19 | 330.51 | 119.42 | 143.76 | 140.81 | 189.47 | 203.21 | 191.14 |
\({\widehat{\mathcal{F}}}_{GK}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(6)}(\mathcal{Y})\) | 301.81 | 321.63 | 329.93 | 120.76 | 148.63 | 145.52 | 189.46 | 203.19 | 191.12 |
\({\widehat{\mathcal{F}}}_{GK}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(7)}(\mathcal{Y})\) | 303.13 | 323.35 | 330.67 | 110.97 | 119.80 | 117.47 | 189.47 | 203.21 | 191.14 |
\({\widehat{\mathcal{F}}}_{GK}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(8)}(\mathcal{Y})\) | 303.62 | 324.54 | 331.89 | 118.76 | 141.50 | 138.62 | 189.50 | 203.28 | 191.21 |
\({\widehat{\mathcal{F}}}_{GK}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(9)}(\mathcal{Y})\) | 301.63 | 321.22 | 329.51 | 110.95 | 119.75 | 117.63 | 189.45 | 203.17 | 191.10 |
\({\widehat{\mathcal{F}}}_{GK}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(10)}(\mathcal{Y})\) | 301.52 | 321.99 | 329.74 | 110.93 | 119.70 | 117.38 | 189.45 | 203.17 | 191.10 |
| Â | \(\widehat{\mathcal{F}}(y)\) | Â | Â | 100.00 | Â | Â | 100.00 | Â | Â | Â | 100.00 |
| Â | \({\widehat{\mathcal{F}}}_{R}(\mathcal{Y})\) | Â | Â | 280.87 | Â | Â | 34.370 | Â | Â | Â | 17.380 |
| Â | \({\widehat{\mathcal{F}}}_{P}(\mathcal{Y})\) | Â | Â | 28.490 | Â | Â | 51.640 | Â | Â | Â | 107.62 |
| Â | \({\widehat{\mathcal{F}}}_{BT,R}(\mathcal{Y})\) | Â | Â | 224.30 | Â | Â | 63.690 | Â | Â | Â | 189.38 |
| Â | \({\widehat{\mathcal{F}}}_{BT,P}(\mathcal{Y})\) | Â | Â | 49.400 | Â | Â | 83.380 | Â | Â | Â | 189.45 |
| Â | \({\widehat{\mathcal{F}}}_{Reg}(\mathcal{Y})\) | Â | Â | 299.22 | Â | Â | 101.28 | Â | Â | Â | 189.13 |
| Â | \({\widehat{\mathcal{F}}}_{R,D}(\mathcal{Y})\) | Â | Â | 301.52 | Â | Â | 110.93 | Â | Â | Â | 41.680 |
