Table 10 Percentage relative efficiency using Population 1, 2, 3 when \(\left\{x=\widetilde{\mathcal{X}},y=\widetilde{\mathcal{Y}}\right\}\).
From: Construction of improved comprehensive classes of estimators for population distribution function
Estimators | Population 1 | Population 2 | Population 3 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\widehat{\mathcal{F}}}_{GK}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | |||
\({\widehat{\mathcal{F}}}_{GK}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(1)}(\mathcal{Y})\) | 351.58 | 358.79 | 404.92 | 488.43 | 498.33 | 551.21 | 140.84 | 898.79 | 913.16 |
\({\widehat{\mathcal{F}}}_{GK}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(2)}(\mathcal{Y})\) | 351.58 | 358.79 | 404.92 | 488.43 | 498.33 | 551.21 | 140.56 | 898.77 | 913.10 |
\({\widehat{\mathcal{F}}}_{GK}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(3)}(\mathcal{Y})\) | 351.78 | 358.79 | 404.92 | 488.43 | 498.33 | 551.21 | 140.86 | 898.79 | 913.17 |
\({\widehat{\mathcal{F}}}_{GK}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(4)}(\mathcal{Y})\) | 351.58 | 358.79 | 404.92 | 488.43 | 498.33 | 551.21 | 140.32 | 898.75 | 913.05 |
\({\widehat{\mathcal{F}}}_{GK}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(5)}(\mathcal{Y})\) | 351.59 | 358.81 | 404.94 | 488.45 | 498.35 | 551.24 | 141.67 | 898.97 | 913.56 |
\({\widehat{\mathcal{F}}}_{GK}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(6)}(\mathcal{Y})\) | 351.59 | 358.81 | 404.94 | 488.44 | 498.35 | 551.23 | 141.41 | 898.94 | 913.50 |
\({\widehat{\mathcal{F}}}_{GK}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(7)}(\mathcal{Y})\) | 351.57 | 358.77 | 404.89 | 488.43 | 498.30 | 551.19 | 138.82 | 898.60 | 911.74 |
\({\widehat{\mathcal{F}}}_{GK}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(8)}(\mathcal{Y})\) | 351.59 | 358.81 | 404.94 | 488.45 | 498.35 | 551.24 | 141.70 | 898.98 | 913.57 |
\({\widehat{\mathcal{F}}}_{GK}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(9)}(\mathcal{Y})\) | 351.57 | 358.77 | 404.89 | 488.43 | 498.30 | 551.19 | 138.56 | 989.59 | 911.69 |
\({\widehat{\mathcal{F}}}_{GK}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(10)}(\mathcal{Y})\) | 351.53 | 358.69 | 404.80 | 488.37 | 489.19 | 551.07 | 101.36 | 896.49 | 908.20 |
| 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 | 324.29 | Â | Â | 461.49 | Â | Â | Â | 861.32 |
| Â | \({\widehat{\mathcal{F}}}_{P}(\mathcal{Y})\) | Â | Â | 27.060 | Â | Â | 26.450 | Â | Â | Â | 25.790 |
| Â | \({\widehat{\mathcal{F}}}_{BT,R}(\mathcal{Y})\) | Â | Â | 248.08 | Â | Â | 279.06 | Â | Â | Â | 324.69 |
| Â | \({\widehat{\mathcal{F}}}_{BT,P}(\mathcal{Y})\) | Â | Â | 47.640 | Â | Â | 46.690 | Â | Â | Â | 45.620 |
| Â | \({\widehat{\mathcal{F}}}_{Reg}(\mathcal{Y})\) | Â | Â | 351.08 | Â | Â | 487.23 | Â | Â | Â | 888.06 |
| Â | \({\widehat{\mathcal{F}}}_{R,D}(\mathcal{Y})\) | Â | Â | 351.53 | Â | Â | 488.37 | Â | Â | Â | 896.49 |
