Table 8 Percentage relative efficiency using Population 1, 2, 3 when \(\{ x=\overline{{\mathcal{X}}},y=\overline{{\mathcal{Y}}}\}\).
From: Construction of improved comprehensive classes of estimators for population distribution function
Estimators | Population 1 | Population 2 | Population 3 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | |||
\({\widehat{\mathcal{F}}}_{GK}^{\left(1\right)}\left(\mathcal{Y}\right)\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(1)}(\mathcal{Y})\) | 493.99 | 511.31 | 517.30 | 419.78 | 475.32 | 431.20 | 181.17 | 220.67 | 228.54 |
\({\widehat{\mathcal{F}}}_{GK}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(2)}(\mathcal{Y})\) | 493.94 | 511.19 | 517.18 | 419.74 | 475.20 | 431.10 | 180.82 | 219.78 | 227.61 |
\({\widehat{\mathcal{F}}}_{GK}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(3)}(\mathcal{Y})\) | 494.05 | 511.47 | 517.46 | 419.83 | 475.45 | 431.31 | 181.53 | 221.65 | 229.55 |
\({\widehat{\mathcal{F}}}_{GK}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(4)}(\mathcal{Y})\) | 493.93 | 511.17 | 517.17 | 419.73 | 475.19 | 431.09 | 180.78 | 219.68 | 227.51 |
\({\widehat{\mathcal{F}}}_{GK}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(5)}(\mathcal{Y})\) | 493.97 | 511.25 | 517.25 | 419.77 | 475.27 | 431.16 | 181.11 | 220.51 | 228.37 |
\({\widehat{\mathcal{F}}}_{GK}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(6)}(\mathcal{Y})\) | 493.94 | 511.20 | 517.19 | 419.75 | 475.23 | 431.12 | 180.95 | 220.08 | 227.93 |
\({\widehat{\mathcal{F}}}_{GK}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(7)}(\mathcal{Y})\) | 493.98 | 511.29 | 517.29 | 419.78 | 475.30 | 431.18 | 181.04 | 220.32 | 228.17 |
\({\widehat{\mathcal{F}}}_{GK}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(8)}(\mathcal{Y})\) | 494.02 | 511.38 | 517.38 | 419.80 | 475.38 | 431.26 | 181.47 | 221.47 | 229.37 |
\({\widehat{\mathcal{F}}}_{GK}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(9)}(\mathcal{Y})\) | 493.93 | 511.18 | 517.18 | 419.74 | 475.20 | 431.09 | 180.79 | 219.70 | 227.53 |
\({\widehat{\mathcal{F}}}_{GK}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(10)}(\mathcal{Y})\) | 493.93 | 511.17 | 517.16 | 419.73 | 475.18 | 431.08 | 180.76 | 219.63 | 227.46 |
| 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 | 465.57 | Â | Â | 336.04 | Â | Â | Â | 161.16 |
| Â | \({\widehat{\mathcal{F}}}_{P}(\mathcal{Y})\) | Â | Â | 25.470 | Â | Â | 23.310 | Â | Â | Â | 33.340 |
| Â | \({\widehat{\mathcal{F}}}_{BT,R}(\mathcal{Y})\) | Â | Â | 281.07 | Â | Â | 296.44 | Â | Â | Â | 164.00 |
| Â | \({\widehat{\mathcal{F}}}_{BT,P}(\mathcal{Y})\) | Â | Â | 46.570 | Â | Â | 43.750 | Â | Â | Â | 55.940 |
| Â | \({\widehat{\mathcal{F}}}_{Reg}(\mathcal{Y})\) | Â | Â | 493.79 | Â | Â | 419.59 | Â | Â | Â | 177.46 |
| Â | \({\widehat{\mathcal{F}}}_{R,D}(\mathcal{Y})\) | Â | Â | 493.93 | Â | Â | 419.73 | Â | Â | Â | 180.76 |
