Table 9 Percentage relative efficiency using Population 1, 2, 3 when \(\left\{x={Q}_{1}(x),y={Q}_{1}(y)\right\}\).
From: Construction of improved comprehensive classes of estimators for population distribution function
Estimators | Population 1 | Population 2 | Population 3 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | |||
\({\widehat{\mathcal{F}}}_{GK}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(1)}(\mathcal{Y})\) | 415.95 | 418.83 | 449.59 | 105.10 | 119.99 | 227.16 | 268.65 | 273.50 | 297.65 |
\({\widehat{\mathcal{F}}}_{GK}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(2)}(\mathcal{Y})\) | 415.94 | 418.80 | 449.57 | 105.09 | 119.98 | 227.15 | 268.54 | 273.28 | 297.40 |
\({\widehat{\mathcal{F}}}_{GK}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(3)}(\mathcal{Y})\) | 416.02 | 418.96 | 449.74 | 105.12 | 120.03 | 227.23 | 269.51 | 275.29 | 299.59 |
\({\widehat{\mathcal{F}}}_{GK}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(4)}(\mathcal{Y})\) | 415.96 | 418.85 | 449.62 | 105.10 | 119.99 | 227.17 | 268.60 | 273.83 | 298.00 |
\({\widehat{\mathcal{F}}}_{GK}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(5)}(\mathcal{Y})\) | 416.00 | 418.92 | 449.69 | 105.20 | 120.24 | 227.67 | 269.45 | 275.16 | 299.46 |
\({\widehat{\mathcal{F}}}_{GK}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(6)}(\mathcal{Y})\) | 416.09 | 419.10 | 449.89 | 105.27 | 120.39 | 227.96 | 270.78 | 277.99 | 301.54 |
\({\widehat{\mathcal{F}}}_{GK}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(7)}(\mathcal{Y})\) | 415.95 | 418.82 | 449.58 | 105.09 | 119.97 | 227.13 | 268.55 | 273.3) | 297.43 |
\({\widehat{\mathcal{F}}}_{GK}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(8)}(\mathcal{Y})\) | 416.16 | 419.27 | 450.07 | 105.29 | 120.46 | 228.13 | 271.88 | 280.38 | 305.18 |
\({\widehat{\mathcal{F}}}_{GK}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(9)}(\mathcal{Y})\) | 415.94 | 418.80 | 449.57 | 105.93 | 119.97 | 227.13 | 268.48 | 273.15 | 297.27 |
\({\widehat{\mathcal{F}}}_{GK}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(10)}(\mathcal{Y})\) | 415.93 | 418.78 | 449.54 | 105.09 | 119.97 | 227.13 | 268.39 | 271.97 | 297.06 |
| 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 | 381.08 | Â | Â | 61.280 | Â | Â | Â | 213.53 |
| Â | \({\widehat{\mathcal{F}}}_{P}(\mathcal{Y})\) | Â | Â | 18.950 | Â | Â | 25.700 | Â | Â | Â | 19.220 |
| Â | \({\widehat{\mathcal{F}}}_{BT,R}(\mathcal{Y})\) | Â | Â | 267.67 | Â | Â | 94.190 | Â | Â | Â | 206.54 |
| Â | \({\widehat{\mathcal{F}}}_{BT,P}(\mathcal{Y})\) | Â | Â | 46.700 | Â | Â | 69.100 | Â | Â | Â | 49.600 |
| Â | \({\widehat{\mathcal{F}}}_{Reg}(\mathcal{Y})\) | Â | Â | 414.63 | Â | Â | 103.79 | Â | Â | Â | 241.84 |
| Â | \({\widehat{\mathcal{F}}}_{R,D}(\mathcal{Y})\) | Â | Â | 415.93 | Â | Â | 105.09 | Â | Â | Â | 268.39 |
