Table 14 Percentage relative efficiency using Population 4, 5, 6 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 4 | Population 5 | Population 6 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
\({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{GK}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}(\mathcal{Y})\) | |||
\({\widehat{\mathcal{F}}}_{GK}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(1)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(1)}(\mathcal{Y})\) | 210.65 | 225.70 | 301.93 | 120.44 | 126.31 | 123.83 | 241.45 | 243.84 | 281.75 |
\({\widehat{\mathcal{F}}}_{GK}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(2)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(2)}(\mathcal{Y})\) | 21.64 | 225.69 | 301.91 | 120.45 | 126.33 | 123.85 | 241.45 | 243.84 | 281.75 |
\({\widehat{\mathcal{F}}}_{GK}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(3)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(3)}(\mathcal{Y})\) | 210.65 | 225.70 | 301.93 | 120.44 | 126.31 | 123.83 | 241.45 | 243.84 | 281.75 |
\({\widehat{\mathcal{F}}}_{GK}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(4)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(4)}(\mathcal{Y})\) | 210.64 | 225.68 | 301.89 | 120.46 | 126.35 | 123.87 | 241.45 | 243.84 | 281.75 |
\({\widehat{\mathcal{F}}}_{GK}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(5)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(5)}(\mathcal{Y})\) | 210.92 | 226.31 | 301.77 | 131.42 | 155.44 | 151.23 | 241.47 | 243.87 | 281.79 |
\({\widehat{\mathcal{F}}}_{GK}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(6)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(6)}(\mathcal{Y})\) | 210.91 | 226.30 | 301.75 | 131.34 | 155.16 | 151.95 | 241.47 | 243.87 | 281.79 |
\({\widehat{\mathcal{F}}}_{GK}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(7)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(7)}(\mathcal{Y})\) | 210.45 | 225.26 | 301.34 | 119.85 | 125.07 | 121.61 | 241.44 | 243.81 | 281.72 |
\({\widehat{\mathcal{F}}}_{GK}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(8)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(8)}(\mathcal{Y})\) | 210.92 | 226.31 | 301.77 | 131.42 | 155.44 | 151.23 | 241.47 | 243.87 | 281.79 |
\({\widehat{\mathcal{F}}}_{GK}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(9)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(9)}(\mathcal{Y})\) | 210.44 | 225.26 | 301.32 | 119.85 | 125.07 | 121.61 | 241.44 | 243.81 | 281.72 |
\({\widehat{\mathcal{F}}}_{GK}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{1}}^{(10)}(\mathcal{Y})\) | \({\widehat{\mathcal{F}}}_{P{r}_{2}}^{(10)}(\mathcal{Y})\) | 210.13 | 224.58 | 300.42 | 119.83 | 125.03 | 111.57 | 241.41 | 243.75 | 281.65 |
| 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 | 171.46 | Â | Â | 44.640 | Â | Â | Â | 28.330 |
| Â | \({\widehat{\mathcal{F}}}_{P}(\mathcal{Y})\) | Â | Â | 29.290 | Â | Â | 56.480 | Â | Â | Â | 213.50 |
| Â | \({\widehat{\mathcal{F}}}_{BT,R}(\mathcal{Y})\) | Â | Â | 185.21 | Â | Â | 71.990 | Â | Â | Â | 241.81 |
| Â | \({\widehat{\mathcal{F}}}_{BT,P}(\mathcal{Y})\) | Â | Â | 51.02 | Â | Â | 88.500 | Â | Â | Â | 241.41 |
| Â | \({\widehat{\mathcal{F}}}_{Reg}(\mathcal{Y})\) | Â | Â | 201.70 | Â | Â | 101.46 | Â | Â | Â | 206.53 |
| Â | \({\widehat{\mathcal{F}}}_{R,D}(\mathcal{Y})\) | Â | Â | 210.13 | Â | Â | 119.83 | Â | Â | Â | 49.610 |
