Table 11 Partial and overall ranks for all estimation methods of our proposed model by SRS.
Parameter | n | MLE | ADE | CVME | MPSE | OLSE | PCE | RTADE | WLSE | LTADE | MSADE | MSALDE | ADSOE | KE | MSSD | MSSLD | MSLND |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\alpha =1.5,~\beta =2.0\) | 30 | 4.0 | 3.0 | 10.0 | 2.0 | 7.0 | 1.0 | 8.0 | 5.0 | 11.0 | 13.0 | 9.0 | 16.0 | 12.0 | 14.0 | 6.0 | 15.0 |
80 | 2.0 | 5.0 | 7.5 | 3.0 | 7.5 | 1.0 | 6.0 | 4.0 | 12.0 | 13.0 | 10.0 | 16.0 | 11.0 | 14.0 | 9.0 | 15.0 | |
150 | 1.0 | 6.0 | 8.0 | 2.0 | 7.0 | 3.0 | 4.0 | 5.0 | 9.5 | 13.0 | 11.0 | 16.0 | 12.0 | 15.0 | 9.5 | 14.0 | |
300 | 4.0 | 1.0 | 8.0 | 2.0 | 9.0 | 3.0 | 6.0 | 5.0 | 10.5 | 13.0 | 10.5 | 16.0 | 12.0 | 14.0 | 7.0 | 15.0 | |
400 | 2.0 | 5.0 | 7.0 | 1.0 | 9.5 | 3.0 | 6.0 | 4.0 | 8.0 | 13.0 | 12.0 | 16.0 | 11.0 | 14.0 | 9.5 | 15.0 | |
500 | 1.0 | 3.0 | 8.0 | 2.0 | 9.0 | 5.5 | 5.5 | 4.0 | 10.0 | 13.0 | 11.0 | 16.0 | 12.0 | 15.0 | 7.0 | 14.0 | |
\(\alpha =0.8,~\beta =0.2\) | 30 | 3.0 | 1.0 | 11.0 | 2.0 | 13.0 | 8.0 | 7.0 | 4.0 | 6.0 | 9.0 | 10.0 | 15.0 | 12.0 | 16.0 | 5.0 | 14.0 |
80 | 1.0 | 3.5 | 7.0 | 2.0 | 6.0 | 12.0 | 8.0 | 3.5 | 9.5 | 13.0 | 9.5 | 16.0 | 11.0 | 15.0 | 5.0 | 14.0 | |
150 | 2.0 | 1.0 | 6.0 | 3.0 | 9.0 | 14.0 | 5.0 | 4.0 | 10.0 | 12.0 | 11.0 | 16.0 | 7.0 | 13.0 | 8.0 | 15.0 | |
300 | 1.0 | 4.0 | 6.0 | 3.0 | 7.0 | 13.5 | 5.0 | 2.0 | 8.0 | 12.0 | 11.0 | 16.0 | 10.0 | 15.0 | 9.0 | 13.5 | |
400 | 1.0 | 2.0 | 7.0 | 4.0 | 5.0 | 13.0 | 6.0 | 3.0 | 8.0 | 12.0 | 11.0 | 16.0 | 9.0 | 15.0 | 10.0 | 14.0 | |
500 | 1.0 | 2.0 | 8.5 | 3.0 | 6.0 | 13.0 | 5.0 | 4.0 | 7.0 | 12.0 | 11.0 | 16.0 | 10.0 | 14.0 | 8.5 | 15.0 | |
\(\alpha =1.0,~\beta =1.5\) | 30 | 4.0 | 3.0 | 10.0 | 1.5 | 5.0 | 6.0 | 7.0 | 1.5 | 9.0 | 13.0 | 11.0 | 16.0 | 12.0 | 15.0 | 8.0 | 14.0 |
80 | 3.0 | 1.5 | 7.0 | 1.5 | 6.0 | 8.0 | 5.0 | 4.0 | 10.0 | 13.0 | 11.0 | 14.0 | 12.0 | 15.0 | 9.0 | 16.0 | |
150 | 1.0 | 4.0 | 8.0 | 2.0 | 6.0 | 10.0 | 5.0 | 3.0 | 7.0 | 13.0 | 11.0 | 14.0 | 12.0 | 15.0 | 9.0 | 16.0 | |
300 | 1.0 | 4.0 | 9.0 | 2.0 | 7.0 | 11.0 | 5.0 | 3.0 | 6.0 | 13.0 | 12.0 | 14.0 | 10.0 | 16.0 | 8.0 | 15.0 | |
400 | 1.0 | 2.0 | 6.0 | 3.0 | 7.0 | 10.0 | 5.0 | 4.0 | 8.0 | 13.0 | 12.0 | 15.0 | 11.0 | 16.0 | 9.0 | 14.0 | |
500 | 1.0 | 2.0 | 8.0 | 3.0 | 6.0 | 12.0 | 5.0 | 4.0 | 7.0 | 13.0 | 11.0 | 14.0 | 10.0 | 15.0 | 9.0 | 16.0 | |
\(\alpha =1.25,~\beta =0.3\) | 30 | 2.0 | 3.0 | 7.0 | 4.0 | 10.0 | 1.0 | 11.0 | 5.0 | 12.0 | 13.0 | 8.0 | 15.0 | 9.0 | 16.0 | 6.0 | 14.0 |
80 | 4.0 | 2.0 | 12.0 | 3.0 | 6.0 | 1.0 | 7.0 | 5.0 | 11.0 | 13.0 | 9.0 | 16.0 | 10.0 | 15.0 | 8.0 | 14.0 | |
150 | 4.5 | 4.5 | 12.0 | 2.0 | 11.0 | 1.0 | 7.0 | 3.0 | 9.0 | 13.0 | 10.0 | 16.0 | 6.0 | 14.0 | 8.0 | 15.0 | |
300 | 3.0 | 5.0 | 10.5 | 2.0 | 6.5 | 1.0 | 6.5 | 4.0 | 9.0 | 13.0 | 10.5 | 16.0 | 12.0 | 15.0 | 8.0 | 14.0 | |
400 | 2.0 | 4.0 | 8.0 | 3.0 | 9.0 | 1.0 | 6.0 | 5.0 | 10.0 | 13.0 | 11.0 | 16.0 | 12.0 | 14.0 | 7.0 | 15.0 | |
500 | 2.0 | 5.0 | 10.0 | 3.0 | 7.0 | 1.0 | 6.0 | 4.0 | 12.0 | 13.0 | 11.0 | 16.0 | 9.0 | 15.0 | 8.0 | 14.0 | |
\(\alpha =0.9,~\beta =2.5\) | 30 | 1.0 | 6.0 | 7.0 | 2.0 | 5.0 | 8.0 | 4.0 | 10.0 | 12.0 | 11.0 | 3.0 | 16.0 | 13.0 | 15.0 | 9.0 | 14.0 |
80 | 1.0 | 2.5 | 6.0 | 2.5 | 4.0 | 13.0 | 5.0 | 8.0 | 10.0 | 15.0 | 11.0 | 16.0 | 9.0 | 14.0 | 7.0 | 12.0 | |
150 | 1.0 | 3.0 | 6.0 | 2.0 | 7.0 | 10.0 | 5.0 | 4.0 | 13.0 | 12.0 | 9.0 | 16.0 | 11.0 | 15.0 | 8.0 | 14.0 | |
300 | 1.0 | 2.5 | 9.0 | 5.0 | 10.0 | 11.0 | 2.5 | 4.0 | 7.5 | 13.0 | 12.0 | 16.0 | 6.0 | 14.0 | 7.5 | 15.0 | |
400 | 2.0 | 4.0 | 6.5 | 5.0 | 10.0 | 12.0 | 1.0 | 6.5 | 9.0 | 13.0 | 11.0 | 16.0 | 8.0 | 14.0 | 3.0 | 15.0 | |
500 | 1.0 | 7.0 | 8.0 | 2.0 | 11.0 | 12.0 | 5.0 | 3.0 | 10.0 | 13.0 | 9.0 | 16.0 | 4.0 | 14.0 | 6.0 | 15.0 | |
\(\sum\) Ranks | 58.5 | 101.5 | 244.0 | 77.5 | 228.5 | 219.0 | 169.5 | 128.5 | 281.0 | 381.0 | 309.5 | 469.0 | 305.0 | 441.0 | 231.0 | 435.5 | |
Overall Rank | 1 | 3 | 9 | 2 | 7 | 6 | 5 | 4 | 10 | 13 | 12 | 16 | 11 | 15 | 8 | 14 |
