Table 6 Partial and overall rankings of all estimation methods for the proposed distribution under various values of model parameters.
Parameter | n | \(M_1\) | \(M_2\) | \(M_3\) | \(M_4\) | \(M_5\) | \(M_6\) |
|---|---|---|---|---|---|---|---|
\(\gamma _{1}=0.10,~\gamma _{2}=0.25\) | 50 | 6.0 | 3.0 | 4.5 | 1.5 | 4.5 | 1.5 |
100 | 6.0 | 2.0 | 4.0 | 1.0 | 5.0 | 3.0 | |
250 | 6.0 | 3.0 | 4.0 | 1.0 | 5.0 | 2.0 | |
350 | 6.0 | 2.0 | 4.0 | 1.0 | 5.0 | 3.0 | |
400 | 6.0 | 3.0 | 5.0 | 1.0 | 4.0 | 2.0 | |
450 | 6.0 | 2.5 | 4.0 | 1.0 | 5.0 | 2.5 | |
\(\gamma _{1}=0.5,~\gamma _{2}=0.75\) | 50 | 6.0 | 1.0 | 4.0 | 3.0 | 5.0 | 2.0 |
100 | 6.0 | 2.0 | 5.0 | 1.0 | 4.0 | 3.0 | |
250 | 6.0 | 1.0 | 5.0 | 3.5 | 3.5 | 2.0 | |
350 | 6.0 | 3.5 | 3.5 | 1.0 | 5.0 | 2.0 | |
400 | 6.0 | 3.0 | 5.0 | 2.0 | 4.0 | 1.0 | |
450 | 6.0 | 3.0 | 4.0 | 2.0 | 5.0 | 1.0 | |
\(\gamma _{1}=1.0,~\gamma _{2}=1.25\) | 50 | 6.0 | 2.0 | 4.5 | 1.0 | 4.5 | 3.0 |
100 | 6.0 | 2.0 | 4.0 | 1.0 | 5.0 | 3.0 | |
250 | 6.0 | 4.0 | 2.0 | 1.0 | 5.0 | 3.0 | |
350 | 6.0 | 1.5 | 4.0 | 3.0 | 5.0 | 1.5 | |
400 | 6.0 | 3.0 | 5.0 | 1.0 | 4.0 | 2.0 | |
450 | 6.0 | 2.0 | 5.0 | 1.0 | 3.0 | 4.0 | |
\(\gamma _{1}=1.5,~\gamma _{2}=2.0\) | 50 | 4.0 | 2.0 | 5.0 | 1.0 | 3.0 | 6.0 |
100 | 3.0 | 2.0 | 5.0 | 1.0 | 4.0 | 6.0 | |
250 | 2.0 | 2.0 | 4.5 | 2.0 | 4.5 | 6.0 | |
350 | 3.0 | 1.5 | 5.0 | 1.5 | 4.0 | 6.0 | |
400 | 3.0 | 1.5 | 5.0 | 1.5 | 4.0 | 6.0 | |
450 | 3.0 | 1.5 | 4.0 | 1.5 | 5.0 | 6.0 | |
\(\gamma -{1}=2.0,~\gamma _{2}=3.0\) | 50 | 1.0 | 3.0 | 5.5 | 2.0 | 5.5 | 4.0 |
100 | 2.5 | 2.5 | 6.0 | 1.0 | 4.5 | 4.5 | |
250 | 2.0 | 5.0 | 4.0 | 1.0 | 6.0 | 3.0 | |
350 | 4.0 | 5.0 | 3.0 | 1.0 | 6.0 | 2.0 | |
400 | 6.0 | 2.0 | 4.0 | 1.0 | 5.0 | 3.0 | |
450 | 5.0 | 3.0 | 4.0 | 1.0 | 6.0 | 2.0 | |
\(\sum\) Ranks | Â | 146.5 | 74.5 | 131.5 | 42.5 | 139 | 96 |
Overall Rank | Â | 6 | 2 | 4 | 1 | 5 | 3 |
