Research Article
Exponentiated Gamma Distribution: Different Methods of Estimations
Table 1
Bias estimates and MSEs of
are presented, when
is known.
| | Method | = 0.25 | = 0.5 | = 1 | = 2 | = 2.5 |
| 10 | MLE | 0.13269 | 0.31581 | 0.12298 | 0.19146 | 0.24863 | 0.04193 | 0.15449 | 0.15997 | 0.59425 | 0.95929 | MME | 0.14114 | 0.24936 | 0.76652 | − 0.76236 | 1.21176 | 0.01992 | 0.06218 | 0.58756 | 0.58119 | 1.46835 | PCE | 0.05443 | 0.22400 | − 0.05708 | − 0.18646 | − 0.19735 | 0.02452 | 0.08653 | 0.11220 | 0.47012 | 0.75097 | LSE | 1.25613 | 0.92901 | 1.18688 | 0.20133 | 0.18193 | 1.57786 | 0.86305 | 1.58971 | 1.02132 | 1.43291 | WLSE | 1.21698 | 0.90029 | 1.13884 | 0.17699 | 0.16053 | 1.48105 | 0.81052 | 1.47831 | 0.82830 | 1.32242 | UBE | 0.09442 | 0.23423 | 0.01069 | − 0.02769 | − 0.02624 | 0.02862 | 0.09922 | 0.11744 | 0.45242 | 0.72764 |
| 20 | MLE | 0.01488 | 0.02848 | 0.06164 | 0.09579 | 0.14010 | 0.00356 | 0.01578 | 0.06943 | 0.23892 | 0.40589 | MME | − 0.01385 | − 0.00755 | 0.09627 | 0.07783 | 0.06881 | 0.01186 | 0.03202 | 0.12147 | 0.47954 | 0.72776 | PCE | − 0.05946 | − 0.05620 | − 0.06172 | − 0.15758 | − 0.22235 | 0.00671 | 0.02036 | 0.06388 | 0.23730 | 0.39565 | LSE | 1.62596 | 1.36431 | 0.02848 | 0.07049 | 0.10051 | 2.64656 | 1.86404 | 0.09260 | 0.32610 | 0.55121 | WLSE | 2.21133 | 1.87305 | 0.02495 | 0.06392 | 0.29974 | 4.89475 | 3.51203 | 0.08449 | 0.29810 | 0.90352 | UBE | 0.00164 | 0.00206 | 0.00856 | − 0.00900 | 0.00809 | 0.00302 | 0.01351 | 0.05930 | 0.20743 | 0.34867 |
| 50 | MLE | 0.01029 | 0.01194 | 0.02556 | 0.03783 | 0.05525 | 0.00135 | 0.00541 | 0.02171 | 0.09390 | 0.12927 | MME | − 0.02304 | −0.01614 | 0.02354 | 0.03965 | − 0.01924 | 0.00476 | 0.01191 | 0.03931 | 0.16665 | 0.23736 | PCE | − 0.06374 | −0.05750 | − 0.04838 | − 0.10306 | − 0.19602 | 0.00523 | 0.01070 | 0.02443 | 0.10966 | 0.18408 | LSE | 1.58813 | 1.04030 | 0.02102 | 0.01700 | 0.03799 | 2.52287 | 1.08322 | 0.03064 | 0.11586 | 0.17602 | WLSE | 2.20514 | 1.85472 | 0.01968 | 0.01582 | − 0.49704 | 4.87453 | 3.44050 | 0.02725 | 0.10712 | 0.39058 | UBE | 0.00508 | 0.00170 | 0.00505 | −0.00292 | 0.00414 | 0.00122 | 0.00506 | 0.02025 | 0.08881 | 0.12124 |
| 100 | MLE | 0.03297 | 0.14041 | 0.01201 | 0.02151 | 0.00560 | 0.00109 | 0.00197 | 0.01105 | 0.04172 | 0.06166 | MME | 0.07016 | 0.04276 | 0.03428 | 0.04947 | − 0.04117 | 0.00492 | 0.00183 | 0.00117 | 0.00245 | 0.00170 | PCE | 0.03915 | 0.16972 | − 0.03748 | − 0.07757 | − 0.10999 | 0.00308 | 0.02880 | 0.01317 | 0.05372 | 0.08057 | LSE | 0.19718 | 0.17144 | 0.00963 | 0.01773 | − 0.00567 | 0.03888 | 0.03338 | 0.01525 | 0.05612 | 0.08245 | WLSE | 0.16700 | 0.22510 | 0.00934 | 0.01664 | − 0.00374 | 0.02789 | 0.05388 | 0.01365 | 0.05063 | 0.07397 | UBE | 0.03014 | 0.13401 | 0.00189 | 0.00129 | − 0.01945 | 0.00091 | 0.00180 | 0.01069 | 0.04044 | 0.06078 |
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The first entry is the simulated bias. The second entry is simulated MSE.
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