Table 4.
Alternative estimator results for log-normal, gamma and weibull distributions for n=100
| Data | Estimator | MPE | MPAE | MSE(β) | 95% CI | AIC | Prob. H.Lsignif | |
|---|---|---|---|---|---|---|---|---|
| Lower | upper | |||||||
| Log normal σ2=0.5 | OLS for Ln(y) | -0.03144 | 0.56088 | 0.06312 | 0.953 | 1.049 | 217.5766 | 0.0391 |
| Gamma | -0.00007 | 0.55234 | 0.05761 | 0.942 | 1.052 | 168.199 | 0.0361 | |
| Weibull | -0.11282 | 0.58936 | 0.06098 | 0.935 | 1.057 | 175.260 | 0.0417 | |
| Cox | -1.34295 | 3.32199 | 5.63414 | -1.423 | -1.263 | 716.154 | 0.0481 | |
| Log normal σ2=1 | OLS for Ln(y) | -0.03161 | 0.77499 | 0.12623 | 0.933 | 1.069 | 286.891 | 0.0365 |
| Gamma | -0.00020 | 0.76419 | 0.10963 | 0.907 | 1.081 | 192.904 | 0.0333 | |
| Weibull | -0.00812 | 0.76533 | 0.12196 | 0.908 | 1.080 | 193.907 | 0.0330 | |
| Cox | -0.94387 | 3.19872 | 3.91711 | -1.020 | -0.868 | 722.133 | 0.0479 | |
| Log normal σ2=1.5 | OLS for Ln(y) | -0.03195 | 0.93383 | 0.18935 | 0.917 | 1.085 | 327.438 | 0.0335 |
| Gamma | -0.00038 | 0.92175 | 0.15884 | 0.873 | 1.107 | 189.222 | 0.0300 | |
| Weibull | 0.11681 | 0.86782 | 0.18295 | 0.887 | 1.099 | 185.001 | 0.0294 | |
| Cox | -0.76851 | 3.15738 | 3.26405 | -0.844 | -0.694 | 724.207 | 0.0531 | |
| Log normal σ2=2 | OLS for Ln(y) | -0.03217 | 1.05939 | 0.25247 | 0.904 | 1.098 | 356.206 | 0.0320 |
| Gamma | -0.00068 | 1.04672 | 0.20674 | 0.840 | 1.132 | 172.665 | 0.0283 | |
| Weibull | 0.23968 | 0.92933 | 0.24393 | 0.869 | 1.113 | 163.925 | 0.0276 | |
| Cox | -0.66436 | 3.13647 | 2.90548 | -0.738 | -0.590 | 725.262 | 0.0544 | |
| Gamma α=0.5 | OLS for Ln(y) | -0.06210 | 0.98793 | 0.924 | 0.842 | 1.149 | 444.474 | 0.1015 |
| Gamma | -0.00071 | 0.95946 | 0.382 | 0.899 | 1.099 | 151.970 | 0.0366 | |
| Weibull | 0.25749 | 0.88296 | 0.456 | 0.896 | 1.102 | 154.259 | 0.0380 | |
| Cox | 0.69973 | 3.18874 | 2.997 | -0.700 | -0.626 | 724.990 | 0.050 | |
| Gamma α =1 | OLS for Ln(y) | -0.03843 | 0.74577 | 0.307 | 0.915 | 1.093 | 335.557 | 0.0569 |
| Gamma | -0.00026 | 0.73384 | 0.185 | 0.934 | 1.072 | 196.691 | 0.0391 | |
| Weibull | -0.00460 | 0.73458 | 0.185 | 0.934 | 1.072 | 196.682 | 0.0395 | |
| Cox | -1.02065 | 3.27855 | 4.182 | -1.095 | -0.947 | 721.285 | 0.0518 | |
| Gamma α =2 | OLS for Ln(y) | -0.03271 | 0.54277 | 0.120 | 0.946 | 1.057 | 242.168 | 0.0504 |
| Gamma | -0.00011 | 0.53579 | 0.092 | 0.950 | 1.494 | 171.847 | 0.0434 | |
| Weibull | -0.11069 | 0.56268 | 0.087 | 0.949 | 1.049 | 172.908 | 0.0471 | |
| Cox | -1.44678 | 3.44580 | 6.080 | -1.525 | -1.369 | 714.645 | 0.0503 | |
| Gamma α =4 | OLS for Ln(y) | -0.03138 | 0.39126 | 0.053 | 0.966 | 1.040 | 160.228 | 0.0436 |
| Gamma | -0.00001 | 0.38627 | 0.046 | 0.967 | 1.037 | 122.262 | 0.0403 | |
| Weibull | -0.13163 | 0.41676 | 0.044 | 0.964 | 1.038 | 125.708 | 0.0515 | |
| Cox | -2.05432 | 3.72857 | 9.359 | -2.138 | -1.970 | 702.730 | 0.0506 | |
| Wiebull α=0.5 | OLS for Ln(y) | -0.07169 | 1.20997 | 0.82955 | 0.830 | 1.186 | 473.993 | 0.0833 |
| Gamma | -0.00180 | 1.16992 | 0.36191 | 0.839 | 1.145 | 83.622 | 0.032 | |
| Weibull | 0.48656 | 0.96925 | 0.50264 | 0.856 | 1.138 | 79.302 | 0.0345 | |
| Cox | -0.49779 | 3.13454 | 2.38376 | -0.668 | -0.330 | 726.558 | 0.0485 | |
| Wiebull α =1 | OLS for Ln(y) | -0.03853 | 0.74709 | 0.20739 | 0.915 | 1.093 | 335.3635 | 0.0574 |
| Gamma | -0.00025 | 0.73522 | 0.12587 | 0.928 | 1.068 | 196.7417 | 0.0399 | |
| Weibull | -0.00400 | 0.73582 | 0.12566 | 0.928 | 1.068 | 196.7316 | 0.0397 | |
| Cox | -1.00326 | 3.28425 | 4.16180 | -1.176 | -0.834 | 721.3257 | 0.0505 | |
| Wiebull α =5 | OLS for Ln(y) | -0.03115 | 0.18335 | 0.00829 | 0.983 | 1.019 | 13.476 | 0.0480 |
| Gamma | -0.00001 | 0.18277 | 0.00738 | 0.984 | 1.016 | -7.0357 | 0.0437 | |
| Weibull | -0.08850 | 0.19266 | 0.00503 | 0.986 | 1.014 | -16.598 | 0.0639 | |
| Cox | -5.04559 | 6.57363 | 36.88155 | -5.160 | -4.932 | 636.392 | 0.0472 | |