Research Article
Maximum Likelihood Estimator of AUC for a Bi-Exponentiated Weibull Model
Table 1
ARB and RMSE of five estimated parameters
and
, when
and with different values of
.
| | MLE | | | | |
| | (50, 50) | | 0.3721 (1.6569) | 0.35630 (2.211) | 0.3607 (1.5814) | 0.3995 (1.950) | | 0.2556 (1.1068) | 0.3645 (1.2601) | 0.4204 (1.5814) | 0.5547 (2.1276) | | 0.0801 (0.7525) | 0.0675 (0.6655) | 0.0615 (0.6679) | 0.0525 (0.6243) | | 0.0842 (0.5661) | 0.0756 (0.5421) | 0.961 (0.5442) | 0.0979 (0.5683) | | 0.0913 (0.5235) | 0.0805 (0.5493) | 0.0916 (0.560) | 0.119 (0.6189) | | 0.0309 (0.0648) | 0.0187 (0.0734) | 0.0074 (0.08) | 0.0078 (0.0648) |
| | (50, 100) | | 0.1872 (1.6205) | 0.3035 (2.1506) | 0.2333 (1.5885) | 0.2205 (1.9536) | | 0.0823 (0.4995) | 0.2404 (1.8192) | 0.2507 (2.6231) | 0.2896 (2.1170) | | 0.0636 (0.5464) | 0.0293 (0.5054) | 0.0271 (0.4935) | 0.0467 (0.5228) | | 0.0348 (0.4380) | 0.0985 (0.4777) | 0.0859 (0.4421) | 0.0653 (0.4614) | | 0.0217 (0.3694) | 0.0751 (0.4532) | 0.0762 (0.4510) | 0.0612 (0.4861) | | 0.0072 (0.060) | 0.005 (0.0591) | 0.0037 (0.0565) | 0.0058 (0.0424) |
| | (100, 50) | | 0.1609 (1.3638) | 0.1689 (1.5535) | 0.1774 (1.3754) | 0.1731 (1.4751) | | 0.1379 (0.5709) | 0.2031 (1.6370) | 0.2773 (1.9342) | 0.3209 (1.7746) | | 0.0467 (0.5281) | 0.0455 (0.4998) | 0.0320 (0.4814) | 0.0425 (0.5079) | | 0.0399 (0.4085) | 0.0430 (0.4129) | 0.0602 (0.3962) | 0.0461 (0.4191) | | 0.0709 (0.4078) | 0.0524 (0.4300) | 0.0824 (0.4498) | 0.0668 (0.4889) | | 0.0048 (0.0519) | 0.0031 (0.0489) | 0.0017 (0.0469) | 0.0056 (0.0435) |
| | (100, 100) | | 0.1205 (1.1180) | 0.1322 (1.2528) | 0.1396 (1.2052) | 0.1276 (1.1109) | | 0.0726 (0.4195) | 0.1291 (1.2499) | 0.1842 (2.1241) | 0.1295 (2.0528) | | 0.0367 (0.4324) | 0.0346 (0.4317) | 0.0290 (0.4219) | 0.0323 (0.4281) | | 0.0318 (0.3521) | 0.0354 (0.3687) | 0.0469 (0.3720) | 0.0369 (0.3644) | | 0.029 (0.3286) | 0.0323 (0.3739) | 0.0593 (0.3962) | 0.0452 (0.3954) | | 0.0036 (0.0412) | 0.003 (0.0458) | 0.0018 (0.0331) | 0.0031 (0.040) |
| | (200, 200) | | 0.0668 (0.6871) | 0.0569 (0.6666) | 0.0700 (0.6368) | 0.0602 (0.6553) | | 0.0404 (0.2707) | 0.0637 (0.6581) | 0.0833 (1.1019) | 0.0965 (0.7324) | | 0.0152 (0.2879) | 0.0135 (0.2853) | 0.0090 (0.2791) | 0.0102 (0.2756) | | 0.0214 (0.2487) | 0.0215 (0.2457) | 0.0324 (0.2399) | 0.0217 (0.2430) | | 0.0162 (0.2274) | 0.0222 (0.2419) | 0.0292 (0.2562) | 0.0280 (0.2715) | | 0.0021 (0.0256) | 0.0033 (0.0267) | 0.0031 (0.0270) | 0.0013 (0.0264) |
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