Research Article
Estimation for Parameters of Life of the Marshall-Olkin Generalized-Exponential Distribution Using Progressive Type-II Censored Data
Table 2
The APEs (first-line), RMSEs (second-line), and MRABs (third-line) of
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| | FP | Scheme | MLE | SEL | LL | Prior | I | II | I | II | | −3 | −0.03 | +3 | −3 | −0.03 | +3 |
| 30 | 30% | 1 | 1.9985 | 0.5629 | 0.5427 | 0.5691 | 0.5630 | 0.5571 | 0.5471 | 0.5428 | 0.5390 | | | 1.9726 | 0.0894 | 0.0749 | 0.0692 | 0.0630 | 0.0571 | 0.0480 | 0.0432 | 0.0402 | | | 2.4722 | 0.1327 | 0.1067 | 0.1383 | 0.1260 | 0.1142 | 0.0941 | 0.0855 | 0.0788 | | 2 | 1.8432 | 0.5834 | 0.5514 | 0.5870 | 0.5834 | 0.5804 | 0.5586 | 0.5515 | 0.5449 | | | 1.5105 | 0.0957 | 0.0859 | 0.0874 | 0.0836 | 0.0805 | 0.0741 | 0.0680 | 0.0643 | | | 2.1497 | 0.1668 | 0.1355 | 0.1739 | 0.1668 | 0.1608 | 0.1454 | 0.1350 | 0.1282 | | 3 | 6.0528 | 0.5304 | 0.4064 | 0.5336 | 0.5304 | 0.5279 | 0.4145 | 0.4065 | 0.4009 | | | 1.6522 | 0.1195 | 0.1161 | 0.0899 | 0.0904 | 0.0961 | 0.0835 | 0.0954 | 0.1001 | | | 2.9469 | 0.2079 | 0.2070 | 0.1710 | 0.1777 | 0.1914 | 0.1539 | 0.1870 | 0.1983 | 60% | 1 | 1.0393 | 0.5479 | 0.4952 | 0.5490 | 0.5480 | 0.5470 | 0.5055 | 0.4953 | 0.4887 | | | 1.7948 | 0.0672 | 0.0546 | 0.0493 | 0.0482 | 0.0472 | 0.0381 | 0.0392 | 0.0393 | | | 1.5525 | 0.0973 | 0.0961 | 0.0980 | 0.0959 | 0.0940 | 0.0729 | 0.0762 | 0.0780 | | 2 | 0.9105 | 0.5565 | 0.5675 | 0.5583 | 0.5565 | 0.5548 | 0.5727 | 0.5675 | 0.5641 | | | 1.4539 | 0.0852 | 0.0660 | 0.0592 | 0.0566 | 0.0549 | 0.0586 | 0.0522 | 0.0458 | | | 1.3115 | 0.1350 | 0.1129 | 0.1171 | 0.1129 | 0.1097 | 0.1167 | 0.1030 | 0.0898 | | 3 | 1.6928 | 0.4110 | 0.5678 | 0.4243 | 0.4111 | 0.4043 | 0.5715 | 0.5678 | 0.5641 | | | 2.1120 | 0.0841 | 0.0612 | 0.0715 | 0.0679 | 0.0642 | 0.0353 | 0.0316 | 0.0286 | | | 2.1506 | 0.1420 | 0.0803 | 0.1429 | 0.1356 | 0.1282 | 0.0671 | 0.0609 | 0.0557 | 90% | 1 | 0.8250 | 0.5188 | 0.4619 | 0.5214 | 0.5188 | 0.5169 | 0.4635 | 0.4619 | 0.4606 | | | 1.1076 | 0.0501 | 0.0429 | 0.0238 | 0.0201 | 0.0177 | 0.0282 | 0.0168 | 0.0155 | | | 1.1141 | 0.0873 | 0.0490 | 0.0427 | 0.0376 | 0.0339 | 0.0408 | 0.0305 | 0.0289 | | 2 | 0.8093 | 0.4851 | 0.5093 | 0.4869 | 0.4851 | 0.4837 | 0.5117 | 0.5093 | 0.5071 | | | 0.9211 | 0.0409 | 0.0363 | 0.0158 | 0.0163 | 0.0171 | 0.0154 | 0.0125 | 0.0100 | | | 1.0725 | 0.0623 | 0.0484 | 0.0295 | 0.0302 | 0.0326 | 0.0233 | 0.0186 | 0.0142 | | 3 | 0.7959 | 0.4810 | 0.5145 | 0.4866 | 0.4811 | 0.4770 | 0.5180 | 0.5145 | 0.5122 | | | 0.8940 | 0.0536 | 0.0461 | 0.0261 | 0.0254 | 0.0270 | 0.0229 | 0.0170 | 0.0136 | | | 1.1052 | 0.0696 | 0.0413 | 0.0486 | 0.0460 | 0.0478 | 0.0359 | 0.0290 | 0.0245 | 60 | 30% | 1 | 0.8289 | 0.4609 | 0.5271 | 0.4696 | 0.4609 | 0.4563 | 0.5292 | 0.5271 | 0.5254 | | | 1.2792 | 0.0775 | 0.0648 | 0.0484 | 0.0458 | 0.0457 | 0.0302 | 0.0312 | 0.0347 | | | 1.1895 | 0.1102 | 0.0973 | 0.0955 | 0.0910 | 0.0874 | 0.0584 | 0.0606 | 0.0688 | | 2 | 0.8221 | 0.5196 | 0.5524 | 0.5226 | 0.5197 | 0.5177 | 0.5534 | 0.5524 | 0.5515 | | | 1.0056 | 0.0674 | 0.0582 | 0.0536 | 0.0525 | 0.0522 | 0.0246 | 0.0206 | 0.0181 | | | 1.1491 | 0.1150 | 0.1069 | 0.1048 | 0.1049 | 0.1031 | 0.0451 | 0.0393 | 0.0353 | | 3 | 2.3964 | 0.4963 | 0.4363 | 0.4996 | 0.4964 | 0.4943 | 0.4451 | 0.4363 | 0.4319 | | | 1.2605 | 0.0918 | 0.0505 | 0.0275 | 0.0279 | 0.0289 | 0.0632 | 0.0661 | 0.0691 | | | 1.7870 | 0.1550 | 0.0725 | 0.0508 | 0.0512 | 0.0551 | 0.1159 | 0.1273 | 0.1361 | 60% | 1 | 0.6404 | 0.5408 | 0.4696 | 0.5440 | 0.5408 | 0.5387 | 0.4756 | 0.4697 | 0.4656 | | | 0.6240 | 0.0585 | 0.0582 | 0.0452 | 0.0435 | 0.0440 | 0.0280 | 0.0277 | 0.0258 | | | 0.7339 | 0.0910 | 0.0817 | 0.0880 | 0.0817 | 0.0876 | 0.0519 | 0.0543 | 0.0509 | | 2 | 0.6507 | 0.4515 | 0.5102 | 0.4552 | 0.4515 | 0.4490 | 0.5145 | 0.5102 | 0.5072 | | | 0.6429 | 0.0503 | 0.0485 | 0.0475 | 0.0504 | 0.0516 | 0.0203 | 0.0136 | 0.0093 | | | 0.7673 | 0.0564 | 0.0897 | 0.0477 | 0.0970 | 0.1020 | 0.0290 | 0.0205 | 0.0145 | | 3 | 0.8705 | 0.4746 | 0.5283 | 0.4780 | 0.4747 | 0.4725 | 0.5325 | 0.5283 | 0.5257 | | | 1.2345 | 0.0552 | 0.0500 | 0.0212 | 0.0207 | 0.0217 | 0.0355 | 0.0294 | 0.0293 | | | 1.5016 | 0.0726 | 0.0595 | 0.0404 | 0.0385 | 0.0421 | 0.0651 | 0.0566 | 0.0562 | 90% | 1 | 0.5737 | 0.5100 | 0.5455 | 0.5139 | 0.5100 | 0.5078 | 0.5478 | 0.5455 | 0.5438 | | | 0.4576 | 0.0458 | 0.0447 | 0.0438 | 0.0414 | 0.0390 | 0.0197 | 0.0129 | 0.0091 | | | 0.6049 | 0.0639 | 0.0317 | 0.0820 | 0.0794 | 0.0773 | 0.0277 | 0.0201 | 0.0155 | | 2 | 0.5792 | 0.4880 | 0.5030 | 0.4920 | 0.4881 | 0.4857 | 0.5072 | 0.5030 | 0.5004 | | | 0.4528 | 0.0478 | 0.0448 | 0.0182 | 0.0156 | 0.0157 | 0.0179 | 0.0107 | 0.0068 | | | 0.6110 | 0.0440 | 0.0462 | 0.0342 | 0.0294 | 0.0291 | 0.0208 | 0.0140 | 0.0105 | | 3 | 0.6153 | 0.4814 | 0.4741 | 0.4855 | 0.4814 | 0.4790 | 0.4780 | 0.4742 | 0.4719 | | | 0.5390 | 0.0523 | 0.0421 | 0.0143 | 0.0100 | 0.0085 | 0.0284 | 0.0284 | 0.0261 | | | 0.7138 | 0.0596 | 0.0348 | 0.0235 | 0.0184 | 0.0159 | 0.0531 | 0.0525 | 0.0514 |
| 90 | 30% | 1 | 0.6918 | 0.4963 | 0.4965 | 0.4988 | 0.4963 | 0.4947 | 0.4989 | 0.4966 | 0.4950 | | | 1.0070 | 0.0400 | 0.0370 | 0.0184 | 0.0138 | 0.0110 | 0.0143 | 0.0097 | 0.0070 | | | 0.8784 | 0.0299 | 0.0305 | 0.0271 | 0.0221 | 0.0190 | 0.0186 | 0.0150 | 0.0132 | | 2 | 0.6603 | 0.5138 | 0.4904 | 0.5163 | 0.5138 | 0.5122 | 0.4936 | 0.4904 | 0.4885 | | | 0.7114 | 0.0442 | 0.0435 | 0.0283 | 0.0245 | 0.0223 | 0.0222 | 0.0163 | 0.0131 | | | 0.8485 | 0.0469 | 0.0285 | 0.0518 | 0.0467 | 0.0435 | 0.0343 | 0.0276 | 0.0245 | | 3 | 1.4694 | 0.4988 | 0.5048 | 0.5026 | 0.4988 | 0.4967 | 0.5082 | 0.5049 | 0.5029 | | | 1.2001 | 0.0448 | 0.0425 | 0.0181 | 0.0154 | 0.0149 | 0.0176 | 0.0112 | 0.0075 | | | 1.0183 | 0.0425 | 0.0250 | 0.0334 | 0.0288 | 0.0272 | 0.0190 | 0.0136 | 0.0106 | 60% | 1 | 0.5322 | 0.5110 | 0.5059 | 0.5136 | 0.5111 | 0.5095 | 0.5083 | 0.5059 | 0.5044 | | | 0.4071 | 0.0387 | 0.0365 | 0.0159 | 0.0107 | 0.0083 | 0.0120 | 0.0082 | 0.0067 | | | 0.5394 | 0.0277 | 0.0198 | 0.0225 | 0.0181 | 0.0158 | 0.0166 | 0.0125 | 0.0099 | | 2 | 0.5573 | 0.5193 | 0.5138 | 0.5212 | 0.5194 | 0.5181 | 0.5171 | 0.5138 | 0.5118 | | | 0.3903 | 0.0440 | 0.0391 | 0.0234 | 0.0205 | 0.0187 | 0.0171 | 0.0143 | 0.0130 | | | 0.5467 | 0.0399 | 0.0388 | 0.0424 | 0.0387 | 0.0362 | 0.0317 | 0.0270 | 0.0237 | | 3 | 0.6249 | 0.4900 | 0.5005 | 0.4935 | 0.4901 | 0.4879 | 0.5033 | 0.5005 | 0.4988 | | | 0.8033 | 0.0442 | 0.0403 | 0.0175 | 0.0104 | 0.0076 | 0.0155 | 0.0096 | 0.0061 | | | 1.0769 | 0.0251 | 0.0204 | 0.0247 | 0.0178 | 0.0141 | 0.0187 | 0.0126 | 0.0088 | 90% | 1 | 0.5475 | 0.5075 | 0.5008 | 0.5103 | 0.5075 | 0.5057 | 0.5029 | 0.5008 | 0.4994 | | | 0.3430 | 0.0377 | 0.0345 | 0.0133 | 0.0098 | 0.0075 | 0.0110 | 0.0080 | 0.0059 | | | 0.4828 | 0.0228 | 0.0171 | 0.0206 | 0.0150 | 0.0114 | 0.0165 | 0.0118 | 0.0087 | | 2 | 0.5332 | 0.4969 | 0.5234 | 0.5004 | 0.4969 | 0.4948 | 0.5259 | 0.5234 | 0.5217 | | | 0.3258 | 0.0426 | 0.0378 | 0.0198 | 0.0156 | 0.0138 | 0.0165 | 0.0110 | 0.0088 | | | 0.4729 | 0.0296 | 0.0281 | 0.0325 | 0.0276 | 0.0252 | 0.0264 | 0.0199 | 0.0166 | | 3 | 0.5489 | 0.5036 | 0.5049 | 0.5073 | 0.5036 | 0.5015 | 0.5079 | 0.5049 | 0.5031 | | | 0.4135 | 0.0438 | 0.0390 | 0.0168 | 0.0101 | 0.0064 | 0.0137 | 0.0088 | 0.0060 | | | 0.5669 | 0.0203 | 0.0198 | 0.0198 | 0.0126 | 0.0085 | 0.0162 | 0.0102 | 0.0067 |
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