Research Article
A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application
Table 3
ML and Bayesian estimations of parameters and reliability based on nonfuzzy and fuzzy: I.
| | | Parameter | Nonfuzzy | Fuzzy |
| | n | | | | | | | | | α = 0.25 | α = 0.55 | α = 0.9 | 0.5 | 50 | ML | AAB | 0.0315 | 0.5563 | 1.0294 | 0.0121 | 0.0030 | 0.0007 | 0.0037 | 0.0023 | 0.0079 | MSE | 0.2332 | 0.5967 | 2.4594 | 0.0008 | 0.0046 | 0.0070 | 0.0004 | 0.0017 | 0.0058 | LACI | 1.8889 | 2.1017 | 4.6401 | 0.0922 | 0.2657 | 0.3274 | 0.0771 | 0.1632 | 0.2892 | Bayesian | AAB | 0.0589 | 0.0884 | 0.0658 | 0.0131 | 0.0242 | 0.0206 | 0.0082 | 0.0120 | 0.0094 | MSE | 0.0274 | 0.0623 | 0.0763 | 0.0006 | 0.0035 | 0.0039 | 0.0003 | 0.0010 | 0.0020 | LCCI | 0.5927 | 0.8852 | 0.9128 | 0.0823 | 0.2153 | 0.2354 | 0.0577 | 0.1155 | 0.1712 | 150 | ML | AAB | 0.0042 | 0.3571 | 0.6636 | 0.0170 | 0.0060 | 0.0017 | 0.0026 | 0.0032 | 0.0153 | MSE | 0.0661 | 0.2163 | 0.7759 | 0.0005 | 0.0017 | 0.0025 | 0.0001 | 0.0006 | 0.0021 | LACI | 1.0085 | 1.1686 | 2.2720 | 0.0550 | 0.1584 | 0.1945 | 0.0441 | 0.0963 | 0.1706 | Bayesian | AAB | 0.0480 | 0.0695 | 0.0120 | 0.0128 | 0.0127 | 0.0064 | 0.0051 | 0.0044 | 0.0034 | MSE | 0.0232 | 0.0289 | 0.0514 | 0.0004 | 0.0014 | 0.0018 | 0.0001 | 0.0004 | 0.0013 | LCCI | 0.5617 | 0.6001 | 0.7586 | 0.0557 | 0.1403 | 0.1673 | 0.0364 | 0.0794 | 0.1383 | 1 | 50 | ML | AAB | 0.0470 | 0.7050 | 1.2235 | 0.0157 | 0.0084 | 0.0022 | 0.0055 | 0.0017 | 0.0133 | MSE | 0.2524 | 0.7991 | 3.0997 | 0.0007 | 0.0043 | 0.0069 | 0.0004 | 0.0016 | 0.0054 | LACI | 1.9617 | 2.1556 | 4.9653 | 0.0796 | 0.2549 | 0.3260 | 0.0737 | 0.1560 | 0.2821 | Bayesian | AAB | 0.0674 | 0.1034 | 0.0456 | 0.0109 | 0.0221 | 0.0189 | 0.0075 | 0.0115 | 0.0098 | MSE | 0.0310 | 0.0751 | 0.0872 | 0.0005 | 0.0034 | 0.0041 | 0.0003 | 0.0010 | 0.0022 | LCCI | 0.6211 | 0.9587 | 1.0448 | 0.0695 | 0.2097 | 0.2425 | 0.0543 | 0.1127 | 0.1821 | 150 | ML | AAB | 0.0448 | 0.5815 | 1.0702 | 0.0153 | 0.0064 | 0.0005 | 0.0027 | 0.0014 | 0.0128 | MSE | 0.0930 | 0.5231 | 1.7384 | 0.0004 | 0.0016 | 0.0026 | 0.0001 | 0.0005 | 0.0020 | LACI | 1.1688 | 1.6869 | 3.0202 | 0.0470 | 0.1525 | 0.1982 | 0.0409 | 0.0900 | 0.1692 | Bayesian | AAB | 0.0635 | 0.0782 | 0.0098 | 0.0103 | 0.0136 | 0.0083 | 0.0052 | 0.0061 | 0.0006 | MSE | 0.0296 | 0.0337 | 0.0659 | 0.0003 | 0.0015 | 0.0019 | 0.0001 | 0.0004 | 0.0012 | LCCI | 0.5937 | 0.6331 | 0.9222 | 0.0482 | 0.1403 | 0.1680 | 0.0365 | 0.0792 | 0.1342 |
| 2 | 50 | ML | AAB | 0.0465 | 0.8958 | 1.4360 | 0.0126 | 0.0072 | 0.0088 | 0.0063 | 0.0046 | 0.0137 | MSE | 0.3169 | 1.2278 | 3.6640 | 0.0003 | 0.0033 | 0.0070 | 0.0003 | 0.0011 | 0.0048 | LACI | 2.2003 | 2.5577 | 4.9638 | 0.0507 | 0.2219 | 0.3268 | 0.0595 | 0.1314 | 0.2674 | Bayesian | AAB | 0.0699 | 0.1272 | 0.0335 | 0.0066 | 0.0188 | 0.0179 | 0.0058 | 0.0106 | 0.0120 | MSE | 0.0310 | 0.0945 | 0.0944 | 0.0002 | 0.0025 | 0.0037 | 0.0002 | 0.0007 | 0.0020 | LCCI | 0.6255 | 1.0813 | 1.1544 | 0.0435 | 0.1778 | 0.2240 | 0.0420 | 0.0933 | 0.1676 | 150 | ML | AAB | 0.0335 | 0.8512 | 1.4411 | 0.0123 | 0.0071 | 0.0008 | 0.0048 | 0.0026 | 0.0086 | MSE | 0.1257 | 0.9823 | 3.0928 | 0.0002 | 0.0012 | 0.0024 | 0.0001 | 0.0004 | 0.0017 | LACI | 1.3841 | 1.9909 | 3.9532 | 0.0285 | 0.1305 | 0.1930 | 0.0336 | 0.0761 | 0.1586 | Bayesian | AAB | 0.0608 | 0.0954 | 0.0003 | 0.0062 | 0.0142 | 0.0106 | 0.0049 | 0.0079 | 0.0058 | MSE | 0.0305 | 0.0412 | 0.0657 | 0.0001 | 0.0012 | 0.0018 | 0.0001 | 0.0003 | 0.0011 | LCCI | 0.6253 | 0.6868 | 0.9670 | 0.0328 | 0.1191 | 0.1594 | 0.0284 | 0.0633 | 0.1238 |
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