Research Article
A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector
Table 1
The results of the simulation study of the NGen-Weibull model for
.
| n | Parameters | MLEs | MSEs | Biases |
| 25 | | 1.57272700 | 0.10565145 | 0.17272731 | | 1.15407200 | 0.06573026 | 0.15407212 | | 3.230664 00 | 6.47732440 | 2.03066430 |
| 50 | | 1.52288400 | 0.05360254 | 0.12288441 | | 1.13838900 | 0.04414655 | 0.13838869 | | 2.69624200 | 4.51638700 | 1.49624160 |
| 75 | | 1.49738600 | 0.03260828 | 0.09738595 | | 1.12120700 | 0.03170536 | 0.12120685 | | 2.50034400 | 3.78230730 | 1.30034420 |
| 100 | | 1.48435200 | 0.02587331 | 0.08435211 | | 1.10939400 | 0.02752766 | 0.10939399 | | 2.24930400 | 2.82126370 | 1.04930410 |
| 150 | | 1.46361500 | 0.01655346 | 0.06361484 | | 1.09583800 | 0.02307459 | 0.09583788 | | 2.16424400 | 2.76536040 | 0.96424440 |
| 200 | | 1.45604900 | 0.01408698 | 0.05604902 | | 1.08893700 | 0.02016455 | 0.08893705 | | 2.02291800 | 2.18558790 | 0.82291830 |
| 300 | | 1.44233200 | 0.00948109 | 0.04233205 | | 1.07478400 | 0.01469160 | 0.07478449 | | 1.80914600 | 1.47998310 | 0.60914590 |
| 400 | | 1.43438700 | 0.00710442 | 0.03438667 | | 1.06524200 | 0.01251653 | 0.06524163 | | 1.67936500 | 1.08931920 | 0.47936480 |
| 500 | | 1.43820200 | 0.00648074 | 0.03820168 | | 1.06577600 | 0.01241515 | 0.06577620 | | 1.67539100 | 1.02479190 | 0.47539100 |
| 600 | | 1.43061800 | 0.00528021 | 0.03061809 | | 1.06079900 | 0.01133082 | 0.06079897 | | 1.64763900 | 1.01068440 | 0.44763910 |
| 700 | | 1.43231000 | 0.00516572 | 0.03231025 | | 1.05961300 | 0.01092145 | 0.05961322 | | 1.62284000 | 0.91456200 | 0.42284040 |
| 750 | | 1.41498100 | 0.00400002 | 0.02498083 | | 1.04965000 | 0.00870671 | 0.04964955 | | 1.51043600 | 0.63627510 | 0.32043650 |
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