Table 5 Case 3. Parameter estimates for different simulated data sets
From: Perturbative method for maximum likelihood estimation of the Weibull distribution parameters
CR (%) | M | L-Moments method | Approximate analytical method | ||
|---|---|---|---|---|---|
\(\alpha\) | \(\beta\) | \(\alpha\) | \(\beta\) | ||
0 | 10 | 3.0522 | 2.1521 | 3.0563 | 2.5286 |
20 | 3.4026 | 1.3887 | 3.4289 | 1.4851 | |
50 | 2.7332 | 1.3915 | 2.7112 | 1.3497 | |
100 | 2.9970 | 1.5129 | 2.9860 | 1.4877 | |
500 | 3.1178 | 1.5677 | 3.0670 | 1.4772 | |
1000 | 3.0152 | 1.5289 | 2.9624 | 1.4342 | |
20 | 10 | 2.6830 | 1.9116 | 2.9353 | 1.7227 |
20 | 2.9035 | 1.8576 | 3.3553 | 1.4175 | |
50 | 2.5856 | 1.8822 | 2.8145 | 1.5906 | |
100 | 2.8119 | 2.1616 | 2.9557 | 1.9031 | |
500 | 2.7591 | 1.8930 | 3.0847 | 1.4296 | |
1000 | 2.7483 | 1.9360 | 3.0350 | 1.5349 | |
80 | 10 | 1.0279 | 4.5619 | 1.4874 | 2.1709 |
20 | 1.0871 | 12.9564 | 2.4157 | 2.2982 | |
50 | 1.0709 | 7.8137 | 3.0147 | 1.4884 | |
100 | 1.0553 | 6.1198 | 3.4455 | 1.2138 | |
500 | 1.0757 | 9.3024 | 2.8698 | 1.6711 | |
1000 | 1.0709 | 8.2974 | 2.9130 | 1.5363 | |