Table 3 Summary statistics for the MLEs of θ,γ and τ under Case 3: all parameters are unknown
From: The linearly decreasing stress Weibull (LDSWeibull): a new Weibull-like distribution
True values | Sample size | MLE summary statistics | |||
|---|---|---|---|---|---|
(θ0,γ0,τ0) | n | Bias | Variance | MSE | CV (%) |
(1, 2.1, 4) | 10 | 3.2041×10−01 | 4.3806×10−01 | 5.41×10−01 | 50.1 |
|  | 100 | 5.8064×10−02 | 1.7228×10−02 | 2.06×10−02 | 12.4 |
(1, 2.1, 4) | 10 | −1.0850×10−03 | 4.3741×10−01 | 4.37×10−01 | 31.5 |
|  | 100 | −3.3220×10−02 | 1.8676×10−02 | 1.98×10−02 | 6.6 |
(1, 2.1, 4) | 10 | 8.0234 | 1.2209×1003 | 1.29×1002 | 290.6 |
|  | 100 | −1.7590×10−01 | 1.5449 | 1.58 | 32.5 |
(5, 2.1, 0.5) | 10 | 1.0691×10−01 | 3.6471×10−01 | 3.76×10−01 | 11.8 |
|  | 100 | 4.4063×10−02 | 1.1865×10−02 | 1.38×10−02 | 2.2 |
(5, 2.1, 0.5) | 10 | 1.3436×10−01 | 1.9815 | 2.00 | 63 |
|  | 100 | −5.8553×10−02 | 5.0993×10−02 | 5.44×10−02 | 11.1 |
(5, 2.1, 0.5) | 10 | 7.9145 | 7.9433×1002 | 8.57×1002 | 334.9 |
|  | 100 | −2.3851×10−02 | 2.5798×10−02 | 2.64×10−02 | 33.7 |
(0.01, 2, 1) | 10 | 6.2834×10−02 | 7.2434×10−03 | 1.1191×10−02 | 116.9 |
|  | 100 | 6.3975×10−03 | 9.8491×10−05 | 1.39×10−04 | 60.5 |
(0.01, 2, 1) | 10 | −6.0908×10−02 | 1.5017×10−01 | 1.54×10−01 | 20 |
|  | 100 | −2.3752×10−02 | 7.3364×10−03 | 7.90×10−03 | 4.3 |
(0.01, 2, 1) | 10 | −1.0817×10−01 | 2.1851×10−01 | 2.30×10−01 | 52.4 |
|  | 100 | −2.4058×10−02 | 1.1661×10−02 | 1.22×10−02 | 11.1 |