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Generalized Gamma Distribution with MLE Solution
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This example validates the calculations for the MLE solution for the Generalized-Gamma distribution in Weibull++ standard folios.
Reference Case
The data set from Table 1.1 on page 4 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used.
Data
| Failures
|
| 17.88 |
28.92 |
33
|
| 41.52 |
42.12 |
45.6
|
| 48.4 |
51.84 |
51.96
|
| 54.12 |
55.56 |
67.8
|
| 68.64 |
68.64 |
68.88
|
| 84.12 |
93.12 |
98.64
|
| 105.12 |
105.84 |
127.92
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| 128.04 |
173.4 |
|
Result
The solution is given on page 257, Example 11.2. The ML estimates are [math]\displaystyle{ \mu\,\! }[/math] = 4.23, [math]\displaystyle{ \sigma\,\! }[/math] = 0.51 and [math]\displaystyle{ \alpha\,\! }[/math] = 0.3076.
Results in Weibull++
The following picture shows the results in Weibull++:
