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Gamma Distribution with MLE Solution |
This example compares the MLE solution for the Gamma distribution.
Reference Case
The data 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 |
| 128.04 | 173.4 | |
Result
The solution is given on page 257, Example 11.1. The ML estimates are [math]\displaystyle{ \theta \,\! }[/math] = 17.94, k = 4.025.
Results in Weibull++
In Weibull++, the parameter [math]\displaystyle{ \mu\,\! }[/math] is used instead of [math]\displaystyle{ \theta \,\! }[/math]. The relation between them is [math]\displaystyle{ \theta = exp(\mu)\,\! }[/math].
We can see [math]\displaystyle{ \mu\,\! }[/math] = 2.8873. Therefore, [math]\displaystyle{ \theta = exp(\mu)\,\! }[/math] = 17.94, which is the same as the results in the book.