Gamma Distribution with MLE Solution

This example validates the calculations for the MLE solution for the Gamma distribution in Weibull++ standard folios.

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.

The solution is given on page 257, Example 11.1. The ML estimates are $$\theta \,\!$$ = 17.94, k = 4.025.

In Weibull++, the parameter $$\mu\,\!$$ is used instead of $$\theta \,\!$$. The relation between them is $$\theta = exp(\mu)\,\!$$.

The following picture shows that in Weibull++, $$\mu\,\!$$ = 2.8873. Therefore, $$\theta = exp(\mu)\,\!$$ = 17.94, which is the same as the results in the book.