Gamma Distribution with MLE Solution

From ReliaWiki
Jump to navigation Jump to search
Weibull Reference Examples Banner.png


Gamma Distribution with MLE Solution

This example validates the calculations for the MLE solution for the 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
128.04 173.4


Result

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


Results in Weibull++

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

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

Gamma MLE.png