# Gamma Distribution with MLE Solution

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.