Generalized Gamma Distribution with MLE Solution: Difference between revisions

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{{Reference Example}}
{{Reference Example}}


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




{{Reference_Example_Heading1}}
{{Reference_Example_Heading1}}


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.
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.




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{{Reference_Example_Heading4}}
{{Reference_Example_Heading4}}


The following picture shows the results in Weibull++:


[[Image:GenGamma_MLE.png|center|500px]]
[[Image:GenGamma_MLE.png|center|550]]

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Generalized Gamma Distribution with MLE Solution

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
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++:

550