Gamma Distribution with MLE Solution: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
(Created page with '{{Reference Example}} This example compares the MLE solution for the Gamma distribution. {{Reference_Example_Heading1}} The data from Table 1.1 on page 4 in the book ''Statis…')
 
No edit summary
Line 6: Line 6:
{{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.




Line 41: Line 41:


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


[[Image:Gamma_MLE.png|center]]
[[Image:Gamma_MLE.png|center]]
We can see <math>\mu\,\!</math> = 2.8873. Therefore, <math>\theta = exp(\mu)\,\!</math> = 17.94, which is the same as the results in the book.

Revision as of 16:20, 9 June 2014

Weibull Reference Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at Weibull examples and Weibull reference examples.



Gamma Distribution with MLE Solution

This example compares the MLE solution for the Gamma distribution.


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]\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].

The following picture shows that in Weibull++, [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.

Gamma MLE.png
Retrieved from "https://www.reliawiki.com/index.php?title=Gamma_Distribution_with_MLE_Solution&oldid=55298"