The Generalized Gamma Distribution Notes

The Generalized Gamma Distribution Notes

The Generalized Gamma Distribution

Compared to the other distributions previously discussed, the generalized gamma distribution is not as frequently used for modeling life data; however, it has the the ability to mimic the attributes of other distributions, such as the Weibull or lognormal, based on the values of the distribution’s parameters. This offers a compromise between two lifetime distributions. The generalized gamma function is a three-parameter distribution with parameters 74b8eddf4b37de80c7c8eed1b64e46fc5b33f39cef9df8c1d0386c99deb5c8d9 and b5d9e5a9ecd98ded0a1c6f439321904a. The pdf of the distribution is given by,

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where 24b4737f4100228c545e66234e3de28a is the gamma function, defined by:

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This distribution behaves as do other distributions based on the values of the parameters. For example, if 602aa81fe407ee5b3959f53f9f6e38ad, then the distribution is identical to the Weibull distribution. If both 602aa81fe407ee5b3959f53f9f6e38ad and 77c071d59ea999493bfda7e1e5724973, then the distribution is identical to the exponential distribution, and for 1ce5f9e0e28cbb07bc0d56dfcd824889 it is identical to the lognormal distribution. While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.

The generalized gamma distribution and its characteristics are presented in The Generalized Gamma Distribution.

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