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 
, 
and 
. The pdf of the distribution is given by,
where 
is the gamma function, defined by:
This distribution behaves as do other distributions based on the values of the parameters. For example, if 
, then the distribution is identical to the Weibull distribution. If both and 
, then the distribution is identical to the exponential distribution, and for 
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.