Gamma and generalized gamma distributions
We present the Generalized Gamma Distribution, study its properties and derive the estimators of the parameters. This distribution includes many standard forms, like: Gamma, Exponential, Weibull, Half Normal and others. Sum and ratios of independent generalized gamma lead to intractable forms. However approximation works well. In particular two-moment gamma and three moment normal approximations are shown to approximate the sum of k independent gamma as well as generalized gamma distributions.^
Jimenez Nava, Victor Hugo, "Gamma and generalized gamma distributions" (2011). ETD Collection for University of Texas, El Paso. AAI1503731.