Describing the Flexibility of the Generalized Gamma and Related Distributions

The generalized gamma (GG) distribution is a widely used, flexible tool for parametric survival analysis. Many alternatives and extensions to this family have been proposed. This paper characterizes the flexibility of the GG by the quartile ratio relationship, log(Q2/Q1)/log(Q3/Q2), and compares the GG on this basis with two other three-parameter distributions and four parent distributions of four or five parameters. For most parameter combinations of other distributions, a very similar GG, as assessed by the Kullback-Liebler distance, can be found by matching the three quartiles; extreme cases where this fails are examined. Limited additional flexibility is observed, supporting the basic GG family as an ideal platform for parametric survival analysis.