Uncovering a generalised gamma distribution : from shape to interpretation

Abstract

In this paper, we introduce the flexible interpretable gamma (FIG) distribution, with origins in Weibulisation, power weighting, and a stochastic representation. The FIG parameters have been verified graphically, mathematically, and through simulation as having separable roles in influencing the left tail, body, and right tail shape. The generalised gamma (GG) distribution has become a standard model for positive data in statistics due to its interpretable parameters and tractable equations. Although there are many generalised forms of the GG that can provide a better fit to data, none of them extend the GG so that the parameters are interpretable. We conduct simulation studies on the maximum likelihood estimates and respective sub-models of the FIG. Finally, we assess the flexibility of the FIG relative to existing models by applying the FIG model to hand grip strength and insurance loss data.