Uncovering a generalised gamma distribution: from shape to interpretation

TL;DR

This paper introduces the flexible interpretable gamma (FIG) distribution, derived from the generalised normal, with interpretable parameters controlling different distribution parts, and demonstrates its application to real data for improved modeling.

Contribution

The paper presents the FIG distribution with interpretable parameters, extending the GG distribution, and proves its mathematical properties and applicability to real-world data.

Findings

FIG distribution has interpretable parameters for different distribution parts.

The model fits hand grip strength and insurance loss data effectively.

Mathematical properties and identifiability of FIG are established.

Abstract

In this paper, we introduce the flexible interpretable gamma (FIG) distribution which has been derived by Weibullisation of the body-tail generalised normal distribution. The parameters of the FIG have been verified graphically and mathematically as having interpretable roles in controlling the left-tail, body, and right-tail shape. The generalised gamma (GG) distribution has become a staple model for positive data in statistics due to its interpretable parameters and tractable equations. Although there are many generalised forms of the GG which can provide better fit to data, none of them extend the GG so that the parameters are interpretable. Additionally, we present some mathematical characteristics and prove the identifiability of the FIG parameters. Finally, we apply the FIG model to hand grip strength and insurance loss data to assess its flexibility relative to existing models.