Mastering the body and tail shape of a distribution

TL;DR

This paper introduces a novel integration approach for flexible distribution modeling that separately visualizes and controls the body and tail shapes, enhancing interpretability and inference.

Contribution

It proposes a new generalized distribution framework that distinctly models body and tail shapes, demonstrated through two specific models and applications to various data types.

Findings

Effective separation of body and tail shape modeling

Enhanced interpretability of distribution parameters

Successful application to heavy and light-tailed data

Abstract

The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to distinguish between changes in the relative body and tail shapes when using these generalizations. What we propose is a neat integration approach generalization which enables the visualization and control of the body and the tail shape separately. This provides a flexible modeling opportunity with an emphasis on parameter inference and interpretation. Two related models, the two-piece body-tail generalized normal and the two-piece tail adjusted normal are swiftly introduced to demonstrate this inferential potential. The methodology is then demonstrated on heavy and light-tailed data.