A new asymmetric generalisation of the t-distribution

TL;DR

This paper introduces a flexible 6-parameter asymmetric distribution that generalizes the t-distribution, allowing for asymmetry and heavier tails, with applications demonstrated through data fitting examples.

Contribution

It proposes a novel 6-parameter distribution that extends the t-distribution by incorporating asymmetry and tail power control, avoiding previous discontinuities.

Findings

Distribution reduces to t-distribution when parameters are set to default.

Allows heavier tails than the t-distribution by adjusting the sixth parameter.

Demonstrated effective data fitting with real examples.

Abstract

A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With the sixth parameter set to unity and no asymmetry, the distribution reduces to a t-distribution, but with the sixth parameter reduced, fatter tails than those of the t-distribution are allowed (the tails start earlier) and the distribution generalises Johnson's $S_U$ distribution. Data fitting is illustrated with examples.