Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions

TL;DR

This paper introduces a flexible family of univariate double two-piece distributions that model skewness and kurtosis, with applications in finance, internet traffic, and medicine, supported by Bayesian inference methods.

Contribution

It formalizes and generalizes double two-piece distributions with interpretable parameters and develops Bayesian priors and posterior conditions for these models.

Findings

Distributions effectively model asymmetry in diverse data.

Bayesian priors enable meaningful model comparisons.

Applications demonstrate practical utility in real-world data.

Abstract

We formalise and generalise the definition of the family of univariate double two--piece distributions, obtained by using a density--based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.