On modelling asymmetric data using two-piece sinh-arcsinh distributions

TL;DR

This paper introduces a new univariate two-piece sinh-arcsinh distribution with two shape parameters for skewness and kurtosis, offering enhanced asymmetry modeling while maintaining tail flexibility and tractability.

Contribution

The paper presents a novel two-piece sinh-arcsinh distribution that better captures asymmetry compared to the original, with potential multivariate extensions.

Findings

The new distribution captures higher asymmetry levels than previous models.

It maintains tail flexibility and tractability.

Performance demonstrated with real data comparisons.

Abstract

We introduce the univariate two--piece sinh-arcsinh distribution, which contains two shape parameters that separately control skewness and kurtosis. We show that this new model can capture higher levels of asymmetry than the original sinh-arcsinh distribution (Jones and Pewsey, 2009), in terms of some asymmetry measures, while keeping flexibility of the tails and tractability. We illustrate the performance of the proposed model with real data, and compare it to appropriate alternatives. Although we focus on the study of the univariate versions of the proposed distributions, we point out some multivariate extensions.