Skew t distributions via the sinh-arcsinh transformation

Rosco, J. F.; Jones, M. C. and Pewsey, Arthur (2011). Skew t distributions via the sinh-arcsinh transformation. TEST, 20(3) pp. 630–652.

DOI: https://doi.org/10.1007/s11749-010-0222-2

Abstract

A version of the sinh-arcsinh transformation is used to generate a skew extension of Student’s t distribution which provides an alternative to previously proposed skew t distributions. The basic properties of the resulting sinh-arcsinhed t family of distributions are presented, many of them effectively having the same level of complexity as their Student t counterparts. Quantile-based measures, which come to the fore due to the non-existence of moments, are readily available. The parameters of the distribution have clear interpretations. Limiting distributions as shape parameters tend to their extreme values are especially appealing. The family’s simplest sub-class is closely related to a sub-class of the LU family. Likelihood based inference is considered and applied in the analysis of heavy-tailed and skew data on fibre glass strengths. Comparisons are made throughout with two of the most popular existing competitors to this distribution: it scores very well relative to them on a number of tractability grounds.

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