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arXiv · 2310.11779

A Multivariate Skew-Normal-Tukey-h Distribution

Sagnik Mondal·Marc G. Genton
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Abstract

We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and is an extension of the skew-normal distribution for handling heavy-tailed data. We compare this proposed distribution to the skew-t distribution, which is another extension of the skew-normal distribution for modeling tail-thickness, and demonstrate that when there are substantial differences in marginal kurtosis, the proposed distribution is more appropriate. Moreover, we derive many appealing stochastic properties of the proposed distribution and provide a methodology for the estimation of the parameters in which the computational requirement increases linearly with the dimension. Using simulations, as well as a wine and a wind speed data application, we illustrate how to draw inferences based on the multivariate skew-normal-Tukey-h distribution.

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Sagnik Mondal, Marc G. Genton. 2023-10-18. A Multivariate Skew-Normal-Tukey-h Distribution. https://arxiv.org/abs/2310.11779

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