A Multivariate Skew-Normal-Tukey-h Distribution
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.
Cite
@article{arxiv.2310.11779,
title = {A Multivariate Skew-Normal-Tukey-h Distribution},
author = {Sagnik Mondal and Marc G. Genton},
journal= {arXiv preprint arXiv:2310.11779},
year = {2023}
}