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A multivariate skew-normal-Tukey-h distribution

Author

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  • Mondal, Sagnik
  • Genton, Marc G.

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 with an alternative parameterization. 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 that can be applied to large dimensions. 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.

Suggested Citation

  • Mondal, Sagnik & Genton, Marc G., 2024. "A multivariate skew-normal-Tukey-h distribution," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:jmvana:v:200:y:2024:i:c:s0047259x23001069
    DOI: 10.1016/j.jmva.2023.105260
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