A multivariate skew-normal-Tukey-h distribution

Sagnik Mondal*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number105260
StatePublished - Mar 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.


  • Heavy-tails
  • Lambert's-W
  • Non-gaussian distribution
  • Skew-normal
  • Skew-t
  • Tukey-h

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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