The multivariate g-and-h distribution

Christopher Field*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


In this article we consider a generalization of the univariate g-and-h distribution to the multivariate situation with the aim of providing a flexible family of multivariate distributions that incorporate skewness and kurtosis. The approach is to modify the underlying random variables and their quantiles, directly giving rise to a family of distributions in which the quantiles rather than the densities are the foci of attention. Using the ideas of multivariate quantiles, we show how to fit multivariate data to our multivariate g-and-h distribution. This provides a more flexible family than the skew-normal and skew-elliptical distributions when quantiles are of principal interest. Unlike those families, the distribution of quadratic forms from the multivariate g-and-h distribution depends on the underlying skewness. We illustrate our methods on Australian athletes data, as well as on some wind speed data from the northwest Pacific.

Original languageEnglish (US)
Pages (from-to)104-111
Number of pages8
Issue number1
StatePublished - Feb 2006
Externally publishedYes


  • Kurtosis
  • Multivariate
  • Quantiles
  • Shape
  • Skewness
  • Transformation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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