Scale mixtures of Kotz-Dirichlet distributions

  • Authors:

  • N. Balakrishnan;E. Hashorva

  • Affiliations:

  • Department of Mathematics and Statistics, McMaster University, 1280 Main Street West Hamilton, Ontario, Canada L8S 4K1;Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne Bítiment Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerland

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2013

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Abstract

In this paper, we first show that a k-dimensional Dirichlet random vector has independent components if and only if it is a Kotz Type I Dirichlet random vector. We then consider in detail the class of k-dimensional scale mixtures of Kotz-Dirichlet random vectors, which is a natural extension of the class of Kotz Type I random vectors. An interesting member of the Kotz-Dirichlet class of multivariate distributions is the family of Pearson-Kotz Dirichlet distributions, for which we present a new distributional property. In an asymptotic framework, we show that the Kotz Type I Dirichlet distributions approximate the conditional distributions of scale mixtures of Kotz-Dirichlet random vectors. Furthermore, we show that the tail indices of regularly varying Dirichlet random vectors can be expressed in terms of the Kotz Type I Dirichlet random vectors.