Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution

2009/11/12 by Adelchi Azzalini, Antonella Capitanio · 5 citations
Mathematics · #stat.ME

paper · pdf · doi:10.1111/1467-9868.00391

published as J. Royal Statistical Society, series B, 65 (2003), 367-389 · full-length version of the published paper, 31 pages with 9 figures

arxiv created 2009/11/12 · arxiv updated 2009/12/01

Abstract

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.

Cited by

• Sharpe Ratio and Return-VaR Ratio Maximization for Option Portfolios with Skew-Elliptical t Underlying Returns
• Laplace and skew-Laplace approximations for Dirichlet process mixture posterior density
• Sub-Cauchy Sampling: Escaping the Dark Side of the Moon
• Optimal Option Portfolios for Skew-Elliptical t Returns
• Diffeomorphic Markov Chain Monte Carlo: fast mixing for heavy-tailed distributions

Related

• Statistical applications of the multivariate skew-normal distribution
• Selection models under generalized symmetry settings
• Tail Densities of Skew-Elliptical Distributions
• Some properties of skew-symmetric distributions
• Family of multivariate extended skew-elliptical distributions: Statistical properties, inference and application