Noncentral quadratic forms of the skew elliptical variables

Authors:
B. Q. Fang
Affiliations:
Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 2
Cited 2

A general class of multivariate skew-elliptical distributions

Journal of Multivariate Analysis
The skew elliptical distributions and their quadratic forms

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Sample mean, covariance and T2 statistic of the skew elliptical model

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Noncentral matrix quadratic forms of the skew elliptical variables

Journal of Multivariate Analysis

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Abstract

In this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution.