The skew elliptical distributions and their quadratic forms

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:
2003

Citing 2
Cited 4

Multivariate Liouville distributions

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A general class of multivariate skew-elliptical distributions

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Noncentral quadratic forms of the skew elliptical variables

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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

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Distribution of quadratic forms under skew normal settings

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Abstract

In this paper, a family of the skew elliptical distributions is defined and investigated. Some basic properties, such as stochastic representation, marginal and conditional distributions, distribution under linear transformations, moments and moment generating function are derived. The joint distribution of several quadratic forms is obtained. An example is given to show that the distributions of some statistics as the functions of the quadratic forms can be derived for various applications.