文章基本信息

标题：The Distribution of Quadratic Expressions in Elliptically Contoured Vectors
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作者：Serge Provost ; Ali Mohsenipour
期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2012
卷号：1
期号：2
页码：103
DOI：10.5539/ijsp.v1n2p103
出版社：Canadian Center of Science and Education
摘要：A general representation of quadratic expressions in possibly singular elliptically contoured random vectors, as well as a procedure for the numerical evaluation of their distributions, are proposed in this paper. First, such quadratic expressions are represented as the difference of two positive definite elliptically contoured quadratic forms plus an independently distributed linear combination of spherically distributed random variables. Their distributions are then determined from a representation of elliptically contoured vectors in terms of scale mixtures of Gaussian vectors. Quadratic forms and quadratic expressions in various types of elliptically contoured vectors are considered. An accurate moment-based approximation to their density function is also provided. Several numerical examples illustrate the results.