Journal ArticleDOI
Characterization of normality within the class of elliptical contoured distributions
C.G Khatri,Rahul Mukerjee +1 more
TLDR
In this paper, the necessary and sufficient conditions for a quadratic form x′Ax to be distributed as chi-square were established when μ = 0 and Σ = I.About:
This article is published in Statistics & Probability Letters.The article was published on 1987-04-01. It has received 9 citations till now. The article focuses on the topics: Quadratic form (statistics).read more
Citations
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Journal ArticleDOI
On some characterizations of the t-distribution
TL;DR: In this article, three different characterizations of the generalized t-distribution within the class of the eliptical distributions were discussed, including unconditional and conditional marginals and quadratic forms.
Journal ArticleDOI
On some characterizations of spherical distributions
TL;DR: In this article, a characterization for each spherical distribution is presented, and a representation as a scale mixture of the Pearson type II distribution is obtained, and some extensions to the multivariate case are also considered.
Book ChapterDOI
Mixtures of Normal Distributions
TL;DR: In this paper, the scale mixture of matrix variate normal distributions is defined using Corollary 2.6, and the Laplace transform is used to obtain the p.d.f. of a matrix variately elliptically contoured distribution.
Book ChapterDOI
Application in Portfolio Theory
TL;DR: An exact test for the weights of the global minimum variance portfolio and the characteristics of the efficient frontier are presented as well as the inferences for Markowitz’s efficient frontier.
Book ChapterDOI
Skew Elliptically Contoured Distributions
TL;DR: In this article, the authors deal with matrix variate closed skew normal distributions and their distributional properties are presented and an application to portfolio theory is provided, and the extension to matrix variates closed skew elliptically contoured distributions is suggested.
References
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Journal ArticleDOI
On the theory of elliptically contoured distributions
TL;DR: The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity as mentioned in this paper, where the distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg on spherically symmetric distributions.