On Elliptical and Inverse Elliptical Wishart distributions: Review, new results, and applications
arxiv(2024)
摘要
This paper deals with matrix-variate distributions, from Wishart to Inverse
Elliptical Wishart distributions over the set of symmetric definite positive
matrices. Similar to the multivariate scenario, (Inverse) Elliptical Wishart
distributions form a vast and general family of distributions, encompassing,
for instance, Wishart or t-Wishart ones. The first objective of this study is
to present a unified overview of Wishart, Inverse Wishart, Elliptical Wishart,
and Inverse Elliptical Wishart distributions through their fundamental
properties. This involves leveraging the stochastic representation of these
distributions to establish key statistical properties of the Normalized Wishart
distribution. Subsequently, this enables the computation of expectations,
variances, and Kronecker moments for Elliptical Wishart and Inverse Elliptical
Wishart distributions. As an illustrative application, the practical utility of
these generalized Elliptical Wishart distributions is demonstrated using a real
electroencephalographic dataset. This showcases their effectiveness in
accurately modeling heterogeneous data.
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