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We study the singular values of certain triangular random matrices. When their elements are i.i.d. standard complex Gaussian random variables, the squares of the singular values form a biorthogonal ensemble, and with an appropriate change…

Probability · Mathematics 2014-04-21 Dimitris Cheliotis

Although there is ample work in the literature dealing with skewness in the multivariate setting, there is a relative paucity of work in the matrix variate paradigm. Such work is, for example, useful for modelling three-way data. A matrix…

Methodology · Statistics 2017-10-09 Michael P. B. Gallaugher , Paul D. McNicholas

Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…

Methodology · Statistics 2018-08-15 Michael P. B. Gallaugher , Paul D. McNicholas

This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…

Statistics Theory · Mathematics 2024-05-14 José A. Díaz-García , Francisco J. Caro-Lopera

We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…

Probability · Mathematics 2009-06-16 Wlodzimierz Bryc , Virgil U. Pierce

Recently the termed \emph{multimatrix variate distributions} were proposed in \citet{dgcl:24a} as an alternative for univariate and vector variate copulas. The distributions are based on sample probabilistic dependent elliptically countered…

Statistics Theory · Mathematics 2024-08-06 Francisco J. Caro-Lopera , José A. Díaz-García

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments.…

Statistics Theory · Mathematics 2023-06-09 Koki Shimizu , Hiroki Hashiguchi

This paper proposes a unified approach to enable the study of diverse distributions in the real, complex, quaternion and octonion cases, simultaneously. In particular, the central, nonsingular matricvariate and matrix multivariate Pearson…

Statistics Theory · Mathematics 2010-11-24 Jose A. Diaz-Garcia , Ramon Gutierrez-Jaimez

The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…

Methodology · Statistics 2014-09-17 Ingram Olkin , Thomas A. Trikalinos

In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…

Methodology · Statistics 2025-01-03 Roberto Vila , Felipe Quintino

The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…

Statistics Theory · Mathematics 2022-09-26 Hidemasa Oda , Fumiyasu Komaki

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

Statistics Theory · Mathematics 2020-05-15 Sharon X. Lee , Geoffrey J. McLachlan

Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…

Statistics Theory · Mathematics 2016-03-03 Hazhir Homei

This paper introduces four matrix normal distributions on analytic bundles of flag varieties, extending the separable covariance $\varPhi \otimes \varPsi$ with potentially variable-level ($\varPsi$) and/or sample-level ($\varPhi$)…

Algebraic Geometry · Mathematics 2026-04-24 Haoming Wang

In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…

Statistical Finance · Quantitative Finance 2015-12-09 Frederik Meudt , Martin Theissen , Rudi Schäfer , Thomas Guhr

We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…

Statistics Theory · Mathematics 2014-04-18 Amadou Sarr

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the…

Information Theory · Computer Science 2014-10-21 Marco Chiani

Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart distribution. The Wishart distribution is a matrix…

Probability · Mathematics 2012-01-17 Oliver Pfaffel

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…

Statistics Theory · Mathematics 2021-06-03 Susanne Trick , Frank Jäkel , Constantin A. Rothkopf

We analytically compute the large-deviation probability of a diagonal matrix element of two cases of random matrices, namely $\beta=[\vec H^\dagger\vec H]^{-1}_{11}$ and $\gamma=[\vec I_N+\rho\vec H^\dagger\vec H]^{-1}_{11}$, where $\vec H$…

Information Theory · Computer Science 2011-06-15 Aris L. Moustakas