Related papers: About the matrix variate problem involved in the d…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
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…
We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss.…
Large H-selfadjoint random matrices are considered. The matrix $H$ is assumed to have one negative eigenvalue, hence the matrix in question has precisely one eigenvalue of nonpositive type. It is showed that this eigenvalue converges in…
We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1F_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions…
This work sets the matrix variate Birnbaum-Saunders theory in the context of singular distributions and elliptical models. The so termed singular matrix variate generalised Birnbaum-Saunders distribution is obtained with respect the…
Consider random matrices $A$, of dimension $m\times (m+n)$, drawn from an ensemble with probability density $f(\rmtr AA^\dagger)$, with $f(x)$ a given appropriate function. Break $A = (B,X)$ into an $m\times m$ block $B$ and the…
Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
The variance of a linear statistic defined on the symmetric group endowed with the Ewens probability is examined. Despite the dependence of the summands, it can be bounded from above by a constant multiple of the sum of variances. We find…
The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.
In this article, we define a matrix variate asymmetric Laplace distribution. We prove some properties of the matrix variate asymmetric Laplace distribution. We prove the relationship between the matrix variate asymmetric Laplace…
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…