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We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
The binomial and Poisson distributions have interesting relationships with the beta and gamma distributions, respectively, which involve their cumulative distribution functions and the use of conjugate priors in Bayesian statistics. We…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
Matrix variate beta (MVB) distributions are used in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. In this approach a unified methodology is proposed to…
In this article, a general family of bivariate distributions is used to model competing risks data with dependent factors. The general structure of competing risks data considered here includes ties. A comprehensive inferential framework…
We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present…
We study multilevel matrix ensembles at general beta by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For beta = 1, 2, we express the joint…
We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
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…
We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…
Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
In this paper we provide a matrix extension of the scalar binomial series under elliptical contoured models and real normed division algebras. The classical hypergeometric series…
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.…
This note introduces a new range of modified gamma and beta $k$ functions. The authors present new modified gamma and beta $k$-functions, first and second summation relations, various functionals, Mellin transforms, and integral…
This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
In this paper, we introduce a new bivariate distribution we called it bivariate expo- nentiated modified Weibull extension distribution (BEMWE). The model introduced here is of Marshall-Olkin type. The marginals of the new bivariate…
This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…