Fractional operators in the matrix variate case

Evaluation of matrix-variate gamma and beta integrals as multiple integrals and Kober fractional integral operators in the complex matrix variate case

Matrix-variate Beta Distribution

We propose matrix-variate beta type III distribution. Several properties of this distribution including Laplace transform, marginal distribution and its relationship with matrix-variate beta type I and type II distributions are also studied.

Matrix-Variate Beta Generator - Developments and Application

Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, exten...

Dynamic Matrix-Variate Graphical Models

This paper introduces a novel class of Bayesian models for multivariate time series analysis based on a synthesis of dynamic linear models and graphical models. The synthesis uses sparse graphical modelling ideas to introduce structured, conditional independence relationships in the time-varying, cross-sectional covariance matrices of multiple time series. We define this new class of models and...

Matrix Variate Kummer-dirichlet Distributions

(1.1) { Γ(α)Ψ(α,α−γ+1;ξ) }−1 exp(−ξv)v(1+v), v > 0, (1.2) respectively, where α > 0, β > 0, ξ > 0, −∞ < γ,λ < ∞, 1F1, and Ψ are confluent hypergeometric functions. These distributions are extensions of Gamma and Beta distributions, and for α < 1 (and certain values of λ and γ) yield bimodal distributions on finite and infinite ranges, respectively. These distributions are used (i) in the Bayesi...