Extended Matrix Variate Beta Distributions

In this paper, we study the  matrix variate generalization of the extended beta type 1 distribution. We also define extended  matrix variate beta type 2 and type 3 distributions and derive several of their properties. We also establish relationship between these three matrix variate distributions

Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions

In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with a set of complex Dirichlet type I matrices have been derived.In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with a set of complex Dirichlet type I matrices have been derived

Non-Central Beta Type 3 Distribution

Let $X$ and $Y$ be independent random variables, $X$ having a gamma distribution with  shape parameter  $a$ and $Y$ having a non-centralgamma distribution with shape and non-centrality parameters $b$ and$\delta$, respectively. Define $W ={X}/(X + 2 Y)$. Then, the randomvariable $W$ has a non-central beta type 3 distribution, $W\sim\textnormal{NCB3} (a,b;\delta)$. In this article we study several of itsproperties. We also give a multivariate generalization of thenon-central beta type 3 distribution and derive its properties

Distribución Kummer-beta bivariada generalizada

A new bivariate beta distribution based on the Humbert’s confluent hypergeometric function of the second kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and entropies. En este artículo se propone una nueva distribución beta bivariada basada en distribuciones hipergeométricas Humbert de segundo tipo. También se derivan las representaciones de las densidades marginales, momentos marginales y productos, densidades condicionales y entropía.&nbsp

Generalized Bivariate Kummer-Beta Distribution

A new bivariate beta distribution based on the Humbert’s confluent hypergeometric function of the second kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and entropies.En este artículo se propone una nueva distribución beta bivariada basadaen distribuciones hipergeométricas Humbert de segundo tipo. Tambiénse derivan las representaciones de las densidades marginales, momentosmarginales y productos, densidades condicionales y entropía

Funciones Beta y Gama Generalizadas Extendidas y sus Aplicaciones

In this article, we define and study generalized forms of extended matrix variate gamma and beta functions. By using a number of results from matrix algebra, special functions of matrix arguments and zonal polynomials we derive a number of properties of these newly defined functions. We also give some applications of these functions to statistical distribution theory.En este artículo definimos y estudiamos formas generalizadas de las funciones gama y beta matriz variadas extendidas. Utilizando varios resultados del álgebra matricial, funciones especiales de argumento matricial y polinomios zonales, derivamos algunas de las propiedades de estas funciones. También mostramos algunas aplicaciones de estas funciones a la teoría de distribuciones

Null distribution of multiple correlation coefficient under mixture normal model

The multiple correlation coefficient is used in a large variety of statistical tests and regression problems. In this article, we derive the null distribution of the square of the sample multiple correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1−R2 and inverse Mellin transform have been used to derive the density of R2

Distribución de la traza de la matriz de sumas de cuadrados y productos bajo el modelo normal mixto

En este artículo se deriva la distribución de la traza de A, tr(A), donde A es la matriz de sumas de cuadrados y productos cuando la muestra proviene de la mezcla de dos distribuciones normales multivariadas

Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry

The non-null distribution of the modified likelihood ratio test statistic Λ∗ for testing multisample compound symmetry of q multivariate Gaussian models is derived. The non-null moments of Λ∗ are obtained in terms of Lauricella's hypergeometric function. The non-null distribution is expressed in terms of H-function.&nbsp

Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry

The non-null distribution of the modified likelihood ratio test statistic Λ∗ for testing multisample compound symmetry of q multivariate Gaussian models is derived. The non-null moments of Λ∗ are obtained in terms of Lauricella's hypergeometric function. The non-null distribution is expressed in terms of H-function.