Daya K. Nagar

Matrix-variate Kummer-Beta distribution

This paper proposes matrix variate generalization of Kummer-Beta family of distributions which has been studied recently by Ng and Kotz. This distribution is an extension of Beta distribution. Its characteristic function has been derived and it is shown that the distribution is orthogonally invariant. Some results on distribution of random quadratic forms have also been derived.

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.

Extended matrix variate gamma and beta functions

The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In this article, we define extended matrix variate gamma and extended matrix variate beta functions thereby generalizing multivariate gamma and multivariate beta functions defined by Ingham and Siegel. We study a number of properties of these newly defined functions. We also give some applications of these functions to statistical distribution theory.

Matrix variate Kummer-Gamma distribution

In this article we propose matrix variate Kummer-Gamma distribution which is an extension of matrix variate Gamma distribution. Several properties of this distribution have been studied. Distributional results on randorn quadratic forms involving Kummer-Gamma matrix have also been derived.

Properties of Matrix Variate Beta Type 3 Distribution

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appells first hypergeometric function and Humberts confluent hypergeometric function of matrix arguments. Further, a bimatrix variate generalization of the beta type 3 distribution is also defined and studied.

Matrix variate Kummer-Dirichlet distributions

The multivariate Kummer-Beta and multivariate Kummer-Gamma families of distributions have been proposed and studied recently by Ng and Kotz. These distributions are extensions of Kummer-Beta and Kummer-Gamma distributions. In this article we propose and study matrix variate generalizations of multivariate Kummer-Beta and multivariate Kummer-Gamma families of distributions.

Product and quotient of correlated beta variables

Abstract Let U , V , W be independent random variables having a standard gamma distribution with respective shape parameters a , b , c , and define X = U / ( U + W ) , Y = V / ( V + W ) . Clearly, X and Y are correlated each having a beta distribution, X ∼ B ( a , c ) and Y ∼ B ( b , c ) . In this article we derive probability density functions of X Y , X / Y and X / ( X + Y ) .

Distribution and percentage points of the likelihood ratio statistic for testing circular symmetry

Abstract In this paper, the distribution of the likelihood ratio statistic for testing the hypothesis that the covariance matrix of a p -variate normal distribution is circular symmetric has been derived. The distribution is obtained in series form using the inverse Mellin transform and the residue theorem. Percentage points for p =4,5,6 and 7 have been computed using distributional results derived in this article.

Likelihood Ratio Test for Multisample Sphericity

This article deals with the null and nonnull distributions of the likelihood ratio criterion for testing multisample sphericity in q multinormal populations. Nonnull moments have been obtained using a simple and shortcut method. The null density has been derived using inverse Mellin transform and the calculus of residues. The nonnull density is given in a series involving zonal polynomials and generalized hypergeometric functions.

Distribution of LRC for testing sphericity of a complex multivariate Gaussian model

In this paper, exact null distribution of the likelihood ratio criterion for testing sphericity structure in a complex multivariate normal covariance matrix is obtained in computable series form. The method of inverse Mellin transform and contour integration has been used. Certain special cases are given explicitly in terms of the hypergeometric functions.