Showing papers on "Multivariate gamma function published in 1997"
TL;DR: In this paper, the joint probability density function (pdf) and the moments of order h of the general multivariate statistic defined by Y (p) (a,b) = П p i = 1 l a i (1 - l i ) b, where a and b are positive real numbers, are obtained in the canonical correlation case and expressed in terms of the H-function.
21 Apr 1997
TL;DR: A derivation of the probability density function of complex inverse Wishart distributed random matrices is given and strategies are outlined for the calculation of the moments of complex Wishart and complex inverse wishart distributed matrices.
Abstract: This paper addresses the calculation of moments of complex Wishart and complex inverse Wishart distributed random matrices. Complex Wishart and complex inverse Wishart distributed random matrices are used in applications like radar, sonar, or seismology in order to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively. The moments of these random matrices are often needed e.g. in studies of asymptotic properties of parameter estimates. This paper gives a derivation of the probability density function of complex inverse Wishart distributed random matrices. Furthermore, strategies are outlined for the calculation of the moments of complex Wishart and complex inverse Wishart distributed matrices.
Book•
1 Jan 1997TL;DR: In this article, the authors present a concise review of developments on discrete multivariate distributions and present some basic definitions and notations, and present several important discrete multiivariate distributions with significant properties and characteristics.
Abstract: In this article, we present a concise review of developments on discrete multivariate distributions. We first present some basic definitions and notations. Then, we present several important discrete multivariate distributions and list their significant properties and characteristics.
Keywords:
generating function;
moments;
stirling numbers;
regression;
inflated distributions;
truncated forms;
compound distributions;
multinomial;
negative multinomial;
multivariate poisson;
multivariate hypergeometric;
multivariate Polya–Eggenberger;
multivariate discrete exponential;
multivariate power series;
multivariate hermite;
multivariate occupancy;
multivariate weighted;
dirichlet;
multivariate run-related distributions
TL;DR: In this paper, the inverted Wishart distribution was obtained with the help of a factorization theorem, and moments for normally distributed variables and inverse moments for chi-square variables were obtained.
Abstract: Moments of arbitrary order for the inverted Wishart distribution are obtained with the help of a factorization theorem, moments for normally distributed variables and inverse moments for chi-square ...