No abstract

No abstract

In this paper a bivariate generalisation of the gamma distribution is proposed by using an unsymmetrical bivariate characteristic function; an extension to the noncentral case also receives attention. The probability density functions of the product and ratio of the correlated components of this distribution are also derived. The benefits of introducing this generalised bivariate gamma distribution and the distributions of the product and the ratio of its components will be demonstrated by graphical representations of their density functions. An example of this generalised bivariate gamma distribution to rainfall data for two specific districts in the North West province is also given to illustrate the greater versatility of the new distribution. Mathematical subject classification: 62E20

Abstract-In this paper the bimatrix variate beta type IV distribution is derived from independent Wishart distributed matrix variables. We explore specific properties of this distribution which is then used to derive the exact expressions of the densities of the product and ratio of two dependent Wilks's statistics and to define the bimatrix Kummer-beta type IV distribution.

Key Words and Phrases: 3a.yesian posterior; Bessel function of the second kind with matris argument; mullivam'ate normal distribution; multivariate quadratic loss finction; Wishart prior. ABSTRACT This paper considers the Bayesian analysis of the multivariate normal distribution when its covariance matrix has a Wishar.t prior density under the assumption of a multivariate quadratic loss function. New flexible marginal posterior distributions of the mean and of the covariance matrix C are developed and univarjate cases with graphical representations are given.