Characterizations of probability distributions is a topic of great popularity in applied probability and reliability literature for over last 30 years. Beside the intrinsic mathematical interest (often related to functional equations) the results in this area are helpful for probabilistic and...

A new family of continuous multivariate distributions is introduced, generalizing the canonical form of the multivariate normal distribution. The well-known univariate version of this family, as developed by Box, Tiao and Lund, among others, has proven a valuable tool in Bayesian analysis and...

Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method utilized for this procedure is to embed the spherical distribution quantile transformation of each...

In this paper we provide rather weak conditions on a distribution which would guarantee that the t-statistic of a random vector of order n follows the t-distribution with n-1 degrees of freedom. The results sharpen the earlier conclusions of Mauldon [Characterizing properties of statistical...

A vector definition of multivariate hazard rate, and associated definitions of increasing and decreasing multivariate hazard rate distributions are presented. Consequences of these definitions are worked out in a number of special cases. Relationships between hazard rate and orthant dependence...

The distributions of the ratio X/Y are derived when (X,Y) has the elliptically symmetric Pearson-type II distribution, elliptically symmetric Pearson-type VII distribution and the elliptically symmetric Kotz-type distribution.

Mehler gave an expansion for the standard bivariate normal density. Kibble extended it to a multivariate normal density whose covariance is a correlation matrix. We give extensions of these expansions for general covariances.

The recent paper by Alshabani et al. [Partial size-and-shape distributions, J. Multivariate Anal. (2006), in press] derived the partial size-and-shape distributions motivated by a study in human movement analysis. The paper contained three main results (referred to as Results 1-3), each deriving...