For random variables T1,...,Tn, the gradient of R(t) = -logP{T1 t1,...,Tn tn} is called the hazard gradient. Some properties of this multivariate version of the hazard rate are demonstrated, and some examples are given to show the usefulness of the hazard gradient in characterizing...

A large number of characterizations of univariate exponential distributions are known; these often lead to a functional equation, relatively few of which have been extended to the multivariate case. This paper is an exposition of multivariate extensions and relatives of the functional equation...

In several classic papers, Pólya and Eggenberger used urn models to generate distributions that could be used to model contagion processes. Three bivariate versions are investigated together with their limiting distributions. In this way a large class of bivariate distributions (beta, Pareto,...