In this note, we present some relationships between moments, central moments and cumulants from multivariate distributions. Recently, Smith (1995) presented four simple recursive formulas that translate moments to cumulants and vice versa. Here, we derive similar recursive formulas between the...

In recent papers, Johnson and Kotz (Amer. Statist.44, 245-249 (1990); Math. Sci.15, 42-52 (1990)) have explored the utility of moment calculations as a simple way of establishing distributional forms. In particular a characterization theorem for beta distributions has been proved. In this paper...

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 purpose of this note is to clarify certain ambiguities in definition of failure rate of discrete distributions in a paper by Nair and Hitha (1989) and to suggest a possible bivariate extension of renewal (partial sum) distributions.

A method of calculating moments of distributions of limit points of certain procedures for iterated random subdivision of finite intervals is applied to some specific examples. Since the ranges of these distributions are finite, the moments, in principle determine the limit distributions....