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...