On a Characterization of Multivariate Distributions with Applications in Reliability and Epidemiology.

Abstract

Abstract : Let T sub 1,...,T sub n be positive random variables with finite means. Further let I be the collection of all subsets of (1,...,n), and let xi be a function from the nth Euclidian space to I. It is proved that the minimum of (a sub i) (T sub i) over i from 1 to n and xi (a sub 1,...,a sub n) are independent random variables for every n real numbers a sub 1,...,a sub n iff for every n positive real numbers b sub 1,...,b sub n and r = 1,...,n the random variables and T sub r/ET sub r are identically distributed. Further we provide an explicit formula for the distribution of xi(a sub 1,...,a sub n). Multivariate distributions that possess the independence property are presented. Their use in Reliability growth or decay models as well as in Mathematical Epidemiology are discussed.