Discrete Schur-constant models

Abstract

This paper introduces a class of Schur-constant survival models, of dimension $n$, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be $n$-monotone. Two general representations are obtained, by conditioning on the sum of the $n$ variables or through a doubly mixed multinomial distribution. Several other properties including correlation measures are derived. Three processes in insurance theory are discussed for which the claim interarrival periods form a Schur-constant model.