Discrete Schur-constant models

This paper introduces a class of Schur-constant survival models, of dimension nn, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be nn-monotone. Two general representations are obtained, by conditioning on the sum of the nn 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.