Résumé : 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.
This is a joint work with A. Castaner, M.M. Claramunt and S. Loisel.

Keywords: Schur-constant property; survival function; multiple monotonicity; mixed multinomial distribution; insurance risk theory