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.
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Anna Castañer, Maria Mercè Claramunt, Claude Lefèvre, Stéphane Loisel. Discrete Schur-constant models. Journal of Multivariate Analysis, Elsevier, 2015, 140 (September 2015), pp.343-362. ⟨hal-01081756⟩

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