A Model for Positively Correlated Count Variables

P>An alpha-permanental random field is briefly speaking a model for a collection of non-negative integer valued random variables with positive associations. Though such models possess many appealing probabilistic properties, many statisticians seem unaware of alpha-permanental random fields and their potential applications. The purpose of this paper is to summarize useful probabilistic results, study stochastic constructions and simulation techniques, and discuss some examples of alpha-permanental random fields. This should provide a useful basis for discussing the statistical aspects in future work.Resume Un champ aleatoire alpha-permanental est la modelisation d'une collection de variables aleatoires entieres non negatives positivement associees. Malgre leurs attrayantes proprietes probabilistes et leurs nombreuses applications potentielles, ces modeles restent ignores de la majorite des statisticiens. Le but de cet article est de fournir les resultats probabilistes utiles, d'etudier les constructions stochastiques et les techniques de simulation, ainsi que de discuter quelques exemples, de facon a fournir une base utile a une discussion future des aspects statistiques des champs permanentaux.