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A Model for Positively Correlated Count Variables

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  • Jesper Møller
  • Ege Rubak

Abstract

An α‐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 α‐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 α‐permanental random fields. This should provide a useful basis for discussing the statistical aspects in future work. Un champ aléatoire α‐permanental est la modélisation d'une collection de variables aléatoires entières non négatives positivement associées. Malgré leurs attrayantes propriétés probabilistes et leurs nombreuses applications potentielles, ces modèles restent ignorés de la majorité des statisticiens. Le but de cet article est de fournir les résultats probabilistes utiles, d'étudier les constructions stochastiques et les techniques de simulation, ainsi que de discuter quelques exemples, de façon à fournir une base utile à une discussion future des aspects statistiques des champs permanentaux.

Suggested Citation

  • Jesper Møller & Ege Rubak, 2010. "A Model for Positively Correlated Count Variables," International Statistical Review, International Statistical Institute, vol. 78(1), pages 65-80, April.
  • Handle: RePEc:bla:istatr:v:78:y:2010:i:1:p:65-80
    DOI: 10.1111/j.1751-5823.2009.00091.x
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    References listed on IDEAS

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    1. Griffiths, R. C., 1984. "Characterization of infinitely divisible multivariate gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 13-20, August.
    2. Griffiths, R. C. & Milne, R. K., 1987. "A class of infinitely divisible multivariate negative binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 13-23, June.
    3. S. C. Kou & P. McCullagh, 2009. "Approximating the α-permanent," Biometrika, Biometrika Trust, vol. 96(3), pages 635-644.
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