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Exponential families of mixed Poisson distributions

Ferrari, André and Letac, Gérard and Tourneret, Jean-Yves Exponential families of mixed Poisson distributions. (2007) Journal of Multivariate Analysis, vol. 9 (n° 6). pp. 1283-1292.

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Official URL: http://dx.doi.org/10.1016/j.jmva.2006.03.005

Abstract

If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Journal of Multivariate Analysis website: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Université de Toulouse I-Sciences Sociales - UT1
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA
French research institutions > Centre National de la Recherche Scientifique - CNRS
Other partners > Université Nice Sophia Antipolis (FRANCE)
Université de Toulouse > Université de Toulouse II-Le Mirail - UTM
Laboratory name:
Statistics:download
Deposited By: Jean-yves TOURNERET

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