OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

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, 9 (6). 1283-1292.

(Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader

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


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:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Other partners > Université Nice Sophia Antipolis (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Laboratoire de recherche en télécommunications spatiales et aéronautiques - TéSA (FRANCE)
Laboratory name:
Deposited On:08 Sep 2008 08:25

Repository Staff Only: item control page