Paper Info
Title
Multivariate mixed poisson distributions
Abstract
Univariate Mixed Poisson distributions (MPDs) are commonly used to model data recorded from low flux objects or with short exposure times. They assume that the number of recorded events, conditioned on the received random intensity, is Poisson distributed. This communication focuses on the generalization of the MPDs to the multivariate case. This generalization is required to tackle new challenging problems such as exo-planet detection using direct imaging. The joint moments and the moment generating function of a multivariate mixed Poisson distribution (MMPD) are derived. These quantities allow to characterize the over-dispersion, dependency or unicity properties of the distribution. The important example of negative multinomial distributions is considered. These distributions are obtained when the mixing distribution is a multivariate Gamma distribution. Conditions ensuring that MMPDs belong to a natural exponential family (NEF) are finally investigated.
Year
Venue
Keywords
2004
EUSIPCO
poisson distribution,gamma distribution,mmpd,direct imaging,exoplanet detection,multinomial distributions,multivariate gamma distribution,multivariate mixed poisson distribution,natural exponential family,received random intensity
Field
DocType
ISBN
Multivariate t-distribution,Compound Poisson distribution,Applied mathematics,Multivariate stable distribution,Exponential family,Univariate distribution,Poisson distribution,Gamma distribution,Statistics,Mathematics,Matrix t-distribution
Conference
978-320-0001-65-7
Citations 
PageRank 
References 
4
0.81
0
Authors
3
Name
Order
Citations
PageRank
André Ferrari1322.79
Gérard Letac242.50
Jean-Yves Tourneret383564.32