Decomposition d'une loi de poisson ponderee en une combinaison convexe de lois duales

Abstract

The probability distribution of a set of observation is most often dened as a convex combination of probability laws. To highlight this mixture of the laws, MCMC (Monte Carlo Markov Chain) which is an algorithm that generates a stationary Markov chain is often used; laws being considered as normal laws. In this paper, the observations are positive integer, so it is assumed that the mixture law is a Poisson weighted law and Blending laws are dual. The purpose of this work is to determine the dual laws by simple algebraic properties.

Key words: Count Data; Exponetial Family; Weighted Poisson Distribution; Fisher Index; Overdispersion; Underdispersion; Dual Distribution; Convex Combination.