A Characterization of Multivariate Binomial Distribution by Univariate Marginals 1

Abstract

Abstract

A distribution P₀ of a random vector X = (X₁,...,X _n ) is said to be linear exponential in a parameter θ = (θ₁,...,θ _n ) if $d{P}_{\theta }\left(x_1,\dots ,x_n\right)=\exp \left({\displaystyle \sum _{i=1}^n{\theta }_i{x}_i}\right){\left[f\left(\theta \right)\right]}^{-1}d\pi \left(x_1,\dots ,x_n\right).$ .

A multivariate linear exponential distribution is binomial if and only if its univariate marginals are binomial.