Canonical Expansion of a Mixed Bivariate Distribution with Negative Binomial and Gamma Marginals

Abstract

For the following mixed bivariate probability distribution between a discrete random variable X and a continuous random variable Λ: ▪ where α, β > 0, 0 < p = 1 − q < 1, x=0,1,2,..., ▪ a canonical expansion is obtained in terms of the Laguerre and Meixner orthogonal polynomials. The chance mechanisms giving rise to this mixed bivariate distribution are also discussed.