A Contruction of Lacaster Probabilities with Margins in the Multidimensional Meixner Class.

The well-known Meixner class (Meixner, 1934) of probabilities on R has been recently extended to R^d (Pommeret, 1996). This generalized Meixner class corresponds to the simple quadratic natural exponential families charaterized by Casalis (1996). Following Lancaster (1975), we offer a characterization of the joint probability of a random variable (X,Y), such that the two variables X and Y on R^d belong to this multidimensional Meixner class and fulfill a biorthogonality condition involving orthogonal polynomials.