Generalized Laguerre expansions of multivariate probability densities with moments

We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an approximation to the conditional PDFs is derived. Numerical results first showed the superiority of the Gamma expansion over other numerical methods. The ability of the Gamma expansion to fit mixtures of Gaussian ans super Gaussian PDFs, univariate and multivariate Lognormal PDFs, and complex geologic media is shown through different examples.