Properties and applications of the Sarmanov family of bivariate distributions

We discuss properties of the bivariate family of distributions introduced by Sarmanov (1966). It is shown that correlation coefficients of this family of distributions have wider range than those of the Farlie-Gumbel-Morgenstern distributions. Possible applications of this family of bivariate distributions as prior distributions in Bayesian inference are discussed. The density of the bivariate Sarmanov distributions with beta marginals can be expressed as a linear combination of products of independent beta densities. This pseudo-conjugate property greatly reduces the complexity of posterior computations when this bivariate beta distribution is used as a prior. Multivariate extensions are derived.