Identifiability of Modified Power Series Mixtures via Posterior Means

Problems of specification of discrete bivariate statistical models by a modified power series conditional distribution and a regression function are studied. An identifiability result for a wide class of such mixtures with infinite support is obtained. Also the finite support case within a more specific model is considered. Applications for Poisson, (truncated) geometric, and binomial mixtures are given. From the viewpoint of Bayesian analysis unique determination of the prior by a Bayes estimate of the mean for modified power series mixtures is investigated.