Symmetric Bernoulli Distributions and Generalized Binomial Distributions

Abstract

Abstract The generalized binomial distribution is defined as the distribution of a sum of symmetrically distributed Bernoulli random variates. Several two‐parameter families of generalized binomial distributions have received attention in the literature, including the Polya urn model, the correlated binomial model and the latent variable model. Some properties and limitations of the three distributions are described. An algorithm for maximum likelihood estimation for two‐parameter generalized binomial distributions is proposed. The Polya urn model and the latent variable model were found to provide good fits to sub‐binomial data given by Parkes. An extension of the latent variable model to incorporate heterogeneous response probabilities is discussed.