Binomial and Negative Binomial Analogues under Correlated Bernoulli Trials

Several statistical applications demand the adoption of models in which the response is binary but the outcomes of different trials exhibit some degree of correlation. Although the independent case is well known and treated even in elementary textbooks, results on correlated Bernoulli trials are hardly found in the literature. Analogues of the binomial and negative binomial distributions are presented in this article when the correlation is of …