BINOMIAL AND NEGATIVE BINOMIAL ANALOGS UNDER CORRELATED BERNOULLI TRIALS

Several statistical applications demand the adoption of models in whic h the response is binary but the outcomes of different trials exhibit some degree of correlation. Although the independent case is well know n and treated even in elementary textbooks, results on correlated Bern oulli trials are hardly found in the literature. Analogues of the bino mial and negative binomial distributions are presented in this article when the correlation is of the Markovian type. Probability-generating function, probability mass function, mean, and variance are derived. The analysis allows illustration of a variety of techniques useful in the study of discrete distributions appropriate for second-level proba bility courses. An example on customer brand switching discussed by Ol kin, Glesser, and Derman is presented as illustration.