Binomial and Negative Binomial Analogues under Correlated Bernoulli Trials

Publisher Website
Google Scholar
Abstract
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 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 probability courses. An example on customer brand switching discussed by Olkin, Glesser, and Derman is presented as illustration.

This publication has 8 references indexed in Scilit: