Abstract
The convolution of two binomial random variables has appeared in various settings such as a model in machine maintenance and as a Markov chain model. This article presents a bivariate distribution with this convolution of binomials as marginal distributions. This bivariate distribution arises from sampling with partial classification, and this has potentially useful applications in diverse areas. The distribution generalizes the bivariate binomial distribution and its variants. Some properties of the bivariate distribution have been obtained. A mixture formulation of the distribution has been derived which facilitates computation of probabilities and computer sampling. An application to a real data set is presented to illustrate its usefulness in empirical modeling.
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