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A Bivariate Geometric Distribution with Applications to Reliability

This article studies a bivariate geometric distribution (BGD) as a plausible reliability model. Maximum likelihood and Bayes estimators of parameters and various reliability characteristics are obtained. Approximations to the mean, variance, and Bayes risk of these estimators have been derived using Taylor's expansion. A Monte-Carlo simulation study has been performed to compare these estimators. At the end, the theory is illustrated with a real data set example of accidents.