A Bivariate Geometric Distribution with Applications to Reliability

Abstract

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.

Keywords:

• Bayes estimation
• Bayes risk
• Bivariate Dirichlet distribution
• Bivariate geometric distribution
• Maximum likelihood estimation

Mathematics Subject Classification:

• Primary 62N05, 66F12
• Secondary 65C05, 65D30

Acknowledgment

The second author is thankful to the “University Grants Commission, India” for providing financial support.