Modeling with Bivariate Geometric Distributions

Abstract

This article describes two bivariate geometric distributions. We investigate characterizations of bivariate geometric distributions using conditional failure rates and study properties of the bivariate geometric distributions. The bivariate models are fitted to real-life data using the Method of Moments, Maximum Likelihood, and Bayes Estimators. Two methods of moments estimators, in each bivariate geometric model, are compared and evaluated for their performance in terms of bias vector and covariance matrix. This comparison is done through a Monte Carlo simulation. Chi-square goodness-of-fit tests are used to evaluate model performance.

Keywords:

• Bivariate geometric distribution
• Bayes estimation
• Conditional failure rate
• Maximum likelihood estimation

Mathematics Subject Classification:

• 62E10
• 62F10

Acknowledgments

This research is part of the first author's Ph.D. dissertation. The author is most grateful to the thesis advisor and the reviewers for their helpful suggestions and comments.