A bivariate geometric distribution allowing for positive or negative correlation

Abstract

In this paper, we propose a new bivariate geometric model, derived by linking two univariate geometric distributions through a specific copula function, allowing for positive and negative correlations. Some properties of this joint distribution are presented and discussed, with particular reference to attainable correlations, conditional distributions, reliability concepts, and parameter estimation. A Monte Carlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. Finally, in order to demonstrate its usefulness, the model is applied to a real data set.

Keywords:

• Attainable correlations
• correlated counts
• Farlie-Gumbel-Morgenstern copula
• method of moments
• two-step maximum likelihood

Acknowledgements

I would like to thank the Editor and two anonymous reviewers for their constructive comments, which helped me to improve the final version of the paper.