A bivariate generalized geometric distribution with applications

ABSTRACT

This paper proposes a bivariate version of the univariate discrete generalized geometric distribution considered by Gómez–Déniz (2010). The proposed bivariate distribution can have a positive or negative correlation coefficient which can be used for modeling bivariate-dependent count data. After discussing some of its properties, maximum likelihood estimation is discussed. Two illustrative examples are given for fitting and demonstrating the usefulness of the new bivariate distribution proposed here.

KEYWORDS:

• Geometric distribution
• joint distributions
• marginal distributions
• Marshall and Olkin family of distributions
• overdispersion
• underdispersion.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62E99
• 62H12

Acknowledgments

The authors are thankful to the associate editor and the referee for some useful comments which enhanced the presentation.

Funding

EGD work is funded by ECO2013–47092 (Ministerio de Economía y Competitividad, Spain). EGD also acknowledges the Department of Statistics and Operations Research at Kuwait University for their special support, as part of this paper was done while EGD was visiting Kuwait University in 2012.