Journal of Mathematics and Statistics

Bivariate Poisson-Lindley Distribution with Application

Hossein Zamani, Pouya Faroughi and Noriszura Ismail

DOI : 10.3844/jmssp.2015.1.6

Journal of Mathematics and Statistics

Volume 11, Issue 1

Pages 1-6


This study applies a Bivariate Poisson-Lindley (BPL) distribution for modeling dependent and over-dispersed count data. The advantage of using this form of BPL distribution is that the correlation coefficient can be positive, zero or negative, depending on the multiplicative factor parameter. Several properties such as mean, variance and correlation coefficient of the BPL distribution are discussed. A numerical example is given and the BPL distribution is compared to Bivariate Poisson (BP) and Bivariate Negative Binomial (BNB) distributions which also allow the correlation coefficient to be positive, zero or negative. The results show that BPL distribution provides the smallest Akaike Information Criterion (AIC), indicating that the distribution can be used as an alternative for fitting dependent and over-dispersed count data, with either negative or positive correlation.


© 2015 Hossein Zamani, Pouya Faroughi and Noriszura Ismail. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.