Comparison of Discrete Bivariate Beta - Binomial Distributions Based on Correlation Between Marginal Variables

The aim of this study was to compare fitting of different discrete bivariate beta-binomial distributions based on correlation between marginal variables. The models included bivariate beta-binomial distribution proposed by Bibby and Væth (2011) (with three parameters), Danaher and Hardie (2005) (with five parameters) and generalized model of the classical bivariate beta-binomial distribution proposed by Olmo - Jimenez et al. (2011). Based on results obtained from goodness of fit test, Olmo - Jimenez et al’s model was found to be more appropriate than other models when correlation between marginal variables was high. Also Danaher and Hardie’s model were found to be more appropriate than other models when correlation between marginal variables was low. The results were presented by using three real data set.