Bivariate Poisson–XLindley Distribution and Its Application in Sport

The Poisson–XLindley distribution (PXLD), which can be used to characterize count data that is overly dispersed or dependent, is presented in the present study. It is displayed in its bivariate form. Among the characteristics that are considered are the correlation coefficient, mean, and variance of the distribution. A comparison with various bivariate distributions is included. The goodness of fit of this new model is evaluated using data from one season in the Italian Series A and one season in the German Bundesliga using the bivariate Poisson, bivariate negative binomial, and bivariate Poisson–Lindley distributions.