On bivariate alpha logarithmic series distribution and its properties

Abstract

Here we propose a bivariate version of the alpha logarithmic series distribution (ALSD) of Kumar and Riyaz (South African Statist. J., 2014) and shown that its marginals are also ALSD. We study some of its important properties by deriving expressions for its probability mass function, factorial moments, conditional probability generating function, covariance etc. The parameters of the model are estimated by the method of maximum likelihood and the distribution has been fitted to certain real life data sets.