Bivariate Version of Yule Distribution and Some of its Properties

Abstract

Here, we introduce bivariate Yule distribution (BYD), as the distribution of the random sum of certain types of independent and identically distributed bivariate Bernoulli random variables. A genesis of the distribution and explicit closed form expressions for its probability mass function, factorial moments and the p.g.f.s of its conditional distributions are derived. Certain recurrence relations for probabilities, raw moments and factorial moments of the BYD are also obtained. The method of maximum likelihood estimation is employed for estimating the parameter of the distribution. All these procedures are illustrated with the help of a real life data set.