Bivariate Extended Yule Distribution

Abstract

Here we introduce a bivariate version of the extended Yule distribution (EYD) of Martinez-Rodriguez et al (Computational Statistics and Data Analysis, 2011). The EYD has been found suitable for heavy tailed distributions. For emphasizing the practical relevance of the model, it is shown that the proposed distribution can be viewed as the distribution of the random sum of independently and identically distributed bivariate Bernoulli random variables. It is also observed that the proposed bivariate distribution is a very flexible distribution and it includes the bivariate geometric distribution as its special case. A genesis of the distribution and explicit closed form expressions for its probability mass function, factorial moments and the probability generating function of its conditional distributions are derived. Certain recurrence relations for probabilities, raw moments and factorial moments of the BEYD are also obtained. The method of maximum likelihood estimation is employed for estimating the parameters of the distribution. Some examples of application using data from different fields are included in order to illustrate all these procedures.

KEYWORDS AND PHRASES:

• Bivariate Bernoulli distribution
• factorial moments
• generalized hypergeometric function
• model selection
• probability generating function
• simulation

Acknowledgements

Authors are highly thankful to Editor-in-Chief, the Associate Editor and the anonymous referees for their valuable comments on an earlier version of this paper that greatly improved the quality and presentation of the manuscript.