On some aspects of a bivariate alternative zero-inflated logarithmic series distribution

Abstract

In this paper, we discuss some important aspects of the bivariate alternative zero-inflated logarithmic series distribution (BAZILSD) of which the marginals are the alternative zero-inflated logarithmic series distributions of Kumar and Riyaz (2015. An alternative version of zero-inflated logarithmic series distribution and some of its applications. Journal of Statistical Computation and Simulation, 85(6), 1117–1127). We study some important properties of the distribution by deriving expressions for its probability mass function, factorial moments, conditional probability generating functions, and recursion formulae for its probabilities, raw moments and factorial moments. The parameters of the BAZILSD are estimated by the method of maximum likelihood and certain test procedures are also considered. Further certain real-life data applications are cited for illustrating the usefulness of the model. A simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the BAZILSD.

KEYWORDS:

• Factorial moments
• generalized likelihood ratio test
• probability generating function
• Rao’s score test
• zero-inflated distributions

Acknowledgements

The authors are grateful to the Editor-in-Chief and the anonymous Referees for their valuable comments on an earlier version which helped to improve the quality of this article.