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.

References

• Ghosh, I., & Balakrishnan, N. (2015). Study of incompatibility or near compatibility of bivariate discrete conditional probability distributions through divergence measures. Journal of Statistical Computation and Simulation, 85(1), 117–130. https://doi.org/10.1080/00949655.2013.806509 
• Hassan, M. Y., & El-Bassiouni, M. Y. (2013). Modelling Poisson marked point processes using bivariate mixture transition distributions. Journal of Statistical Computation and Simulation, 83(8), 1440–1452. https://doi.org/10.1080/00949655.2012.662683
• Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions. 3rd ed. Wiley. 
• Kemp, A. W. (2013). New discrete Appell and Humbert distributions with relevance to bivariate accident data. Journal of Multivariate Analysis, 113, 2–6. https://doi.org/10.1016/j.jmva.2011.08.011 
• Kocherlakota, S., & Kocherlakota, K. (1992). Bivariate discrete distributions. Marcel Dekker. 
• Kumar, C. S. (2007). Some properties of bivariate generalized hypergeometric probability distribution. Journal of the Korean Statistical Society, 36, 349–355. http://koreascience.or.kr/article/JAKO200734515966569.page?&lang=ko. 
• Kumar, C. S. (2008). A unified approach to bivariate discrete distributions. Metrika, 67(1), 113–121. https://doi.org/10.1007/s00184-007-0125-8 
• Kumar, C. S. (2013). The bivariate confluent hypergeometric series distribution. Economic Quality Control, 28(2), 23–30. https://doi.org/10.1515/eqc-2013-0009 
• Kumar, C. S., & Riyaz, A. (2013). On the zero-inflated logarithmic series distribution and its modification. Statistica, 73(4), 477–492. https://doi.org/10.6092/issn.1973-2201/4498 
• Kumar, C. S., & Riyaz, A. (2014). On a bivariate version of zero-inflated logarithmic series distribution and its applications. Journal of Combinatorics, Information and System Science, 39(4), 249–262. 
• Kumar, C. S., & Riyaz, A. (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. https://doi.org/10.1080/00949655.2013.867347 
• Kumar, C. S., & Riyaz, A. (2016). An order k version of the alternative zero-inflated logarithmic series distribution and its applications. Journal of Applied Statistics, 43(14), 2681–2695. https://doi.org/10.1080/02664763.2016.1142949 
• Kumar, C. S., & Riyaz, A. (2017). On some aspects of a generalized alternative zero-inflated logarithmic series distribution. Communications in Statistics – Simulation and Computations, 46(4), 2689–2700. https://doi.org/10.1080/03610918.2015.1057287 
• Mathai, A. M., & Haubold, H. J. (2008). Special functions for applied scientists. Springer. 
• MitchelL, C. R., & Paulson, A. S. (1981). A new bivariate negative binomial distribution. Naval Research Logistics Quarterly, 28(3), 359–374. https://doi.org/10.1002/nav.3800280302 
• Partrat, C. (1993). Compound model for two dependent kinds of clam. XXIVe ASTIN Colloquium. 
• Rao, C. R. (1973). Linear statistical inference and its applications. John Wiley. 
• Subrahmaniam, K. (1966). A test for intrinsic correlation in the theory of accident proneness. Journal of the Royal Statistical Society B, 35(1), 131–146. https://doi.org/10.1111/j.2517-6161.1966.tb00631. 

To cite this article: C. Satheesh Kumar & A. Riyaz (2023) On some aspects of a bivariate alternative zero-inflated logarithmic series distribution, Statistical Theory and Related Fields, 7:2, 130-143, DOI: 10.1080/24754269.2023.2179324

To link to this article: https://doi.org/10.1080/24754269.2023.2179324