A new general class of discrete bivariate distributions constructed by using the likelihood ratio

  • Hyunju Lee
  • Ji Hwan Cha
Regular Article


In statistics, stochastic orders formalize such a concept that one random variable is bigger than another. In this paper, we develop a new class of discrete bivariate distributions based on a stochastic order defined by the likelihood ratio. We derive general formula for the joint distributions belonging to the class. It will be seen that, from the proposed class, specific families of distributions can be efficiently generated just by specifying the ‘baseline seed distributions’. An important feature of the proposed discrete bivariate model is that, unlike other discrete bivariate models already proposed in the literature such as the well-known and most popular bivariate Poisson distribution by Holgate, it can model both positive and negative dependence. A number of new families of discrete bivariate distributions are generated from the proposed class. Furthermore, the generated bivariate distributions are applied to analyze real data sets and the results are compared with those obtained from some conventional models.


Stochastic order Likelihood ratio order Joint distribution Positive and negative dependence Baseline seed distribution 



The authors thank the reviewers for helpful comments and suggestions, which have improved the presentation of this paper. This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of StatisticsEwha Womans UniversitySeoulRepublic of Korea

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