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.

中文翻译：

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使用似然比构造的一类新的离散二元分布

在统计学中，随机命令形式化了这样一个概念，即一个随机变量大于另一个。在本文中，我们基于由似然比定义的随机顺序开发了一类新的离散双变量分布。我们推导出属于该类的联合分布的一般公式。可以看出，从建议的类中，可以通过指定“基线种子分布”有效地生成特定的分布族。所提出的离散双变量模型的一个重要特征是，与文献中已经提出的其他离散双变量模型（例如 Holgate 著名且最受欢迎的双变量泊松分布）不同，它可以对正相关和负相关进行建模。从提议的类中生成了许多新的离散双变量分布族。此外，生成的双变量分布用于分析真实数据集，并将结果与​​从一些传统模型中获得的结果进行比较。