In this paper, a new bivariate discrete distribution is defined and studied in-detail, in the so-called the bivariate exponentiated discrete Weibull distribution. Several of its statistical properties including the joint cumulative distribution function, joint probability mass function, joint hazard rate function, joint moment generating function, mathematical expectation and reliability function for stress–strength model are derived. Its marginals are exponentiated discrete Weibull distributions. Hence, these marginals can be used to analyze the hazard rates in the discrete cases. The model parameters are estimated using the maximum likelihood method. Simulation study is performed to discuss the bias and mean square error of the estimators. Finally, two real data sets are analyzed to illustrate the flexibility of the proposed model.

中文翻译：

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二元指数指数离散Weibull分布：统计性质，估计，模拟和应用

在本文中，定义了一种新的双变量离散分布，并进行了详细研究，即所谓的双变量指数离散Weibull分布。推导了它的几个统计特性，包括联合强度分布函数，联合概率质量函数，联合危险率函数，联合矩生成函数，数学期望和可靠性函数。它的边际是指数离散的威布尔分布。因此，这些边际可用于分析离散情况下的危险率。使用最大似然法估计模型参数。进行仿真研究以讨论估计量的偏差和均方误差。最后，分析了两个实际数据集以说明所提出模型的灵活性。