Discrete double factors of a family of odd Weibull-G distributions: features and modeling

Recently, an increasing volume of complex bivariate data has been generated from diverse sources, particularly within applied sciences. These datasets demand a flexible probabilistic framework for comprehensive analysis and discussion of their characteristics. Consequently, this article introduces and extensively explores a novel bivariate discrete distribution. Various distributional properties, including the joint probability mass function, joint survival function, joint hazard rate function, conditional expectation, and joint probability generating function, are derived and thoroughly discussed. Within this general class, two specific models of the new bivariate distribution are investigated in depth. It is demonstrated that the underlying distribution within this proposed discrete bivariate framework is suitable for modeling both asymmetric and symmetric bivariate data. Furthermore, the joint hazard rate function is employed as a statistical tool for analyzing diverse patterns in failure rates across different surfaces. The maximum likelihood approach is employed to estimate the parameters of this bivariate distribution, yielding the most accurate estimators for fitting real datasets. A comprehensive simulation study is conducted to assess the bias and mean squared errors of these maximum likelihood estimators across various sample sizes. Finally, the utility and significance of this novel bivariate discrete distribution class are exemplified through the analysis of two distinct real-world datasets.