Developing New Bivariate Distributions With Advanced Estimation Methods for Interdisciplinary Data Analysis

This paper proposes a novel bivariate odd beta prime Fréchet (BOBPF) distribution constructed through the application of the Farlie–Gumbel–Morgenstern (FGM) copula function. The new model, called the BOBPF-FGM, is engineered to address the persistent challenge of modeling positively skewed and heavy-tailed bivariate data that exhibit complex interdependency structures. The study provides a derivation of the joint probability density function, the cumulative distribution function, and the joint survival function. Essential mathematical properties are derived, including moments, moment-generating function, conditional density function, conditional expectations, and a detailed exposition of the dependence structure. Parameters are efficiently estimated using the maximum likelihood estimation method, and the performance of the estimators is formally verified through a Monte Carlo simulation study. The practical utility and superior performance of the BOBPF-FGM model are demonstrated through its application to several real-world datasets across different disciplines, where it consistently provides a more favorable fit compared to numerous established competing bivariate models. Hence, this study provides strong evidence of the adaptability and accuracy of BOBPF in handling diverse real-world datasets, making it a valuable tool for statistical modeling across multiple fields.