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

Aliyu Ismail Ishaq, Ahmad Abubakar Suleiman, Hana N. Alqifari, Amani Almohaimeed, Hanita Daud and Sani I. Abba

Journal of Mathematics, 2026, vol. 2026, 1-38

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5518563

DOI: 10.1155/jom/5518563

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