Bivariate Discrete Burr Lifetime Distribution: A Mathematical and Statistical Framework for Modeling Medical and Engineering Data

Authors

Mohamed El-Dawoody, Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaFollow
Mohamed S. Eliwa, Department of Statistics and Operation Research, College of Science,Qassim University, Buraydah 51482, Saudi Arabia\\ Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptFollow

Abstract

The central role of modeling discrete bivariate data in enhancing understanding, facilitating informed decision-making, and advancing knowledge spans various fields. This modeling allows the depiction of the intricate relationship between two variables and finds applications in diverse domains. The focus of this study is on introducing a novel statistical model, specifically the bivariate discrete Burr distribution, an unexplored entity in existing statistical literature. This model is presented as the discrete counterpart of the Burr distribution, and we explore its essential statistical characteristics. This exploration includes the derivation of the joint probability mass function, joint survival function, joint hazard rate function along with its reversed counterpart, conditional expectations, and positive quadrant dependence. For parameter estimation of the model, maximum likelihood estimation is employed. Additionally, an extensive simulation study is conducted to evaluate the bias and mean square error of the maximum likelihood estimators. Finally, two real-world datasets are examined to demonstrate the practical applicability of the model.

Recommended Citation

El-Dawoody, Mohamed and S. Eliwa, Mohamed (2023) "Bivariate Discrete Burr Lifetime Distribution: A Mathematical and Statistical Framework for Modeling Medical and Engineering Data," Information Sciences Letters: Vol. 12 : Iss. 11 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss11/29