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Mathematics
Volume 14
Issue 1
10.3390/math14010120
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Dependent Bivariate Burr XII Inverse Weibull Model: Application to Diabetic Retinopathy and Dependent Competing Risks Data

by
Ammar M. Sarhan
1,2,*,
Ahlam H. Tolba
2,
Dina A. Ramadan
2 and
Thamer Manshi
3
1
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 4R2, Canada
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3
Department of Statistics & Operation Research, King Saud University, Riyadh 11451, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 120; https://doi.org/10.3390/math14010120 (registering DOI)
Submission received: 22 November 2025 / Revised: 22 December 2025 / Accepted: 23 December 2025 / Published: 28 December 2025
(This article belongs to the Special Issue Advances in Statistical Approaches with Applications for Multivariate Data Analysis)
Versions Notes

Abstract

This paper introduces a novel bivariate distribution, referred to as the Bivariate Burr XII Inverse Weibull (BBXII-IW) distribution, constructed via the Marshall–Olkin approach from the univariate Burr XII Inverse Weibull (BXII-IW) distribution. The proposed BBXII-IW model provides a flexible framework for modeling dependent bivariate data, including competing risk scenarios. The key statistical properties of the distribution are derived, and parameter estimation is conducted using the maximum likelihood method. The model’s performance is evaluated using two types of real-world datasets: (1) bivariate data and (2) dependent competing risk data related to diabetic retinopathy. The results demonstrate that the BBXII-IW distribution offers an improved fit compared to existing models, highlighting its flexibility and practical relevance in modeling complex dependent structures.
Keywords: maximum likelihood method; reliability analysis; Marshall–Olkin family; statistical inferences maximum likelihood method; reliability analysis; Marshall–Olkin family; statistical inferences

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MDPI and ACS Style

Sarhan, A.M.; Tolba, A.H.; Ramadan, D.A.; Manshi, T. A Dependent Bivariate Burr XII Inverse Weibull Model: Application to Diabetic Retinopathy and Dependent Competing Risks Data. Mathematics 2026, 14, 120. https://doi.org/10.3390/math14010120

AMA Style

Sarhan AM, Tolba AH, Ramadan DA, Manshi T. A Dependent Bivariate Burr XII Inverse Weibull Model: Application to Diabetic Retinopathy and Dependent Competing Risks Data. Mathematics. 2026; 14(1):120. https://doi.org/10.3390/math14010120

Chicago/Turabian Style

Sarhan, Ammar M., Ahlam H. Tolba, Dina A. Ramadan, and Thamer Manshi. 2026. "A Dependent Bivariate Burr XII Inverse Weibull Model: Application to Diabetic Retinopathy and Dependent Competing Risks Data" Mathematics 14, no. 1: 120. https://doi.org/10.3390/math14010120

APA Style

Sarhan, A. M., Tolba, A. H., Ramadan, D. A., & Manshi, T. (2026). A Dependent Bivariate Burr XII Inverse Weibull Model: Application to Diabetic Retinopathy and Dependent Competing Risks Data. Mathematics, 14(1), 120. https://doi.org/10.3390/math14010120

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