OICC Press Mathematical Sciences 2251-7456 20 3 2026 09 30 Proportional Hazard Bivariate Chen Model and Its Mathematical Features with Applications on Environmental, Climatic and Medical Data 10.57647/mathsci.2026.2003.37 EN N. M. Kilany Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt Asamh Saleh M. Al Luhayb Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia https://orcid.org/0000-0002-1272-1265 Reid Alotaibi Department of Mathematics, College of Science and Humanities, Shaqra University, Saudi Arabia Lobna H. El-Refai Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt Journal Article 2026 09 30 This paper introduces a new bivariate model, the Bivariate Chen Proportional Hazard Rate (BCPH) model, designed to effectively model diverse real-life datasets. This model is formulated within the proportional hazard framework, employing Chen marginal distributions. Its main statistical and reliability characteristics such as product moments, Pearson’s correlation, survival, and hazard functions are thoroughly derived and analyzed. Parameter estimation is accomplished through the maximum likelihood method and inference functions for margins, with simulation studies confirming the consistency and efficiency of the estimators. The BCPH model is further applied to various environmental, climatic, and medical datasets, including mercury fish length, precipitation temperature, and kidney infection recurrence times. Comparative evaluations using AIC, BIC, CAIC, and HQIC criteria demonstrate that the BCPH distribution provides a superior fit compared to existing bivariate models, highlighting its robustness, flexibility, and suitability for real world applications.