10.57647/mathsci.2026.2003.37

Proportional Hazard Bivariate Chen Model and Its Mathematical Features with Applications on Environmental, Climatic and Medical Data

XML PDF
  • N. M. Kilany1,
  • Asamh Saleh M. Al Luhayb2,
  • Reid Alotaibi3,
  • Lobna H. El-Refai1,
  1. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt
  2. Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
  3. Department of Mathematics, College of Science and Humanities, Shaqra University, Saudi Arabia

Received: 2025-11-09

Revised: 2026-02-09

Accepted: 2026-02-19

Published in Issue 2026-09-30

Copyright (c) 2026 N. M. Kilany, Asamh Saleh M. Al Luhayb, Reid Alotaibi, Lobna H. El-Refai (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Kilany, N. M., Al Luhayb, A. S. M., Alotaibi, R., & El-Refai, L. H. (2026). Proportional Hazard Bivariate Chen Model and Its Mathematical Features with Applications on Environmental, Climatic and Medical Data. Mathematical Sciences, 20(3). https://doi.org/10.57647/mathsci.2026.2003.37
Crossref
Scopus
Google Scholar
Europe PMC

PDF views: 12

Abstract

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.

Keywords

  • Bivariate Chen distribution,
  • Proportional hazard rate model,
  • Simulation,
  • Maximum likelihood estimation,
  • Inference functions for margins
PDF

References

  1. Balakrishnan N and Lai CD. Continuous Bivariate Distributions. 2nd ed. Springer, 2009
  2. Kundu D and Gupta RD. A class of bivariate models with proportional reversed hazard marginal. Sankhya B 2010; 72:236–53
  3. Gupta R and Gupta PL. Modelling failure time data by Lehmann alternatives. Communications in Statistics - Theory and Methods 1998; 27:887–904
  4. Mirhosseini SM, Dolati A, and Amini M. On a bivariate Kumaraswamy type exponential distribution. Communications in Statistics - Theory and Methods 2015. DOI: 10.1080/03610926.2014.944664
  5. Hassanein WAA and Seyam MMA. Structure of bivariate Rayleigh proportional hazard rate model with its associated copula applied on COVID-19 data. Quality and Reliability Engineering International 2022; 38:3451–69. DOI: 10.1002/qre.3143
  6. Hassanein WAA, Sobhy AM, and Abd El-Monsef MME. Proportional hazard bivariate Kumaraswamy model applied on fish mercury concentration. Journal of Statistics Application and Probability 2023. DOI: 10.18576/jasp/120307
  7. Abd Elgawad MA, Alawady MA, Barakat HM, Mansour GM, Husseiny IA, Alyami SA, Hashem AF, and Mohamed MO. Bivariate power Lomax
  8. Sarmanov distribution: Statistical properties, reliability measures, and parameter estimation. Alexandria Engineering Journal 2025; 113:593–610
  9. Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics and Probability Letters 2000; 49:155–61
  10. Bhatt FA, Hamedani GG, Najibi SM, and Ahmad M. On the extended Chen distribution: Development, properties, characterizations and applications. Annals of Data Science 2019. DOI: 10.1007/s40745-019-00202-x
  11. Basu A. Bivariate failure rate. Journal of the American Statistical Association 1971; 66:103–4
  12. Johnson N and Kotz S. A vector multivariate hazard rates. Journal of Multivariate Analysis 1975; 5:53–66
  13. Joe H. Multivariate Models and Dependence Concepts. CRC Press, 1997
  14. Storelli M, Giacominelli-Stuffler R, and Marcotrigiano G. Relationship between total mercury concentration and fish size in two pelagic fish species: Implications for consumer health. Journal of Food Protection 2006; 69:1402–5
  15. Ghosh I and Ray S. Some alternative bivariate Kumaraswamy-type distributions via copula with application in risk management. Journal of Statistical Theory and Practice 2016; 10:693–706
  16. Thomas PY and Jose J. A new bivariate distribution with Rayleigh and Lindley distributions as marginals. Journal of Statistical Theory and Practice 2020; 14:1–38
  17. El-Sherpieny EA. FGM bivariate Weibull distribution: Properties and applications. Journal of Advanced Research in Statistics and Probability
  18. 2018; 3:79–96
  19. McGilchrist CA and Aisbett CW. Regression with frailty in survival analysis. Biometrics 1991; 47:461–6
  20. Kundu D and Dey AK. Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm. Computational Statistics and Data Analysis 2009; 53:956–65
  21. Tahmasebi S, Jafari AA, and Ahsanullah M. Reliability characteristics of bivariate Rayleigh distribution and concomitants of its order statistics and record values. Studia Scientiarum Mathematicarum Hungarica 2017; 54:151–70