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Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

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  • Ehab M. Almetwally

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11153, Egypt)

  • Aisha Fayomi

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Maha E. Qura

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

Abstract

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients.

Suggested Citation

  • Ehab M. Almetwally & Aisha Fayomi & Maha E. Qura, 2024. "Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings," Mathematics, MDPI, vol. 12(12), pages 1-35, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1774-:d:1410459
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    References listed on IDEAS

    as
    1. Hiba Z. Muhammed & Ehab M. Almetwally, 2023. "Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 10(2), pages 481-512, April.
    2. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    3. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    4. Rainer Winkelmann, 2012. "Copula Bivariate Probit Models: With An Application To Medical Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 21(12), pages 1444-1455, December.
    5. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    6. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    7. Hanan Haj Ahmad & Ehab M. Almetwally & Dina A. Ramadan, 2023. "Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach," Mathematics, MDPI, vol. 11(9), pages 1-23, May.
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