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Bivariate Power Lindley Models Based on Copula Functions Under Type‐II Censored Samples With Applications in Industrial and Medical Data

Author

Listed:
  • Ehab M. Almetwally
  • Aisha Fayomi
  • Maha E. Qura

Abstract

This study introduces three innovative bivariate models to address complex dependencies between random variables in real‐world applications. Specifically, we develop bivariate power Lindley (BPL) distribution models utilizing the Gumbel, Frank, and Clayton copulas. These models effectively capture the underlying relationships between variables, particularly under a Type‐II censored sampling scheme. Parameter estimation is performed using both maximum likelihood and Bayesian methods, with asymptotic and credible confidence intervals computed. We also employ the Markov Chain Monte Carlo method for numerical analysis. The proposed methodology is demonstrated through the analysis of multiple datasets: the first investigates burr formation in manufacturing with two sets of observations, while the second and third datasets explore medical data on diabetic nephropathy and infection recurrence times in kidney patients, respectively. The results highlight the practical applicability and robustness of these newly proposed bivariate models.

Suggested Citation

  • Ehab M. Almetwally & Aisha Fayomi & Maha E. Qura, 2025. "Bivariate Power Lindley Models Based on Copula Functions Under Type‐II Censored Samples With Applications in Industrial and Medical Data," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5904687
    DOI: 10.1155/jom/5904687
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    References listed on IDEAS

    as
    1. 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.
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    4. Maha E Qura & Aisha Fayomi & Mutua Kilai & Ehab M Almetwally, 2023. "Bivariate power Lomax distribution with medical applications," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-32, March.
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