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Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions

Author

Listed:
  • Aisha Fayomi

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

  • Ehab M. Almetwally

    (Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt)

  • Maha E. Qura

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

Abstract

In survival analyses, infections at the catheter insertion site among kidney patients using portable dialysis machines pose a significant concern. Understanding the bivariate infection recurrence process is crucial for healthcare professionals to make informed decisions regarding infection management protocols. This knowledge enables the optimization of treatment strategies, reduction in complications associated with infection recurrence and improvement of patient outcomes. By analyzing the bivariate infection recurrence process in kidney patients undergoing portable dialysis, it becomes possible to predict the probability, timing, risk factors and treatment outcomes of infection recurrences. This information aids in identifying the likelihood of future infections, recognizing high-risk patients in need of close monitoring, and guiding the selection of appropriate treatment approaches. Limited bivariate distribution functions pose challenges in jointly modeling inter-correlated time between recurrences with different univariate marginal distributions. To address this, a Copula-based methodology is presented in this study. The methodology introduces the Kavya–Manoharan transformation family as the lifetime model for experimental units. The new bivariate models accurately measure dependence, demonstrate significant properties, and include special sub-models that leverage exponential, Weibull, and Pareto distributions as baseline distributions. Point and interval estimation techniques, such as maximum likelihood and Bayesian methods, where Bayesian estimation outperforms maximum likelihood estimation, are employed, and bootstrap confidence intervals are calculated. Numerical analysis is performed using the Markov chain Monte Carlo method. The proposed methodology’s applicability is demonstrated through the analysis of two real-world data-sets. The first data-set, focusing on infection and recurrence time in kidney patients, indicates that the Farlie–Gumbel–Morgenstern bivariate Kavya–Manoharan–Weibull (FGMBKM-W) distribution is the best bivariate model to fit the kidney infection data-set. The second data-set, specifically that related to UEFA Champions League Scores, reveals that the Clayton Kavya–Manoharan–Weibull (CBKM-W) distribution is the most suitable bivariate model for fitting the UEFA Champions League Scores. This analysis involves examining the time elapsed since the first goal kicks and the home team’s initial goal.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2986-:d:1186626
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    References listed on IDEAS

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    1. Debasis Kundu & Rameshwar Gupta, 2011. "Absolute continuous bivariate generalized exponential distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 169-185, June.
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    3. Ranadeera Gamage Madhuka Samanthi & Jungsywan Sepanski, 2022. "On bivariate Kumaraswamy-distorted copulas," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2477-2495, April.
    4. M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    5. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    6. 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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    1. 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.

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