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

Ehab M. Almetwally, Aisha Fayomi and Maha E. Qura ()
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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
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

Mathematics, 2024, vol. 12, issue 12, 1-35

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.

Keywords: XLindley distribution; Censoring scheme; kidney patients; Frank copula; type II censored samples; Clayton copula; Markov Chain Monte Carlo; Gumbel copula; Bayesian estimation; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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