Bayesian Estimation of the Lomax Distribution Parameters under Progressive Type-II Censoring

Document Type : Original Article

Authors

1 Associate Professor of Mathematical Statistics, Department of Mathematics Faculty of Science, Helwan University, Egypt

2 Professor. Dept. of Mathematics Faculty of Science. Helwan University

3 Department of Mathematics, College of Science, Hafar Al-Batin, Saudi Arabia.

10.21608/abas.2025.411161.1075

Abstract

This paper presents approximate Bayesian estimators for the unknown parameters of the Lomax distribution using progressive Type II censored samples, which are commonly encountered in reliability testing scenarios and lifetime data analysis. The study explores both maximum likelihood and Bayesian estimation methods, incorporating informative gamma priors for the parameters to enhance inference accuracy and flexibility. Additionally, the reliability function and the reversed hazard rate function are thoroughly examined to provide deeper insights into system failure behavior over time. To compute the Bayesian estimates, Lindley’s approximation (1980) and Markov Chain Monte Carlo (MCMC) techniques are employed, offering computational solutions for analytically intractable integrals. The estimators are derived under symmetric and asymmetric loss functions, including linex and general entropy loss functions to accommodate varied decision-making criteria. A comprehensive simulation study is conducted to evaluate the practical performance of the proposed estimators, and numerical results are provided to demonstrate their robustness and effectiveness under different progressive censoring schemes.

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