Bayesian Estimation under a Censoring-Adjusted Loss Function for Theakash Distribution with Progressive First-Failure Censoring
- 1Troy University
Abstract
This paper studies Bayesian estimation for the Akash distribution under progressive first-failure censoring (PFFC), a censoring scheme commonly encountered in reliability and life-testing experiments. The objective is to improve point estimation and interval efficiency through a loss function that adapts to censoring severity. In addition to the conventional squared-error (SE) and LINEX loss functions, a new censoring-adjusted linear-exponential quadratic (CALQ) loss function is proposed. The CALQ loss incorporates censoring information through an adaptive weighting mechanism that varies with censoring intensity. Maximum likelihood estimation is obtained using the expectation-maximization (EM) algorithm, while Bayesian estimators are computed via Markov Chain Monte Carlo (MCMC) methods. The proposed methodology is evaluated through an extensive Monte Carlo simulation study covering a wide range of sample sizes and censoring schemes. Its practical applicability is further demonstrated using two real data sets involving tensile-strength and analgesic relief-time observations. The results indicate that Bayesian estimators outperform the EM-based maximum likelihood estimator in terms of mean squared error (MSE) and bias. Among the Bayesian approaches, the CALQ estimator provides the most accurate and stable performance across nearly all scenarios. The improvement is particularly pronounced under moderate to heavy censoring, where classical estimators tend to lose efficiency. For interval estimation, CALQ-based credible intervals achieve shorter average lengths while maintaining coverage probabilities close to the nominal level, indicating improved efficiency compared with existing methods. Overall, the CALQ framework offers a flexible and effective extension of loss-based Bayesian inference by explicitly accounting for censoring severity, resulting in consistent improvements in both point and interval estimation for reliability analysis under complex censoring schemes.
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BibTeX
@article{wijekularathna2026bayesian,
title = {{Bayesian Estimation under a Censoring-Adjusted Loss Function for Theakash Distribution with Progressive First-Failure Censoring}},
author = {Danush Wijekularathna and Nicholas A. Newman},
journal = {Reliability: Theory \& Applications},
year = {2026},
month = jun,
doi = {10.66721/vahcvb18},
url = {https://doi.org/10.66721/vahcvb18},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Bayesian Estimation under a Censoring-Adjusted Loss Function for Theakash Distribution with Progressive First-Failure Censoring
AU - Danush Wijekularathna
AU - Nicholas A. Newman
PY - 2026
DA - 2026/06/01
JO - Reliability: Theory & Applications
DO - 10.66721/vahcvb18
UR - https://doi.org/10.66721/vahcvb18
AB - This paper studies Bayesian estimation for the Akash distribution under progressive first-failure censoring (PFFC), a censoring scheme commonly encountered in reliability and life-testing experiments. The objective is to improve point estimation and interval efficiency through a loss function that adapts to censoring severity. In addition to the conventional squared-error (SE) and LINEX loss functions, a new censoring-adjusted linear-exponential quadratic (CALQ) loss function is proposed. The CALQ loss incorporates censoring information through an adaptive weighting mechanism that varies with censoring intensity. Maximum likelihood estimation is obtained using the expectation-maximization (EM) algorithm, while Bayesian estimators are computed via Markov Chain Monte Carlo (MCMC) methods. The proposed methodology is evaluated through an extensive Monte Carlo simulation study covering a wide range of sample sizes and censoring schemes. Its practical applicability is further demonstrated using two real data sets involving tensile-strength and analgesic relief-time observations. The results indicate that Bayesian estimators outperform the EM-based maximum likelihood estimator in terms of mean squared error (MSE) and bias. Among the Bayesian approaches, the CALQ estimator provides the most accurate and stable performance across nearly all scenarios. The improvement is particularly pronounced under moderate to heavy censoring, where classical estimators tend to lose efficiency. For interval estimation, CALQ-based credible intervals achieve shorter average lengths while maintaining coverage probabilities close to the nominal level, indicating improved efficiency compared with existing methods. Overall, the CALQ framework offers a flexible and effective extension of loss-based Bayesian inference by explicitly accounting for censoring severity, resulting in consistent improvements in both point and interval estimation for reliability analysis under complex censoring schemes.
SN - 1932-2321
ER -