Bayesian Estimation for the Rate Parameter of the Weibull Distribution

Yaghoobzadeh Shahrastani, Shahram; Kazemi, Mohammad

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Bayesian Estimation for the Rate Parameter of the Weibull Distribution

Shahram Yaghoobzadeh Shahrastani

, Mohammad Kazemi ^*

Abstract: (9 Views)

In this paper, the Weibull distribution, which is widely used in various fields such as medicine, engineering, and reliability analysis, is considered with parameters $alpha$ and $beta$. In survival analysis, the parameter $alpha$ represents the mortality rate or level, while the parameter $beta$ reflects the aging effect; therefore, accurate estimation of $alpha$ is of particular importance. Accordingly, the parameter $alpha$ is estimated under two scenarios where $beta$ is assumed to be known and unknown. In addition to the Bayes and $E$-Bayes estimators, a new estimator called the $E^2$-Bayes estimator is proposed for the parameter $alpha$. Specifically, when $beta$ is known, this estimator is derived under the general entropy loss function, whereas in the case of unknown $beta$, it is obtained under the squared error loss function. Subsequently, the performance of the proposed estimators is evaluated and compared using Monte Carlo simulations and a real data set based on the criteria of absolute bias and mean squared error. An estimator with smaller absolute bias and mean squared error is regarded as superior to the others.

Keywords: Weibull distribution, Bayesian estimator, E-Bayesian estimator, E^2-Bayesian estimator, mean squared error

Full-Text [PDF 1195 kb] (9 Downloads)

Type of Study: Research | Subject: Statistical Inference
Received: 2026/02/9 | Accepted: 2027/03/1

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