A simulation study of the Bayes estimator for parameters in Weibull distribution

Year 2019, Volume: 68 Issue: 2, 1664 - 1674, 01.08.2019

Esin Köksal Babacan , Samet Kaya

https://doi.org/10.31801/cfsuasmas.455276

Cited By: 3

Abstract

The Weibull
distribution is one of the most popular distributions in analyzing the lifetime
data. In this study, we consider the Bayes
estimators of the scale and shape parameters of  Weibull distribution under the assumptions of
gamma priors and squared error loss function. While computing the Bayes
estimates for a Weibull distribution, the continuous conjugate joint prior
distribution of the shape and scale parameters does not exist and the closed form
expressions of the Bayes estimators cannot be obtained.

In this study first we
will consider the Bayesian inference of the scale parameter under the
assumption that the shape parameter is known. We will assume that the scale
parameter has a gamma prior. Under these assumptions Bayes estimate can be
obtained in explicit form. When both the parameters are unknown, the Bayes
estimates cannot be obtained in closed form. In this case, we will assume that
the scale parameter has the gamma prior, and the shape parameter also has the gamma
prior and they are independently distributed. We will use the Lindley
approximation to obtain the approximate Bayes estimators.

Under these
assumptions, we will compute approximate Bayes estimators and compare with the
maximum likelihood estimators by Monte Carlo simulations. 

Keywords

Weibull Distribution, Bayes Estimator, Lindley approximation

References

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