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Title: Bayesian estimation for geometric process with the Weibull distribution
Authors: Usta, İlhan
Keywords: Asymptotic normality
Bayesian estimation
geometric process
Markov Chain Monte Carlo
Maximum likelihood estimation
Weibull distribution
Issue Date: 2022
Publisher: Taylor & Francis Inc
Abstract: In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes.
ISSN: 0361-0918
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu
WoS İndeksli Yayınlar Koleksiyonu

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