Volume 9, Issue 12 (December 2022), Pages: 57-67

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 Original Research Paper

 Lindley procedure and MCMC technique in Bayesian estimation for Kumaraswamy Weibull distribution

 Author(s): Fathy H. Eissa ^{1, 2,} *

 Affiliation(s):

 ¹Department of Mathematics, College of Science and Arts-Rabigh, King Abdulaziz University, Jeddah, Saudi Arabia
 ²Department of Mathematics, Faculty of Science, Damanhur University, Damanhur, Egypt

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-3139-8459

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2022.12.008

 Abstract:

In this study, a comparison between three methods for estimating unknown parameters of the Kumaraswamy Weibull distribution for different sample sizes of type II censoring data is presented. Specifically, we compare the behaviors of maximum likelihood estimates, Lindley and Markov chain Monte Carlo (MCMC) estimates as Bayesian estimates. We have not found any work on this topic after reviews of the literature except one with little information about the inference of this important distribution. The simplest form for Lindley approximation of the posterior mean is proposed and approximate closed forms of acceptable Bayes estimates for the models of multi-parameters such as Kumaraswamy Weibull distribution is derived. A Monte Carlo simulation is conducted to investigate the performances of the proposed estimators. Finally, three real data examples are analyzed to illustrate the application possibility of the different proposed estimation methods. The results reveal that, although, good performance of the approximate forms of Lindley estimators, the estimators resulting in the MCMC technique are better in the sense of the mean squared errors.

 © 2022 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Kumaraswamy Weibull distribution, Type II censored data, Reliability characteristics, Lindley procedure, MCMC technique

 Article History: Received 22 January 2022, Received in revised form 15 April 2022, Accepted 20 August 2022

 Acknowledgment 

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant no. (G: 528-662-1439). The authors acknowledge thanks to DSR financial support.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Eissa FH (2022). Lindley procedure and MCMC technique in Bayesian estimation for Kumaraswamy Weibull distribution. International Journal of Advanced and Applied Sciences, 9(12): 57-67

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 Figures

 Fig. 1 Fig. 2

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 

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