Aykroyd, RG orcid.org/0000-0003-3700-0816, Mahmoud, MAW and Aljohani, HM (2017) Bayesian analysis using MCMC methods of record values based on a new generalised Rayleigh distribution. Stochastic Modeling and Applications, 21 (2). pp. 49-66. ISSN 0972-3641
Abstract
In this paper, we extend the Rayleigh distribution to create a generalised Rayleigh distribution which is more flexible than the standard. The general properties of the new distribution are derived and investigated, with properties of more standard distributions, such as the exponential, standard Rayleigh and the Weibull, appearing as special cases. Further, we consider maximum likelihood estimation and Bayesian inference under the assumptions of gamma prior distributions on model parameters. Point estimates and confidence intervals based on maximum likelihood estimation are computed. The main challenge, however, is that the Bayesian estimators cannot easily be found and hence, Markov chain Monte Carlo (MCMC) techniques are proposed to generate samples from the posterior distributions leading to approximate posterior inference. The approximate Bayes estimators are compared with the maximum likelihood estimators using simulated data showing dramatic superiority of the Bayesian approach.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, Author(s). This is an open access article under the terms of the Creative Commons Attribution License (CC-BY)]. |
Keywords: | Bayesian inference; maximum likelihood; life testing; Metropolis-Hastings methods; standard Rayleigh distribution |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Sep 2017 08:34 |
Last Modified: | 16 Nov 2017 12:34 |
Published Version: | http://www.mukpublications.com/smavol-21-no-2.php |
Status: | Published |
Publisher: | MUK Publications |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:121000 |