Bayesian estimation and prediction based on Rayleigh record data with applications

Raed R. Abu Awwad; Omar M. Bdair; Ghassan K. Abufoudeh

doi:10.21307/stattrans-2021-027

Bayesian estimation and prediction based on Rayleigh record data with applications

Raed R. Abu Awwad Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan , Omar M. Bdair Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan. Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada , Ghassan K. Abufoudeh Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan Statistics in Transition new series, vol. 22, 2021, 3, pages: 59–79 Published online: 6 September 2021 DOI 10.21307/stattrans-2021-027

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ARTICLE

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ABSTRACT

Based on a record sample from the Rayleigh model, we consider the problem of estimating the scale and location parameters of the model and predicting the future unobserved record data. Maximum likelihood and Bayesian approaches under different loss functions are used to estimate the model’s parameters. The Gibbs sampler and Metropolis-Hastings methods are used within the Bayesian procedures to draw the Markov Chain Monte Carlo (MCMC) samples, used in turn to compute the Bayes estimator and the point predictors of the future record data. Monte Carlo simulations are performed to study the behaviour and to compare methods obtained in this way. Two examples of real data have been analyzed to illustrate the procedures developed here.

KEYWORDS

Bayesian estimation and prediction, Rayleigh distribution, record values, Markov Chain Monte Carlo samples

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