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Bayesian estimation and prediction based on Rayleigh record data with applications

Author

Listed:
  • Abu Awwad Raed R.

    (Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan .)

  • Bdair Omar M.

    (Faculty of Engineering Technology, Al-Balqa Applied University, Amman, 11134, Jordan . Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4L8, Canada .)

  • Abufoudeh Ghassan K.

    (Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan .)

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.

Suggested Citation

  • Abu Awwad Raed R. & Bdair Omar M. & Abufoudeh Ghassan K., 2021. "Bayesian estimation and prediction based on Rayleigh record data with applications," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 59-79, September.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:3:p:59-79:n:5
    DOI: 10.21307/stattrans-2021-027
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    References listed on IDEAS

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    1. Jafar Ahmadi & M. Doostparast, 2006. "Bayesian estimation and prediction for some life distributions based on record values," Statistical Papers, Springer, vol. 47(3), pages 373-392, June.
    2. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    3. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    4. Soliman, Ahmed A. & Al-Aboud, Fahad M., 2008. "Bayesian inference using record values from Rayleigh model with application," European Journal of Operational Research, Elsevier, vol. 185(2), pages 659-672, March.
    5. Essam Al-Hussaini & Abd Ahmad, 2003. "On Bayesian interval prediction of future records," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 79-99, June.
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