Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm ()

Tahani A. Abushal, Areej M. Al-Zaydi

Department of Mathematics, Taif University, Taif, KSA.

Department of Mathematics, Umm Al-Qura University, Makkah Al-Mukarramah, KSA.

**DOI: **10.4236/ojs.2012.23044
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Department of Mathematics, Taif University, Taif, KSA.

Department of Mathematics, Umm Al-Qura University, Makkah Al-Mukarramah, KSA.

This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.

Keywords

Mixture Distributions; Rayleigh Distribution; Generalized Order Statistics; Record Values; MCMC

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T. Abushal and A. Al-Zaydi, "Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm," *Open Journal of Statistics*, Vol. 2 No. 3, 2012, pp. 356-367. doi: 10.4236/ojs.2012.23044.

Conflicts of Interest

The authors declare no conflicts of interest.

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