A Bayesian analysis for censored Rayleigh model using a generalised hypergeometric prior

P. J. Mostert; A. Bekker; J. J. J. Roux

doi:10.37920/sasj.2016.50.2.2

P. J. Mostert Department of Statistics and Actuarial Science, Stellenbosch University
A. Bekker Department of Statistics, University of Pretoria
J. J. J. Roux Department of Statistics, University of South Africa

DOI: https://doi.org/10.37920/sasj.2016.50.2.2

Keywords: Bayesian estimation, Bayesian prediction bounds, Frequentist coverage, Generalised hypergeometric distribution, H-function, Metropolis-Hastings algorithm, Rayleigh model, Squared error loss function, Type II censored data

Abstract

Based on a type II censored sample, Bayesian estimation for the scale parameter of the Rayleigh model is carried out under the assumption of the squared error loss function. A generalised hypergeometric distribution with its versatile shape of tails is introduced as a prior, and beta special cases are examined. A simulation study is carried out to investigate the sensitivity of four special cases of this beta prior family in terms of bias, frequentist coverage and mean square error and to determine their effect on robustness. Prediction bounds are derived for the lifetime of unused components using this beta prior family. A data set is used to illustrate and support some of the findings.

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