Bayesian estimation and prediction based on Rayleigh sample quantiles

Ordered data arise naturally in many fields of statistical practice. Often some sample values are unknown or disregarded due to various reasons. On the basis of some sample quantiles from the Rayleigh distribution, the problems of estimating the Rayleigh parameter, hazard rate and reliability function, and predicting future observations are addressed using a Bayesian perspective. The construction of β-content and β-expectation Bayes tolerance limits is also tackled. Under squared-error loss, Bayes estimators and predictors are deduced analytically. Exact tolerance limits are derived by solving simple nonlinear equations. Highest posterior density estimators and credibility intervals, as well as Bayes estimators and predictors under linear loss, can easily be computed iteratively.