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Using squared-error loss function and Jeffreys' noninformative prior, a Bayes estimator of the Rayleigh parameter and the associated reliability function have been obtained and the estimators compared with their maximum likelihood and uniformly minimum variance unbiased counterparts. Credible intervals and the highest posterior density intervals for the scale parameter and the reliability function are derived. A numerical example is given.
Sinha et al. (1983) studied this question.