Bayesian estimation of the Rayleigh distribution under different loss function

In a Rayleigh distribution, we interesting of the estimation of the parameter and some feature of reliability, as, the reliability function and the failure rate function. We used the Bayesian approach under different loss function (squared loss and Linex loss) with a type II censored data. the prior law of the parameter is uninformative prior then a natural conjugated prior. The estimators of s, S(t) and h(t) are obtained with the exact analytic expression, the posterior risks are calculated in each case. A simulation study was carried out as well as real data analysis. A comparaison between the different estimators from there posterior risks leads us to conclude that the best estimator is obtained under the Linex loss.