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In this paper, maximum likelihood and Bayes estimators of the scale parameter, survival function and hazard rate function are obtained for the Rayleigh failure time distribution, when the life test is progressively first-failure censored. Bayes estimators have been developed using the standard Bayes method under square error and LINEX loss functions, using inverted gamma prior for the parameter. Asymptotic confidence intervals and two bootstrap confidence intervals for the parameter are also proposed. We give an example to illustrate our proposed methods. Results from simulation studies assessing the performance of our proposed method are included. The Bayes estimates are found to be, generally, better than the maximum likelihood estimates against the proposed prior, in the sense of having smaller mean square errors.

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