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This paper aims to estimate the unknown parameters, survival and hazard functions for exponentiated Rayleigh distribution based on unified hybrid censored data. The maximum likelihood and Bayes methods are used for estimating the two unknown parameters as well as survival and hazard functions. Lindley’s approximation and Markov Chain Monte Carlo (MCMC) method applied to find the Bayes estimation. Approximate confidence intervals for the unknown parameters moreover survival and hazard functions are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimates (MLEs). The approximate Bayes estimators have been obtained under the assumptions of non-informative priors depending on symmetric and asymmetric loss functions via the Gibbs within Metropolis-Hasting samplers procedure. Finally, the proposed methods can be understood through illustrating the results of the real data analysis.

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