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In this paper, the problem of estimation for the new Weibull-Pareto distribution based on progressive Type-II censored sample is studied. The maximum likelihood, Bayes and parametric bootstrap methods are used for estimating the three unknown parameters as well as some lifetime parameters reliability and hazard functions. Based on the asymptotic normality of maximum likelihood estimators we construct the approximate confidence intervals of the parameters. Futhermor, depending on the delta and parametric bootstrap methods we calculate the approximate confidence intervals (ACIs) of the reliability and hazard functions. Markov chain Monte Carlo (MCMC) technique is applied to computing the Bayes estimate and the credible intervals of the unknown parameters as well as reliability and hazard functions which are obtained under the assumptions of informative and non-informative priors based on the Gibbs within Metropolis-Hasting samplers procedure. The results of Bayes methed are obtained under squared error loss (SEL) function. Finally, Two examples used to a simulated data and a real life data sets have been presented for illustrative purposes.

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