Applied Mathematics & Information Sciences

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Comparative lifetime experiments are vital when the interest is in learning the overall benefits of two competing products with respect to their reliability. In this article, point and interval estimations for the unknown parameters of two Weibull- Fre ́chet populations based on joint progressive Type-II censoring samples are discussed. The point estimations for the two distribution parameters are obtained by the maximum likelihood, Bayes and parametric bootstrap methods. Moreover, approximate confidence intervals and credible intervals of the estimators have been obtained and compared with four bootstrap confidence intervals. Furthermore, Bayes estimators have been developed under squared error loss and linear exponential loss functions using independent gamma prior distributions when Gibbs sampler within the Metropolis-Hasting algorithm is applied to generate Markov chain Monte Carlo samples from the posterior density functions. A real data set is studied to illustrate the application of the proposed criteria. Finally, extensive simulation experiments have been performed to study the performances of the different methods.

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