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The focus of this book is the mixtures of distributions: mixture of two Weibull distributions, mixture of Frechet and Weibull distributions. The elegant closed-form Bayes estimators are derived for each of these mixtures assuming informative (Inverted-Gamma, Inverted-Chi Squared, Gumbel Type II and Levy) and non-informative (Uniform and Jeffreys) priors. Also, an extensive simulation study is conducted to highlight some interesting properties and comparison of Bayes estimates under Type-I censored mixture data. Some real life examples are also presented. Moreover, we have developed the limiting expressions for the Bayes estimators and their posterior risks. The Bayesian approach of life testing for the Weibull distribution is also used for simple Weibull model. The closed form expressions are derived for posterior distributions under the different priors, Bayes estimators and their posterior risks are obtained under different loss functions. Efficiency comparison of Bayes estimator with respect to ML estimator is also made. Efficiency comparison of Bayes estimator with respect to ML estimator is also made.