Unified Treatment for a Class of Extreme Value Distributions

In this paper, we introduce new family depends on Fréchet distribution. A sub-model of the new family called the composed- Fréchet exponential (C-FE) distribution is presented to provide the flexibality of the family. The point and interval estimation based on maximum likelihood are proposed. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in a closed form. So, Markov Chain Monte Carlo (MCMC) method has been used to compute the approximate Bayes estimates under the squared error loss function and also the highest posterior density (HPD) intervals have been constructed. Further, a simulation study has been conducted to compare the performances of the Bayes estimators with corresponding maximum likelihood estimators.