Journal of Statistics Applications & Probability

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The bivariate Fre ́chet distribution is an important lifetime distribution in survival analysis. In this paper, Farlie-Gumbel- Morgenstern (FGM), Ali-Mikhail-Haq (AMH) copulas and univariate Fre ́chet distribution are used for creating bivariate distributions which will be called FGM bivariate Fre ́chet (FGMBF) and AMH Bivariate Fre ́chet (AMHBF) distributions. The reliability function and hazard function will be obtained for Bivariate Fre ́chet distributions. Some properties of the FGMBF distribution are obtained such as product moments and moment generation function. Two different estimation methods for the unknown parameters of the two bivariate Fre ́chet models will be discussed. Asymptotic and bootstrap confidence intervals for the models parameter are also considered. To evaluate the performance of the estimators, a Monte Carlo simulations study is conducted to compare the efficiency between the two models and the preferences between estimation methods. Also, a two real data sets are analyzed to investigate the models and useful results are obtained for illustrative purposes.

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