Estimation of stress-strength reliability from exponentiated Fréchet distribution

In this paper, we are mainly concerned in estimating the reliability R = P(Y < X) in the exponentiated Fréchet distribution, recently proposed by Nadarajah and Kotz (2006), Acta Appl Math 92:97–111. The model arises as a generalization of the standard Fréchet distribution in the same way the exponentiated exponential distribution introduced by Gupta et al. (1998), Commun Stat Theory Methods 27:887–904. The maximum likelihood estimator and its asymptotic distribution are used to construct an asymptotic confidence interval of R. Assuming that the common scale and shape parameters are known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator of R are discussed. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulation. Using real data, we illustrate the procedure.