  In this article, we consider the problem of estimating the parameters of the
Fr\'echet distribution from both frequentist and Bayesian points of view. First
we briefly describe different frequentist approaches, namely, maximum
likelihood, method of moments, percentile estimators, L-moments, ordinary and
weighted least squares, maximum product of spacings, maximum goodness-of-fit
estimators and compare them with respect to mean relative estimates, mean
squared errors and the 95\% coverage probability of the asymptotic confidence
intervals using extensive numerical simulations. Next, we consider the Bayesian
inference approach using reference priors. The Metropolis-Hasting algorithm is
used to draw Markov Chain Monte Carlo samples, and they have in turn been used
to compute the Bayes estimates and also to construct the corresponding credible
intervals. Five real data sets related to the minimum flow of water on
Piracicaba river in Brazil are used to illustrate the applicability of the
discussed procedures.
