The Fréchet distribution: Estimation and application - An overview

Abstract

In this article we consider the problem of estimating the parameters of the Fréchet 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 using extensive numerical simulations. Next, we consider the Bayesian infer- ence approach using reference priors. 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.

Subject Classification (2010):

• 62F10
• 62P12

Keywords:

• Bayesian Inference
• Fréchet distribution
• Hydrological applications
• Maximum product of spacings
• Reference prior