The Frechet distribution: Estimation and Application an Overview

TL;DR

This paper reviews methods for estimating the parameters of the Fréchet distribution, comparing frequentist and Bayesian approaches through simulations and real data applications.

Contribution

It provides a comprehensive comparison of various estimation techniques for the Fréchet distribution, including new Bayesian inference methods with reference priors.

Findings

Frequentist estimators vary in bias and variance

Bayesian estimates are effective with MCMC methods

Real data applications demonstrate practical utility

Abstract

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.