&lt;b&gt;Is the Conditional Density Network more suitable than the Maximum likelihood for fitting the Generalized Extreme Value Distribution?

Monica Cristina Meschiatti,Gabriel Constantino Blain

doi:10.4025/actascitechnol.v37i4.27660

<b>Is the Conditional Density Network more suitable than the Maximum likelihood for fitting the Generalized Extreme Value Distribution?

Monica Cristina Meschiatti, Gabriel Constantino Blain

Open Access

https://doi.org/10.4025/actascitechnol.v37i4.27660

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Abstract

The Generalized Extreme value Distribution (GEV) has been widely used to assess the probability of extreme weather events and the parameter estimation method is a key factor for improving its quantile estimates. On such background, this study aimed to indicate under which conditions (sample size and tail behavior) the Conditional Density Network (CDN) leads to better GEV quantile estimates than the widely used Maximum likelihood method (MLE) does. With Monte Carlo simulations and rainfall series of several Brazilians regions, we highlight the following results: the return period and the tail behavior of the GEV (specified by the shape parameter) are two of the main factors affecting the quantile estimates. For -0.1 ≤ shape ≤ 0.1 and sample size ≤ 50, the CDN outperformed the MLE. For shape ≥ 0.20 the CDN outperformed the MLE for all sample sizes (30-90). The results also suggested that the CDN is more suitable than the MLE for fitting the GEV parameter to the Brazilian extreme rainfall series. We conclude that when the shape parameter are equal to or greater than -0.1 the CDN should be preferred over the MLE.

Highlights

The Extremal Types Theorem states that the highest values of independent and identically distributed data converge to one of the three types of extreme value distributions: Gumbel, Fréchet or Weibull
This study aimed to indicate under which conditions the Conditional Density Network (CDN) leads to better quantile estimates than the Maximum Likelihood Estimation (MLE) does
This statement is consistent with the results found by Martins and Stedinger (2000), Coles (2001), El Adlouni et al (2007), Blain (2014), Blain and Meschiatti (2014) and indicates that the magnitude of the errors of the quantile estimates increases as the return period of an extreme event increases

Summary

Introduction

The Extremal Types Theorem states that the highest values of independent and identically distributed data converge to one of the three types of extreme value distributions: Gumbel (type I), Fréchet (type II) or Weibull (type III). Given that the General Extreme Value Distribution (GEV) is capable of representing these three types of extreme distribution into a single equation, several meteorological studies 2000; COLES, 2001; EL ADLOUNI et al, 2007; FELICI et al, 2007; BROWN et al, 2008; CANNON, 2010; DELGADO et al, 2010; ZWIERS et al, 2011; WILKS, 2011; ANDRADE et al, 2012) have used the GEV to assess the probability of extreme weather events in virtually all parts of the Globe

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