Mean and Dispersion Regression Model for Extremes with Application in Humidity

Lara Roberta da Silva Costa, Fernando Ferraz do Nascimento () and Marcelo Bourguignon
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Lara Roberta da Silva Costa: Departamento de Estatística, Universidade Federal do Piauí, Teresina 64049-550, PI, Brazil
Fernando Ferraz do Nascimento: Departamento de Estatística, Universidade Federal do Piauí, Teresina 64049-550, PI, Brazil
Marcelo Bourguignon: Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, RN, Brazil

Mathematics, 2025, vol. 13, issue 18, 1-13

Abstract: The generalized extreme value (GEV) distribution has been extensively applied in predicting extreme events across diverse fields, enabling accurate estimation of extreme quantiles of maxima. Although the mean and variance of the GEV can be expressed as functions of its parameters, a reparameterization that directly uses the mean and standard deviation as parameters provides interpretative advantages. This is particularly useful in regression-based models, as it allows a more straightforward interpretation of how covariates influence the mean and the standard deviation of the data. The proposed models are estimated within the Bayesian framework, assuming normal prior distributions for the regression coefficients. In this work, we introduce a reparameterization of the GEV distribution in terms of the mean and standard deviation, and apply it to minimum humidity data from the northeast region of Brazil. The results highlight the benefits of the proposed methodology, demonstrating clearer interpretability and practical relevance for extreme value modeling, where the influence of seasonal and locality variables on the mean and variance of minimum humidity can be accurately assessed.

Keywords: Bayesian inference; extreme value theory; generalized extreme value distribution; mean and standard deviation modelling; parameterization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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