<p>Extreme value theory (EVT) is a fundamental statistical framework for modeling and analyzing extreme events across diverse scientific domains, including hydrology, meteorology, finance, and environmental sciences. The generalized extreme value (GEV) distribution has been traditionally employed to model the probabilistic behavior of block maxima and minima. Recent extensions of the GEV distribution, including bimodal models, provide greater flexibility to capture heterogeneous extremes. This heterogeneity requires models that incorporate covariates to account for non-stationarity and allow for more accurate risk assessments. Unlike recent approaches based on mixtures of distributions, in this study, we propose a pioneering regression model for heterogeneous and bimodal extremes based on the bimodal GEV distribution, integrating covariates directly into its parameters. Reparameterization in terms of quantiles improves interpretability, and the parameters are estimated using maximum likelihood, which was implemented through the <Emphasis FontCategory="NonProportional">gamlss</Emphasis> package in <Emphasis FontCategory="NonProportional">R</Emphasis>. The model’s performance is evaluated through Monte Carlo simulations and illustrated with climate data, demonstrating adequate fit and practical applicability.</p>

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A regression-type model for bimodal extreme-valued data

  • Cira E. G. Otiniano,
  • Mathews N. S. Lisboa,
  • Terezinha K. A. Ribeiro,
  • Juliana B. Fachini-Gomes

摘要

Extreme value theory (EVT) is a fundamental statistical framework for modeling and analyzing extreme events across diverse scientific domains, including hydrology, meteorology, finance, and environmental sciences. The generalized extreme value (GEV) distribution has been traditionally employed to model the probabilistic behavior of block maxima and minima. Recent extensions of the GEV distribution, including bimodal models, provide greater flexibility to capture heterogeneous extremes. This heterogeneity requires models that incorporate covariates to account for non-stationarity and allow for more accurate risk assessments. Unlike recent approaches based on mixtures of distributions, in this study, we propose a pioneering regression model for heterogeneous and bimodal extremes based on the bimodal GEV distribution, integrating covariates directly into its parameters. Reparameterization in terms of quantiles improves interpretability, and the parameters are estimated using maximum likelihood, which was implemented through the gamlss package in R. The model’s performance is evaluated through Monte Carlo simulations and illustrated with climate data, demonstrating adequate fit and practical applicability.