Practical strategies for generalized extreme value‐based regression models for extremes

The generalized extreme value (GEV) distribution is the only possible limiting of properly normalized maxima a sequence independent and identically distributed random variables. As such, it has been widely applied to approximate over blocks. In these applications, GEV properties such as finite lower endpoint when shape parameter ξ $$ \xi positive or loss moments due magnitude are inherited by finite-sample distribution. extent which realistic for data at hand ignored. Motivated overlooked consequences in regression setting, we here make three contributions. First, propose blended (bGEV) distribution, smoothly combines left tail Gumbel (GEV with = 0 =0 ) right Fréchet > >0 ). Our resulting has, therefore, unbounded support. Second, proposed principled method called property-preserving penalized complexity (P 3 {}^3 C) prior decide on existence first second priori. Third, reparametrization that provides more natural interpretation (possibly covariate-dependent) model parameters, turn helps define meaningful priors. We implement bGEV new parameterization P C approach R-INLA package readily available users. illustrate our methods simulation study reveals distributions comparable estimating under large-sample settings. Moreover, some small-sample settings show fit slightly outperforms fit. Finally, conclude an application NO 2 {}_2 pollution levels California illustrates suitability Bayesian framework.