Regression in extremes using the four-parameter Kappa distribution

Abstract

The four-parameter Kappa distribution (4KD) is known to be flexible and has been used for extreme value analysis, especially in hydrological sciences. This distribution has the great advantage of encompassing the two main distributions of extreme values used in the literature: the Generalized Pareto Distribution (GPD) and the Generalized Extreme Value (GEV) distribution. However, the analyses made in previous works for 4KD in the context of extreme values are based only on models with static parameters, not allowing the capture of covariate effects such as seasonality and location variables in a specific dataset. This study proposes that the inference about the 4KD can be made under the Bayesian paradigm by inserting a regression structure on the parameters to assess possible effects of covariates under the model. This proposal allows us to interpret the parameters and predict extreme events when there are covariates. The estimation of the parameters is performed using Markov Chain Monte Carlo (MCMC) procedures. The model was applied with both approaches in extremes: maximum and exceedance data. In this analysis, the proposed model was compared with models that use a regression structure in the usual extreme values distribution (GEV and GPD), and it presented better results in fit measures.