Regression models for the full distribution to exceedance data

Abstract

The list of occurrences linked to significant climate change has grown in recent decades. These changes can be influenced by a set of covariates, such as temperature, location and period of the year. Analyzing the relation among elements and factors that influence the behavior of such events is extremely important for decision-making in order to minimize damages and losses. Exceedance analysis uses the tail of the distribution based on Extreme Value Theory (EVT). Extensions for these models have been proposed in literature, such as regression models for the tail parameters and a parametric or semi-parametric distribution for the part that comes before the tail (well known as bulk distribution). This work presents a new extension to exceedance model, in which the parameters for the bulk distribution capture the effect of covariates such as location and seasonality. We considered a Bayesian approach in the inference procedure. The estimation was done using MCMC -- Markov Chain Monte Carlo methods. Application results for modeling maximum and minimum temperature data showed an efficient estimation of extreme quantiles and a predictive advantage compared to models previously used in literature.