Selecting “the best” nonstationary Generalized Extreme Value (GEV) distribution: on the influence of different numbers of GEV-models

Abstract

The selection of an appropriate nonstationary Generalized Extreme Value (GEV) distribution is frequently based on methods, such as Akaike information criterion (AIC), second-order Akaike information criterion (AICc), Bayesian information criterion (BIC) and likelihood ratio test (LRT). Since these methods compare all GEV-models considered within a selection process, the hypothesis that the number of candidate GEV-models considered in such process affects its own outcome has been proposed. Thus, this study evaluated the performance of these four selection criteria as function of sample sizes, GEV-shape parameters and different numbers candidate GEV-models. Synthetic series generated from Monte Carlo experiments and annual maximum daily rainfall amounts generated by the climate model MIROC5 (2006-2099; State of São Paulo-Brazil) were subjected to three distinct fitting processes, which considered different numbers of increasingly complex

Improving the interpretation of standardized precipitation index estimates to capture drought characteristics in changing climate conditions

“…The results found in this simulation round indicate that the BIC also tends to perform poorly when the dispersion of the series increases over time. This statement is consistent with results found by Xavier et al (2019b).…”

“…For the highest values of the sample size, μ 0 and σ 0 , the ΔAICc tended to outperform all other methods. The tendency of both AIC and AICc to select more complex models (Panagoulia et al, 2014;Kim et al, 2017;Xavier et al, 2019b) was also observed. These two criteria selected the most complex model (Model 3) at rates considerably higher than the other procedures.…”

“…On the other hand, the success rates of both the AIC and AICc remained below 80% for all sample sizes and gamma‐parameters considered in Experiment 2. These relatively low success rates (Figure 6 and Table S2) are consistent with the statement that both AIC and AICc tend to select more complex models than BIC and LRT (Panagoulia et al ., 2014; Kim et al ., 2017; Xavier et al ., 2019b). The delta method has consistently improved the performance of the Akaike's statistics because both ΔAIC and ΔAICc presented success rates almost as high as those presented by the BIC and LRT.…”

Generalized Pareto distribution applied to the analysis of maximum rainfall events in Uruguaiana, RS, Brazil

“…Regarding simulation studies involving distributions of extreme values, Xavier et al [48] have reported in their simulation studies involving the generalized extreme values distribution, in the presence of covariates to model trend or temporal effect. The one that is more parsimonious is preferable and that according to the subject of study, the method used to select models is an important issue.…”

Changes in Extreme Air Temperatures in One of South America’s Longest Meteorological Records: Campinas, Brazil (1890-2022)

“…From an agrometeorological perspective, this selection process is expected to describe if and how the probability of the Tmax and Tmin events have changed over the last 133 years in Campinas-SP and if these changes are significantly correlated with the global air temperature. As pointed out by authors such as Cannon (2010); Coles (2001);El Adlouni et al (2007) and Xavier et al (2019a), this selection process should be based on the principle of parsimony, which seeks to choose the most parsimonious candidate model. In other words, this principle attempts to select the simplest model that explains as much of the variation in the data as possible (Coles 2001).…”