A note of caution when interpreting parameters of the distribution of excesses

In climatology and hydrology, univariate Extreme Value Theory has become a powerful tool to model the distribution of extreme events. The Generalized Pareto Distribution (GPD) is routinely applied to model excesses in space or time by letting the two GPD parameters depend on appropriate covariates. Two possible pitfalls of this strategy are the modeling and the interpretation of the scale and shape GPD parameters estimates which are often and incorrectly viewed as independent variables. In this note we first recall a statistical technique that makes the GPD estimates less correlated within a Maximum Likelihood (ML) estimation approach. In a second step we propose novel reparametrizations for two method-of-moments particularly popular in hydrology: the Probability Weighted Moment (PWM) method and its generalized version (GPWM). Finally these three inference methods (ML, PWM and GPWM) are compared and discussed with respect to the issue of correlations.

► In climatology and hydrology, Extreme Value Theory is a standard tool to model extreme events. ► The Generalized Pareto Distribution (GPD) is applied to model excesses. ► The scale and shape GPD parameters estimates are correlated. ► We focus on Maximum Likelihood (ML) and Probability Weighted Moments (PWM) methods. ► We propose novel reparametrizations that make the GPD estimates less correlated.