Joint modeling of low and high extremes using a multivariate extended generalized Pareto distribution

Abstract: In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to droughts, while heavy rainfall may generate large floods, and both of these extreme scenarios can have major impacts on the safety of people and infrastructure, as well as agricultural or other economic sectors. In the univariate case, the extended generalized Pareto distribution (eGPD) was specifically developed to accurately model low, moderate, and high precipitation intensities, while bypassing the threshold selection procedure usually conducted in extreme-value analyses. In this work, we extend this approach to the multivariate case. The proposed multivariate eGPD has the following appealing properties: (1) its marginal distributions behave like univariate eGPDs; (2) its lower and upper joint tails comply with multivariate extreme-value theory, with key parameters separately controlling dependence in each joint tail; and (3) the model allows for fast simulation and is thus amenable to simulation-based inference. We propose estimating model parameters by leveraging modern neural approaches, where a neural network, once trained, can provide point estimates, credible intervals, or full posterior approximations in a fraction of a second. Our new methodology is illustrated by application to daily rainfall times series data from the Netherlands. The proposed model is shown to provide satisfactory marginal and dependence fits from low to high quantiles.