Abstract: We propose a novel mixture generalized Pareto model for calibrating extreme precipitation forecasts. This model is able to describe the marginal distribution of observed precipitation and capture the dependence between climate forecasts and observed precipitation under suitable conditions. In addition, the full range distribution of precipitation can be estimated, conditional on grid forecast ensembles. Unlike the classical generalized Pareto distribution that can only model points over a hard threshold, our model takes the threshold as a latent parameter. We study the tail behavior of both univariate and bivariate models. The utility of our model is evaluated using a Monte Carlo simulation study. Lastly, we apply the model to US precipitation data, showing that it outperforms competing methods.

Key words and phrases: Bivariate extreme value model, generalized Pareto distribution, hierarchical model, tail dependence.