Extremes.jl: Extreme Value Analysis in Julia

Abstract

The Extremes.jl package provides exhaustive, high-performance functions by leveraging the multiple-dispatch capabilities in Julia for the analysis of extreme values. In particular, the package implements statistical models for both block maxima and peaks-over-threshold methods, along with several methods for the generalized extreme value and generalized Pareto distributions used in extreme value theory. Additionally, the package offers various parameter estimation methods, such as probability-weighted moments, maximum likelihood, and Bayesian estimation. It also includes tools for handling dependence in excesses over a threshold and methods for managing nonstationary models. Inference for extreme quantiles is available for both stationary and nonstationary models, along with diagnostic figures to assess the goodness of fit of the model to the data.