Extreme Value Analysis in Julia with Extremes.jl

In this talk, we present Extremes.jl, a package that provides exhaustive high-performance functions for the statistical analysis of extreme values with Julia. Parameter estimation, diagnostic tools for assessing model accuracy and high quantile estimation are implemented for stationary and non-stationary extreme value models. The functionalities will be illustrated in this talk by reproducing many results from the popular book of Coles (2001).

Risk assessment and impact analysis of extreme values is an important aspect of climate sciences. Recently, the Intergovernmental Panel on Climate Change (IPCC) reported that extreme meteorological events are expected to increase in frequency and intensity with climate change, leading to important impacts on many sectors of activities (IPCC 2013). The only statistical discipline that develops a rigorous framework for the study of extremes events is Extreme value theory. However, unlike other programming languages commonly used by statisticians, tools for the analysis of extreme values are lacking in Julia despite the growing popularity of the language among scientific community.

In this talk, we present Extremes.jl, a package that provides exhaustive high-performance functions for the statistical analysis of extreme values. In particular, methods for the usual block maxima and peaks-over-threshold models are implemented. Model parameter estimation can be achieved by using the probability weighted moments, the maximum likelihood, and the Bayesian paradigm. Non-stationary models are also implemented as well as diagnostic plots for assessing model accuracy and high quantile estimation.

The proposed package is designed to be used by the statistical community as well as by engineers who need estimations of extremes. We illustrate the package functionalities by reproducing many results obtained by Coles (2001).