Extremes.jl is a package in the Julia programming language ecosystem. It specializes in statistical analysis of extreme values or rare events, particularly in the context of environmental science, finance, and engineering. It 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
- block maxima;
- peaks-over-threshold;
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;
- 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.
See the Package Documentation for details and examples on how to use the package.
Additionally, refer to the related paper by Jalbert et al. (2024, to appear) which describes the package, along with the accompanying Jupyter notebook file that replicates the results and figures. The notebook can be viewed online via nbviewer through this link.
Reference: Jalbert, J., Farmer, M., Gobeil, G., & Roy, P. (2024). Extremes.jl: Extreme Value Analysis in Julia. Journal of Statistical Software, 109(6), 1–35. https://doi.org/10.18637/jss.v109.i06
The following julia command will install the package:
julia> Pkg.add("Extremes")The datasets that are available through this package are the datasets referenced in An Introduction to Statistical Modeling of Extreme Values by Stuart Coles.
They were obtained using the R package ismev.
https://www.rdocumentation.org/packages/ismev/
The package also provides fit functions using maximum likelihood and probability-weighted moments for the Generalized Extreme Value, Gumbel, and Generalized Pareto distributions. They can be used with the fit function for the corresponding type in Distributions.jl. For example:
julia> using Distributions, Extremes
y = rand(GeneralizedExtremeValue(0,1,.1))
fit(GeneralizedExtremeValue, y)
fit(GeneralizedExtremeValue, y, method="mle")
fit(GeneralizedExtremeValue, y, method="pwm")Jalbert, J., Farmer, M., Gobeil, G., & Roy, P. (2024). Extremes.jl: Extreme Value Analysis in Julia. Journal of Statistical Software, 109(6), 1–35. https://doi.org/10.18637/jss.v109.i06
@article{Jalbert2024,
title={Extremes.jl: Extreme Value Analysis in Julia},
volume={109},
url={https://www.jstatsoft.org/index.php/jss/article/view/v109i06},
doi={10.18637/jss.v109.i06},
number={6},
journal={Journal of Statistical Software},
author={Jalbert, Jonathan and Farmer, Marilou and Gobeil, Gabriel and Roy, Philippe},
year={2024},
pages={1–35}
}