Extreme value distributions are used to model the occurrence of extrema (i.e. extreme deviations from the median of a probability distribution). The parameters for GEV Distribution 1 are taken from a model fitted to annual maximum sea level data in Port Pirie, Australia from 1923–1987. GEV Distribution 2 has the same parameters as GEV Distribution 1, only the scale parameter has been increased to create more variability. The return level curves shown in the bottom-left give the expected maximum sea level that will occur once every years. For example, the Port Pirie return curve (blue) indicates that one may expect the sea level to reach 4.3 meters once every ten years, or 4.6 meters once every 100 years.

The purpose of this Demonstration is to show how to interpret PDFs and return level curves for a GEV distribution with a real-world example. Move the sliders to adjust the various parameters and notice how each parameter affects both the PDF and the respective return level curve.

The generalized extreme value distribution is a combined family of three distinct distribution families: Gumbel, Fréchet, and Weibull. It is a distribution function of the form

,

with parameters , , and for location, scale, and shape, respectively. Return level curves for a GEV can be generated by plotting

for the return period . The Port Pirie data and parameters can be found in [1]. Anyone interested in learning more about extreme value theory should also refer to [1]. Coles provides a clear and coherent overview of modeling extreme values and supplements with a variety of examples. The goal of this Demonstration was to put one of those examples into a more tangible form.

Reference

[1] S. Coles, An Introduction to Statistical Modeling of Extreme Values, London: Springer-Verlag, 2001