Exploring extreme values
Worldwide, there are almost a million dams, roughly 5 percent of which are higher than 15 m. A civil engineer designing a dam will have to consider many factors, including rainfall. Let's assume, for the sake of simplicity, that the engineer wants to know the cumulative annual rainfall. We can also take monthly maximums and fit those to a generalized extreme value (GEV) distribution. Using this distribution, we can then bootstrap to get our estimate. Instead, I select values that are above the 95th percentile in this recipe.
The GEV distribution is implemented in scipy.stats and is a mixture of the Gumbel, Frechet, and Weibull distributions. The following equations describe the cumulative distribution function (3.11)
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