# gumbel distribution

A distribution that models the maximum of a number of samples. For example, it might be used to model the max of a number of i.i.d. Gaussian samples. (How the parameters for the Gumbel distribution are found in this case, I do not know).

The Gumbel distribution is parameterized by \(\mu\) and \(\beta\).

The CDF: \[ P(x \leq M) = \exp\left(-\exp\left(-\left(\frac{x-\mu}{\beta}\right)\right)\right) \]