Gumbel Distribution

A probability distribution \(Gumbel(\mu, \sigma)\) having the PDF
\[ p_{\mu,\sigma}(x) = \frac{1}{\sigma} \exp\left(-\frac{x-\mu}{\sigma} - e^{-(x-\mu)/\sigma}\right) \]
that governs the probability of the maximum of many observations of a random variable with an appropriate distribution, such as the exponential distribution.