The Gumbel distribution is a continuous probability distribution with probability density function given by:

subject to the following conditions:

The Gumbel distribution is also known as the type I extreme value distribution.

The Gumbel variate with location parameter a and scale parameter b is related to the Exponential variate with scale parameter b according to the formula:  Gumbel(a,b) ~ a - log(Exponential(b))

Note that the Gumbel command is inert and should be used in combination with the RandomVariable command.

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.