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.
X ≔ RandomVariable⁡Gumbel⁡a,b:
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.
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