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(maximum case) |quantile = |mean =
where is the Euler–Mascheroni constant |median = |mode = |variance = |skewness = |kurtosis = |entropy = |mgf = |char =|notation=}}In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.

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