Extreme Value Distribution
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The shorthand X ∼ extreme value(α, β) is used to indicate that the random variable X has the extreme value distribution with positive scale parameter α and positive shape parameter β. An extreme value random variable X with parameters α and β has probability density function f (x) = (β/α)e x β−e xβ /α − ∞ < x < ∞. The extreme value distribution can be used to model water levels associated with floods and earthquake magnitudes. The probability density function with three different parameter settings is illustrated below.