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gptkbp:instanceOf
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gptkb:organization
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gptkbp:alsoKnownAs
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gptkb:Extreme_Value_Type_I_distribution
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gptkbp:application
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engineering
finance
hydrology
meteorology
material science
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gptkbp:cumulativeDistributionFunction
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F(x) = exp(-exp(-(x-μ)/β))
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gptkbp:entropy
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ln(β) + γ + 1
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gptkbp:familyMember
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gptkb:exponential_family
gptkb:location-scale_family
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gptkbp:hasSpecialCase
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gptkb:generalized_extreme_value_distribution
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|
https://www.w3.org/2000/01/rdf-schema#label
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Gumbel distribution
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gptkbp:kurtosis
|
12/5
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gptkbp:limitingDistributionOf
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maximum of iid random variables
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gptkbp:meaning
|
μ + γβ
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gptkbp:mode
|
μ
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gptkbp:momentGeneratingFunction
|
Γ(1 - βt) exp(μt) for t < 1/β
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gptkbp:namedAfter
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gptkb:Emil_Julius_Gumbel
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gptkbp:parameter
|
location parameter
scale parameter
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gptkbp:probabilityDensityFunction
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f(x) = (1/β) exp(-(z + exp(-z))) where z = (x - μ)/β
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gptkbp:relatedTo
|
gptkb:Weibull_distribution
gptkb:Fréchet_distribution
gptkb:logistic_distribution
|
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gptkbp:skewness
|
12√6 ζ(3)/π^3 ≈ 1.1396
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gptkbp:supports
|
x ∈ ℝ
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gptkbp:usedFor
|
modeling maximum values
modeling minimum values
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gptkbp:usedIn
|
extreme value theory
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gptkbp:variant
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(π^2/6)β^2
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gptkbp:bfsParent
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gptkb:Fisher–Tippett_distribution
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gptkbp:bfsLayer
|
6
|