Extreme Value Type I distribution
GPTKB entity
Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:organization
|
| gptkbp:alsoKnownAs |
gptkb:Gumbel_distribution
|
| gptkbp:category |
Continuous probability distributions
|
| gptkbp:characteristic |
Γ(1-iβt) exp(iμt)
|
| gptkbp:cumulativeDistributionFunction |
F(x) = exp(-exp(-(x-μ)/β))
|
| gptkbp:entropy |
ln(β) + γ + 1
|
| gptkbp:familyMember |
Extreme value distributions
|
| gptkbp:firstPublished |
1932
|
| https://www.w3.org/2000/01/rdf-schema#label |
Extreme Value Type I distribution
|
| gptkbp:kurtosis |
12/5
|
| gptkbp:limitingDistributionOf |
maximum of a large number of i.i.d. random variables with exponential-type tails
|
| gptkbp:meaning |
μ + γβ (γ = Euler–Mascheroni constant)
|
| gptkbp:mode |
μ
|
| gptkbp:momentGeneratingFunction |
Γ(1-tβ) exp(μt), for tβ < 1
|
| gptkbp:namedAfter |
gptkb:Emil_Julius_Gumbel
|
| gptkbp:parameter |
location parameter μ
scale parameter β > 0 |
| gptkbp:probabilityDensityFunction |
f(x) = (1/β) exp(-(x-μ)/β) exp(-exp(-(x-μ)/β))
|
| gptkbp:relatedTo |
Extreme Value Type II distribution
Extreme Value Type III distribution Generalized Extreme Value distribution |
| gptkbp:skewness |
12√6 ζ(3)/π^3 ≈ 1.1396
|
| gptkbp:supports |
x ∈ ℝ
|
| gptkbp:usedFor |
modeling maxima of samples
|
| gptkbp:usedIn |
engineering
finance hydrology meteorology extreme value theory |
| gptkbp:variant |
(π^2/6)β^2
|
| gptkbp:bfsParent |
gptkb:Gumbel_distribution
|
| gptkbp:bfsLayer |
7
|