MaxStableDistribution
Beschikbaar
Max-stable (GEV) distribution with shape-cased forms
MaxStableDistribution[μ, σ, ξ]
Mean[MaxStableDistribution[μ, σ, ξ]]
→ Piecewise[{{μ + EulerGamma*σ, ξ == 0}, {(μ*ξ - σ + σ*Gamma[1 - ξ])/ξ, ξ != 0 && ξ < 1}}, Indeterminate]PDF[MaxStableDistribution[μ, σ, ξ], x]
→ Piecewise[{{E^(-E^((μ - x)/σ) - (-μ + x)/σ)/σ, ξ == 0}, {(1 + (ξ*(-μ + x))/σ)^(-1 - ξ^(-1))/(σ*E^(1 + (ξ*(-μ + x))/σ)^(-ξ^(-1))), ξ != 0 && 1 + (ξ*(-μ + x))/σ > 0}}, 0]CDF[MaxStableDistribution[μ, σ, ξ], x]
→ Piecewise[{{E^(-E^((μ - x)/σ)), ξ == 0}, {E^(-(1 + (ξ*(-μ + x))/σ)^(-ξ^(-1))), ξ != 0 && 1 + (ξ*(-μ + x))/σ > 0}, {0, ξ > 0 && 1 + (ξ*(-μ + x))/σ <= 0}}, 1] Alle 6300 functies ·
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