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gptkbp:instanceOf
|
gptkb:organization
distribution with undefined mean and variance
pathological distribution
|
|
gptkbp:alsoKnownAs
|
gptkb:Breit–Wigner_distribution
gptkb:Lorentz_distribution
|
|
gptkbp:characteristic
|
exp(ixx0 - γ|t|)
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|
gptkbp:continuity
|
true
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|
gptkbp:cumulativeDistributionFunction
|
F(x; x0, γ) = (1/π) arctan((x - x0)/γ) + 1/2
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gptkbp:entropy
|
ln(4πγ)
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|
gptkbp:hasHeavyTails
|
true
|
|
gptkbp:hasNoFiniteMoments
|
true
|
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gptkbp:hasSpecialCase
|
gptkb:t-distribution_(with_1_degree_of_freedom)
stable distribution
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Cauchy distribution
|
|
gptkbp:isHeavyTailed
|
true
|
|
gptkbp:isInfinitelyDivisible
|
true
|
|
gptkbp:isLevyAlphaStable
|
true
|
|
gptkbp:isNotExponentialFamily
|
true
|
|
gptkbp:isNotLightTailed
|
true
|
|
gptkbp:isNotSquareIntegrable
|
true
|
|
gptkbp:isNotSubexponential
|
true
|
|
gptkbp:isSelfSimilar
|
true
|
|
gptkbp:isStableDistribution
|
true
|
|
gptkbp:isUnimodal
|
true
|
|
gptkbp:kurtosis
|
undefined
|
|
gptkbp:locationParameter
|
x0
|
|
gptkbp:meaning
|
undefined
|
|
gptkbp:medium
|
x0
|
|
gptkbp:mode
|
x0
|
|
gptkbp:moments
|
do not exist
|
|
gptkbp:namedAfter
|
gptkb:Augustin-Louis_Cauchy
|
|
gptkbp:parameter
|
location parameter (x0)
scale parameter (γ)
|
|
gptkbp:probabilityDensityFunction
|
f(x; x0, γ) = [1/(πγ)] [γ^2 / ((x - x0)^2 + γ^2)]
|
|
gptkbp:scaleParameter
|
γ
|
|
gptkbp:skewness
|
undefined
|
|
gptkbp:supports
|
real numbers
|
|
gptkbp:symmetry
|
true
|
|
gptkbp:usedIn
|
gptkb:signal_processing
physics
spectroscopy
statistics
resonance phenomena
|
|
gptkbp:variant
|
undefined
|
|
gptkbp:bfsParent
|
gptkb:Augustin-Louis_Cauchy
gptkb:location-scale_family
|
|
gptkbp:bfsLayer
|
5
|