Cauchy distribution

URI: https://gptkb.org/entity/Cauchy_distribution

GPTKB entity

AI-created image

Predicate	Object
gptkbp:instanceOf	gptkb:organization gptkb:distribution_with_undefined_mean_and_variance gptkb:pathological_distribution
gptkbp:alsoKnownAs	gptkb:Breit–Wigner_distribution gptkb:Lorentz_distribution
gptkbp:characteristic	exp(ixx0 - γ\|t\|)
gptkbp:continuity	true
gptkbp:cumulativeDistributionFunction	F(x; x0, γ) = (1/π) arctan((x - x0)/γ) + 1/2
gptkbp:entropy	ln(4πγ)
gptkbp:hasHeavyTails	true
gptkbp:hasNoFiniteMoments	true
gptkbp:hasSpecialCase	gptkb:t-distribution_(with_1_degree_of_freedom) stable 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
https://www.w3.org/2000/01/rdf-schema#label	Cauchy distribution