Lévy alpha-stable distribution

E825429

probability distribution

The Lévy alpha-stable distribution is a family of heavy-tailed probability distributions characterized by a stability parameter α, generalizing the normal and Cauchy distributions and often used to model impulsive or anomalous random phenomena.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Lévy alpha-stable distribution canonical	1
Lévy distribution	1
Lévy flights	1

How this entity was disambiguated

This entity first appeared as the object of triple T9843718 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lévy alpha-stable distribution
Context triple: [Cauchy distribution, isSpecialCaseOf, Lévy alpha-stable distribution]

A. Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
B. Carsey-Werner Distribution
Carsey-Werner Distribution is a television distribution company best known for handling popular sitcoms produced by Carsey-Werner, including major hits from the late 1980s and 1990s.
C. Laplace distribution
The Laplace distribution is a continuous probability distribution with a sharp peak at its mean and heavier tails than the normal distribution, often used to model data with abrupt changes or outliers.
D. Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
E. Student’s t-distribution
Student’s t-distribution is a continuous probability distribution used primarily to estimate population means and conduct hypothesis tests when sample sizes are small and population variance is unknown.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Lévy alpha-stable distribution
Target entity description: The Lévy alpha-stable distribution is a family of heavy-tailed probability distributions characterized by a stability parameter α, generalizing the normal and Cauchy distributions and often used to model impulsive or anomalous random phenomena.

A. Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
B. Carsey-Werner Distribution
Carsey-Werner Distribution is a television distribution company best known for handling popular sitcoms produced by Carsey-Werner, including major hits from the late 1980s and 1990s.
C. Laplace distribution
The Laplace distribution is a continuous probability distribution with a sharp peak at its mean and heavier tails than the normal distribution, often used to model data with abrupt changes or outliers.
D. Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
E. Student’s t-distribution
Student’s t-distribution is a continuous probability distribution used primarily to estimate population means and conduct hypothesis tests when sample sizes are small and population variance is unknown.
F. None of above. chosen

Statements (46)

Predicate	Object
instanceOf	probability distribution ⓘ
alsoKnownAs	Lévy stable distribution ⓘ stable Paretian distribution ⓘ α-stable distribution ⓘ
appearsIn	limit distributions of sums of i.i.d. heavy-tailed variables ⓘ
field	probability theory ⓘ statistics ⓘ
generalizes	Cauchy distribution ⓘ Gaussian distribution ⓘ normal distribution ⓘ
governs	Lévy flights ⓘ linked to: Lévy processes
hasParameter	location parameter δ ⓘ scale parameter γ ⓘ skewness parameter β ⓘ stability parameter α ⓘ
hasProperty	characteristic function known in closed form ⓘ closed under convolution ⓘ heavy tails ⓘ no general closed-form density ⓘ often lacks finite mean ⓘ often lacks finite variance ⓘ power-law tails ⓘ stable under addition ⓘ
hasSupport	real line ⓘ
locationParameterRange	δ ∈ ℝ ⓘ
meanExistsCondition	mean exists only if α > 1 ⓘ
momentProperty	moments of order ≥ α are infinite ⓘ
namedAfter	Paul Lévy ⓘ
parameterization	can be expressed in multiple parameterizations (e.g. Zolotarev forms) ⓘ
relatedTo	generalized central limit theorem ⓘ
scaleParameterRange	γ > 0 ⓘ
simulationMethod	can be simulated via Chambers–Mallows–Stuck algorithm ⓘ
skewnessParameterRange	−1 ≤ β ≤ 1 ⓘ
specialCaseAt	α = 0.5 and β = 1 gives Lévy distribution ⓘ α = 1 and β = 0 gives Cauchy distribution ⓘ α = 2 gives normal distribution ⓘ
stabilityParameterRange	0 < α ≤ 2 ⓘ
tailBehavior	P(\|X\| > x) ~ x^{-α} as x → ∞ ⓘ
usedIn	finance ⓘ modeling anomalous diffusion ⓘ modeling heavy-tailed financial returns ⓘ modeling impulsive noise ⓘ physics ⓘ signal processing ⓘ telecommunications ⓘ
varianceExistsCondition	variance exists only if α = 2 ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Cauchy distribution → isSpecialCaseOf → Lévy alpha-stable distribution ⓘ

Paul Lévy → knownFor → Lévy distribution ⓘ

linked to: Lévy alpha-stable distribution

Paul Lévy → knownFor → Lévy flights ⓘ