Lévy alpha-stable distribution
E825429
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.
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]
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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.
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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.
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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.
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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
NERFINISHED
ⓘ
Gaussian distribution NERFINISHED ⓘ normal distribution ⓘ |
| governs | Lévy flights NERFINISHED ⓘ |
| 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 GENERATED ⓘ |
| meanExistsCondition | mean exists only if α > 1 ⓘ |
| momentProperty | moments of order ≥ α are infinite ⓘ |
| namedAfter | Paul Lévy NERFINISHED ⓘ |
| 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lévy alpha-stable distribution Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.