Pareto distribution
E382868
continuous probability distribution
heavy-tailed distribution
power-law distribution
probability distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Pareto distribution canonical | 7 |
| Lomax distribution | 1 |
| Pareto law | 1 |
| Zipf's law | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3707476 — 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: Pareto distribution Context triple: [Vilfredo Pareto, knownFor, Pareto 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.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
C.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
D.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
-
E.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
- 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: Pareto distribution Target entity description: The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
-
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.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
C.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
D.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
-
E.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
heavy-tailed distribution ⓘ power-law distribution ⓘ probability distribution ⓘ |
| belongsToFamily |
one-parameter shape families
ⓘ
scale distributions ⓘ |
| belongsToField |
econometrics
ⓘ
probability theory ⓘ statistical physics ⓘ statistics ⓘ |
| cumulativeDistributionFunction | F(x) = 1 - (x_m / x)^α for x ≥ x_m ⓘ |
| hasApplication |
actuarial science
ⓘ
network traffic modeling ⓘ risk management ⓘ |
| hasParameter |
scale parameter xm
ⓘ
shape parameter alpha ⓘ |
| hasProperty |
infinite higher moments for small α
ⓘ
scale invariant tail ⓘ |
| inequalityMeasure | generates high Gini coefficients for small α ⓘ |
| isHeavyTailed | true ⓘ |
| kurtosis | high for small α ⓘ |
| logTransform | log X has shifted exponential distribution ⓘ |
| mean | E[X] = α x_m / (α - 1) for α > 1 ⓘ |
| meanExistsIf | α > 1 ⓘ |
| median | x_m 2^{1/α} ⓘ |
| mode | x_m ⓘ |
| namedAfter | Vilfredo Pareto ⓘ |
| parameterConstraint |
x_m > 0
ⓘ
α > 0 ⓘ |
| probabilityDensityFunction | f(x) = α x_m^α / x^{α+1} for x ≥ x_m ⓘ |
| relatedConcept |
80-20 rule
ⓘ
Pareto principle ⓘ |
| relatedDistribution |
Lomax distribution
ⓘ
linked to:
Pareto distribution
generalized Pareto distribution ⓘ power law ⓘ |
| skewness | positive ⓘ |
| support | x ≥ xm > 0 ⓘ |
| survivalFunction | S(x) = (x_m / x)^α for x ≥ x_m ⓘ |
| tailBehavior | P(X > x) ∝ x^{-α} ⓘ |
| type | univariate distribution ⓘ |
| usedToModel |
city sizes
ⓘ
file sizes in computer systems ⓘ income distribution upper tail ⓘ insurance claim sizes ⓘ sizes of human settlements ⓘ wealth distribution ⓘ |
| variance | Var(X) = α x_m^2 / ((α - 1)^2 (α - 2)) for α > 2 ⓘ |
| varianceExistsIf | 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: Pareto distribution Description of subject: The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Pareto distribution
linked to: Pareto distribution
linked to: Pareto distribution