Laplace law of error
E160629
continuous probability distribution
probability distribution
symmetric distribution
two-parameter distribution
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Laplace law of error canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382206 — 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: Laplace law of error Context triple: [Gaussian law of error, contrastedWith, Laplace law of error]
-
A.
Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
-
B.
Théorie analytique des probabilités
Théorie analytique des probabilités is Pierre-Simon Laplace’s foundational treatise that systematically developed probability theory and laid the groundwork for modern statistics.
-
C.
A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
-
D.
Illustrations of the Dynamical Theory of Gases
Illustrations of the Dynamical Theory of Gases is a foundational 1860 scientific paper by James Clerk Maxwell that introduced key ideas of kinetic theory and the statistical behavior of gas molecules.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- 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: Laplace law of error Target entity description: The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
-
A.
Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
-
B.
Théorie analytique des probabilités
Théorie analytique des probabilités is Pierre-Simon Laplace’s foundational treatise that systematically developed probability theory and laid the groundwork for modern statistics.
-
C.
A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
-
D.
Illustrations of the Dynamical Theory of Gases
Illustrations of the Dynamical Theory of Gases is a foundational 1860 scientific paper by James Clerk Maxwell that introduced key ideas of kinetic theory and the statistical behavior of gas molecules.
-
E.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
probability distribution ⓘ symmetric distribution ⓘ two-parameter distribution ⓘ |
| alsoKnownAs |
Laplace distribution
ⓘ
bilateral exponential distribution ⓘ double exponential distribution ⓘ |
| belongsTo |
error theory
ⓘ
exponential family (in a suitable parametrization) ⓘ probability theory ⓘ
linked to:
Probability Theory
statistics ⓘ |
| belongsToFamily | location-scale family ⓘ |
| canBeRepresentedAs | distribution of μ + Y1 - Y2 where Y1,Y2 are i.i.d. exponential(1/b) ⓘ |
| characteristicFunction | φ(t) = 1 / (1 + b^2 t^2) · exp(i μ t) ⓘ |
| cumulativeDistributionFunction |
F(x|μ,b) = 0.5 · exp((x-μ)/b) for x < μ
ⓘ
F(x|μ,b) = 1 - 0.5 · exp(-(x-μ)/b) for x ≥ μ ⓘ |
| entropy | 1 + ln(2b) ⓘ |
| excessKurtosis | 3 ⓘ |
| hasHeavierTailsThan | normal distribution ⓘ |
| hasLogLikelihood | ℓ(μ,b|x) = -n ln(2b) - (1/b) Σ|xi - μ| ⓘ |
| hasParameter |
location parameter μ
ⓘ
scale parameter b ⓘ |
| hasProbabilityDensityShape | sharp peak at the mean and heavier tails than the normal distribution ⓘ |
| hasSharperPeakThan | normal distribution ⓘ |
| hasTailBehavior | exponential tails ⓘ |
| historicalUse |
modeling astronomical observational errors
ⓘ
modeling physical measurement errors ⓘ |
| isLimitOf | difference of two independent exponential distributions ⓘ |
| isMoreRobustTo | outliers than the normal distribution ⓘ |
| isSpecialCaseOf | generalized error distribution ⓘ |
| isSymmetricAbout | μ ⓘ |
| kurtosis | 6 ⓘ |
| maximumLikelihoodEstimatorForLocation | sample median ⓘ |
| maximumLikelihoodEstimatorForScale | (1/n) Σ|xi - μ̂| ⓘ |
| mean | μ ⓘ |
| median | μ ⓘ |
| mode | μ ⓘ |
| momentGeneratingFunction | M(t) = exp(μ t) / (1 - b^2 t^2) for |t| < 1/b ⓘ |
| namedAfter | Pierre-Simon Laplace ⓘ |
| probabilityDensityFunction | f(x|μ,b) = (1/(2b)) · exp(-|x-μ|/b) ⓘ |
| skewness | 0 ⓘ |
| support | all real numbers ⓘ |
| usedFor |
modeling data with outliers
ⓘ
modeling magnitude of observational errors ⓘ robust modeling of error distributions ⓘ |
| variance | 2b^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: Laplace law of error Description of subject: The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.