Laplace distribution
E628628
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Laplace distribution canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6939199 — 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 distribution Context triple: [Laplace law of error, alsoKnownAs, Laplace distribution]
-
A.
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.
-
B.
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.
-
C.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
D.
Pareto 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.
-
E.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
- 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 distribution Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
D.
Pareto 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.
-
E.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
univariate probability distribution ⓘ |
| alsoKnownAs | double exponential distribution NERFINISHED ⓘ |
| belongsTo | location-scale distributions ⓘ |
| belongsToFamily |
generalized error distributions
ⓘ
subbotin distributions NERFINISHED ⓘ |
| characteristicFunction | φ(t) = 1 / (1 + b^2 t^2) ⓘ |
| 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 | proportional to negative L1 norm of residuals ⓘ |
| hasParameter |
location parameter μ
ⓘ
scale parameter b ⓘ |
| hasProbabilityDensityFunctionProperty | piecewise exponential around μ ⓘ |
| isDifferenceOf | two independent exponential distributions with same rate ⓘ |
| isScaleMixtureOf | normal distributions ⓘ |
| isSymmetricAbout | μ ⓘ |
| isUsedIn |
differential privacy mechanisms
ⓘ
financial return modeling with jumps ⓘ signal and image processing ⓘ |
| kurtosis | 6 ⓘ |
| lossFunctionConnection | corresponds to L1 loss in maximum likelihood estimation ⓘ |
| mean | μ ⓘ |
| median | μ ⓘ |
| mode | μ ⓘ |
| momentGeneratingFunction | M(t) = 1 / (1 - b^2 t^2) for |t| < 1/b ⓘ |
| namedAfter | Pierre-Simon Laplace NERFINISHED ⓘ |
| peakShape | sharper peak at mean than normal distribution ⓘ |
| probabilityDensityFunction | f(x|μ,b) = (1/(2b)) exp(-|x-μ|/b) ⓘ |
| skewness | 0 ⓘ |
| specialCaseOf |
asymmetric Laplace distribution
ⓘ
generalized Laplace distribution ⓘ |
| support | all real numbers ⓘ |
| supportLowerBound | -∞ ⓘ |
| supportUpperBound | +∞ ⓘ |
| tailBehavior | exponential tails ⓘ |
| usedFor |
Bayesian L1 regularization priors
ⓘ
modeling abrupt changes ⓘ modeling data with outliers ⓘ robust regression error modeling ⓘ sparse signal modeling ⓘ |
| variance | 2 b^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 distribution Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.