Gaussian distribution
E29361
Gaussian distribution
continuous probability distribution
normal distribution
probability 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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Gaussian distribution canonical | 3 |
| Gaussian | 1 |
| Gaussian random walk | 1 |
| normal distribution | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T228920 — 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: Gaussian distribution Context triple: [Carl Friedrich Gauss, notableWork, Gaussian distribution]
-
A.
Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
-
B.
central limit theorem
The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
-
C.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
- 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: Gaussian distribution Target entity description: 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.
-
A.
Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
-
B.
central limit theorem
The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
-
C.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
D.
Kullback–Leibler divergence
Kullback–Leibler divergence is a fundamental information-theoretic measure that quantifies how one probability distribution differs from a reference distribution.
-
E.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
Gaussian distribution
ⓘ
continuous probability distribution ⓘ normal distribution ⓘ probability distribution ⓘ |
| appliesTo |
measurement errors
ⓘ
sum of many independent random variables ⓘ |
| cumulativeDistributionFunction | Φ((x−μ)/σ) ⓘ |
| definedOn | real numbers ⓘ |
| hasAlias |
Gaussian distribution
self-linksurface differs
ⓘ
surface form:
Gaussian
bell curve ⓘ Gaussian distribution self-linksurface differs ⓘ
surface form:
normal distribution
|
| hasCharacteristicFunction | φ(t) = exp(iμt − ½σ²t²) ⓘ |
| hasExcessKurtosis | 0 ⓘ |
| hasInflectionPointsAt |
μ + σ
ⓘ
μ − σ ⓘ |
| hasMean | 0 ⓘ |
| hasMeanSymbol | μ ⓘ |
| hasMomentGeneratingFunction | M(t) = exp(μt + ½σ²t²) ⓘ |
| hasProperty |
bell-shaped
ⓘ
symmetric ⓘ unimodal ⓘ |
| hasSkewness | 0 ⓘ |
| hasSpecialCase | standard normal distribution ⓘ |
| hasStandardDeviationSymbol | σ ⓘ |
| hasVariance | 1 ⓘ |
| hasVarianceSymbol | σ² ⓘ |
| isFullyDeterminedBy | its mean and variance ⓘ |
| isLimitIn | central limit theorem ⓘ |
| isMaximumEntropyDistributionGiven | fixed mean and variance ⓘ |
| isSymmetricAbout | its mean ⓘ |
| medianEquals | mean ⓘ |
| modeEquals | mean ⓘ |
| originatesFrom | work of Carl Friedrich Gauss ⓘ |
| parameter |
location parameter
ⓘ
mean ⓘ scale parameter ⓘ standard deviation ⓘ variance ⓘ |
| probabilityDensityFunction | f(x) = (1/(σ√(2π))) · exp(−(x−μ)²/(2σ²)) ⓘ |
| support | (−∞, +∞) ⓘ |
| usedIn |
Bayesian inference
ⓘ
engineering ⓘ error analysis ⓘ finance ⓘ hypothesis testing ⓘ machine learning ⓘ natural sciences ⓘ regression analysis ⓘ signal processing ⓘ statistics ⓘ |
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: Gaussian distribution Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
normal distribution
this entity surface form:
Gaussian
this entity surface form:
Gaussian random walk