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.
Aliases (3)
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
→
bell curve → 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 → |
Referenced by (5)
| Subject (surface form when different) | Predicate |
|---|---|
|
Gaussian distribution
("normal distribution")
→
Gaussian distribution ("Gaussian") → |
hasAlias |
|
Gaussian law of error
→
|
connectedTo |
|
Carl Friedrich Gauss
→
|
hasConceptNamedAfter |
|
Carl Friedrich Gauss
→
|
notableWork |