|
gptkbp:instanceOf
|
Probability Distribution
|
|
gptkbp:alsoKnownAs
|
gptkb:Gaussian_Distribution
|
|
gptkbp:areaUnderCurve
|
1
|
|
gptkbp:characteristic
|
exp(iμt - 0.5σ^2t^2)
|
|
gptkbp:continuity
|
true
|
|
gptkbp:cumulativeDistributionFunction
|
Φ((x-μ)/σ)
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:describedBy
|
mean
standard deviation
variance
|
|
gptkbp:describedYear
|
18th century
|
|
gptkbp:entropy
|
0.5*ln(2πeσ^2)
|
|
gptkbp:firstDescribed
|
gptkb:Carl_Friedrich_Gauss
gptkb:Abraham_de_Moivre
|
|
gptkbp:hasFeature
|
gptkb:Standard_Normal_Distribution
|
|
gptkbp:hasInflectionPoints
|
μ ± σ
|
|
gptkbp:hasProbabilityDensityFunction
|
f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
|
|
gptkbp:hasSpecialCase
|
gptkb:exponential_family
stable distributions
elliptical distributions
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Normal Distribution
|
|
gptkbp:isMaximumEntropyDistribution
|
for given mean and variance
|
|
gptkbp:isStableUnderSummation
|
true
|
|
gptkbp:isUnimodal
|
true
|
|
gptkbp:kurtosis
|
3
|
|
gptkbp:limitation
|
gptkb:Central_Limit_Theorem
|
|
gptkbp:meanSymbol
|
μ
|
|
gptkbp:medium
|
mean
|
|
gptkbp:mode
|
mean
|
|
gptkbp:momentGeneratingFunction
|
exp(μt + 0.5σ^2t^2)
|
|
gptkbp:parameter
|
mean
standard deviation
variance
|
|
gptkbp:skewness
|
0
|
|
gptkbp:standardDeviationSymbol
|
σ
|
|
gptkbp:standardFormMean
|
0
|
|
gptkbp:standardFormStandardDeviation
|
1
|
|
gptkbp:standardFormVariance
|
1
|
|
gptkbp:supports
|
(-∞, ∞)
|
|
gptkbp:symmetry
|
true
|
|
gptkbp:usedFor
|
gptkb:signal_processing
statistical analysis
hypothesis testing
modeling measurement errors
statistical inference
quality control
|
|
gptkbp:usedIn
|
gptkb:machine_learning
gptkb:natural_sciences
engineering
finance
statistics
|
|
gptkbp:varianceSymbol
|
σ^2
|
|
gptkbp:bfsParent
|
gptkb:Quasi-Normal_Distribution
|
|
gptkbp:bfsLayer
|
7
|