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gptkbp:instanceOf
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gptkb:organization
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gptkbp:alsoKnownAs
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gptkb:normal_distribution
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gptkbp:application
|
statistical analysis
hypothesis testing
modeling measurement errors
statistical inference
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gptkbp:centralLimitTheorem
|
limit distribution
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gptkbp:characteristic
|
exp(iμt - 0.5σ^2t^2)
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gptkbp:conjugatePriorFor
|
mean of normal distribution
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gptkbp:cumulativeDistributionFunction
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Φ(x) = 0.5[1 + erf((x-μ)/(σ√2))]
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gptkbp:describedBy
|
mean
variance
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gptkbp:entropy
|
0.5*ln(2πeσ^2)
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gptkbp:firstDescribed
|
18th century
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gptkbp:hasFeature
|
mean = 0, variance = 1
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gptkbp:hasSpecialCase
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gptkb:exponential_family
gptkb:location-scale_family
gptkb:elliptical_distribution
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Gaussian distribution
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gptkbp:infiniteDivisibility
|
yes
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gptkbp:kurtosis
|
3
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gptkbp:maximumEntropy
|
for given mean and variance
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gptkbp:meanSymbol
|
μ
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gptkbp:medium
|
μ
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gptkbp:mode
|
μ
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gptkbp:momentGeneratingFunction
|
exp(μt + 0.5σ^2t^2)
|
|
gptkbp:moments
|
all moments exist
|
|
gptkbp:namedAfter
|
gptkb:Carl_Friedrich_Gauss
|
|
gptkbp:parameter
|
mean
standard deviation
variance
|
|
gptkbp:pdfShape
|
bell curve
|
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gptkbp:probabilityDensityFunction
|
f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
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gptkbp:relatedTo
|
gptkb:standard_normal_distribution
gptkb:chi-squared_distribution
gptkb:log-normal_distribution
gptkb:multivariate_normal_distribution
error function
|
|
gptkbp:skewness
|
0
|
|
gptkbp:standardDeviationSymbol
|
σ
|
|
gptkbp:standardFormName
|
gptkb:standard_normal_distribution
|
|
gptkbp:sumOfNormals
|
gptkb:normal_distribution
|
|
gptkbp:supports
|
x ∈ ℝ
|
|
gptkbp:symmetry
|
symmetric about mean
|
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gptkbp:usedIn
|
gptkb:machine_learning
gptkb:natural_sciences
gptkb:signal_processing
engineering
finance
statistics
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gptkbp:varianceSymbol
|
σ^2
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gptkbp:bfsParent
|
gptkb:normal_distribution
|
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gptkbp:bfsLayer
|
4
|