|
gptkbp:instanceOf
|
Probability distribution
|
|
gptkbp:68-95-99.7Rule
|
68% within 1σ
95% within 2σ
99.7% within 3σ
|
|
gptkbp:alsoKnownAs
|
gptkb:Gaussian_distribution
|
|
gptkbp:centralLimitTheoremApplies
|
true
|
|
gptkbp:characteristic
|
exp(iμt - 0.5σ^2t^2)
|
|
gptkbp:continuity
|
true
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:describedBy
|
mean
standard deviation
variance
|
|
gptkbp:entropy
|
0.5*ln(2πeσ^2)
|
|
gptkbp:firstDescribed
|
gptkb:Carl_Friedrich_Gauss
gptkb:Abraham_de_Moivre
|
|
gptkbp:has68-95-99.7Rule
|
true
|
|
gptkbp:hasCumulativeDistributionFunction
|
Φ(x) = 1/2 [1 + erf((x-μ)/(σ√2))]
|
|
gptkbp:hasFeature
|
gptkb:Standard_normal_distribution
|
|
gptkbp:hasInflectionPoints
|
μ ± σ
|
|
gptkbp:hasKurtosis
|
3
|
|
gptkbp:hasProbabilityDensityFunction
|
f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
|
|
gptkbp:hasSkewness
|
0
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Normal distribution
|
|
gptkbp:isBellShaped
|
true
|
|
gptkbp:isLimitOfBinomialDistribution
|
true
|
|
gptkbp:isMaximumEntropyDistribution
|
true
|
|
gptkbp:isStableDistribution
|
true
|
|
gptkbp:isUnimodal
|
true
|
|
gptkbp:meanEqualsMedianEqualsMode
|
true
|
|
gptkbp:momentGeneratingFunction
|
exp(μt + 0.5σ^2t^2)
|
|
gptkbp:parameter
|
μ (mean)
σ (standard deviation)
σ^2 (variance)
|
|
gptkbp:standardFormMean
|
0
|
|
gptkbp:standardFormStandardDeviation
|
1
|
|
gptkbp:supports
|
(-∞, ∞)
|
|
gptkbp:symmetry
|
true
|
|
gptkbp:usedFor
|
gptkb:signal_processing
statistical analysis
hypothesis testing
modeling measurement errors
statistical inference
quality control
probabilistic modeling
|
|
gptkbp:usedIn
|
gptkb:machine_learning
gptkb:natural_sciences
finance
statistics
|
|
gptkbp:bfsParent
|
gptkb:Pearson_distribution
gptkb:Student's_t-distribution
|
|
gptkbp:bfsLayer
|
5
|