univariate normal distribution

URI: https://gptkb.org/entity/univariate_normal_distribution

GPTKB entity

Statements (50)

Predicate	Object
gptkbp:instanceOf	gptkb:organization
gptkbp:alsoKnownAs	gptkb:Gaussian_distribution gptkb:normal_distribution
gptkbp:centralLimitTheorem	limit distribution
gptkbp:characteristic	exp(iμt - 0.5σ^2t^2)
gptkbp:closureUnderAddition	true
gptkbp:closureUnderConvolution	true
gptkbp:closureUnderLinearTransformation	true
gptkbp:cumulativeDistributionFunction	Φ((x-μ)/σ)
gptkbp:entropy	0.5*ln(2πeσ^2)
gptkbp:family	gptkb:exponential_family gptkb:location-scale_family
gptkbp:hasFeature	gptkb:standard_normal_distribution
gptkbp:hasMomentGeneratingFunction	exp(μt + 0.5σ^2t^2)
gptkbp:hasSpecialCase	gptkb:location-scale_family gptkb:multivariate_normal_distribution
https://www.w3.org/2000/01/rdf-schema#label	univariate normal distribution
gptkbp:infiniteDivisibility	true
gptkbp:kurtosis	3
gptkbp:maximumEntropyDistribution	for given mean and variance
gptkbp:meaning	μ
gptkbp:medium	μ
gptkbp:mode	μ
gptkbp:modeledAfter	many natural phenomena
gptkbp:momentExistence	all moments exist
gptkbp:namedAfter	gptkb:Carl_Friedrich_Gauss
gptkbp:notation	N(μ, σ^2)
gptkbp:parameter	mean standard deviation variance
gptkbp:probability_density_function	f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
gptkbp:relatedTo	gptkb:probability_theory error function statistical inference z-score
gptkbp:shape	bell curve
gptkbp:skewness	0
gptkbp:standardNormalCDF	Φ(x)
gptkbp:standardNormalMean	0
gptkbp:standardNormalPDF	f(x) = (1/√(2π)) * exp(-x^2/2)
gptkbp:standardNormalVariance	1
gptkbp:supports	real numbers
gptkbp:symmetry	symmetric about mean
gptkbp:usedIn	gptkb:machine_learning gptkb:natural_sciences gptkb:signal_processing statistics
gptkbp:variant	σ^2
gptkbp:bfsParent	gptkb:multivariate_normal_distribution
gptkbp:bfsLayer	6