Normal distribution (standard parameterization)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	Probability distribution
gptkbp:alsoKnownAs	gptkb:Gaussian_distribution
gptkbp:bell-shaped	yes
gptkbp:characteristic	exp(iμt - 0.5σ^2t^2)
gptkbp:cumulativeDistributionFunction	Φ((x-μ)/σ)
gptkbp:entropy	0.5*ln(2πeσ^2)
gptkbp:family	gptkb:exponential_family gptkb:location-scale_family
gptkbp:form	mean = 0, standard deviation = 1
gptkbp:hasSpecialCase	gptkb:elliptical_distribution stable distribution
https://www.w3.org/2000/01/rdf-schema#label	Normal distribution (standard parameterization)
gptkbp:kurtosis	3
gptkbp:limitation	gptkb:central_limit_theorem
gptkbp:maximum_entropy_distribution	given mean and variance
gptkbp:meaning	μ
gptkbp:medium	μ
gptkbp:mode	μ
gptkbp:moment_generating_function	exp(μt + 0.5σ^2t^2)
gptkbp:namedAfter	gptkb:Carl_Friedrich_Gauss
gptkbp:notation	N(μ,σ^2)
gptkbp:parameter	mean standard deviation variance
gptkbp:pdf	f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
gptkbp:relatedTo	gptkb:log-normal_distribution gptkb:multivariate_normal_distribution standardization error function z-score probability density function normal approximation cumulative distribution function normality test normal quantile normal random variable normal table
gptkbp:skewness	0
gptkbp:standard_normal_distribution	N(0,1)
gptkbp:supports	all real numbers
gptkbp:symmetry	yes
gptkbp:type	continuous
gptkbp:usedIn	gptkb:machine_learning gptkb:natural_sciences social sciences statistics
gptkbp:variant	σ^2
gptkbp:bfsParent	gptkb:Gaussian_distribution_(precision_parameterization)
gptkbp:bfsLayer	8