Normal Distribution Function

URI: https://gptkb.org/entity/Normal_Distribution_Function
GPTKB entity
Statements (49)
Predicate Object
gptkbp:instanceOf Mathematical Function
gptkbp:alsoKnownAs gptkb:Gaussian_Distribution
gptkbp:cdfSymbol Φ(x)
gptkbp:centralLimitTheoremApplies True
gptkbp:characteristic exp(iμt - (σ^2 t^2)/2)
gptkbp:continuity True
gptkbp:definedIn gptkb:Real_Numbers
gptkbp:entropy (1/2)ln(2πeσ^2)
gptkbp:firstDescribed gptkb:Carl_Friedrich_Gauss
gptkbp:hasEquation f(x) = (1/(σ√(2π))) * exp(- (x-μ)^2 / (2σ^2))
gptkbp:hasInflectionPoints μ ± σ
gptkbp:hasKurtosis 3
gptkbp:hasSkewness 0
gptkbp:hasSpecialCase gptkb:Standard_Normal_Distribution
https://www.w3.org/2000/01/rdf-schema#label Normal Distribution Function
gptkbp:isBellShaped True
gptkbp:isClosedUnderConvolution True
gptkbp:isEllipticalDistribution True
gptkbp:isLimitOfBinomial True
gptkbp:isLimitOfPoisson True
gptkbp:isLocationScaleFamily True
gptkbp:isMaximumEntropyDistribution True
gptkbp:isSelfConjugate True
gptkbp:isStableDistribution True
gptkbp:isUnimodal True
gptkbp:kurtosis 3
gptkbp:meanEqualsMedianEqualsMode True
gptkbp:mode μ
gptkbp:momentGeneratingFunction exp(μt + (σ^2 t^2)/2)
gptkbp:momentsExist All Orders
gptkbp:parameter Mean
Variance
Standard Deviation
gptkbp:pdfSymbol φ(x)
gptkbp:skewness 0
gptkbp:standardNormalMean 0
gptkbp:standardNormalStdDev 1
gptkbp:supports (-∞, ∞)
gptkbp:symmetry Mean
gptkbp:totalAreaUnderCurve 1
gptkbp:usedFor gptkb:Statistical_Inference
Hypothesis Testing
Error Analysis
Modeling Random Variables
gptkbp:usedIn Statistics
Probability Theory
gptkbp:variant σ^2
gptkbp:bfsParent gptkb:Gaussian_Function
gptkbp:bfsLayer 8