The Univariate Normal Distribution

Pham-Gia Thu

Chapter 2 in The Multivariate Normal Distribution:Theory and Applications, 2021, pp 11-34 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The following sections are included:IntroductionHow Could the Normal Distribution be Derived?The General CaseAlternative FormulationsProperties of the Standard NormalGraphicsDensityThe general normal distribution and its cumulative distribution functionStandardizing the general normal random variablePosition of the Normal wrt Other DistributionsMain Properties of the General Normal Distribution, X ∼ N(μ, σ2)Other Properties of X ∼ N(μ, σ2)Test on NormalityQuantile FunctionTransformation of Data to Reach NormalityCharacterizationProbability density function (pdf) ϕ(x)Characteristic function φX(t) and moment-generating function MX(t)The cumulant generating functionMoments of order kExponential Family of DistributionsSampling from the NormalConclusionBibliography

Keywords: Univariate Normal; Multivariate; Random Variable; Random Vector; Random Matrix; Applications: Education; Psychology; Quality Control; Pattern Recognition (search for similar items in EconPapers)
JEL-codes: C01 C1 C15 C4 C46 (search for similar items in EconPapers)
Date: 2021
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