Normal Theory in Rp

Pham-Gia Thu

Chapter 9 in The Multivariate Normal Distribution:Theory and Applications, 2021, pp 273-310 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The following sections are included:IntroductionBasic Results in Quadratic Forms in p VariablesExpression of the DensityExpression of the normal densityExamplesSome Integrals Related to the Multivariate NormalGoing from a Normal with Dependent Components to One with Independent Ones and BackPropertiesCharacteristic functionContours of the density surfaceOperations on the Distribution of X ∼ Np(μ, Σ)Linear combinationMatrix transformationsConditionally normal distributionsQuadratic forms in normal variablesComputation of the cdf of the MultinormalSome specific approachesTablesGeneration of Observations from the MultinormalChecking on MultinormalityMultivariate Normal SamplingTest on the Population Mean VectorConfidence Intervals for Mean Vectors and their ComponentsOne multinormal populationTwo multinormal populations and moreCorrelation CoefficientsCorrelation between two univariate rv’sThe multiple correlation coefficient in practiceCoefficient of partial correlationSemi-partial correlation or part correlationSome theory on correlationsCorrelation matrixSimulation of the Multivariate NormalAn Example from MATLABConclusionBibliography

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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