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Normal Theory in Rp

In: THE MULTIVARIATE NORMAL DISTRIBUTION Theory and Applications

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  • PHAM-GIA THU

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

Suggested Citation

  • Pham-Gia Thu, 2021. "Normal Theory in Rp," World Scientific Book Chapters, in: THE MULTIVARIATE NORMAL DISTRIBUTION Theory and Applications, chapter 9, pages 273-310, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811235290_0009
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    Keywords

    Univariate Normal; Multivariate; Random Variable; Random Vector; Random Matrix; Applications: Education; Psychology; Quality Control; Pattern Recognition;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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