Chapter 2 Multivariate Distributions

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Chapter 2Multivariate IntroductionDefinition importantmultivariate location and dispersion modelisa joint distribution with joint probability density function (pdf)f(z| , )for ap 1 random vectorxthat is completely specified by ap 1 populationlocationvector and ap psymmetric positive definite populationdispersionmatrix .ThusP(x A) = Af(z)dzfor suitable :Usually a vectorxwill be column vector, and a row vectorxTwill be the transpose of the vectorx. However, Af(z)dz= Af(z1, ..., zp)dz1 notationf(z1, ..., zp) will be used to write out the componentsziof ajoint pdff(z) although in the formula for the pdf, egf(z) =cexp(zTz),zis a column 1random vectorx= (x1, ..., xp)T= (X1, ..., Xp)TwhereX1, ..., Xpareprandom variables. Acaseorobservationconsists oftheprandom variables measured for one person or thing.

Chapter 2 Multivariate Distributions 2.1 Introduction Definition 2.1. An important multivariate location and dispersion model is a joint distribution with joint probability density function (pdf)

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