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multidimensional ellipsoids

3-dim projections of 4-dim MVN

Covariance matrix of a cut-off Multivariate Normal Distribution – II – integrals over volume and surface of an n-dimensional sphere

In the 1st post of this series, we have posed the following problem: Take the probability density of a Multivariate Normal Distribution [MVN], but set it to zero at Mahalanobis distances bigger than a finite Mahalanobis distance D. Take a respective volume region enclosed by a contour surface of constant probability density, for a Mahalanobis distance dm ≤ D. We… Read More »Covariance matrix of a cut-off Multivariate Normal Distribution – II – integrals over volume and surface of an n-dimensional sphere

Multivariate Normal Distributions – IV – Spectral decomposition of the covariance matrix and rotation of the coordinate system

In the preceding posts of this series we have considered a comprehensible definition and basic properties of a non-degenerate “Multivariate Normal Distribution” of vectors in the ℝn [N-MND]. In this post we will make a step in the direction of a numerical analysis of some given finite vector distribution with properties that indicate an underlying N-MND. We want to find… Read More »Multivariate Normal Distributions – IV – Spectral decomposition of the covariance matrix and rotation of the coordinate system