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normalization

Covariance matrix of a cut-off Multivariate Normal Distribution – IV – theoretical prediction for a 3-dimensional MVN-core

In this post series we study ellipsoidal cores of Multivariate Normal Distributions [MVNs]. We defined a “core” as the volume enclosed by a selected contour surface of constant probability density. We constructed cut-off distributions by setting the probability density to zero outside the core. In previous posts we have already discussed volume integrals which would give us a relation between… Read More »Covariance matrix of a cut-off Multivariate Normal Distribution – IV – theoretical prediction for a 3-dimensional MVN-core

Cut-off BVN limited to an ellipsoidal core

Covariance matrix of a cut-off Multivariate Normal Distribution – III – results for a 2-dimensional BVN-core and proper normalization of its cut-off distribution

In the math section of this blog, we try to cover interesting aspects of Multivariate Normal Distributions [MVNs]. The topic of this post series is the covariance matrix of a MVN-like distribution confined inside a hyper-surface of constant probability density. Outside of the surface we set the probability density to zero. This gives us a “cut-off” MVN- distribution. Contour surfaces… Read More »Covariance matrix of a cut-off Multivariate Normal Distribution – III – results for a 2-dimensional BVN-core and proper normalization of its cut-off distribution

contour ellipsoids of a projected MND

Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians

This post series is about mathematical aspects of so called “Multivariate Normal Distributions“. In respective literature two abbreviations are common: MNDs or MVNs. I will use both synonymously. To get an easy access, I want to introduce a MND as the result of a linear transformations applied to random vectors whose components can be described by independent 1-dimensional normal distributions.… Read More »Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians