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probability density

BVD contour ellipses

Bivariate Normal Distribution – Mahalanobis distance and contour ellipses

I continue with my posts on Bivariate Normal Distributions [BVDs]. In this post we consider the exponent of a BVD’s probability density function [pdf]. This function is governed by a central matrix Σ-1, the inverse of the variance-covariance matrix of the BVD’s random vector. We define the so called Mahalanobis distance dm for BVD vectors. A constant value of the… Read More »Bivariate Normal Distribution – Mahalanobis distance and contour ellipses

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