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eigenvalues

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

confidence ellipses of bivariate normal distribution

Eigenvalues and eigenvector of a positive-definite, real valued and symmetric matrix

A bivariate normal distributions [BVD] is governed by a central positive symmetric matrix. This matrix is a covariance matrix which describes the variances and correlation of the BVD’s marginal distributions. The contour lines of the probabilty density function of a BVD are ellipses. The half axes and the orientation of these ellipses are controlled by the eigenvalues and eigenvectors of… Read More »Eigenvalues and eigenvector of a positive-definite, real valued and symmetric matrix