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integration

Confidence ellipses for an approximate BVD

Bivariate Normal Distribution – integrated probability up to a given Mahalanobis distance, the Chi-squared distribution and confidence ellipses

In previous posts of this blog we have discussed the general form of the probability density function [pdf] of a Bivariate Normal Distribution [BVD]. In this post we consider the integral over a BVD’s pdf up to a defined value of the Mahalanobis Distance. A given value of the latter defines an elliptic contour line of constant probability density. With… Read More »Bivariate Normal Distribution – integrated probability up to a given Mahalanobis distance, the Chi-squared distribution and confidence ellipses

Bivariate Normal Distribution from face data encoded by a CAE

Bivariate Normal Distribution – derivation of the covariance and correlation by integration of the probability density

In a previous post of this blog we have derived a function g2(x,y for the probability density f a Bivariate Normal Distribution [BVD] of two 1-dimensional random variables X and Y). By rewriting the probability density function [pdf] in terms of vectors (x, y)T and a coupling matrix Σ-1 we recognized that a coefficient appearing in a central exponential of… Read More »Bivariate Normal Distribution – derivation of the covariance and correlation by integration of the probability density