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bivariate normal distribution

How to compute confidence ellipses – III – 4 alternative construction methods

In previous mathematical posts of this blog, we have studied some core properties of Bivariate Normal Distributions [BVDs]. During the rather mathematical tour de force we have come across various methods to construct and plot confidence ellipses for a given confidence level and respective Mahalanobis distance from the distribution’s center. We have also covered the mathematical derivation of the methods.… Read More »How to compute confidence ellipses – III – 4 alternative construction methods

How to compute confidence ellipses – II – equivalence of Schelp’s basic construction method for confidence ellipse with other approaches

In the 1st post of this series, I have motivated a simple method for constructing confidence ellipses for assumedly Bivariate Normal Distributions [BVD] or at least approximate BVDs. A reader has asked me, whether one can prove more rigidly that the proposed method of C. Schelp is equivalent to other BVD-based methods. Well, in this post we show that the… Read More »How to compute confidence ellipses – II – equivalence of Schelp’s basic construction method for confidence ellipse with other approaches

Properties of BVD confidence ellipses – II – dependency of half-axes on the correlation coefficient

If you have read my last post on confidence ellipses, you may have tried to derive the result on the longer half-axis for maximum correlation by following an eigenvalue analysis of the (inverse) covariance matrix of a Bivariate Normal Distribution [BVD]. If you have succeeded, jump over this post. If not, the contents my be interesting for you. Its is… Read More »Properties of BVD confidence ellipses – II – dependency of half-axes on the correlation coefficient

BVD confidence ellipses for varying correlation

Properties of BVD confidence ellipses – I – constant limits and tangents in x- and y-direction during variation of the Pearson correlation coefficient

We have gathered a lot of knowledge about Bivariate Normal Distributions [BVDs] and their contour ellipses in the math section of this blog. We can now analyze some secondary and funny properties of BVD contour and confidence ellipses. Among other things the variation of some key properties with the Pearson correlation coefficient ρ is of interest for data analysts. In… Read More »Properties of BVD confidence ellipses – I – constant limits and tangents in x- and y-direction during variation of the Pearson correlation coefficient