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I am trying to find a method to calculate how far a point lies from the mean of a 2D Gaussian in terms of standard deviations. I have drawn a diagram to demonstrate my problem.

Diagram of my problem

I know the position of the mean, the position of the point and the 2x2 Covariance matrix of the Gaussian.

I am currently using the Gaussian Distribution function to determine the (z-axis) height of the Gaussian curve at the given point, but a standard deviation measurement in the x/y plane is far more valuable to me.

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What you are looking for is precisely the Mahalanobis distance of an observation.

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  • $\begingroup$ This is exactly what I am after, thank you! $\endgroup$ – Unl1ght Dec 4 '16 at 7:22

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