How to draw contours over a bi-variate Gaussian so that the lines enclose a certain percentage of the distribution?

I use fitgmdist to get the Gaussian distribution. Then I draw a contour plot of the distribution using fcontour . The problem is that I don't understand at what interval these lines are drawn. I would like the lines to be drawn such that for example 68% of the samples are within the first line, 95% are within the second line and so on.

What I have now looks like this:

What I want is something similar to this:

so that I know which percentage of the distribution the lines are enclosing.

Any help is greatly appreciated.

Answer 1

[James Herman]

Probably no longer in need of a response but...

The way I solved this was to find the "levels" that the contours need to be drawn at to contain a certain percentile of the 2D gaussian. Given "alpha" (%), this depends on critical values of the chi-square distribution, for which you can use "chi2inv". More info here.

Below an example of how to calculate the "levels" for a couple alphas. It's done by using a purely diagonal covariance matrix ("unrotated"). After obtaining "pdlevels" you can feed those to contour...

mu = [7, 3];
cov = [1 0.2; 0.2, 1];

alpha = [0.2 0.7];
nAlpha = length(alpha);

% walk out from the mean to points such that all points closer
% comprise the central alpha% of the distribution; choose the
% direction along which this distance is shortest so that we
% can return the radius
pdpoints = repmat(mu, 2*nAlpha,1) + ...
    repmat(sqrt(chi2inv(alpha, 2))*...
    sqrt(cov),2,1).*sortrows(repmat(eye(2), nAlpha,1));

% calculate the value of the (unrotated) gaussian there.
pdlevels = mvnpdf(pdpoints(1:nAlpha,:), mu, diag(diag(cov)));

[Olga Kashibadze]

Thank you!!!