How to make an ellipse with given standard deviations?

I'm trying to test an algorithm that my lab has written to see how it handles a non-spherical distribution of data. I need to generate a set of n-dimensional elliptical data with a standard deviation of 1 along one major axis, and a standard deviation of something else, let's say 2, along the other major axis.

Then, I need to calculate the exact standard deviation and the standard deviation of skew of the distribution around-the-compass-rose and compare it to that given by my algorithm.

How would I do this in Matlab?

[Image Analyst]

What do you mean by "by my algorithm"? Do you mean by OUR algorithm that we would give you? And if you're getting multiple skewnesses around the data scattered around an elliptical shell, what is the window size that you're computing the skewness in?

[Cynthia Dickerson]

I have an algorithm that my professor wrote that bootstrap replicates spectral data from a training set and tests whether a test sample's spectrum deviates significantly from the training set. It basically creates a hyper-cylinder around the bootstrapped points and then tests whether the test point falls within the hyper-cylinder, and calculates the standard deviation non-parametrically from that.

I'm trying to perform this experiment, but on data that forms an elliptical cluster, rather than a spherical one: http://asrg.contactincontext.org/asrg/pdfs/beast.pdf (Figures 14 and 16 on page 1360)

I need to calculate the algorithm's bias as the number of bootstrap replicates increases and as the radius of the hypercylinder increases.

I don't really understand what you mean by window size. It's not a graphical problem - it's just a non-parametric test. I just need data that fills a normally-distributed ellipse to run it on.

[Image Analyst]

Originally you said " I need to calculate the exact standard deviation......" but now it seems like you're saying that you need code not to do that, but actually, to create the input data - the random points. OK, but we're still not sure if you want a shell (which I think) or a solid ellipse (which I doubt). So which is it?

[Cynthia Dickerson]

I need a solid ellipse.

It would be nice if I could also get the code to calculate the standard deviation of points at the 45-degree angle of the compass rose, but I can do that by hand if I have to, to compare to the algorithm's output.

Answer 1

[John D'Errico]

help mvnrnd

[Cynthia Dickerson]

Thank you!