I am trying to use Alan Genz's mvnlps code as posted here
The aim is to use it to integrate the area of under an ellipse given a bivariate distribution.
I have a bivariate normal distribution with standard deviation [, ] and have an ellipse with major radius = a and minor radius = b
To me, this should be quite a straightforward problem - I simply want to compute a bounded integral of my normal bivariate distribution, which has no skew, without having to resort to numerical integration.
And as such, I would expect that integrating over that surface, with those bounds would give me around 0.6827 (i.e. 1-sigma worth of stuff under my curve). However, I find the following:
e = [1/(135^2),0; 0,1/(3^2)];
mvnval = mvnlps( [0,0]', diag([135, 3]).^2, [0,0]', e, 1, 0.0001)
When to me, that should be around 1-sigma. Am I doing something wrong with my definition of e, my "radius" (I am unsure what that actually means in the context of an ellipse), or indeed something that I haven't even thought of?
Thanks in advance!