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I have two normally distributed random variables (estimated from two different sets of samples), and I'd like to know how "similar" those variables are (in order to compare the sets).
I had the idea of calculating the area common to both the PDFs of those variables, which would be between 0 and 1 (I think).
This would be the integral of the minimum of each PDF on every point (I think). I'm struggling a bit on calculating this, though.
If I was doing this manually, I'd calculate the intersections between the two PDFs, see which was the minimum PDF on each region, and integrate each separately.
However, I need to do this on a computer, for any two normal distributions. Is there a way to compute this easily?
Also, am I on the right track? Are there better ways of comparing two distributions?