It seems that no one has replied to this, perhaps for the reasons I nearly didn't.
I don't know precisely what you are seeking here. Measures of similarity don't always function well as test statistics, and vice versa, and I don't know what you mean by correlated pdfs, as distinct from correlated variables.
But it is not obvious that any such measure or test exists. Even if you have three points in some space, there isn't a unique single distance between them, and you have three functions, which in any case have to be estimated.
Contrary to any intuition that three is only a little more complicated than two, I assert that once you have three variables then your problem is multivariate. Other than treating your problem as related to standard ANOVA (classical or nonparametric) or principal component analysis, I can't see that there is an easy way forward of the kind you seek.
There is a growing field called functional data analysis, but it is does not seem to matched by Stata implementations.
Nick
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I have 3 correlated probability density functions (pdf), and would like to
obtain a simple measure of similarity among them. Cohen�s U statistics do
that, but they look at two pdfs at a time. There are also measures of
intrinsic discrepancy, but I am not sure if they work with 3 pdf.. could
not find any reference.
Are you aware of an alternative test to do what I am looking for using Stata?
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