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st: RE: Is there any test to examine disitribution overlap with Stata?


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Is there any test to examine disitribution overlap with Stata?
Date   Mon, 2 Jun 2008 18:14:10 -0400

>>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?<<<

I'm not entirely sure what you mean by correlated here. I don't understand a measure of one distance though. You have three points in a function space and thus have three distances, dAB, dAC, and dBC. That's just how it is. If you want to define another piont in the function space, e.g., the functional centroid, that's different.  

Anyway, there are many, many possible distance measures, as Nick noted. A natural metric is the max norm, used by the Kolmogorov-Smirnov test. So you could use KS for each. There are lots of other metrics on one dimensional function spaces, with the most obvious one being the Euclidean for functions, i.e.,

           /
d(f,g) = [ | {f(x) - g(x)}^2 dx ]^.5
           / 
           X


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