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Re: st: about -mreldif( )-


From   wgould@stata.com (William Gould, Stata)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: about -mreldif( )-
Date   Thu, 09 Jun 2005 14:19:47 -0500

Katsuhide Isa <katu@ier.hit-u.ac.jp> noted that Stata's (misnamed) 
reldif(X,Y) function returns r, 

                      |X - Y|
                r =  ---------
                      |Y| + 1

and asked about the mathematical justification for this formula.

The formula is simply a mix of the absolute difference,

             r_a   =  |X - Y|

and the relative difference

                      |X - Y|
              r_r =  ---------
                        |Y|
In particular, 

           lim  r =  r_a
           Y->0

           lim  r =  r_r
         Y->inf

When Y is small, then r is approximately the absolute difference (r is
exactly the absolute difference when Y==0), and when Y is large, then
r is approximately the relative difference.

This function is often used in numerical programming to test whether a 
value has changed much from one iteration to the next, and when one 
does not know whether the paramter will be large or small.

-- Bill
wgould@stata.com
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