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st: RE: Does invnormal have a symbol?


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Does invnormal have a symbol?
Date   Thu, 31 Jul 2008 10:39:32 +0100

People often represent it using capital phi and a superscript power -1.
No doubt there is cause for feeling queasy about that, as the idea of an
inverse and the idea of a reciprocal are not the same (although they
overlap). Nevertheless you'd be in very good company in using such a
symbol. 

Although the inverse cdf terminology is clearly very common, there is a
good case for using the terminology of quantile functions. Stata's
function terminology is, in this respect, I believe inferior to that of
S and now R, which has clean conventions using p, q and r to indicate
kinds of functions. However, that does not help you much in your search
for symbols. It seems quite common to use Q() rather than F^{-1}() to
indicate quantile functions in general, but I don't think that would be
common for the normal quantile function. 

The inverse cdf terminology is particularly strained if you have cause
to discuss the inverse of the inverse gamma or inverse Gaussian
cumulative distribution function. 

Nick
n.j.cox@durham.ac.uk 

tiago.pereira@incor.usp.br

I am using the inverse normal cumulative distribution function
(invnormal
in Stata), and would like to know if there is a way to represent it
using
a symbol like the cumulative normal distribution, which is usually
represented by the greek letter phi.

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