From smyth at wehi.edu.au  Fri Apr 22 11:17:17 2005
From: smyth at wehi.edu.au (Gordon Smyth)
Date: Fri Apr 22 11:17:34 2005
Subject: [Rd] Infinite degrees of freedom for F-distribution
Message-ID: <6.2.1.2.1.20050422190734.02174a88@imaphost.wehi.edu.au>

This is just a suggestion/wish that it would be nice for the F-distribution 
functions to recognize limiting cases for infinite degrees of freedom, as 
the t-distribution functions already do.

The t-distribution functions recognize that df=Inf is equivalent to the 
standard normal distribution:

 > pt(1,df=Inf)
[1] 0.8413447
 > pnorm(1)
[1] 0.8413447

On the other hand, pf() will accept Inf for df1, but returns the wrong result:

 > pf(1,df1=Inf,df2=1)
[1] 1

whereas the correct limiting value is

 > pchisq(1,df=1,lower.tail=FALSE)
[1] 0.3173105

pf() returns NaN when df2=Inf:

 > pf(1,df1=1,df2=Inf)
[1] NaN
Warning message:
NaNs produced in: pf(q, df1, df2, lower.tail, log.p)

although the correct value is available as

 > pchisq(1,df=1)
[1] 0.6826895


Gordon

 > version
          _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    1.0
year     2005
month    04
day      18
language R
---------------------------------------------------------------------------------------
Dr Gordon K Smyth, Senior Research Scientist, Bioinformatics,
Walter and Eliza Hall Institute of Medical Research,
1G Royal Parade, Parkville, Vic 3050, Australia
Tel: (03) 9345 2326, Fax (03) 9347 0852,
Email: smyth@wehi.edu.au, www: http://www.statsci.org


[Rd] Infinite degrees of freedom for F-distribution
Gordon Smyth