R devel - Apr 2005 - Infinite degrees of freedom for F-distribution

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

Gordon Smyth <smyth@wehi.edu.au> writes:
> 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
This is actually a regression. It worked as you suggest in 2.0.1, at
least on Linux. Also, somewhat disturbing,
> pf(1,df1=1,df2=Inf)
[1] NaN
Warning message:
NaNs produced in: pf(q, df1, df2, lower.tail, log.p)
> pf(1,df1=1,df2=99999999)
[1] 0.6826895
> pf(1,df1=1,df2=999999999999)
[1] 0.6826841
> pf(1,df1=1,df2=99999999999999999999)
[1] 0

(notice that the middle case has actually begun to diverge from the
limiting value)

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907