From p.dalgaard at biostat.ku.dk  Fri Apr 22 11:36:18 2005
From: p.dalgaard at biostat.ku.dk (Peter Dalgaard)
Date: Fri Apr 22 11:36:26 2005
Subject: [Rd] Infinite degrees of freedom for F-distribution
In-Reply-To: <6.2.1.2.1.20050422190734.02174a88@imaphost.wehi.edu.au>
References: <6.2.1.2.1.20050422190734.02174a88@imaphost.wehi.edu.au>
Message-ID: <x2sm1jkval.fsf@turmalin.kubism.ku.dk>

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


[Rd] Infinite degrees of freedom for F-distribution
Peter Dalgaard