[R] Problems with pf() with certain noncentral values/degrees of freedom combinations

[Ken Kelley]

Hello all.

It seems that the pf() function when used with noncentral parameters can 
behave badly at times. I've included some examples below, but what is 
happening is that with some combinations of df and ncp parameters, 
regardless of how large the quantile gets, the same probability value is 
returned. Upon first glance noncentral values greater than 200 may seem 
large, but they are in some contexts not large at all. The problems with 
pf() can thus have serious implications (for example, in the context of 
sample size planning).

I noticed that in in 1999 and 2000 issues with large degrees of freedom 
came about (PR#138), but I couldn't find the present issue reported 
anywhere.

Might there be a way to make the algorithm more stable? I'm not sure how 
difficult this issue might be to fix, but hopefully it won't be too bad 
and can be easily done. Any thoughts on a workaround until then?

Thanks,
Ken Kelley

# <Begin example code>
X <- seq(10, 600, 10)

# Gets stuck at .99135
############################
round(pf(X, 10, 1000, 225), 5)
round(pf(X, 10, 200, 225), 5)

round(pf(X, 5, 1000, 225), 5)
round(pf(X, 5, 200, 225), 5)

round(pf(X, 1, 1000, 225), 5)
round(pf(X, 1, 200, 225), 5)

# Gets stuck at .97035
############################
round(pf(X, 10, 1000, 250), 5)
round(pf(X, 10, 200, 250), 5)

round(pf(X, 5, 1000, 250), 5)
round(pf(X, 5, 200, 250), 5)

round(pf(X, 1, 1000, 250), 5)
round(pf(X, 1, 200, 250), 5)

# Gets stuck at .93539
############################
round(pf(X, 10, 1000, 275), 5)
round(pf(X, 10, 200, 275), 5)

round(pf(X, 5, 1000, 275), 5)
round(pf(X, 5, 200, 275), 5)

round(pf(X, 1, 1000, 275), 5)
round(pf(X, 1, 200, 275), 5)
# <end example code>

 > version
          _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    2.0
year     2005
month    10
day      06
svn rev  35749
language R

-- 
Ken Kelley, Ph.D.
Inquiry Methodology Program
Indiana University
201 North Rose Avenue, Room 4004
Bloomington, Indiana 47405
http://www.indiana.edu/~kenkel