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

From: Ken Kelley <KKIII_at_indiana.edu>
Date: Tue 25 Oct 2005 - 03:01:10 EST

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

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