[R] Noncentral t & F distributions

[Alan Arnholt]

Dear List:

The square of the noncentral t-statistic with noncentrality parameter 
\delta is a noncentral F with noncentrality parameter \lambda=\delta^2. 
So, t^2_{\nu,\delta} = F_{1,\nu,\lambda=\delta^2}.  Consequently, it 
should follow that t^2_{1-\alpha/2,\nu,\delta} = 
f_{1-alpha,1,\vu,\lambda=\delta^2}.  However, this is not what is 
happening with the following code.  The central distributions agree as 
they should but the noncentral distributions do not.  Am I missing 
something or is there a bug in the code?

> alpha <- 0.05
> nu <- 10
> NCP <- c(0,1,2,3)
> TV <- (qt(1-alpha/2,nu,NCP))^2
> FV <- qf(1-alpha,1,nu,NCP^2)
> rbind(TV,FV)
        [,1]      [,2]     [,3]     [,4]
TV 4.964603 12.535179 24.58013 41.71937
FV 4.964603  9.285829 18.98771 32.97855
> TV <- (qt(1-alpha/2,nu,NCP))^2
> FV <- qf(1-alpha/2,1,nu,NCP^2)
> rbind(TV,FV)
        [,1]     [,2]     [,3]     [,4]
TV 4.964603 12.53518 24.58013 41.71937
FV 6.936728 12.56450 24.58023 41.71937

Thanks,

Alan-

> version
                _
platform       i386-pc-mingw32
arch           i386
os             mingw32
system         i386, mingw32
status
major          2
minor          4.0
year           2006
month          10
day            03
svn rev        39566
language       R
version.string R version 2.4.0 (2006-10-03)


Alan T. Arnholt
Associate Professor
Dept. of Mathematical Sciences
Appalachian State University
TEL: 828 262 2863
FAX: 828 265 8617