Thank you very much for your kind reply. It solved the problem of rt( ). :D
But it seems that the qt( ) also have problems:
I modified the rt( ) function as you suggested,
rt <- function (n, df, ncp = 0)
{
if (ncp == 0)
.Internal(rt(n, df))
else rnorm(n, ncp)/sqrt(rchisq(n, df)/df)
}
Then I increase the number of random variables to 10000, and made a QQ-plot:
> qqplot(rt(10000,df=20,ncp=3),qt(runif(10000),df=20,ncp=3))
I've got some spurious points at lower-left corner. It seems that qt( )
results were truncated.
I also tried this with another df and ncp:
> pt(-.75,df=2,ncp=1)
[1] 0.05726429
> sum(qt(1:10000/10001,df=2,ncp=1)< -.75)
[1] 0
where I'd expected the last number should be > 550 or so, not 0.
Thanks again, the modified rt( ) is now OK for my work.
Long
Thomas Lumley <[EMAIL PROTECTED]> wrote£º
On Fri, 30 Jun 2006, Long Qu wrote:
> Hi there:
>
> I'd thought these two versions of noncentral t-distribution are essentially
> the same:
> > qqplot(rt(1000,df=20,ncp=3),qt(runif(1000),df=20,ncp=3))
>
> But, the scales of the x-axis and the y-axis are quite different according to
> the QQ-plot.
>
> Did I make any mistakes somewhere?
>
No, I think we did.
We have
> rt
function (n, df, ncp = 0)
{
if (ncp == 0)
.Internal(rt(n, df))
else rnorm(n, ncp)/(rchisq(n, df)/sqrt(df))
}
and the rchisq() in the denominator should be inside the sqrt().
-thomas
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