[R] Non-central distributions

[(Ted Harding)]

On 18-Oct-02 Bill.Venables at cmis.csiro.au wrote:
> As far as I know, percentage points of the non-central
> distributions are not much used, but what would be very
> useful would be to have the percentage points (with respect
> to the non-centrality parameter) of the distribution function
> G(delta) = 1-P(X^2, n, delta), (i.e. you take the upper tail
> area as defining a distribution function in delta.  Such a
> distributon has a finite probability at the origin, of course.
> These are the quantities you need, for example, for things
> like sample size determination and power calculations.

Yes, this is precisely why I was looking for non-central t.
(Your "fiducial" inversion of the distribution function would
of course give confidence limits for delta at the percentiles.)

>> Anyway, in this respect R is still ahead of S-Plus, which
>> doesn't seem to carry ANY non-centrality as standard!
>> (Except possibly obscurely tucked away in some add-on library).
>       [WNV]  Tsk tsk, Ted.  They are there for pf and pchisq, at least.
> 
>       Bill Venables.

OOPS! Yes, you are right, now that I look properly. In fact it
is there for pf, pchisq and pbeta. (Having failed with pt, and
adopted a misguided search strategy in S-Plus's on-line Language
Reference -- namely, hoping that "full-text search" for "central"
would hit it -- I concluded that it wasn't there ... ).

But, as Martin Maechler says, R is still ahead on that front!

Best wishes,
Ted.

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Date: 18-Oct-02                                       Time: 09:45:52
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