[R] Non-central distributions
Bill.Venables@cmis.csiro.au
Bill.Venables at cmis.csiro.au
Fri Oct 18 06:19:26 CEST 2002
Ted Harding says:
> -----Original Message-----
> From: Ted.Harding at nessie.mcc.ac.uk
> [mailto:Ted.Harding at nessie.mcc.ac.uk]
> Sent: Friday, October 18, 2002 2:14 AM
> To: Peter Dalgaard BSA
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] Non-central distributions
>
> Thanks, Peter! (Must try to give this some thought ...).
[WNV] The density functions for the t and F distributions are in
fact quite easy and only require hypergeometric functions in addition to
standard things. These could be useful anyway for all sorts of things.
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.
Random numbers from the non-central distributions are easy enough to
generate, of course, using the central ones. Again, I'm not sure just how
much slick versions of them would be useful, though.
> 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.
> Ted.
>
> On 17-Oct-02 Peter Dalgaard BSA wrote:
> > (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> writes:
> >
> >> only the CDF functions 'pt' and 'pf' allow this parameter to
> >> be set. (If you try in the others, you get the message
> >> "unused argument(s) (ncp ...)").
> >>
> >> Why is this? Being able to set it would be just as useful ...
> >
> > We don't have any references on how to calculate them! (Except for the
> > brute-force approaches of numeric differentiation, root finding, and
> > transformation of uniform distributions.)
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
> Fax-to-email: +44 (0)870 167 1972
> Date: 17-Oct-02 Time: 17:13:30
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