[R] Non-central distributions

[Bill.Venables@cmis.csiro.au]

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
> ------------------------------ XFMail ------------------------------
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
> -.-.-
> r-help mailing list -- Read
> http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
> Send "info", "help", or "[un]subscribe"
> (in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
> _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.
> _._._
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._