-----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.)
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Date: 17-Oct-02 Time: 17:13:30
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"Bill" == Bill Venables <Bill.Venables at cmis.csiro.au>
on Fri, 18 Oct 2002 14:19:26 +1000 writes:
Bill> Ted Harding says:
>> -----Original Message-----
>> From: 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 ...).
Bill> [WNV] The density functions for the t and F
Bill> distributions are in fact quite easy and only require
Bill> hypergeometric functions in addition to standard
Bill> things. These could be useful anyway for all sorts of
Bill> things. As far as I know, percentage points of the
Bill> non-central distributions are not much used, but what
Bill> would be very useful would be to have the percentage
Bill> points (with respect to the non-centrality parameter)
Bill> of the distribution function G(delta) = 1-P(X^2, n,
Bill> delta), (i.e. you take the upper tail area as defining
Bill> a distribution function in delta. Such a distributon
Bill> has a finite probability at the origin, of course.
Bill> These are the quantities you need, for example, for
Bill> things like sample size determination and power calculations.
probably an exercise of reading the sections in Johnson et al
(see "HRK" below). I remember having seen quite a few references there.
Contributions are welcome..
Bill> Random numbers from the non-central distributions are
Bill> easy enough to generate, of course, using the central
Bill> ones. Again, I'm not sure just how much slick
Bill> versions of them would be useful, though.
In the next major version of R, 1.7.x,
I plan to have finished the code for rchisq(*, ncp = *)
{and possibly for some of ?chisq(*, df = 0, *) }
thanks to a suggestion from Hans R. Kuensch:
HRK> I think the help file for the Chisquare distribution should
HRK> indicate clearly whether df has to be a natural number or can be
HRK> any positive number. Also I don't understand why rchisq works
HRK> only in the central case. It should be easy to do the general
HRK> case by decomposing it as the sum of a central chisquare with df
HRK> degrees of freedom plus a noncentral chisquare with zero degrees
HRK> of freedom (which is a Poisson mixture of central chisquares
HRK> with integer degrees of freedom), see Formula (29.5b-c) in
HRK> Johnson, Kotz, Balakrishnan (1995). The noncentral chisquare
HRK> with arbitary degrees of freedom is of interest for simulating
HRK> the Cox-Ingersoll-Ross model for interest rates in finance.
>> 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).
Bill> [WNV] Tsk tsk, Ted. They are there for pf and pchisq, at least.
[ but of course, R is still ahead ;-) ;-) ]
Martin Maechler <maechler at stat.math.ethz.ch> http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum LEO C16 Leonhardstr. 27
ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND
phone: x-41-1-632-3408 fax: ...-1228 <><
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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.
--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 18-Oct-02 Time: 09:45:52
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In message <15791.44578.187614.230488 at gargle.gargle.HOWL> you write:
probably an exercise of reading the sections in Johnson et al
(see "HRK" below). I remember having seen quite a few references there.
Contributions are welcome..
...
In the next major version of R, 1.7.x,
I plan to have finished the code for rchisq(*, ncp = *)
{and possibly for some of ?chisq(*, df = 0, *) }
thanks to a suggestion from Hans R. Kuensch:
I haven't followed this entire thread, so I apologize if I'm
completely off the mark, especially since I strongly suspect that
Martin and others would be aware of this information already.
Still, FWIW, probably all of these routines are available, albeit in
Fortran, in Barry W. Brown, James Lovato, and Kathy Russell's cdflib,
which seems to be unencumbered by any license restrictions. I have
used this library before without any problems, and I'm sure that I
have dynloaded it into Splus, and probably into R as well. Maybe it
would at least be useful as a reference while you code this up in C?
Should be on statlib.
Brett Presnell
Department of Statistics
University of Florida
http://www.stat.ufl.edu/~presnell/
"We don't think that the popularity of an error makes it the truth."
-- Richard Stallman
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