From: Clark Allan <Allan_at_stats.uct.ac.za>

Date: Tue 28 Jun 2005 - 20:43:44 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jun 28 20:50:38 2005

Date: Tue 28 Jun 2005 - 20:43:44 EST

**HI ALL
**
i would like to solve a complex set of equations. i have four parameters
and four equations. i could set up more equations since they are derived
from the momnets of a particular distribution.

the parameters are NON LINEAR!!!

AND the eqautions are of the form:

phi(i)=function(a,x,y,z)

is there a package or group of commands that might be used in order to solve the system directly?

thanking you in advance

/

allan

Spencer Graves wrote:

*>
*

> Have you considered writing a function to compute the sum of squares

*> of deviations from equality and using "optim"? I use sum of squares not
**> sum of absolute values, because if my functions are differentiable, the
**> sum of squares will also be differentible while the sum of absolute
**> values will not be. This means that sum of absolute values will not
**> work well with a quasi-Newton algorithm.
**>
**> Also, have you considered making plots? If I understand your
**> example, you can solve for lambda using (II) as lambda = x/mean(X).
**> Then you can use (I) to solve for "c". To understand this, it would
**> help to plot the digamma function. If you do this (e.g.,
**> http://mathworld.wolfram.com/DigammaFunction.html), you will see that
**> there are countably infinite solutions to this equation. If you want
**> the positive solution, I suggest you try to solve for ln.c = log(c)
**> rather than "c" directly, because that should make "optim" more stable.
**> More generally, it often helps to make, e.g., contour or perspective
**> plots and to try to find a parameterization that will make the sum of
**> squares of errors approximatly parabolic in your parameters.
**>
**> My favorite reference on this is Bates and Watts (1988) Nonlinear
**> Regression Analysis and Its Applications (Wiley). There may be better,
**> more recent treatments of this subject, but I am not familiar with them.
**>
**> spencer graves
**> p.s. I never (no never, not ever) use "c" as a variable name, because
**> it is the name of a common R function. R is smart enough to distinguish
**> between a function and a non-function in some contexts but not in all.
**> When I want a name for a new object, I routinely ask R to print my
**> proposed name. If it returns "Error: object ... not found", I can use
**> "...".
**>
**> Carsten Steinhoff wrote:
**>
**> > Hello,
**> >
**> > I want to solve some two dimensional equation system with R. Some systems
**> > are not solvable analytically.
**> >
**> > Here is an example:
**> >
**> > (I) 1/n*sum{from_i=1_to_n}(Xi) = ln lambda + digamma(c)
**> >
**> > (II) mean(X) = x / lambda
**> >
**> > I want to find lambda and c,
**> >
**> > which R-function could do that task?
**> >
**> > Carsten
**> >
**> > [[alternative HTML version deleted]]
**> >
**> > ______________________________________________
**> > R-help@stat.math.ethz.ch mailing list
**> > https://stat.ethz.ch/mailman/listinfo/r-help
**> > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
**>
**> --
**> Spencer Graves, PhD
**> Senior Development Engineer
**> PDF Solutions, Inc.
**> 333 West San Carlos Street Suite 700
**> San Jose, CA 95110, USA
**>
**> spencer.graves@pdf.com
**> www.pdf.com <http://www.pdf.com>
**> Tel: 408-938-4420
**> Fax: 408-280-7915
**>
**> ______________________________________________
**> R-help@stat.math.ethz.ch mailing list
**> https://stat.ethz.ch/mailman/listinfo/r-help
**> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jun 28 20:50:38 2005

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