R help - Apr 2008 - Simulation study in R

Here I am in a simulation study where I want to find different values
of x and y such that f(x,y)=c (some known constant) w.r.t. x, y >0,
y<=x and x<=c1 (another known constant). Can anyone please tell me how
to do it efficiently in R. One way I thought that I will draw
different random numbers from uniform dist according to that
constraints and pick those which satisfy f(x,y)=c. However it is not I
think computationally efficient. Can anyone here suggest me any other
efficient approach?

Regards,

Are the pairs (x,y) belong to some lattice or can
change continuously?
Does f assume some discrete values (or is constant on
sets of positive measure)? If not then it will be hard
to randomly select x and y which satisfy the exact
equality (this still can happen since there are
finitely many computer numbers, but their number is
quite large!). So if f change continuously you may
need the condition |f(x,y) - c| < epsilon for some
epsilon > 0.

Regards,

Moshe.

--- Arun Kumar Saha <arun.kumar.saha at gmail.com> wrote:
> Here I am in a simulation study where I want to find
> different values
> of x and y such that f(x,y)=c (some known constant)
> w.r.t. x, y >0,
> y<=x and x<=c1 (another known constant). Can anyone
> please tell me how
> to do it efficiently in R. One way I thought that I
> will draw
> different random numbers from uniform dist according
> to that
> constraints and pick those which satisfy f(x,y)=c.
> However it is not I
> think computationally efficient. Can anyone here
> suggest me any other
> efficient approach?
> 
> Regards,
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>

x, y are cont. variable, and f also have to be cont.. And your second
suggestion is correct of course, it actually should be |f(x,y) - c| <
epsilon

Thanks

On Tue, Apr 29, 2008 at 12:34 PM, Moshe Olshansky <m_olshansky at
yahoo.com> wrote:
> Are the pairs (x,y) belong to some lattice or can
> change continuously?
> Does f assume some discrete values (or is constant on
> sets of positive measure)? If not then it will be hard
> to randomly select x and y which satisfy the exact
> equality (this still can happen since there are
> finitely many computer numbers, but their number is
> quite large!). So if f change continuously you may
> need the condition |f(x,y) - c| < epsilon for some
> epsilon > 0.
>
> Regards,
>
> Moshe.
>
>
> --- Arun Kumar Saha <arun.kumar.saha at gmail.com> wrote:
>
> > Here I am in a simulation study where I want to find
> > different values
> > of x and y such that f(x,y)=c (some known constant)
> > w.r.t. x, y >0,
> > y<=x and x<=c1 (another known constant). Can anyone
> > please tell me how
> > to do it efficiently in R. One way I thought that I
> > will draw
> > different random numbers from uniform dist according
> > to that
> > constraints and pick those which satisfy f(x,y)=c.
> > However it is not I
> > think computationally efficient. Can anyone here
> > suggest me any other
> > efficient approach?
> >
> > Regards,
> >
> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> > reproducible code.
> >
>
>


--

At 02:40 AM 4/29/2008, Arun Kumar Saha wrote:
>Here I am in a simulation study where I want to find different values
>of x and y such that f(x,y)=c (some known constant) w.r.t. x, y >0,
>y<=x and x<=c1 (another known constant). Can anyone please tell me how
>to do it efficiently in R. One way I thought that I will draw
>different random numbers from uniform dist according to that
>constraints and pick those which satisfy f(x,y)=c. However it is not I
>think computationally efficient. Can anyone here suggest me any other
>efficient approach?
You have not specified the distributions proper for X and Y. Using a 
uniform distribution is only appropriate when it meets requirements.

One obvious approach is to sample one of the variables, say X, and 
then solve your equation for Y. If you're going to draw a lot of 
samples, it would pay to develop y = g(x) first.

But you need to know how to sample X in the first place. Is its 
distribution uniform, or something else?

===============================================================Robert A.
LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
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