R help - Jun 2013 - Simulating from a special type of bivariate exponential distribution

Hi,
I have the following problem in simulating samples from a bivariate
exponential distribution with the following construction:

Start with three independent exponential random variables say W1,W2 and W3
with intensity parameters lambda 1, lambda 2 and lambda 3 respectively.

Now I construct a bivariate distribution (X,Y) such that

(X,Y) is distributed as (W1,W2  given that W0<min(W1,W2)).

The resulting distribution has the form

f(x,y)=((lambda 1+lambda 2+lambda 3)/lambda 3)*exp(-lambda 1*x-lambda 2*y)
*(1-exp(lambda 3*min(x,y)), with the joint support x>0, y>0.

Any suggestion is appreciated.

Thanks,


-- 
Indranil

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This looks like a homework problem, and has no R question in it.

If it is homework, ask your professor or fellow students for help.  

If not, and you have a question about R, please post that.

On Jun 15, 2013, at 8:17 PM, INDRANIL GHOSH <jamesbond.indranil at
gmail.com> wrote:
> Hi,
> I have the following problem in simulating samples from a bivariate
> exponential distribution with the following construction:
> 
> Start with three independent exponential random variables say W1,W2 and W3
> with intensity parameters lambda 1, lambda 2 and lambda 3 respectively.
> 
> Now I construct a bivariate distribution (X,Y) such that
> 
> (X,Y) is distributed as (W1,W2  given that W0<min(W1,W2)).
> 
> The resulting distribution has the form
> 
> f(x,y)=((lambda 1+lambda 2+lambda 3)/lambda 3)*exp(-lambda 1*x-lambda 2*y)
> *(1-exp(lambda 3*min(x,y)), with the joint support x>0, y>0.
> 
> Any suggestion is appreciated.
> 
> Thanks,
> 
> 
> -- 
> Indranil
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> 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.
Don McKenzie, Research Ecologist
Pacific WIldland Fire Sciences Lab
US Forest Service

Affiliate Professor
School of Forest Resources, College of the Environment
CSES Climate Impacts Group
University of Washington

phone: 206-732-7824
dmck at uw.edu

If your goal is to simulate data from the given distribution in R then
there are a couple of approaches.  You have the distribution function
derived, so you can use any technique that just need the distribution
function.  This could be rejection sampling or Metropolis-Hastings sampling
or others.  Both the methods I have mentioned have examples of use in past
R posts and probably various tutorials.  Adapt the R code from any of those
to your distribution.


On Sat, Jun 15, 2013 at 9:17 PM, INDRANIL GHOSH <
jamesbond.indranil@gmail.com> wrote:
> Hi,
> I have the following problem in simulating samples from a bivariate
> exponential distribution with the following construction:
>
> Start with three independent exponential random variables say W1,W2 and W3
> with intensity parameters lambda 1, lambda 2 and lambda 3 respectively.
>
> Now I construct a bivariate distribution (X,Y) such that
>
> (X,Y) is distributed as (W1,W2  given that W0<min(W1,W2)).
>
> The resulting distribution has the form
>
> f(x,y)=((lambda 1+lambda 2+lambda 3)/lambda 3)*exp(-lambda 1*x-lambda 2*y)
> *(1-exp(lambda 3*min(x,y)), with the joint support x>0, y>0.
>
> Any suggestion is appreciated.
>
> Thanks,
>
>
> --
> Indranil
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help@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.
>


-- 
Gregory (Greg) L. Snow Ph.D.
538280@gmail.com

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