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
>
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>
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>



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

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