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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