# [R] Simulating from a special type of bivariate exponential distribution

Don McKenzie dmck at u.washington.edu
Sun Jun 16 16:05:47 CEST 2013

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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]]
>
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> 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

```