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.indra...@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. 538...@gmail.com [[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.
