Simulation of remission and after remission times under specific conditions

This is basically a data generation problem.

Say, $t$ is an exponential lifetime with mean two years. $tr$ is the remission time and $ts$ is the after remission time. So, $t=tr+ts$. I need to simulate these quantities for $100$ patients. Now in real life, usually when $tr$ is smaller, that is when the patients remit quickly, their after remission time $ts$ are longer (so that the lifetimes $t$ are also longer). When $tr$ are longer, that is the patients remit slowly, their after remission times $ts$ are shorter.

One thing is known that the distribution of the lifetimes, $t$ is exponential with mean two years. I don't have any information about their exact relationship but I know, this is the scenario in real life. I need to simulate data under this scenario because I want to see the performance of an estimator under these conditions. So any feasible assumption regarding how they are correlated is absolutely okay for me. But I cannot understand how to generate data from the above mentioned scenario. If some sort of randomness can be put along with maintaining the conditions, that will be great!

Your suggestion will be a great help.

• By the way, I am using R. – Blain Waan Mar 17 '13 at 15:08