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I am trying to simulate remission times for 100 patients from an exponential distribution with mean 1 year. I also want to simulate after-remission times for these 100 patients. But it is very much likely in the real life scenario that those who remit quickly are likely to have comparatively longer after-remission times and those who remit slowly are likely to have comparatively shorter after-remission times. So the after-remission time is likely to be correlated negatively to the remission time.

I want to test the performance of an estimator at certain levels of correlation (say, r=-0.5, r=-0.8 etc.). Could you please suggest how should I simulate the remission times and the after-remission times imposing the condition of certain levels of correlations?

Should I consider the relationship to be linear or non-linear?

I know from the real life data that the average after-remission time is about 1.5 years. How can I reflect this information in my simulated data, imposing the level of correlation?

kjetil b halvorsen
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Blain Waan
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  • I am using R for the simulation. Thank you for your suggestion in advance. – Blain Waan Aug 06 '13 at 11:33
  • As a side comment, two exponential random variables cannot have a correlation less than $1-\pi^2/6 \approx -0.645$. – QuantIbex Aug 06 '13 at 17:52
  • Thanks for the information. Could you please explain how? – Blain Waan Aug 07 '13 at 15:44
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    The derivation of this lower bound takes more that just a few lines, and since it was a side comment I provide the development [here](http://stats.stackexchange.com/q/66775/27403). – QuantIbex Aug 07 '13 at 17:52

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