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I have two overlapping gamma distributions, 'a' and 'b', which are correlated but with correlation coefficient < 1. I want to randomly sample pairs of values, one from each distribution.

However, there is a physical relation between all sampled pairs such that 'a' must always be greater than 'b'. How can I enforce this condition without messing up the randomness/distribution of my samples?

[As noted, correlation coefficient = 1 would achieve this i.e. same P(X) used to sample from each distribution, but I don't want fully correlated samples]

henrybish
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  • What if you just sample them normally, and ignore all the cases where `b>a`? Also, you might ask this in the stats forum for better answers, Cross Validated. – K.Cl Apr 02 '21 at 20:50
  • Won't this mess up the randomness/distribution of my samples? It seems that would be artificially sampling 'b' from a specific region (everything < 'a') in each case and so the histogram of 'b' samples will not represent the specified gamma distribution. Thanks for tip on cross validated. – henrybish Apr 02 '21 at 21:00
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    If you are going to ask the same question simultaneously on two different forums, then please reference the other post. Otherwise if an answer or instructive comment appears on one site, the folks on the other site won't know that. That results in you wasting others valuable time. https://stats.stackexchange.com/questions/517976/randomly-sample-from-two-distributions-but-with-one-value-always-greater-than-th – JimB Apr 02 '21 at 23:00

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