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Having multiple streams of pseudo-random numbers known to be independent and with a uniform distribution I want to do Monte Carlo simulations in parallel.

In other words, one thread will have a full-period independent and uniformly distributed stream of pseudo-random numbers. Each thread will consume these numbers in four different functions (a,b,c,d).

My concern is about the distribution across threads for each function. Thread.1 func_a.1, thread.2 func_a.2... and so on. Do I still need to make sure this distribution is indeed uniform across func_a1, func_a2, etc? Failing to do so can make my simulation have flaws?

In summary,if I start using the pseudo-random numbers in a "random" fashion, rejection sampling. Can I still be sure of the uniform distribution among the different parts?

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with a uniform distribution

uniformly distributed stream

distribution is indeed uniform

still be sure of the normal distribution

You seem to be using "independent", "uniform", and "normal" interchangeably, but in statistics these each have different technical meanings. The one that is probably of the most concern in your situation is "independent".

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  • $\begingroup$ I think the key issue relating to independence is if separate random number streams are independent with respect to each other. In creating multiple streams, one may need to take care exactly how they're created to guarantee inter-stream independence. I believe that this is often accomplished via jump functions used to create substreams. In Matlab at least, the documentation points out that "new streams are not necessarily independent from streams created at other times" (more details in my answer here). In practice, I've no idea, however. $\endgroup$ – horchler Nov 15 '13 at 23:52
  • $\begingroup$ The normal at the end was a typo error. The distribution is uniform. Independent from stream to stream. $\endgroup$ – mrei Nov 18 '13 at 18:24

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