QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: outrunQuoteOriginally posted by: quartzQuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaBut if you want samples drawn from NORMINV(f(rng)) to have the same moments as a regular normal distribution, then you'll need something a bit different. In fact, I suspect you will need a non-linear transform to get the 2nd the 4th moment to behave.that exactly what I was thinking!Nobody is talking about this choice.. Maybe because with 32 or 64 bit resolution this doesn't matter much (assuming you have at least the mean set at 0.5)You raised a good point!And we should still care about it for QMC, where (e.g. in a large CreditVaR, but in general anyway) we might want to use just a few thousand samples per instrument. so sampling virtually only the most significant bits!Indeed,.. or just grid integration for low dimensional problems. For uniform distributions on [0,1], and N samples, we can see if we can define the mapping to [0,1] based on Simpson's, or Trapezoid etc Uniform grids or low discrepancy uniform sampling might miss or underrepresent the "most significant bits" of the system. That is, it might miss the bits in the tail where the pay-off function takes on extreme values.I think that a general issue, also for random sampling (except that you can't catch them on anything). I would say it depend of the ratio of probabilty decay vs payoff growth.Isn't this an orthogonal discussion that call for importance sampling and the likes?Whether this is orthogonal to the "Parallel RNG and distributed MC" discussion depends on how we decompose the system. If we view the job of the RNG and MC system to generate nice uniform samples and paths and relegate adjustment/weighting of the population of MC results in the pay-off's tails to some post process, then, yes, it's orthogonal. But if we want an RNG and MC process that samples in an application-specific, tail-dependent way to intelligently sample a nonlinear pay-off function, then this discussion is germane.For simplicity sake in version 1.0, I'd probably create a simple uniform sampler and defer weighting/tweaking of the MC results for later versions.