I'm implementing a Monte Carlo simulation in 3 variables in Excel. I've used the RAND() function to sample from Weibull distributions (with long tails). The functions applied to the samples are non-linear but smooth (exp, ln, cos, etc). The result for each sample is a pass/fail, and the overall result is a probability of failure.
I have also implemented this by both numerical integration and Monte Carlo in MathCad, getting the same result both times. MathCad uses (I think) a Mersenne Twister random number generator.
My excel spreadsheet is getting consistently different results (ie always larger). I have checked the equations are the same.
What random number generator does Excel use, and how good is it? Is it possible that this is the source of my problem? I have assumed the Excel implementations of exp, cos etc are ok.
Finally, is there a way to implement Monte Carlo to mitigate against the (known) poor properties of a particular random number generator? (I've heard of Markov chains, random walks etc, but don't really know much about them)
Many thanks.