Is there a point at which the statistical properties of the random number generator will start to influence the results of Monte Carlo simulation?
I have a scenario where I need to calculate the distribution functions of the $i^{th}$ order statistic with non-identically distributed random variables. They all follow the exponential distribution, but they have different rate parameters. Rather than trying to compute these probabilities analytically, I think it would be better to approximate them through simulation. Eventually the goal is to maximize an expected value for a certain set of parameters. I will be doing this through some numerical optimization approximation method. This could potentially result in hundreds of iterations each with a thousand or so random variables to approximate the probabilities.
Should I be concerned that the entropy generated through standard language libraries (like python's numpy.random which uses the Mersenne Twister PRG) is not enough for the quantity of random variables I may need to sample? More generally, at what point might it make sense to call the operating system's /dev/random or /dev/urandom for random number generation?
