Random Numbers and Generation

Random Numbers and Generation

Random numbers drive simulation. We use PRNGs since true randomness is computationally difficult.

Good PRNGs

Uniform on [0,1], long period, pass statistical tests, reproducible, efficient.

LCG

X(n+1) = (aX(n) + c) mod m. Period at most m. Parameter selection is critical.

Other Generators

Multiplicative congruential, combined generators, Mersenne Twister (period 2^19937-1), PCG, xorshift.

Tests for Randomness

Chi-square, Kolmogorov-Smirnov, runs test, autocorrelation test.

Variate Generation

Inverse transform, acceptance-rejection, composition, Box-Muller for normal distribution.

Summary

Random number generation underpins all stochastic simulation.