Random Number Generation and Quasi‐ M onte C arlo
Pierre L’Ecuyer · Wiley StatsRef: Statistics Reference Online · 2015
Abstract Probability theory defines random variables and stochastic processes in terms of probability spaces, an abstract notion whose concrete and exact realization on a computer is far from obvious. (Pseudo) random number generator s ( RNG s) implemented on computers are actually deterministic programs that imitate, to some extent, independent random variables uniformly distributed over the interval (i.i.d. , for short). RNGs are a key ingredient for Monte Carlo simulations, probabilistic algorithms, computer games, cryptography, casino machines, and so on. In this article, we outline the main principles underlying the design and testing of RNGs for statistical computing and simulation. Then, we indicate how random numbers can be transformed to generate random variates from other distributions. Finally, we summarize the main ideas on quasi‐random points, which are more evenly distributed than independent random point and permit one to estimate integrals more accurately for the same number of function evaluations.