30. MONTE CARLO TECHNIQUES

Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions. 30.1. Sampling the uniform distribution Most Monte Carlo sampling or integration techniques assume a “random number generator ” which generates uniform statistically independent values on the half open interval [0,1). Although such a generator is, strictly speaking, impossible on a finite digital computer, generators are nevertheless available which pass extensive batteries of tests for statistical independence and which have periods which are so long that, for practical purposes, values from these generators can be considered to be uniform and statistically independent. In particular, the lagged-Fibonacci based generator introduced by Marsaglia, Zaman, and Tsang [1] is efficient, has a period of approximately 10 43, produces identical sequences on a wide variety of computers and, passes the extensiv