RECOMMENDATIONS ON THE TESTING AND USE OF PSEUDORANDOM NUMBER GENERATORS USED IN MONTE-CARLO ANALYSIS FOR RISK ASSESSMENT

Monte Carlo simulation requires a pseudo-random number generator with good statistical properties. Linear congruential generators (LCGs) are the most popular and well-studied computer method for generating pseu do-random numbers used in Monte Carlo studies. High quality LCGs are a vailable with sufficient statistical quality to satisfy all but the mo st demanding needs of risk assessors. However, because of the discrete , deterministic nature of LCGs, it is important to evaluate the random ness and uniformity of the specific pseudo-random number subsequences used in important risk assessments. Recommended statistical tests for uniformity and randomness include the Kolmogorov-Smirnov test, extreme values test, and the runs test, including runs above and runs below t he mean tests. Risk assessors should evaluate the stability of their r isk model's output statistics, paying particular attention to instabil ities in the mean and variance. When instabilities in the mean and var iance are observed, more stable statistics, e.g., percentiles, should be reported. Analyses should be repeated using several non-overlapping pseudo-random number subsequences. More simulations than those tradit ionally used are also recommended for each analysis.