Fast poisson and binomial algorithms for correlationinduction**This research is partially supported by the Office of Naval Research contract N00014-7942-0832 through Purdue University$ef:

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Abstract
Traditionally, exactness, numerical stability and speed are the three main criteria for evaluating algorithms for random variate generation. However, it is sometimes required that the algorithms provide correlation between generated variates for the purpose of inducing dependence among the output of simulation runs. The inverse transformation, which produces optimal correlation induction, often performs poorly in terms of the first three criteria. Algorithms based on composition, rejection, and special properties which often excel in terms of the first three criteria, tend to scramble the use of random numbers, causing many attempts at common random numbers, antithetic variates and external control variates to fail. The concept of obtaining correlation via algorithms other than the inverse transformation is examined here. To demonstrate feasibility, previously developed algorithms for Poisson and binomial random variate generation are modified to obtain both positive and negative correlation between runs. The modifications slow down the execution by less than fifteen percent, which is still much faster than the inverse transformation. The modified algorithms typically obtain between 50 and 95 percent of the correlation obtained by the inverse transformation. Therefore, the modified algorithms are useful when correlation induction is desirable and when the random variate generation requires a substantial part of the computer time, such as in Monte Carlo distribution-sampling experiments.

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