Monte Carlo Simulation for Perusal and Practice / Gordon P. Brooks, Robert S. Barcikowski and Randall R. Robey.

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are observed in many samples drawn from that known population. The statistic's sampling distribution is then estimated by the relative frequency distribution actually observed in the study. The many samples are usually generated artificially through the use of computer algorithms. This paper discusses how one chooses a pseudo-random number generator, and then discusses how to use these generators to simulate data from normal and multivariate normal distributions. Several examples are provided of how one might sample from a pseudo population and the statistics that are commonly calculated during a Monte Carlo investigation. The many trials that might be used when investigating Type I and Type II errors are outlined. The paper ends with a discussion of the processes that might be used to verify that a researcher's simulation process is doing what it was intended to do. Four appendixes contain Statistical Analysis System programming code examples and a FORTRAN code example for generating data. (Contains 1 table and 38 references.) (SLD)

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