The method of sequential systematic sampling in digital simulation

Abstract

This dissertation presents a methodology for the statistical analysis of simulation output data. The analysis deals with the predictability of statistical inferential procedures for means and variances when the data are realizations of correlated and nonnormally distributed random variables. The purpose of the methodology is to improve the predictability of an inferential procedure with respect to the level of confidence in confidence interval analysis, or the power function in hypothesis testing.

Conventional methods of statistical analysis for means lead to poor performance in their predictability if the sample observations are subject to strong autocorrelation. In addition, the predictability problem with respect to inferential procedures for variances is compounded by violation of the normality assumption.

The methodology presented in this dissertation sets forth a sampling procedure to collect sequences of essentially uncorrelated observations. With these observations at hand, the statistical formulation presented leads to an estimator of the variance of the sample mean, thus yielding inferential procedures for means through the classical techniques. The formulation also leads to an estimator of the variance of the population and inferential procedures for variances are developed with an improved property of robustness. The bias in each estimator is greatly reduced due to the sampling procedure employed. Finally the research includes an algorithm for testing the lag correlation such that the sampling procedure can be actually implemented.

The methods for means and variances developed in this research have been compared with corresponding conventional procedures. The comparison is based upon the predictability of the inferential procedure applied to the sample observations generated from autoregressive, simple moving average and M/M/1 queueing models. From the computational and simulation results reported in this research, the methods for means and variances suggested by this research have led to an improvement in the predictability of the analysis.