| Quantiles are convenient indices to describe simulation output data and are more practical than the mean and standard deviation in many applications. However, quantiles are very seldom used in practice. So far, the reason has been that quantile estimation is regarded as a cumbersome task, but the advancement of computer technology has alleviated some of the computational issues.; Simulated estimates of tolerance intervals can be computed using standard nonparametric estimators of quantiles based on order statistics, which can be used not only when the data are independent and identically distributed, but also when the data are drawn from a stationary, &phis;-mixing process of continuous random variables. However, when the random variables are highly positively correlated, the sample sizes needed for estimating extreme quantiles become computationally unmanageable.; This dissertation gives two practical schemes that reduce the number of observations needed to be stored and sorted. We propose two methods for determining the length of a simulation run so that the estimated quantiles and tolerance intervals satisfy a pre-specified precision requirement.; The empirical portion of the research employs the ideas of classical statistical experimental design in a controlled simulation study of the finite sampling properties and techniques for developing quantile and tolerance-interval estimators of discrete event simulation output data. The focus is on the analysis of AR(1), MA(1), and queuing simulation output, but the results have applicability to all disciplines in which the estimation of the quantile and tolerance interval of a stationary stochastic process are of interest. |
