Quantile and tolerance-interval estimation in simulation

Abstract

This paper discusses two sequential procedures to construct proportional half-width confidence intervals for a simulation estimator of the steady-state quantile and tolerance intervals for a stationary stochastic process having the (reasonable) property that the autocorrelation of the underlying process approaches zero with increasing lag. At each quantile to be estimated, the marginal cumulative distribution function must be absolutely continuous in some neighborhood of that quantile with a positive, continuous probability density function. These algorithms sequentially increase the simulation run length so that the quantile and tolerance-interval estimates satisfy pre-specified precision requirements. An experimental performance evaluation demonstrates the validity of these procedures.