Estimating steady-state distributions via simulation-generated histograms

This paper discusses a unified approach for estimating, via a histogram, the steady-state distribution of a stochastic process observed by simulation. The quasi-independent (QI) procedure increases the simulation run length progressively until a certain number of essentially independent and identically distributed samples are obtained. It is known that order-statistics quantile estimators are asymptotically unbiased when the output sequences satisfy certain conditions. We compute sample quantiles at certain grid points and use Lagrange interpolation to estimate any p quantile. Our quantile estimators satisfy a proportional-precision requirement at the first phase, and a relative- or absolute-precision requirement at the second phase. An experimental performance evaluation demonstrates the validity of using the QI procedure to estimate quantiles and construct a histogram to estimate the steady-state distribution.