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 pp 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.