Quantile and histogram estimation

This paper discusses implementation of a sequential procedure to construct proportional half-width confidence intervals for a simulation estimator of the steady-state quantiles and histograms of a stochastic process. Our quasi-independent (QI) procedure increases the simulation run length progressively until a certain number of essentially independent and identically distributed samples are obtained. We compute sample quantiles at certain grid points and use Lagrange interpolation to estimate the p quantile. It is known that order statistics quantile estimator is asymptotically unbiased when the output sequences satisfy certain conditions. Even though the proposed sequential procedure is a heuristic procedure, it does have strong basis. Our empirical results show that the procedure gives quantile estimates and histograms that satisfy a pre-specified precision requirement. An experimental performance evaluation demonstrates the validity of using the QI procedure to estimate the quantiles and histograms