Considering extreme quantiles is a popular way to understand the tail of a distribution. While they have been extensively studied for univariate distributions, much less has been done for multivariate ones, primarily because there is no universally accepted definition of what a multivariate quantile or a multivariate distribution tail should be. In this paper, we focus on extreme geometric quan...

Simulation results are often limited to mean values, even though this provides very limited information about the analyzed systems’ performance. Quantile analysis provides much deeper insights into the performance of simulation system of interest. A set of quantiles can be used to approximate a cumulative distribution function, providing full information about a given performance characteristic...

Production cycle time is an important performance measure in manufacturing systems, and thus it is of interest to characterize distributional properties, such as quantiles, for informative decision making. This article proposes a non-linear quantile regression model for the relationship between stationary cycle time quantiles and corresponding throughput rates of a manufacturing system. The sta...

This paper introduces a new technique for estimating cycle time quantiles from discrete event simulation models run at a single traffic intensity. The Cornish-Fisher expansion is used as a vehicle for this approximation, and it is shown that for an M/M/1 system and a full factory simulation model, the technique provides accurate results with low variability for the most commonly estimated quant...

A time-varying quantile can be …tted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modi…ed state space signal extraction algorithm. It is shown that such quantiles satisfy the de…ning property of …xed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estima...

VARIANCE-REDUCTION TECHNIQUES FOR ESTIMATING QUANTILES AND VALUE-AT-RISK by Fang Chu Quantiles, as a performance measure, arise in many practical contexts. In finance, quantiles are called values-at-risk (VARs), and they are widely used in the financial industry to measure portfolio risk. When the cumulative distribution function is unknown, the quantile can not be computed exactly and must be ...

In this paper, we are interested in estimating geometric quantiles when data are obtained in a complex survey. Geometric quantiles defined by Chaudhuri (1996) are an extension of univariate quantiles in the multivariate set-up that uses the geometry of multivariate data clouds. A very important application of them is the detection of outliers in multivariate data through quantile contours. This...

Quantiles, especially the medians, of survival times are often used as summary statistics to compare the survival experiences between different groups. Quantiles are robust against outliers and preferred over the mean. Multivariate failure time data often arise in biomedical research. For example, in clinical trials, each patient in the study may experience multiple events which may be of the s...

This paper discusses the implementation of a two-phase procedure to construct confidence intervals for a simulation estimator of the steady-state quantiles of stochastic processes. We compute sample quantiles at certain grid points and use Lagrange interpolation to estimate the p quantile. The algorithm dynamically increases the sample size so that quantile estimates satisfy the proportional pr...

Multiple Imputation (MI) is an established approach for handling missing values. We show that MI for continuous data under the multivariate normal assumption is susceptible to generating implausible values. Our proposed remedy, is to 1) transform the observed data into quantiles of the standard normal distribution, 2) obtain a functional relationship between the observed data and it’s correspon...