The estimation of quantiles is one the most fundamental data mining tasks. As real-time streams vary dynamically over time, there a quest for adaptive quantile estimators. well-known type estimators incremental which documents state-of-the art performance in tracking quantiles. However, absolute vast majority fail to jointly estimate multiple consistent manner without violating monotone propert...

Quantiles of customer based performance characteristics have been adopted in many areas for measuring the quality of service. Recently, sensitivity analysis of quantiles has attracted quite some attention. Sensitivity analysis of quantiles is particularly challenging as quantiles cannot be expressed as the expected value of some sample performance function, and it is therefore not evident how s...

The design quantiles of storms are derived directly in terms of design life and the risk of occurrence. Estimators for these quantiles based on exceedance series are discussed for the cases of Poisson and negative binomial storm arrival processes. The use of Bootstrap methods to estimate confidence intervals for the design quantiles is demonstrated. Interval de confiance "bootstrap" pour les av...

The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous distributions. However, this is no longer true for discrete distributions or sampleswith ties.We show that the definition of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic properties of sample q...

Spatial quantiles, based on the L1 norm in a certain sense, provide an appealing vector extension of univariate quantiles and generate a useful “volume” functional based on spatial “central regions” of increasing size. A plot of this functional as a “spatial scale curve” provides a convenient twodimensional characterization of the spread of a multivariate distribution of any dimension. We discu...