Incremental quantile estimation

Quantiles play an important role in data analysis. On-line estimation of quantiles for streaming data- i.e.data arriving step by step over time-especially with devices with limited memory and computation capacity like electronic control units is not as simple as incremental or recursive estimation of characteristics like the mean (expected value) or the variance. In this paper, we propose an algorithm for incremental quantile estimation that overcomes restrictions of previously described techniques. We also develop a statistical test for our algorithm to detect changes, so that the on-line estimation of the quantiles can be carried out in an adaptive or evolving manner. Besides a statistical analysis of our algorithm, we also provide experimental results comparing our algorithm with a recursive quantile estimation technique which is restricted to continuous random variables. © Springer-Verlag 2010.