QRP05-2: Time-Exponentially Weighted Moving Histograms (TEWMH) for Application in Adaptive Systems

The distribution of a stationary point process can be sampled by an ordinary histogram. If the distribution of the process varies over time, a static histogram still yields results that are averaged over time since the beginning of the data collection. In this paper, we propose the time-exponentially weighted moving histogram (TEWMH) to derive an estimate for the time-dependent distribution of an instationary point process. The importance of the samples decays exponentially over time such that young samples contribute more to the empirical distribution than old ones. The strength of the decay can be controlled by a simple parameter which determines the memory of the histogram. We present a simple implementation of the TEWMH such that this mechanism can be well applied in practice. The empirical distribution serves for the derivation of other time-dependent statistical measures such as time-dependent percentiles of the observed random variable. These provide useful feedback in adaptive systems. We illustrate the application of the TEWMH for experience-based admission control (EBAC) and show its benefits.