Uncertainty of quantile estimates in the measurement of self-similar processes

Scaling phenomena can be found in a variety of physical situations, ranging from applications in hydrology to communication traffic measurements. This paper focuses on quantiles estimation for a self-similar time series and in particular on the uncertainty that affects their estimates. Quantiles provide in fact additional information about the distribution of the measurements and in certain cases they may be of more interest than the mean or variance. Finally, theoretical results will be applied in the estimation of the scaling exponent of a self-similar time series.