Quantile estimation: A minimalist approach

Managing telecommunication networks involves collecting and analyzing large amounts of statistical data. The standard approach to estimating quantiles involves capturing all the relevant data (what may require significant storage/processing capacities), and performing an off-line analysis (what may delay management actions). It is often essential to estimate quantiles as the data are collected, and to take management actions promptly. Towards this goal, we present a minimalist approach to sequentially estimating constant/changing over time quantiles. We follow prior work and devise a fixed-point algorithm, which does not estimate the unknown probability density function at the quantile. Instead, our algorithm uses the log-odds transformation of the observed fractions, and the exponentially smoothed estimates of the standard deviation to update the quantile estimate. For large data streams, this algorithm can significantly reduce the amount of collected data and the complexity of data analysis.