The Scaling Estimator

Mark E. Crovella and Murad S. Taqqu

A Tool For Estimating the Heavy Tail Index from Scaling Properties

The software available from this page provides an estimation of the tail index alpha for empirical heavy-tailed distributions, such as have been encountered in telecommunication systems. It uses a method (called the ``scaling estimator'') based on the scaling properties of sums of heavy-tailed random variables. It has the advantages of being nonparametric, of being easy to apply, of yielding a single value, and of being relatively accurate on synthetic datasets. Since the method relies on the scaling of sums, it measures a property that is often one of the most important effects of heavy-tailed behavior. Most importantly, the scaling estimator increases in accuracy as the size of the dataset grows, meaning that it is particularly suited for large datasets, as are increasingly encountered in measurements of telecommunications and computing systems.

This software ("aest") is written in C for Unix operating systems. To date it has been tested on SGI systems running IRIX 5.3 and Sun systems running SunOS 5.4. To retrieve the software, click on the link below, save the result to a file (say aest.tar) type "tar xvf aest.tar", then type "make".

In addition to providing an estimate of the tail index, aest can provide graphical output that can help interpret its results. This figure shows an example of the graphical output from aest (Figure 12 from the paper below). The dataset used is a set of files stored on Web servers and the figure shows the LLCD plots of successive aggregations of the dataset, along with the portion of the tail judged by aest to be the region over which power-law scaling is taking place.