Wavelet-based detection of scaling behavior in noisy experimental data.

Abstract

The detection of power laws in real data is a demanding task for several reasons. The two most frequently met are that (i) real data possess noise, which affects the power-law tails significantly, and (ii) there is no solid tool for discrimination between a power law, valid in a specific range of scales, and other functional forms like log-normal or stretched exponential distributions. In the present report we demonstrate, employing simulated and real data, that using wavelets it is possible to overcome both of the above-mentioned difficulties and achieve secure detection of a power law and an accurate estimation of the associated exponent.