Wavelet based detection of scaling behaviour in noisy experimental data

The detection of power-laws in real data is a demanding task for several reasons. The two, more frequently met, being: (i) real data possess noise which affects significantly the power-law tails and (ii) there is no solid tool for the discrimination between a power-law, valid in a specific range of scales, from 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 a secure detection of a power-law and an accurate estimation of the associated exponent.