# Wavelet based detection of scaling behaviour in noisy experimental data

## TL;DR

This paper demonstrates that wavelet analysis can effectively detect power-law behavior in noisy experimental data and accurately estimate the exponent, overcoming common challenges posed by noise and alternative distributions.

## Contribution

It introduces a wavelet-based method for reliable detection and characterization of power-laws in noisy data, addressing key limitations of existing techniques.

## Key findings

- Wavelet analysis successfully detects power-laws in noisy data.
- The method accurately estimates the power-law exponent.
- It distinguishes power-laws from other distributions like log-normal.

## Abstract

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.