Overview

This project provides implementations of the plfit and plpva functions, which are essential tools for fitting power-law distributions to empirical data. Power-law distributions are significant in various fields, including physics, biology, economics, and social sciences, due to their ability to describe a wide range of natural and man-made phenomena. Understanding and accurately fitting these distributions allows researchers to better model complex systems and predict future events based on observed data.

The plfit function is designed to fit a power-law distribution to a given data set using maximum likelihood estimation (MLE). This method is known for providing robust parameter estimates, particularly in the presence of large fluctuations in the tail of the distribution, which are characteristic of power-law behaviors. The function determines the scaling parameter alpha and the lower bound xmin​, above which the power-law behavior holds. This is crucial for accurately characterizing the distribution and ensuring the reliability of the model.

The plpva function complements plfit by performing a statistical test to assess the goodness-of-fit of the power-law model. Using a p-value derived from the Kolmogorov–Smirnov (KS) statistic and likelihood ratios, plpva quantifies how well the power-law distribution matches the empirical data compared to synthetic datasets generated from the fitted model. This allows researchers to determine the plausibility of the power-law hypothesis and rule out alternative distributions.

This project builds upon the methodologies presented in the research paper Power-Law Distributions in Empirical Data by Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman (2009). The paper provides a principled statistical framework for detecting and quantifying power-law behavior in empirical data, combining MLE with goodness-of-fit tests. Our MATLAB implementation closely follows the algorithms and statistical techniques discussed in the paper, ensuring accurate and reliable power-law fits.

The MATLAB code for this project has been further developed based on the work presented in another notable research titled Molecular motors robustly drive active gels to a critically connected state. This research used the power-law fit MATLAB code to produce significant figures, demonstrating the practical application of these functions in cutting-edge scientific studies. This project aims to document and expand upon this code, providing detailed explanations and enhanced usability for researchers and analysts.

By documenting and explaining the power-law fitting process in detail, this project serves as a comprehensive resource for those looking to understand and apply power-law models to their data. Whether for academic research, data analysis, or practical applications, the tools provided here offer robust solutions for fitting and validating power-law distributions.

To learn more about this project, visit its Github repository at Power-Law Fit Distribution using MATLAB. You will be able to find relevant literature, code, and a scientific (mathematical and statistical) background overview of the subject of matter and how the code functions.