Speeding up lower bound estimation in powerlaw distributions

TL;DR

This paper introduces two new methods to estimate the lower bound in powerlaw distributions more efficiently, significantly improving speed and accuracy over traditional approaches for large datasets.

Contribution

The paper proposes two alternative methods for lower bound estimation in powerlaw distributions that are faster and more accurate than the traditional Kolmogorov-Smirnov based method.

Findings

Proposed methods outperform traditional method in speed.

New methods achieve higher accuracy in large datasets.

Performance tested on datasets with 500,000 elements.

Abstract

The traditional lower bound estimation method for powerlaw distributions based on the Kolmogorov-Smirnov distance proved to perform better than other competing methods. However, if applied to very large collections of data, such a method can be computationally demanding. In this paper, we propose two alternative methods with the aim to reduce the time required by the estimation procedure. We apply the traditional method and the two proposed methods to large collections of data ($N = 500,000$) with varying values of the true lower bound. Both the proposed methods yield a significantly better performance and accuracy than the traditional method.