# Parameter estimation for power-law distributions by maximum likelihood methods

@article{Bauke2007ParameterEF, title={Parameter estimation for power-law distributions by maximum likelihood methods}, author={Heiko Bauke}, journal={The European Physical Journal B}, year={2007}, volume={58}, pages={167-173} }

Abstract.Distributions following a power-law are an ubiquitous phenomenon. Methods
for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods.

## 167 Citations

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A more computationally efficient method of approximate Bayesian computation is described that estimates Zipf exponents for large datasets without bias.

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An empirical study illustrates that the maximum likelihood estimator outperforms traditional Fourier transform based estimators, and achieves the Cramér-Rao bound.

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This work proposes a principled statistical framework for discerning and quantifying power-law behavior in empirical data by combining maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios.

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This paper presents a novel maximum likelihood estimation approach that exploits the friendship paradox to sample more efficiently from the tail of the degree distribution and results in a smaller bias, variance and a Cramer-Rao lower bound compared to the maximum-likelihood estimate obtained with uniformly sampled nodes.

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Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to ﬁrst…

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- 2017

This work first derives the appropriate ML estimator for arbitrary exponents of power-law distributions on bounded discrete sample spaces, and shows that an almost identical estimator also works perfectly for continuous data.

Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated.

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- 2014

An alternative series of maximum likelihood estimators for discrete, continuous, bounded, and censored data are developed and it is shown that these estimators lead to accurate evaluations of power-law distributions, improving on common approaches.

Penalized KS method to fit data sets with power law distribution over a bounded subinterval

- Mathematics, Computer Science
- 2021

It is shown through simulation studies that an adaptively penalized Kolmogorov-Smirnov (apKS) method improves the estimation of the power law interval on random samples from various theoretical probability distributions.

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