Parameter estimation for power-law distributions by maximum likelihood methods

2007/04/30 by Heiko Bauke, H. Bauke · 4 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Estimation theory #Estimator #Exponent #Graphical model #Likelihood function #Maximum likelihood #Maximum likelihood sequence estimation #Quasi-maximum likelihood #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.other #physics.data-an

paper · pdf · doi:10.1140/epjb/e2007-00219-y

published as The European Physical Journal B, vol. 58, no. 2, pp. 167-173 (2007) · Supplementary software: http://www.physics.ox.ac.uk/users/bauke/Publications/index.html#powerlaws

openalex publication_date 2007/07/01 · arxiv created 2007/08/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Power laws, Pareto distributions and Zipf's law

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• Power law distribution and multi-scale analysis in Earth sciences, finance, and other fields: Some guidelines to parameter estimation
• Tail of the distribution of fatalities in epidemics
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• Power law [wikipedia]

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