Power-Law Distributions in Empirical Data

@article{Clauset2007PowerLawDI,
  title={Power-Law Distributions in Empirical Data},
  author={Aaron Clauset and Cosma Rohilla Shalizi and Mark E. J. Newman},
  journal={SIAM Rev.},
  year={2007},
  volume={51},
  pages={661-703}
}
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing… 

Tunable robustness in power-law inference

Power-law probability distributions arise often in the social and natural sciences. Statistics have been developed for estimating the exponent parameter as well as gauging goodness-of-fit to a power

Universality of power-law exponents by means of maximum-likelihood estimation.

By means of the procedure proposed in this manuscript, it is found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent, whereas Vycorlabquakes exhibit a significantly different exponent.

A practical recipe to fit discrete power-law distributions

Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even

On estimating the exponent of power-law frequency distributions.

More sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation are discussed, demonstrating their superior performance at estimating known exponents and providing details on how and when ecologists should use them.

Power-law distributions in geoscience revisited

The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can

Power Law Size Distributions in Geoscience Revisited

The size or energy of diverse structures or phenomena in geoscience appears to follow power law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can

From the power law to extreme value mixture distributions

Two extreme value mixture distributions are proposed, in one of which the power law is incorporated, without the need of pre-specifying the threshold, and the proposed distributions are shown to fit the data well, quantify the threshold uncertainty in a natural way, and satisfactorily answer whether the powerLaw is useful enough.

Discovery of Power-Laws in Chemical Space

Several examples of power-law distributions arising from the features of small, organic molecules are presented, showing how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases.

Underestimating extreme events in power-law behavior due to machine-dependent cutoffs.

  • F. Radicchi
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2014
The findings indicate possible reinterpretations of numerical results obtained through flawed sampling methodologies and pave the way for the search for a concrete solution to this central issue shared by all quantitative sciences dealing with complexity.

Bayesian inference of power law distributions

A Bayesian inference approach is developed, with Markov chain Monte Carlo sampling, to accurately estimate power law exponents, the number of mixtures, and their weights, for both discrete and continuous data.
...

References

SHOWING 1-10 OF 119 REFERENCES

Problems with fitting to the power-law distribution

Abstract.This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and

Power laws, Pareto distributions and Zipf's law

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the

A Brief History of Generative Models for Power Law and Lognormal Distributions

A rich and long history is found of how lognormal distributions have arisen as a possible alternative to power law distributions across many fields, focusing on underlying generative models that lead to these distributions.

Empirical distributions of stock returns: between the stretched exponential and the power law?

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. We develop a battery of

Estimating Heavy-Tail Exponents Through Max Self–Similarity

In this paper, a novel approach to the problem of estimating the heavy-tail exponent α >; 0 of a distribution is proposed. It is based on the fact that block-maxima of size m scale at a rate m1/α for

A practical guide to heavy tails: statistical techniques and applications

Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al

Parameter estimation for power-law distributions by maximum likelihood methods

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

Dynamics of Bayesian Updating with Dependent Data and Misspecified Models

This work establishes sufficient conditions for posterior convergence when all hypotheses are wrong, and the data have complex dependencies, and derives a kind of large deviations principle for the posterior measure, extending in some cases to rates of convergence, and discusses the advantages of predicting using a combination of models known to be wrong.

Are citations of scientific papers a case of nonextensivity?

Abstract:The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner (Eur. Phys. J. B 4, 131 (1998)). To fit the data, a

The Minimum Description Length Principle

This extensive, step-by-step introduction to the MDL Principle provides a comprehensive reference that is accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.
...