Probability distributions

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see: Kolmogorov-Smirnov: do two distributions differ?

Review Articles

Probability Distributions in Complex Systems D. Sornette http://arxiv.org/abs/0707.2194 Review article: Encyclopedia of Complexity and System Science forthcoming 2009.

Types of Distributions

(Wikipedia) [List of probability distributions]

R programs for Pareto I and II

The Pareto I is the power-law distribution and Pareto II is the Tsallis q-exponential distribution.

2007 Cosma Shalizi. Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions. http://www.cscs.umich.edu/~crshalizi/research/tsallis-MLE These are classically known as Pareto II distributions (Examples). For a standard book on Pareto II see Extreme Value Distributions: Theory and Applications 2001 Samuel Kotz and Saralees Nadarajah. (See: Wikipedia:Variational inequality theory.

Ms. in preparation (CRS Website) Cosma R. Shalizi, Laurent Tambayong, Aaron Clauset and Douglas R. White, "Consistent Estimators of q-Exponential Distributions"
Ms. in preparation (CRS Website) Laurent Tambayong, Aaron Clauset, Cosma R. Shalizi, and Douglas R. White, "q-Exponential Distributions in Empirical Data"
Kausik Gangopadhyay and B. Basu. 2009. City size distributions for India and China. Physica A: Statistical Mechanics and its Applications 388(13):2682-2688. physa.2009.03.019

http://intersci.ss.uci.edu/wiki/drwData/Pareto/pareto.R (copyright Cosma Shalizi, now for distribution along with Matlab software of Aaron Clauset)

Power laws, Pareto distributions and Zipf's law, M. E. J. Newman, Contemporary Physics 46, 323–351 (2005)

Sample data for cities

http://intersci.ss.uci.edu/wiki/drwData/ChandlerDataSortByCity.xls Chandler city size data in Excel

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Links

Power laws compared to other distributions (R programs)

Power laws compared to other distributions (Matlab programs

Tsallis q distribution project

Tsallis q historical cities and city-sizes