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