# Probability distributions

see: Kolmogorov-Smirnov: do two distributions differ?

## 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.

- 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)

## Sample data for cities

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

back to InterSciWiki:Community Portal#Tools

## Links

Power laws compared to other distributions (R programs)

Power laws compared to other distributions (Matlab programs