Advanced methods for fitting competing models of degree distributions from networks and city size distributions

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Notes for seminar on Advanced Statistics, Sociology Dept, U Geneva. 12:00 June 12, invitation of Eric Widmer.

Dear Eric,

For the seminar next week, "Advanced methods for fitting competing models of degree distributions from networks and city size distributions" the background papers are:

1) Power-law distributions in empirical data, 2007, by Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman. Under review by a statistical journal, listed by lots of google sites as well. The auxiliary package includes R and Matlab software and documentation (Updated 29 June 2007) for this 2007 review article. THIS (1) WOULD BE THE FIRST OF TWO PAPERS FOR SEMINAR MEMBERS TO READ.

It sets the context in which I will talk about fitting another heavy-tailed distribution, the q-expoonential. Examples will include A) the sample of distributions discussed in (1), B) historical changes of city-size distributions, and in C) network distributions in studies of Chinese Rural-Urban migrant networks. THE SECOND PAPER TO READ IS THIS - IT IS SHORTER AND THE FOCUS OF THE TALK BUT WILL NOT BE FULLY UNDERSTOOD WITHOUT (1).

2) q-Exponential Distributions in Empirical Data (c) 2008 Laurent Tambayong, Aaron Clauset, Cosma Shalizi, and Douglas R. White. For this paper there are new (2008-05-19) R codes programmed and submitted to the wiki site by Cosma Shalizi to extend his preliminary package for fitting univariate distributions. The previous package (1) applied only to continuous data.

ABOUT THE NEW R CODE (available on this wiki)

3) Shalizi’s new tsal.R code extended (1) for use with (2) and has been replaced by tsal-v0.2.2.R for q-exponential continuous distributions. The earlier version is decribed in Cosma Shalizi. 2007 Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions. http://www.cscs.umich.edu/~crshalizi/research/tsallis-MLE

4) An additional code for discrete distribution q-exponential MLE fit by Shalizi will be used for extending our results in (2), including network degree distributions

5) In a third paper on the qlog method used by most physicists we show these estimates are not MLE and have biases toward much greater standard errors than the discrete MLE.

6) No claims or guarantees are made for these new routines and we are still testing them but the early results in pareto2_v0.4-2008-05-19 and its extensions look good.

7) We used the first MLE q-exponential fits using method (3) for our longitudinal city size distributions paper which showed historical oscillations over 50 year periods, 900-1970 from Chandler’s data (e.g. for China and Europe). 2008 Oscillatory dynamics of city-size distributions in world historical systems. (drw, L. Tambayong, and N. Kejžar). In, G. Modelski, T. Devezas and W. Thompson, eds. Globalization as Evolutionary Process: Modeling, Simulating, and Forecasting Global Change. pp. 190-225. London: Routledge. http://intersci.ss.uci.edu/wiki/pw/ModelskiCh9WTK.pdf

[edit] Related links

Using the new discrete estimator and producing sampling distribution plots