ABS: Rousseau,LOTKA: A program to fit a power l aw distribution to observedfrequency data

[Isidro F. Aguillo]

Dear colleagues:

The Lotka and Zipf "laws" has been the subject of discussion for long
time, as many of the informetric distributions. The paper we accepted
for publication is from a well known expert in the field with relevant
contributions on this topic (see informetrics section in
http://linkage.rockefeller.edu/wli/zipf/). Editor contacted several
reviewers prior to publication mainly regarding advice about considering
specialised software distribution as a valid scientific publication. The
answers were diverse about the innovation degree of the paper but
consensus existed about taking advantage of new ways of communication
provided by electronic journals. My personal opinion is that Rousseau´s
article offers original discussion and not only a program to calculate
regressions of power-law distributions. However Cybermetrics will
publish any commentaries about this topic anyone send to the Editor.

> Eric Archambault wrote:
>
> Many users have been using Excel to calculate regressions of
> hyperbolic (power-law) distributions a la Lotka.
>
> This can be performed in either of two ways.
>
> Method 1
>
> 1) Plot the data on a XY (Scatter) graph
> 2) Select the data series on the graph and "Add Trendline..." in the
> "Chart" menu.
> 3) Select "Power" type of regression curve, in the Option Tab, select
> "Display equation on chart" as well as "Display R-squared value on
> chart"
>
> Method 2
>
> 1) Select a two column by five rows area on the spreadsheet where you
> data is
> 2) Type "=Linest(log(Y:Yn);log(X:Xn);1;1)" where Y:Yn is the range of
> the Y-data (frequencies) and X:Xn is the range of the X data (number).
>
> 3) Press simultaneously Ctrl-Shift-Enter to create an array-formula.
> Read Excel's help to interpret the stats. To convert the b of the
> intercept, raise 10 to the power of b to obtain the constant of the
> power law (c=10^b.
>
> The advantage of using these methods based on the least-square fit is
> to obtain the R-Value as well as, in the case of spreadsheet based
> method (Method 2) the F-statistics. The t-test can also be calculated
> from the results of the formula array.
>
> People who are interested can send an email and I'll send them a
> template that calculate regressions from the original Lotka (1926)
> data in both the number-frequency (as in Lotka's paper) and
> rank-frequency (as in the form used by Auerbach long before Zipf)
> forms. The rank-frequency form of Lotka falsify the assertion of Zipf
> that data following Lotka's law (not really a law since it fits only
> his data) would produce a rank-frequency distribution with a power of
> 1.
>
> Cheers
>
> Eric Archambault, Ph. D.
> Associate researcher
> Observatoire des sciences et des technologies
> Institut national de la recherche scientifique
> 3465, rue Durocher
> Montreal, Quebec
> Canada  H2X 2C6
>
> Tel  (1 514) 499-4071
> Fax  (1 514) 499-4065
>
> eric.archambault at inrs-urb.uquebec.ca
>
> -----Original Message-----
> From: Isidro F. Aguillo [mailto:isidro at CINDOC.CSIC.ES]
> Sent: 23 janvier, 2001 14:33
> To: SIGMETRICS at LISTSERV.UTK.EDU
> Subject: [SIGMETRICS] ABS: Rousseau, LOTKA: A program to fit a power
> law
> distribution to observed frequency data
>
> Dear all:
>
> We recently published new papers in the ejournal Cybermetrics,
> including
> a innovative one that includes a software program. It is not usual in
> paper format but it is an important added value of electronic sources.
>
> We will very happy to publish similar contributions.
>
> Authors:
> Brendan Rousseau and Ronald Rousseau (oak at pandora.be)
>
> Title:
> LOTKA: A program to fit a power law distribution to observed frequency
>
> data.
>
> Source:
> Cybermetrics, Vol. 4 (2000). Issue 1. Paper 4
>
> http://www.cindoc.csic.es/cybermetrics/articles/v4i1p4.html
>
> Abstract
> LOTKA, a computer program for fitting a power law distribution such as
>
> Lotka's is presented. It basically follows Nicholl's methodology :
> using
> a maximum likelihood approach to estimate parameters, and a
> Kolmogorov-Smirnov test for goodness-of-fit. When input data are
> converted (from rank-frequency to size-frequency) this program can
> also
> be used to test Zipf's law.
>
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>    Isidro F. AGUILLO                      isidro at cindoc.csic.es
> ------------------------------------------------------------------
>  CINDOC-CSIC                              Tel: +34-91-563.54.82
>  Joaquin Costa, 22                        Móvil: +34-630.858997
>  28002 Madrid. ESPAÑA/SPAIN               Fax: +34-91-564.26.44
>  Editor
>  Cybermetrics, e-Journal (http://www.cindoc.csic.es/cybermetrics)
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   Isidro F. AGUILLO                      isidro at cindoc.csic.es
------------------------------------------------------------------
 CINDOC-CSIC                              Tel: +34-91-563.54.82
 Joaquin Costa, 22                        Móvil: +34-630.858997
 28002 Madrid. ESPAÑA/SPAIN               Fax: +34-91-564.26.44
 Editor
 Cybermetrics, e-Journal (http://www.cindoc.csic.es/cybermetrics)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++