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

Isidro F. Aguillo isidro at CINDOC.CSIC.ES
Fri Jan 26 07:26:30 EST 2001

```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
specialised software distribution as a valid scientific publication. The
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

> 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
> 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
>
> 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