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

Eric Archambault Eric_Archambault at INRS-URB.UQUEBEC.CA
Wed Jan 24 17:24:48 EST 2001

```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"
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)
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