Egghe L, Rao IKR "Duality revisited: Construction of fractional frequency distributions based on two dual Lotka laws" JASIST 53(10):789-801, Aug. 2002.

[Eugene Garfield]

Leo Egghe - e-mail -  leo.egghe at luc.ac.be

Title    Duality revisited: Construction of fractional frequency
         distributions based on two dual Lotka laws
Author   Egghe L, Rao IKR
Journal  JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND
         TECHNOLOGY 53 (10): 789-801 AUG 2002

 Document type: Article    Language: English
 Cited References: 15      Times Cited: 0


Abstract:
Fractional frequency distributions of, for example, authors with a certain
(fractional) number of papers are very irregular and, therefore, not easy to
model or to explain. This article gives a first attempt to this by assuming
two simple Lotka laws (with exponent 2): one for the number of authors with
n papers (total count here) and one for the number of papers with n authors,
n is an element of N. Based on an earlier made convolution model of Egghe,
interpreted and reworked now for discrete scores, we are able to produce
theoretical fractional frequency distributions with only one parameter,
which are in very close agreement with the practical ones as found in a
large dataset produced earlier by Rao. The article also shows that
(irregular) fractional frequency distributions are a consequence of Lotka's
law, and are not examples of breakdowns of this famous historical law.

KeyWords Plus:
COUNTS, ATTRIBUTION, AUTHORSHIP

Addresses:
Egghe L, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium
Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium
Univ Instelling Antwerp, B-2610 Wilrijk, Belgium
DRTC, ISI, Bangalore, Karnataka, India
LUC, B-3590 Diepenbeek, Belgium

Publisher:
JOHN WILEY & SONS INC, NEW YORK

IDS Number:
578GG

ISSN:
1532-2882


 Cited Author            Cited Work                Volume      Page
Year

 AJIFERUKE I           J AM SOC INFORM SCI           42       279      1991
 BLOM G                PROBABILITY STAT THE                            1989
 BURRELL Q             J AM SOC INFORM SCI           46        97      1995
 CHUNG KL              COURSE PROBABILITY T                            1974
 EGGHE L               ELEMENTARY STAT EFFE                            2001
 EGGHE L               INTRO INFORMETRICS Q                            1990
 EGGHE L               J INFORM SCI                  16        17      1990
 EGGHE L               MATH COMPUT MODEL             18        63      1993
 EGGHE L               SCIENTOMETRICS                53       371      2002
 EGGHE L               SCIENTOMETRICS                48       345      2000
 EGGHE L               THESIS CITY U LONDON                            1989
 LOTKA AJ              J WASHINGTON ACADEMY          16       317      1926
 RAO IKR               P 5 INT C INT SOC SC                   455      1995
 ROUSSEAU R            J AM SOC INFORM SCI           43       645      1992
 ROUSSEAU R            J DOC                         50       134      1994


FROM JASIST....

Duality Revisited Construction of Fractional Frequency Distributions Based
on
         Two Dual Lotka Laws
         L. Egghe and I.K. Ravichandra Rao
         Published online 11 June 2002

         Egghe and Rao are able to present evidence that frequency
distributions of author productivity, where productivity is fractionally
assigned from multiple author papers, are a consequence of Lotka's law
rather than exceptions to it. Occurrences of fractional scores will be
influenced by low frequency of papers with a higher number of authors, and
the higher frequency of papers with a low number of authors, while multiple
combinations of papers with different numbers of authors can produce the
same score. Calculation of the fractional frequency distribution is very
difficult since any positive rational number is a possible frequency and the
shapes of simulated and of empirically derived fractional distributions have
been shown to be quite irregular. By grouping data and allowing for only
 a limited number of fractional scores, an analytical formula is produced
for the probability of each allowed score, which nicely fits the grouped
empirical data.