Burrell, QL (Burrell, Quentin L.) Extending Lotkaian informetrics INFORMATION PROCESSING & MANAGEMENT, 44 (5): 1794-1807 SEP 2008

[Eugene Garfield]

E-mail Address: q.burrell at ibs.ac.im 

Author(s): Burrell, QL (Burrell, Quentin L.)
 
Title: Extending Lotkaian informetrics 

Source: INFORMATION PROCESSING & MANAGEMENT, 44 (5): 1794-1807 SEP 2008 

Language: English 

Document Type: Article 

Author Keywords: Lotkaian informetrics; Pareto type II distribution; 
statistical estimation methods; concentration measures 

Keywords Plus: SCIENTOMETRIC MEASUREMENT; EGGHES CONSTRUCTION; LORENZ 
CURVES; GINI INDEX; LAW; DISTRIBUTIONS; AMBIGUITY 

Abstract: The continuous version of the Lotka distribution, more generally 
referred to outside of informetrics as the Pareto distribution, has long 
enjoyed a central position in the theoretical development of informetrics 
despite several reported drawbacks in modelling empirical data 
distributions, most particularly that the inverse power form seems mainly 
to be evident only in the upper tails. We give a number of published 
examples graphically illustrating this shortcoming. In seeking to overcome 
this, we here draw attention to an intuitively reasonable generalization 
of the Pareto distribution, namely the Pareto type II distribution, of 
which we consider two versions. We describe its basic properties and some 
statistical features together with concentration aspects and argue that, 
at least in qualitative terms, it is better able to describe many observed 
informetric phenomena over the full range of the distribution. Suggestions 
for further investigations, including truncated and time-dependent 
versions, are also given. (c) 2008 Elsevier Ltd. All rights reserved. 

Addresses: Nunnery, Isle Man Int Business Sch, Douglas IM2 1QB, Isle Of 
Man, England 

Reprint Address: Burrell, QL, Nunnery, Isle Man Int Business Sch, Old 
Castletown Rd, Douglas IM2 1QB, Isle Of Man, England. 

E-mail Address: q.burrell at ibs.ac.im 

Cited Reference Count: 60 

Times Cited: 0 

Publisher: PERGAMON-ELSEVIER SCIENCE LTD 

Publisher Address: THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 
1GB, ENGLAND 

ISSN: 0306-4573 

DOI: 10.1016/j.ipm.2008.03.002 

29-char Source Abbrev.: INFORM PROCESS MANAGE 

ISO Source Abbrev.: Inf. Process. Manage. 

Source Item Page Count: 14 

Subject Category: Computer Science, Information Systems; Information 
Science & Library Science 

ISI Document Delivery No.: 342UA 

ARNOLD BC
ENCY STAT SCI : 568 1985 

ARNOLD BC
INT STUDIES EC 10 : 1977 

ATKINSON AB
MEASUREMENT OF INEQUALITY
JOURNAL OF ECONOMIC THEORY 2 : 244 1970 

BAIN LJ
INTRO PROBABILITY MA : 1992 

BOOKSTEIN A
Implications of ambiguity for scientometric measurement 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
52 : 74 2001
 
BOOKSTEIN A
Informetric distributions .3. Ambiguity and randomness 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 48 : 2 1997 

BOOKSTEIN A
INFORMETRIC DISTRIBUTIONS .1. UNIFIED OVERVIEW 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 41 : 368 1990 

BOOKSTEIN A
INFORMETRIC DISTRIBUTIONS .2. RESILIENCE TO AMBIGUITY 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 41 : 376 1990 

BOYACK K
P ISSI 2007 CSIC MAD 1 : 124 2007 

BURRELL QL
Symmetry and other transformation features of Lorenz/Leimkuhler 
representations of informetric data 
INFORMATION PROCESSING & MANAGEMENT 41 : 1317 DOI 
10.1016/j.ipm.2005.03.016 2005 

BURRELL QL
THE GINI INDEX AND THE LEIMKUHLER CURVE FOR BIBLIOMETRIC PROCESSES 
INFORMATION PROCESSING & MANAGEMENT 28 : 19 1992 

BURRELL QL
Egghe's construction of Lorenz curves resolved 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
58 : 2157 DOI 10.1002/asi.20674 2007 

BURRELL QL
On Egghe's version of continuous concentration theory 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
57 : 1406 DOI 10.1002/asi.20402 2006
 
BURRELL QL
"Ambiguity" and scientometric measurement: A dissenting view 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
52 : 1075 2001 

BURRELL QL
P ISSI 10 1 : 129 2005 

BURRELL QL
Measuring concentration within and co-concentration between informetric 
distributions: An empirical study 
SCIENTOMETRICS 68 : 441 DOI 10.1007/s11192-006-0122-0 2006 

BURRELL QL
Modelling citation age data: Simple graphical methods from reliability 
theory 
SCIENTOMETRICS 55 : 273 2002 

BURRELL QL
THE BRADFORD DISTRIBUTION AND THE GINI INDEX 
SCIENTOMETRICS 21 : 181 1991 

COHEN AC
PARAMETRIC ESTIMATIO : 1988 

CORVELLA ME
PRACTICAL GUIDE HEAV : 3 1998 

COTHEY V
P ISSI 2005 10 INT C 1 : 212 2005 

DEGROOT MH
PROBABILITY STAT : 1986 

DORFMAN R
FORMULA FOR THE GINI COEFFICIENT
REVIEW OF ECONOMICS AND STATISTICS 61 : 146 1979 

EGGHE L
INTRO INFORMETRICS Q : 1990 

EGGHE L
Zipfian and Lotkaian continuous concentration theory 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
56 : 935 DOI 10.1002/asi.20186 2005 

EGGHE L
POWER LAWS INFORM PR : 2005 

GASTWIRTH JL
GENERAL DEFINITION OF LORENTZ CURVE
ECONOMETRICA 39 : 1037 1971 

GOLDBERG G
PARETO LAW PYRAMID D : 1967 

HARRIS CM
PARETO DISTRIBUTION AS A QUEUE SERVICE DISCIPLINE
OPERATIONS RESEARCH 16 : 307 1968 

JOHNSON NL
CONTINUOUS UNIVARIAT 1 : 1994 

KLEIBER C
STAT SIZE DISTRIBUTI : 2003 

LAFOUGE T
The source-item coverage of the exponential function 
JOURNAL OF INFORMETRICS 1 : 59 2007 

LAMBERT PJ
DISTRIBUTION REDISTR : 2001 

LAVALETTE D
U350 INSERM I CUR RE : 1996 

LETA J
P ISSI 2007 11 INT C 1 : 480 2007 

LOMAX KS
BUSINESS FAILURES - ANOTHER EXAMPLE OF THE ANALYSIS OF FAILURE DATA
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 49 : 847 1954 

LORENZ MO
Methods of measuring the concentration of wealth.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 9 : 209 1905 

LOTKA AJ
J WASHINGTON ACADEMY 16 : 317 1926 

MAGUIRE BA
THE TIME INTERVALS BETWEEN INDUSTRIAL ACCIDENTS
BIOMETRIKA 39 : 168 1952 

NICHOLLS PT
EMPIRICAL VALIDATION OF LOTKA LAW 
INFORMATION PROCESSING & MANAGEMENT 22 : 417 1986
 
NICHOLLS PT
BIBLIOMETRIC MODELING PROCESSES AND THE EMPIRICAL VALIDITY OF LOTKA LAW 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 40 : 379 1989 

NICHOLLS PT
ESTIMATION OF ZIPF PARAMETERS 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 38 : 443 1987 

PAO ML
LOTKA LAW - A TESTING PROCEDURE 
INFORMATION PROCESSING & MANAGEMENT 21 : 305 1985 

PAO ML
AN EMPIRICAL-EXAMINATION OF LOTTKA LAW 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE 37 : 26 1986 

PARETO V
COURS EC POLITIQUE : 1897 

PARETO V
RIV POLITICA EC 87 : 647 1997 

PARETO V
RIV POLITICA EC 87 : 691 1997 

POPESCU II
LAVALETTES NONLINEAR : 2002 

POPESCU II
ROM REP PHYS 49 : 3 1997 

PRIME C
P 8 INT C SCI INF 2 : 529 2001 

ROUSSEAU B
CYBERMETRICS 4 : 2000 

ROUSSEAU R
On Egghe's construction of Lorenz curves 
JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY 
58 : 1551 DOI 10.1002/asi.20615 2007 

ROUSSEAU R
A TABLE FOR ESTIMATING THE EXPONENT IN LOTKA LAW 
JOURNAL OF DOCUMENTATION 49 : 409 1993 

SINGH SK
ASA P BUS EC STAT SE : 551 1975 

SINGH SK
FUNCTION FOR SIZE DISTRIBUTION OF INCOMES
ECONOMETRICA 44 : 963 1976 

VANRAAN AFJ
Reference-based publication networks with episodic memories 
SCIENTOMETRICS 63 : 549 DOI 10.1007/s11192-005-0227-x 2005 

VINCI F
GIORNALE EC RIV STAT 61 : 365 1921 

VOSS J
P ISSI 2005 10 INT C 1 : 221 2005 

YITZHAKI S
RES EC INEQ 8 : 13 1998 

ZIPF G
HUMAN BEHAV PRINCIPL : 1949