"The source-item coverage of the Lotka function " by Leo Egghe. SCIENTOMETRICS 61 (1). 2004. p.103-115

Eugene Garfield garfield at CODEX.CIS.UPENN.EDU
Wed Sep 29 12:09:32 EDT 2004

The author, Leo Egghe, has kindly provided a more descriptive
(nonmathematical)abstract of his paper "The source-item coverage of the
Lotka function" (SCIENTOMETRICS 61 (1). 2004. p.103-115).
The abstract, which was inadvertently omitted in the previous posting of the
paper, follows.

"The source-item coverage of the Lotka function"
L. Egghe

The law of Lotka is a decreasing power function describing the production of
sources (e.g. journals, authors, ...), i.e. the items (e.g. articles,
publications, ...) in the sources. Given a concrete situation of a total
number of sources T and a total number of items in these sources A, the
problem is to determine the types of power functions that describe this
situation, i.e. that yield T and A as defined above.

The paper presents necessary and sufficient conditions for this problem both
in the case of finite or infinite item densities. A crucial role is played
(as always) by the exponent of the power function, in the paper denoted by
alpha. As ever, a turning point is alpha = 2.

So the paper completely describes the limitations of the parameter values in
Lotka's law, given an informetric production process (hence given A and T).


Leo Egghe : leo.egghe at luc.ac.be

TITLE:          The source-item coverage of the Lotka function (Article,

AUTHOR:         Egghe, L

SOURCE:         SCIENTOMETRICS 61 (1). 2004. p.103-115 KLUWER ACADEMIC
                PUBL, DORDRECHT

ABSTRACT:       The following problem has never been studied : Given A,
the total number of items (e.g. articles) and T, the total number of
sources (e.g. journals that contain these articles) (hence A>T), when is
there a Lotka function f(j) = D/j(alpha)

that represents this situation (i.e. where to) denotes the density of the
sources in the item-density j)? And, if it exists, what are the formulae
for D and alpha? This problem is solved in both cases with j is an
element of [1, rho]: where (a) rho = infinity and where (b) rho < &INFIN;
. Note that p = the maximum density of the items. If ρ = &INFIN;,
then A and T determine uniquely D and α. If ρ < infinity, then
we have, for every alpha less than or equal to 2, a solution for D and
rho, hence for f. If rho < &INFIN; and α > 2 then we show that a
solution exists if and only if

mu = A/T < α-1/α-2.

This sheds some light on the source-item coverage power of Lotka's law.

AUTHOR ADDRESS: L Egghe, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek,
(IDS: 844RQ 00008)  ISSN: 0138-9130

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