Title
The theorem of Fellman and Jakobsson: a new proof and dual theory The theorem of Fellman and Jakobsson: a new proof and dual theory
Author
Faculty/Department
Faculty of Social Sciences. Instructional and Educational Sciences
Publication type
article
Publication
Oxford ,
Subject
Computer. Automation
Source (journal)
Mathematical and computer modelling. - Oxford
Volume/pages
50(2009) :11/12 , p. 1595-1605
ISSN
0895-7177
ISI
000271340200005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The Fellman and Jakobsson theorem of 1976 deals with transformations ö of the rankfrequency function g and with their Lorenz curves L(ög) and L(g). It states (briefly) that L(ög) is monotonous (in terms of the Lorenz dominance order) with . In this paper we present a new, elementary proof of this important result. The main part of the paper is devoted to the dual transformation gø−1, where ø is a transformation acting on source densities (instead of item densities as is the case with the transformation ö). We prove that, if the average number of items per source is changed after application of the transformation ø, we always have that L(gø) and L(g) intersect in an interior point of [0,1], i.e. the theorem of Fellman and Jakobsson is not true for the dual transformation. We also show that this includes all convex and concave transformations. We also show that all linear transformations ø yield the same Lorenz curve. We also indicate the importance of both transformations ö and ø in informetrics.
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