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Title:  Exact probabilistic and mathematical proofs of the relation between the meanmu and the generalized 80/20rule 
Authors:  EGGHE, Leo 
Issue Date:  1993 
Publisher:  JOHN WILEY & SONS INC 
Citation:  JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE, 44(7). p. 369375 
Abstract:  The generalized 80/20rule states that 100 x % of the most productive sources in (for example) a bibliography produce 100 y % of the items and one is interested in the relation between y and x. The following (intuitively clear) property (*) is investigated: suppose we have two bibliographies with average number of items per source mu1, mu2, respectively, such that mu1 < mu2. Then y1 = y2 implies x1 > x2, i.e., in the second bibliography we need a smaller fraction of the most productive sources than in the first one in order to have the same fraction of the items produced by these sources. First, we prove this theorem in a probabilistic way for the geometric distribution and for the Lotka distribution with power alpha > 2. A remarkable result is found, when allowing for zeroitem sources in case of the geometric distribution: the opposite property (*) is found to be true (x1 < x2 instead Of x1 > x2). Then a mathematical proof of property follows for Lotka's function with powers alpha = 0, alpha = 1, alpha = 1.5, alpha = 2, where the problem remains open for the other alpha's. The difference between both approaches lies in the fact that the probabilistic proofs use distributions with arguments until infinity, while the mathematical proofs use exact functions with finite arguments. 
Notes:  UIA,B2610 WILRIJK,BELGIUM.EGGHE, L, LUC,UNIV CAMPUS,B3590 DIEPENBEEK,BELGIUM. 
URI:  http://hdl.handle.net/1942/3671 
DOI:  10.1002/(SICI)10974571(199308)44:7<369::AIDASI1>3.0.CO;2B 
ISI #:  A1993LN64400001 
ISSN:  00028231 
Type:  Journal Contribution 
Appears in Collections:  Research publications

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