Structuring Tchebycheff-Type Inequalities – A Systematical Approach / Systematisierung tschebyscheffartiger Ungleichungen – Ein Überblick

Strotmann Harald ()
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Strotmann Harald: Universität Hohenheim, Institut für Volkswirtschaftslehre (520B), Lehrstuhl für Statistik und Ökonometrie, D-70593 Stuttgart, Germany

Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), 1999, vol. 219, issue 3-4, 468-493

Abstract: Though there is a huge variety of different Tchebycheff-type inequalities in the literature a systematised structuring is missing. The few existing surveys remain rather enumerative. Therefore in this paper a structuring of Tchebycheff-type inequalities is suggested which is based on three complementary criteria, with the type of the available information serving as the main criterion. This structuring is used as a basis for a review on important Tchebycheff-type inequalities, some of which are almost forgotten in the literature. A special emphasis is met on the various relationships between different Tchebycheff-type inequalities, with some figures illustrating the results.

Keywords: Bienayme-Tchebycheff inequality; Markoff inequality; Tchebycheff-type inequality; probability; distribution-free probability bounds; criteria for structuring Tchebycheff-type inequalities; Gini’s mean difference; unimodality; symmetry; Bienayme-Tschebyscheff-Ungleichung; Markoff-Ungleichung; Wahrscheinlichkeiten; Verteilungsfreie Wahrscheinlichkeitsabschätzung; Strukturierung tschebyscheffartiger Ungleichungen; Mittlere Differenz von Gini; Unimodalität; Symmetrie; Bienayme-Tchebycheff inequality; Markoff inequality; Tchebycheff-type inequality; probability; distribution-free probability bounds; criteria for structuring Tchebycheff-type inequalities; Gini’s mean difference; unimodality; symmetry (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:jns:jbstat:v:219:y:1999:i:3-4:p:468-493:n:1015

DOI: 10.1515/jbnst-1999-3-430

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