Optimal quantization of probabilities concentrated on small balls

  • We consider probability distributions which are uniformly distributed on a disjoint union of balls with equal radius. For small enough radius the optimal quantization error is calculated explicitly in terms of the ball centroids. We apply the results to special self-similar measures.

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Metadaten
Author:Wolfgang Kreitmeier
URN:urn:nbn:de:bvb:739-opus-12010
Document Type:Preprint
Language:English
Year of Completion:2007
Date of Publication (online):2008/06/18
Publishing Institution:Universität Passau
Release Date:2008/06/18
Tag:centroid; optimal quantization; self-similar probabilities
GND Keyword:Iteriertes Funktionensystem; Maßtheorie; Quantisierung; Schwerpunkt
Source:This is a preprint of an article accepted for publication in Forum Mathematicum, ISSN (Print) 0933-7741, ISSN (Online) 1435-5337 Copyright (c) by de Gruyter. http://www.degruyter.de/journals/forum/detailEn.cfm. The digital object identifier (DOI) of the definitive article is 10.1515/FORUM.2010.017
Institutes:Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx]
62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10]
Licence (German):License LogoStandardbedingung laut Einverständniserklärung

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