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.
| 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: | Maßtheorie; Quantisierung; Iteriertes Funktionensystem; 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] | |
| open_access (DINI-Set): | open_access |
| Licence (German): |  Standardbedingung laut Einverständniserklärung |
