The Quantization of the Cantor Distribution
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Auteurs : S. Graf ; H. LuschgySource :
- Mathematische Nachrichten [ 0025-584X ] ; 1997.
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Abstract
For a real‐valued random variable whose distribution is the classical Cantor probability, the n ‐ quantization error and the n ‐ optimal quantization rules are calculated for every natural number n. Moreover, the connection between the rate of convergence of the logarithms of the quantization errors for n going to infinity and the Hausdorff dimension of the Cantor set is indicated.
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DOI: 10.1002/mana.19971830108
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Theory</title></host><title>Multidimensional Asymptotic Quantization with r‐th Power Distortion Measures</title></json:item><json:item><host><author></author><title>Foundations of Quantization for Random Vectors</title></host></json:item><json:item><author><json:item><name>S. Graf</name></json:item><json:item><name>H. Luschgy</name></json:item></author><host><pages><last>87</last><first>84</first></pages><author></author><title>Transactions of the 12th Prague Conference on Information Theory, Statistical Decission Functions, Random Processes</title></host><title>Consistent Estimation in the Quantization Problem for Random Vectors</title></json:item><json:item><author><json:item><name>J. Hutchinson</name></json:item></author><host><volume>30</volume><pages><last>747</last><first>713</first></pages><author></author><title>Indiana Univ. J.</title></host><title>Fractals and Self‐Similarity</title></json:item><json:item><author><json:item><name>D. Pollard</name></json:item></author><host><volume>28</volume><pages><last>205</last><first>199</first></pages><author></author><title>Inform. Theor</title></host><title>Quantization and the Method of k‐means, IEEE Trans</title></json:item><json:item><author><json:item><name>P. L. Zador</name></json:item></author><host><volume>28</volume><pages><last>249</last><first>139</first></pages><author></author><title>Inform. 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