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Optimal Quantization for Uniform Distributions on

✍ Scribed by Wolfgang Kreitmeier

Publisher
Springer Netherlands
Year
2008
Tongue
English
Weight
637 KB
Volume
105
Category
Article
ISSN
0167-8019

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πŸ“œ SIMILAR VOLUMES

Optimal quantization for dyadic homogene
Optimal quantization for dyadic homogeneous Cantor distributions
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## Abstract For a large class of dyadic homogeneous Cantor distributions in ℝ, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class

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Denoting by \(X_{(1,} \leqslant X_{t 2} \leqslant \cdots \leqslant X_{(n)}\) the order statistic based on a random sample \(X_{1}, X_{2}, \ldots, X_{n}\) drawn from a distribution \(F\), it is shown that the property " \(E\left(X_{1} \mid X_{(1)}, X_{(n)}\right)=\frac{1}{2}\left(X_{(1)}+X_{(n)}\righ