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arXiv · 2401.01958

Constrained quantization for the Cantor distribution with a family of constraints

Megha Pandey·Mrinal Kanti Roychowdhury
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Abstract

In this paper, for a given family of constraints and the classical Cantor distribution we determine the constrained optimal sets of $n$-points, $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient, and see that the constrained quantization dimension $D(P)$ exists as a finite positive number, but the $D(P)$-dimensional constrained quantization coefficient does not exist.

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Megha Pandey, Mrinal Kanti Roychowdhury. 2024-01-03. Constrained quantization for the Cantor distribution with a family of constraints. https://arxiv.org/abs/2401.01958

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