School of Mathematical & Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
7-23-2025
Abstract
Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in this paper, we have shown that the quantization coefficients for absolutely continuous probability measures defined on the same Euclidean space can be different. We have taken uniform distribution as a prototype of an absolutely continuous probability measure. In addition, we have also calculated the conditional optimal sets of n-points and the nth conditional quantization errors for the uniform distributions in constrained and unconstrained scenarios.
Recommended Citation
Nyanney, Evans, Megha Pandey, and Mrinal Kanti Roychowdhury. 2025. "Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions" Mathematics 13, no. 15: 2350. https://doi.org/10.3390/math13152350
Publication Title
Mathematics
DOI
10.3390/math13152350
Comments
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).