Constrained quantization for a uniform distribution with respect to a family of constraints

Authors

Megha Pandey
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

9-2023

Abstract

In this paper, with respect to a family of constraints for a uniform probability distribution we determine the optimal sets of n-points and the nth constrained quantization errors for all positive integers n. We also calculate the constrained quantization dimension and the constrained quantization coefficient. The work in this paper shows that the constrained quantization dimension of an absolutely continuous probability measure depends on the family of constraints and is not always equal to the Euclidean dimension of the underlying space where the support of the probability measure is defined.

Recommended Citation

Pandey, Megha, and Mrinal K. Roychowdhury. "Constrained quantization for a uniform distribution with respect to a family of constraints." arXiv preprint arXiv:2309.11498 (2023).