Conditional optimal sets and the quantization coefficients for some uniform distributions

Authors

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

Document Type

Article

Publication Date

2-2024

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. "Conditional optimal sets and the quantization coefficients for some uniform distributions." arXiv preprint arXiv:2402.16783 (2024).