Conditional Constrained and Unconstrained Quantization for Uniform Distributions on Regular Polygons

Authors

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

Document Type

Article

Publication Date

5-24-2025

Abstract

We consider a uniform distribution on a regular polygon with k sides for some k⩾3 and the set of all its k vertices as a conditional set. For the uniform distribution under a given conditional set, we first obtain the conditional optimal sets of nn points and the corresponding nnth conditional quantization errors for all positive integers n⩾k. Then, we calculate the conditional quantization dimension and the conditional quantization coefficient in the unconstrained scenario. Next, for the uniform distribution on a polygon with the same conditional set, we investigate the conditionally constrained optimal sets of n points and the conditional constrained quantization errors for all n⩾6, under constraints such as the circumcircle, the incircle, and various diagonals of the polygon.

Comments

© 2025 Michigan State University Press

Recommended Citation

Hamilton, Christina, Evans Nyanney, Megha Pandey, and Mrinal K. Roychowdhury. "Conditional Constrained and Unconstrained Quantization for Uniform Distributions on Regular Polygons." Real Analysis Exchange 1, no. 1 (2025): 1-45. https://doi.org/10.14321/realanalexch.1725509532

Publication Title

Real Analysis Exchange

DOI

10.14321/realanalexch.1725509532