Constrained Quantization for Infinite Discrete Distributions

Author

• Bismark Bimpong, The University of Texas Rio Grande Valley

Date of Award

8-1-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Statistics and Data Science

First Advisor

Mrinal Roychowdhury

Second Advisor

Hansapani Rodrigo

Third Advisor

Josef Sifuentes

Abstract

This thesis presents a detailed study of constrained quantization for infinite discrete probability distributions supported on subsets of the real line. Two infinite discrete distributions are analyzed: one supported on the set {1/n : n ∈ N} and the other on the set of natural numbers N. Explicit constructions and numerical computations of optimal quantizers and the corresponding quantization errors are provided. Furthermore, for the infinite discrete distribution supported on N, we develop a general framework for constrained quantization under the linear constraint y = mx+c and prove that the constrained quantization dimension in this setting is zero. These results demonstrate how geometric constraints influence the structure and existence of optimal quantizers and provide directions for further investigation in constrained quantization theory.

Comments

Copyright 2026 Bismark Bimpong. All Rights Reserved. https://proquest.com/docview/3409129347

Recommended Citation

Bimpong, B. (2026). Constrained Quantization for Infinite Discrete Distributions [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1982