Conditional Constrained and Unconstrained Quantization for a Uniform Distribution on a Hexagon

Author

Christina Hamilton, The University of Texas Rio Grande Valley

Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Mrinal K. Roychowdhury

Second Advisor

Santanu Chakraborty

Third Advisor

Hansapani Rodrigo

Abstract

In this thesis, we have considered a uniform distribution on a regular hexagon and the set of all its six vertices as a conditional set. For the uniform distribution under the conditional set first, for all positive integers n ≥ 6, we obtain the conditional optimal sets of n-points and the nth conditional quantization errors, and then we calculate the conditional quantization dimension and the conditional quantization coefficient in the unconstrained scenario. Then, for the uniform distribution on the hexagon taking the same conditional set, we investigate the conditional constrained optimal sets of n-points and the conditional constrained quantization errors for all n ≥ 6, taking the constraint as the different diagonals of the hexagon.

Comments

Copyright 2024 Christina Hamilton.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/pqdtglobal1/dissertations-theses/conditional-constrained-unconstrained/docview/3085283636/sem-2?accountid=7119

Recommended Citation

Hamilton, Christina, "Conditional Constrained and Unconstrained Quantization for a Uniform Distribution on a Hexagon" (2024). Theses and Dissertations. 1516.
https://scholarworks.utrgv.edu/etd/1516