Conditional Quantization for Some Discrete Distributions

Authors

Edgar A. Gonzalez, The University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow
David A. Salinas, The University of Texas Rio Grande Valley
Vishal Veeramachaneni, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

5-23-2025

Abstract

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the finite support are preselected, then the quantization is called a conditional quantization. In this paper, we have determined the conditional quantization, first for two different finite discrete distributions with a same conditional set, and for a finite discrete distribution with two different conditional sets. Next, we have determined the conditional and unconditional quantization for an infinite discrete distribution with support {12𝑛:𝑛∈ℕ}. We have also investigated the conditional quantization for an infinite discrete distribution with support {1𝑛:𝑛∈ℕ}. At the end of the paper, we have given a conjecture and discussed about some open problems based on the conjecture.

Comments

© 2025 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Recommended Citation

Gonzalez, Edgar A., Mrinal Kanti Roychowdhury, David A. Salinas, and Vishal Veeramachaneni. 2025. "Conditional Quantization for Some Discrete Distributions" Mathematics 13, no. 11: 1717. https://doi.org/10.3390/math13111717

Publication Title

Mathematics

DOI

10.3390/math13111717