Quantization for the mixtures of overlap probability distributions

Authors

Asha Barua, The University of Texas Rio Grande Valley
Angelina Chavera, The University of Texas Rio Grande Valley
Ivan Djordjevic, The University of Texas Rio Grande Valley
Valerie Manzano, The University of Texas Rio Grande Valley
Sergio Soto Quintero, The University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow
Hilda Tejeda, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-2025

Abstract

Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of n-means and the corresponding nth quantization errors for all positive integers n. Initially, we explicitly determined the optimal sets and quantization errors for 1 < = n < = 6. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal n-means and quantization errors for all n >= 5. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a foundation for further research on quantization in the context of mixed distributions with overlapping supports.

Comments

© 2025 University of Houston

https://www.math.uh.edu/~hjm/restricted/pdf51(1)/02roychowdhury.pdf

Recommended Citation

Barua, Asha, Angelina Chavera, Ivan Djordjevic, et al. 2025. “Quantization for the Mixtures of Overlap Probability Distributions.” Houston Journal of Mathematics 51 (1): 31–54.

First Page

31

Last Page

54

Publication Title

Houston Journal of Mathematics