Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves

Authors

Gabriela Pena
Hansapani Rodrigo, The University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley
Josef A. Sifuentes, The University of Texas Rio Grande Valley
Erwin Suazo, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

10-2020

Abstract

In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form n = 6k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on the boundary of a semicircular disc, and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n-means and the nth quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n.

Comments

© 2020, Springer Science Business Media, LLC, part of Springer Nature

Recommended Citation

Pena, G., Rodrigo, H., Roychowdhury, M.K. et al. Quantization for Uniform Distributions on Hexagonal, Semicircular, and Elliptical Curves. J Optim Theory Appl (2020). https://doi.org/10.1007/s10957-020-01771-1

Publication Title

Journal of Optimization Theory and Application

DOI

10.1007/s10957-020-01771-1