Constrained quantization for the Cantor distribution

Authors

Megha Pandey
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

7-23-2024

Abstract

The theory of constrained quantization has been recently introduced by Pandey and Roychowdhury. In this paper, they have further generalized their previous definition of constrained quantization and studied the constrained quantization for the classical Cantor distribution. Toward this, they have calculated the optimal sets of n-points, nth constrained quantization errors, the constrained quantization dimensions, and the constrained quantization coefficients, taking different families of constraints for all n∈N. The results in this paper show that both the constrained quantization dimension and the constrained quantization coefficient for the Cantor distribution depend on the underlying constraints. It also shows that the constrained quantization coefficient for the Cantor distribution can exist and be equal to the constrained quantization dimension. These facts are not true in the unconstrained quantization for the Cantor distribution.

Comments

© 2024 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license

Recommended Citation

Pandey, Megha, and Mrinal Kanti Roychowdhury. "Constrained quantization for the Cantor distribution." Journal of Fractal Geometry 11, no. 3 (2024): 319-341. https://doi.org/10.4171/jfg/147

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Fractal Geometry

DOI

https://doi.org/10.4171/jfg/147