QUANTIZATION FOR A SET OF DISCRETE DISTRIBUTIONS ON THE SET OF NATURAL NUMBERS

Authors

Juan Gomez
Haily Martinez
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley
Alexis Salazar
Daniel J. Vallez

Document Type

Article

Publication Date

2023

Abstract

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a theorem, and then give a conjecture. We verify the conjecture by a few examples. Assuming that the conjecture is true, for a set of discrete distributions on the set of natural numbers we have calculated the optimal sets of n-means and the nth quantization errors for all positive integers n. In addition, the quantization dimension is also calculated.

Recommended Citation

Gomez, Juan, et al. "Quantization for a set of discrete distributions on the set of natural numbers." arXiv preprint arXiv:2305.02372 (2023).