## School of Mathematical and Statistical Sciences Faculty Publications and Presentations

#### 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).