Quantization for a set of discrete distributions on the set of natural numbers
Probability
2023-05-05 v1
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 -means and the th quantization errors for all positive integers . In addition, the quantization dimension is also calculated.
Keywords
Cite
@article{arxiv.2305.02372,
title = {Quantization for a set of discrete distributions on the set of natural numbers},
author = {Juan Gomez and Haily Martinez and Mrinal K. Roychowdhury and Alexis Salazar and Daniel J. Vallez},
journal= {arXiv preprint arXiv:2305.02372},
year = {2023}
}