English

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 nn-means and the nnth quantization errors for all positive integers nn. 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}
}