OPTIMAL QUANTIZATION FOR DISCRETE DISTRIBUTIONS

Authors

Russel Cabasag, The University of Texas Rio Grande Valley
Samir Huq, The University of Texas Rio Grande Valley
Eric Mendoza, The University of Texas Rio Grande Valley
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2020

Abstract

In this paper, we first determine the optimal sets of n-means and the nth quantization errors for all 1 ≤ n ≤ 6 for two nonuniform discrete distributions with support the set {1, 2, 3, 4, 5, 6}. Then, for a probability distribution P with support { 1 n : n ∈ N} associated with a mass function f, given by f(x) = 1 2k if x = 1 k for k ∈ N, and zero otherwise, we determine the optimal sets of n-means and the nth quantization errors for all positive integers up to n = 300. Further, for a probability distribution P with support the set N of natural number associated with a mass function f, given by f(x) = 1 2k if x = k for k ∈ N, and zero otherwise, we determine the optimal sets of n-means and the nth quantization errors for all positive integers n. At last we discuss for a discrete distribution, if the optimal sets are given, how to obtain the probability distributions.

Recommended Citation

Cabasag, Russel, Samir Huq, Eric Mendoza, and Mrinal Kanti Roychowdhury. 2020. “Optimal Quantization for Discrete Distributions.” ArXiv:2008.03255 [Math], August. http://arxiv.org/abs/2008.03255.