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

### OPTIMAL QUANTIZATION FOR DISCRETE DISTRIBUTIONS

Article

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.

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