Optimal Quantizers for some Absolutely Continuous Probability Measures

Abstract

The representation of a given quantity with less information is often referred to as ‘quantization’ and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of \(n\)-means and the \(n\)th quantization errors are calculated for some positive integers \(n\).