Optimal quantizers for some absolutely continuous probability measures. (English) Zbl 1410.60030

Roychowdhury, Mrinal Kanti

Real Anal. Exch. 43, No. 1, 105-136 (2018).

Summary: 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 \(n\).

MSC:

60E99	Distribution theory
60D05	Geometric probability and stochastic geometry
62E17	Approximations to statistical distributions (nonasymptotic)
94A34	Rate-distortion theory in information and communication theory

Keywords:

uniform and nonuniform distributions; optimal quantizers; quantization error