Constrained quantization for the Cantor distribution with a family of constraints

Abstract

In this paper, for a given family of constraints and the classical Cantor distribution we determine the optimal sets of \(n\)-points, \(n\)th constrained quantization errors for all positive integers \(n\). We also calculate the constrained quantization dimension and the constrained quantization coefficient, and see that the constrained quantization dimension \(D(P)\) exists as a finite positive number, but the \(D(P)\)-dimensional constrained quantization coefficient does not exist.