Quantization for the mixtures of uniform distributions on connected and disconnected line segments

Abstract In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed distributions, we have determined the optimal sets of n -means and the corresponding n th quantization errors for all positive integers n. The methods developed in this paper can be applied more generally to investigate optimal quantization for any mixed distribution P: = pP₁ + (1 - p) P₂, P: = p P 1 + (1 - p) P 2, where P₁ P 1 and P₂ P 2 are arbitrary probability distributions supported on either connected or disconnected line segments, and (p, 1 - p) (p, 1 - p) is any probability vector with 0 0 p 1.