Quantization for a mixture of uniform distributions associated with probability vectors

TL;DR

This paper explores optimal quantization methods for mixed distributions formed by uniform distributions linked to probability vectors, advancing understanding in approximating complex continuous distributions with finite sets.

Contribution

It introduces new approaches for quantizing mixtures of uniform distributions associated with probability vectors, a novel area in optimal quantization research.

Findings

Developed quantization strategies for mixed uniform distributions

Achieved improved approximation accuracy for complex distributions

Extended quantization theory to new classes of mixed distributions

Abstract

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.