# Optimal Quantization For Mixed Distributions

## TL;DR

This paper investigates optimal quantization for mixed probability distributions, determining optimal sets, errors, and dimensions, and exploring the existence of quantization coefficients to advance understanding in this emerging area.

## Contribution

It provides the first comprehensive analysis of optimal quantization parameters for mixed distributions, including existence and calculation of quantization coefficients.

## Key findings

- Determined optimal n-means for various mixed distributions.
- Calculated the nth quantization errors and dimensions.
- Discussed the existence of quantization coefficients for 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. Mixed distributions are an exciting new area for optimal quantization. In this paper, we have determined the optimal sets of $n$-means, the $n$th quantization errors, and the quantization dimensions of different mixed distributions. Besides, we have discussed whether the quantization coefficients for the mixed distributions exist. The results in this paper will give a motivation and insight into more general problems in quantization for mixed distributions.