论文标题
重叠概率分布的混合物的量化
Quantization for the mixtures of overlap probability distributions
论文作者
论文摘要
混合分布的最佳量化已成为一个引人注目的研究领域。在这项工作中，我们专注于由两个统一分布形成的混合分布，并部分重叠。对于此类的分布，我们已经检查了$ n $ -Means的最佳集合以及所有正整数$ n $的相应$ n $ th量化错误的结构。最初，我们明确确定了$ 1 \ leq n \ leq 6 $的最佳集合和量化错误。随后，我们建立了几个关键的引理和命题，并提出了一种算法，该算法有助于计算所有$ n \ geq 5 $的最佳$ n $ - 均值和量化错误。还提供了数值结果，以说明该算法在得出这些数量时的应用。这项研究的发现为在混合分布的背景下和重叠支持的背景下提供了进一步研究量化的基础。
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of $n$-means and the corresponding $n$th quantization errors for all positive integers $n$. Initially, we explicitly determined the optimal sets and quantization errors for $1 \leq n \leq 6$. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal $n$-means and quantization errors for all $n \geq 5$. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a foundation for further research on quantization in the context of mixed distributions with overlapping supports.
