论文标题
连接和断开线段上均匀分布的混合物的量化
Quantization for the mixtures of uniform distributions on connected and disconnected line segments
论文作者
论文摘要
在本文中，我们研究了由两个统一分布产生的各种混合分布：第一，支撑是两个连接的线段，其次，在其中支撑是两个断开的线段。对于这些混合分布，我们已经确定了所有正整数$ n $的最佳集合和相应的$ n $ th量化错误。本文开发的方法可以更普遍地用于调查任何混合分布的最佳量化$ p：= pp_1 +（1-p）p_2，$，其中$ p_1 $和$ p_2 $是在连接或断开的线段上支持的任意概率分布，以及$（p，1- p）$是$ 0 $ $ 0 <p <p <p <p <p <p <p <p <p <p <p <p <p，$ $ 0。
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 $P := pP_1 + (1 - p)P_2,$ where $P_1$ and $P_2$ are arbitrary probability distributions supported on either connected or disconnected line segments, and $(p, 1 - p)$ is any probability vector with $0 < p < 1$.
