论文标题
关于布尔自我复合分布
On Boolean selfdecomposable distributions
论文作者
论文摘要
本文介绍了有关布尔卷积的自我复合分布类别。建立了布尔自制分布的一般规律性属性；特别是原子的数量最多是两个，而单数连续部分为零。然后，我们分析了转移概率如何改变布尔自我分配性。提出了几个示例以补充上述结果。最后，我们证明标准的正态分布$ n（0,1）$是布尔式自我调整，但转移的一个$ n（m，1）$不适合足够大的$ | m | $。
This paper introduces the class of selfdecomposable distributions concerning Boolean convolution. A general regularity property of Boolean selfdecomposable distributions is established; in particular the number of atoms is at most two and the singular continuous part is zero. We then analyze how shifting probability measures changes Boolean selfdecomposability. Several examples are presented to supplement the above results. Finally, we prove that the standard normal distribution $N(0,1)$ is Boolean selfdecomposable but the shifted one $N(m,1)$ is not for sufficiently large $|m|$.
