Abstract The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.

中文翻译：

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来自 Dickman 下属的规模偏差抽样

摘要 Dickman 函数和相关分布在概率数论和 Poisson-Dirichlet 分布理论中发挥着重要作用。这些分布又与从属节点的有序跳跃的性质密切相关。在本文中，我们为 Dickman 从属节点推导出了一些显着的不变性特性和其他恒等式，这些特性与过程的大跳跃有关。这对来自 Dickman 分布的大小偏向抽样的影响被引出。