Size biased sampling from the Dickman subordinator

Yuguang Ipsen, Ross Maller and Soudabeh Shemehsavar

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6880-6900

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.

Keywords: Generalised Dickman distribution; Size-biased sampling; Generalised Poisson–Dirichlet laws; Negative binomial point process (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.07.002

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