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Size biased sampling from the Dickman subordinator

Author

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  • Ipsen, Yuguang
  • Maller, Ross
  • Shemehsavar, Soudabeh

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.

Suggested Citation

  • Ipsen, Yuguang & Maller, Ross & Shemehsavar, Soudabeh, 2020. "Size biased sampling from the Dickman subordinator," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6880-6900.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6880-6900
    DOI: 10.1016/j.spa.2020.07.002
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    References listed on IDEAS

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    1. Perman, Mihael, 1993. "Order statistics for jumps of normalised subordinators," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 267-281, June.
    2. Kevei, Péter & Mason, David M., 2013. "Randomly weighted self-normalized Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 490-522.
    3. Gregoire, Gérard, 1984. "Negative binomial distributions for point processes," Stochastic Processes and their Applications, Elsevier, vol. 16(2), pages 179-188, February.
    Full references (including those not matched with items on IDEAS)

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