IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i11p6880-6900.html
   My bibliography  Save this article

Size biased sampling from the Dickman subordinator

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920303136
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.07.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuguang Ipsen & Ross Maller & Soudabeh Shemehsavar, 2020. "Limiting Distributions of Generalised Poisson–Dirichlet Distributions Based on Negative Binomial Processes," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1974-2000, December.
    2. Nils Lid Hjort & Andrea Ongaro, 2006. "On the distribution of random Dirichlet jumps," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 61-92.
    3. Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    4. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.
    5. Feng, Shui & Gao, Fuqing, 2010. "Asymptotic results for the two-parameter Poisson-Dirichlet distribution," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1159-1177, July.
    6. Shi, Quan, 2015. "On the number of large triangles in the Brownian triangulation and fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4321-4350.
    7. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2019. "Ratios of ordered points of point processes with regularly varying intensity measures," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 205-222.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6880-6900. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.