IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v153y2022icp283-320.html
   My bibliography  Save this article

Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions

Author

Listed:
  • Iksanov, Alexander
  • Kotelnikova, Valeriya

Abstract

A nested Karlin’s occupancy scheme is a symbiosis of classical Karlin’s balls-in-boxes scheme and a weighted branching process. To define it, imagine a deterministic weighted branching process in which weights of the first generation individuals are given by the elements of a discrete probability distribution. For each positive integer j, identify the jth generation individuals with the jth generation boxes. The collection of balls is one and the same for all generations, and each ball starts at the root of the weighted branching process tree and moves along the tree according to the following rule: transition from a mother box to a daughter box occurs with probability given by the ratio of the daughter and mother weights.

Suggested Citation

  • Iksanov, Alexander & Kotelnikova, Valeriya, 2022. "Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 283-320.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:283-320
    DOI: 10.1016/j.spa.2022.08.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001880
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.08.006?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. Mikhail Chebunin & Sergei Zuyev, 2022. "Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models," Journal of Theoretical Probability, Springer, vol. 35(1), pages 1-19, March.
    2. Pierpaolo De Blasi & Ramsés H. Mena & Igor Prünster, 2022. "Asymptotic behavior of the number of distinct values in a sample from the geometric stick-breaking process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 143-165, February.
    3. Durieu, Olivier & Samorodnitsky, Gennady & Wang, Yizao, 2020. "From infinite urn schemes to self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2471-2487.
    4. Chebunin, Mikhail & Kovalevskii, Artyom, 2016. "Functional central limit theorems for certain statistics in an infinite urn scheme," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 344-348.
    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. Igor Borisov & Maman Jetpisbaev, 2022. "Poissonization Principle for a Class of Additive Statistics," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    2. Hatjispyros, Spyridon J. & Merkatas, Christos & Walker, Stephen G., 2023. "Mixture models with decreasing weights," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    4. Mikhail Chebunin & Sergei Zuyev, 2022. "Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models," Journal of Theoretical Probability, Springer, vol. 35(1), pages 1-19, March.
    5. Mikhail Chebunin & Artyom Kovalevskii, 2019. "Asymptotically Normal Estimators for Zipf’s Law," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 482-492, December.

    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:153:y:2022:i:c:p:283-320. 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.