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Functional central limit theorems for certain statistics in an infinite urn scheme

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  • Chebunin, Mikhail
  • Kovalevskii, Artyom

Abstract

We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for any k≥1.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:344-348
    DOI: 10.1016/j.spl.2016.08.019
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    Cited by:

    1. Igor Borisov & Maman Jetpisbaev, 2022. "Poissonization Principle for a Class of Additive Statistics," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    2. 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.
    3. 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.
    4. 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.

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