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Recursive splitting of an interval when the proportions are identical and independent random variables

Author

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  • Lloyd, C. J.
  • Williams, E. J.

Abstract

Imagine a stick broken at a random point according to the known distribution function F, the right hand piece being discarded. The remaining left hand piece is then broken according to the same (but rescaled) distribution F ad infinitum. What is the largest piece discarded and at what stage of the process does it occur? Using a basic recursive property, these and related questions are studied, in particular when the distribution F is uniform.

Suggested Citation

  • Lloyd, C. J. & Williams, E. J., 1988. "Recursive splitting of an interval when the proportions are identical and independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 111-122, April.
    • Handle: RePEc:eee:spapps:v:28:y:1988:i:1:p:111-122
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    Cited by:

    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. Benjamin J Finley & Kalevi Kilkki, 2014. "Exploring Empirical Rank-Frequency Distributions Longitudinally through a Simple Stochastic Process," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-14, April.
    3. 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.

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