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The limit behavior of an interval splitting scheme

Author

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  • Devroye, Luc
  • Letac, Gerard
  • Seshadri, Vanamamalai

Abstract

We split [0,1] in a uniform manner, take the largest of the two intervals thus obtained, split this interval again uniformly, and continue in this fashion ad infinitum. We show that the extremes of this interval converge almost surely to a beta (2,2) random variable.

Suggested Citation

  • Devroye, Luc & Letac, Gerard & Seshadri, Vanamamalai, 1986. "The limit behavior of an interval splitting scheme," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 183-186, June.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:4:p:183-186
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    Citations

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    Cited by:

    1. Johnson, Norman L. & Kotz, Samuel, 1995. "Use of moments in studies of limit distributions arising from iterated random subdivisions of an interval," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 111-119, August.
    2. Margarete Knape & Ralph Neininger, 2008. "Approximating Perpetuities," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 507-529, December.
    3. Stoyanov, Jordan & Pirinsky, Christo, 2000. "Random motions, classes of ergodic Markov chains and beta distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 293-304, November.
    4. McKinlay, Shaun, 2017. "On beta distributed limits of iterated linear random functions," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 33-41.

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