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On random splitting of the interval

Author

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  • Barrera, Javiera
  • Huillet, Thierry

Abstract

We study the colonizing process of space by some populations which can be verbally described as follows: suppose a first incoming species occupies a random fraction of the available unit space. The forthcoming species takes an independent random fraction of the remaining space. There are n species and so there is a fraction of space occupied by no species. This model constitutes an approximation to the celebrated GEM interval partition. Essentially using moments, we study some statistical features of the induced partition structure of space.

Suggested Citation

  • Barrera, Javiera & Huillet, Thierry, 2004. "On random splitting of the interval," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 237-250, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:237-250
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    References listed on IDEAS

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    1. Yamato, Hajime & Sibuya, Masaaki & Nomachi, Toshifumi, 2001. "Ordered sample from two-parameter GEM distribution," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 19-27, November.
    2. Sibuya, Masaaki & Yamato, Hajime, 1995. "Ordered and unordered random partitions of an integer and the GEM distribution," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 177-183, November.
    3. 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.
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    Cited by:

    1. Itoh, Yoshiaki & Mahmoud, Hosam & Smythe, Robert, 2006. "Probabilistic analysis of maximal gap and total accumulated length in interval division," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1356-1363, July.

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