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Discrete Spacings

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  • Chris A.J. Klaassen
  • J. Theo Runnenburg

Abstract

Consider a string of n positions, i.e. a discrete string of length n. Units of length k are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than k. When centered and scaled by n−1/2 the resulting numbers of spacings of length 1, 2,…, k−1 have simultaneously a limiting normal distribution as n→∞. This is proved by the classical method of moments.

Suggested Citation

  • Chris A.J. Klaassen & J. Theo Runnenburg, 2003. "Discrete Spacings," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 470-483, November.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:4:p:470-483
    DOI: 10.1111/1467-9574.00240
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    Cited by:

    1. Shneer, Seva & van de Ven, Peter M., 2017. "Per-site occupancy in the discrete parking problem," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 141-146.

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