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Some further results on random splitting of an interval

Published online by Cambridge University Press:  14 July 2016

Christopher J. Lloyd
Christopher J. Lloyd*
Affiliation:
University of Melbourne
*
∗Present address: Department of Statistics, La Trobe University, Bundoora, VIC 3083, Australia.
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Abstract

The random splitting model of Lloyd and Williams (1988) is generalised, to allow first beta splitting distributions and secondly, discrete splitting distributions. Analogues of some earlier results are developed. In particular, the equality of the average value of the largest split and the probability that this is achieved at the first split continues to hold.

Keywords

BETA DISTRIBUTIONPERMUTATIONCYCLE LENGTHRENEWAL EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 466 - 476
Copyright
Copyright © Applied Probability Trust 1989 

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References

Golomb, S. W. (1964) Random permutations. Bull. Amer. Math. Soc. 70, 747.Google Scholar
Lloyd, C. J. and Williams, E. J. (1988) On recursive random splitting of an interval when the proportions are identical and independent. Stoch. Proc. Appl. 27, 111–122.Google Scholar
Shepp, L. A. and Lloyd, S. P. (1966) Ordered cycle lengths in random permutations. Trans. Amer. Math. Soc. 121, 340–357.CrossRefGoogle Scholar
Vershik, A. M. and Schmidt, A. A. (1977) Limit measures arising in the asymptotic theory of symmetric groups I. Theory Prob. Appl. 22, 79–85.CrossRefGoogle Scholar