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ArticleOriginal scientific text

Title

On an interval-partitioning scheme

Authors 1, 2, 2

Affiliations

  1. Department of Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, U.S.A.
  2. Department of Applied Mathematics, The University of Adelaide, Adelaide, SA 5005, Australia

Abstract

In a recent paper, Neuts, Rauschenberg and Li [10] examined, by computer experimentation, four different procedures to randomly partition the interval [0,1] into m intervals. The present paper presents some new theoretical results on one of the partitioning schemes. That scheme is called Random Interval (RI); it starts with a first random point in [0,1] and places the kth point at random in a subinterval randomly picked from the current k subintervals (1

Keywords

ENG
random partitioning, spacings

Bibliography

  1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1965.
  2. R. L. Adler and L. Flatto, Uniform distribution of Kakutani's interval splitting procedure, Z. Wahrsch. Verw. Gebiete 38 (1977), 253-259.
  3. D. A. Darling, On a class of problems related to the random division of an interval, Ann. Math. Statist. 24 (1953), 239-253.
  4. S. Gutmann, Interval-dividing processes, Z. Wahrsch. Verw. Gebiete 57 (1981), 339-347.
  5. S. Kakutani, A problem of equidistribution on the unit interval [0,1], in: Proc. Oberwolfach Conf. on Measure Theory (1975), Lecture Notes in Math. 541, Springer, Berlin, 1976, 369-376.
  6. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.
  7. R. G. Laha and V. K. Rohatgi, Probability Theory, John Wiley & Sons, New York, 1979.
  8. J. C. Lootgieter, Sur la répartition des suites de Kakutani, C. R. Acad. Sci. Paris 285A (1977), 403-406.
  9. T. S. Mountford and S. C. Port, Random splittings of an interval, J. Appl. Probab. 30 (1993), 131-152.
  10. M. F. Neuts, D. E. Rauschenberg and J.-M. Li, How did the cookie crumble ? Identifying fragmentation procedures, Statist. Neerlandica 51 (1997), 238-251.
  11. R. Pyke, Spacings, J. Roy. Statist. Soc. Ser. B 27 (1965), 395-449.
  12. E. Slud, Entropy and maximal spacings for random partitions, Z. Wahrsch. Verw. Gebiete 41 (1978), 341-352.
  13. W. R. van Zwet, A proof of Kakutani's conjecture on random subdivision of longest intervals, Ann. Probab. 6 (1978), 133-137.
Applicationes Mathematicae
1999/26/3
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Pages:
347-355
Main language of publication
English
Received
1999-03-16
Accepted
1999-05-31
Published
1999
Exact and natural sciences