On an interval-partitioning scheme

Marcel Neuts; Jian-Min Li; Charles Pearce

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 3, page 347-355
  • ISSN: 1233-7234

Abstract

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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

How to cite

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Neuts, Marcel, Li, Jian-Min, and Pearce, Charles. "On an interval-partitioning scheme." Applicationes Mathematicae 26.3 (1999): 347-355. <http://eudml.org/doc/219244>.

@article{Neuts1999,
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},
author = {Neuts, Marcel, Li, Jian-Min, Pearce, Charles},
journal = {Applicationes Mathematicae},
keywords = {random partitioning; spacings},
language = {eng},
number = {3},
pages = {347-355},
title = {On an interval-partitioning scheme},
url = {http://eudml.org/doc/219244},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Neuts, Marcel
AU - Li, Jian-Min
AU - Pearce, Charles
TI - On an interval-partitioning scheme
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 3
SP - 347
EP - 355
AB - 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
LA - eng
KW - random partitioning; spacings
UR - http://eudml.org/doc/219244
ER -

References

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  1. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1965. Zbl0171.38503
  2. [2] R. L. Adler and L. Flatto, Uniform distribution of Kakutani's interval splitting procedure, Z. Wahrsch. Verw. Gebiete 38 (1977), 253-259. Zbl0362.60014
  3. [3] D. A. Darling, On a class of problems related to the random division of an interval, Ann. Math. Statist. 24 (1953), 239-253. Zbl0053.09902
  4. [4] S. Gutmann, Interval-dividing processes, Z. Wahrsch. Verw. Gebiete 57 (1981), 339-347. Zbl0459.60032
  5. [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. [6] S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981. 
  7. [7] R. G. Laha and V. K. Rohatgi, Probability Theory, John Wiley & Sons, New York, 1979. 
  8. [8] J. C. Lootgieter, Sur la répartition des suites de Kakutani, C. R. Acad. Sci. Paris 285A (1977), 403-406. Zbl0367.60018
  9. [9] T. S. Mountford and S. C. Port, Random splittings of an interval, J. Appl. Probab. 30 (1993), 131-152. Zbl0770.60102
  10. [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. Zbl0903.60094
  11. [11] R. Pyke, Spacings, J. Roy. Statist. Soc. Ser. B 27 (1965), 395-449. 
  12. [12] E. Slud, Entropy and maximal spacings for random partitions, Z. Wahrsch. Verw. Gebiete 41 (1978), 341-352. Zbl0353.60019
  13. [13] W. R. van Zwet, A proof of Kakutani's conjecture on random subdivision of longest intervals, Ann. Probab. 6 (1978), 133-137. Zbl0374.60036

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