On an interval-partitioning scheme
Neuts, Marcel ; Li, Jian-Min ; Pearce, Charles
Applicationes Mathematicae, Tome 26 (1999), p. 347-355 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:219244
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Neuts, Marcel; Li, Jian-Min; Pearce, Charles. On an interval-partitioning scheme. Applicationes Mathematicae, Tome 26 (1999) pp. 347-355. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i3p347bwm/

[000] [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1965. | Zbl 0171.38503

[001] [2] R. L. Adler and L. Flatto, Uniform distribution of Kakutani's interval splitting procedure, Z. Wahrsch. Verw. Gebiete 38 (1977), 253-259. | Zbl 0362.60014

[002] [3] D. A. Darling, On a class of problems related to the random division of an interval, Ann. Math. Statist. 24 (1953), 239-253. | Zbl 0053.09902

[003] [4] S. Gutmann, Interval-dividing processes, Z. Wahrsch. Verw. Gebiete 57 (1981), 339-347. | Zbl 0459.60032

[004] [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.

[005] [6] S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.

[006] [7] R. G. Laha and V. K. Rohatgi, Probability Theory, John Wiley & Sons, New York, 1979.

[007] [8] J. C. Lootgieter, Sur la répartition des suites de Kakutani, C. R. Acad. Sci. Paris 285A (1977), 403-406. | Zbl 0367.60018

[008] [9] T. S. Mountford and S. C. Port, Random splittings of an interval, J. Appl. Probab. 30 (1993), 131-152. | Zbl 0770.60102

[009] [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. | Zbl 0903.60094

[010] [11] R. Pyke, Spacings, J. Roy. Statist. Soc. Ser. B 27 (1965), 395-449.

[011] [12] E. Slud, Entropy and maximal spacings for random partitions, Z. Wahrsch. Verw. Gebiete 41 (1978), 341-352. | Zbl 0353.60019

[012] [13] W. R. van Zwet, A proof of Kakutani's conjecture on random subdivision of longest intervals, Ann. Probab. 6 (1978), 133-137. | Zbl 0374.60036