Estimates of some probabilities in multidimensional convex records

Marek Kałuszka

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 1, page 1-11
  • ISSN: 1233-7234

Abstract

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Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability p n ( k ) that in a sequence of random vectors X 1 ,..., X n there are exactly k records.

How to cite

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Kałuszka, Marek. "Estimates of some probabilities in multidimensional convex records." Applicationes Mathematicae 23.1 (1995): 1-11. <http://eudml.org/doc/219113>.

@article{Kałuszka1995,
abstract = {Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability $p_n(k)$ that in a sequence of random vectors $X_1$,..., $X_n$ there are exactly k records.},
author = {Kałuszka, Marek},
journal = {Applicationes Mathematicae},
keywords = {estimates of probabilities; geometric probability; convex records in Euclidean space; convex hull; record times; records},
language = {eng},
number = {1},
pages = {1-11},
title = {Estimates of some probabilities in multidimensional convex records},
url = {http://eudml.org/doc/219113},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Kałuszka, Marek
TI - Estimates of some probabilities in multidimensional convex records
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 1
SP - 1
EP - 11
AB - Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability $p_n(k)$ that in a sequence of random vectors $X_1$,..., $X_n$ there are exactly k records.
LA - eng
KW - estimates of probabilities; geometric probability; convex records in Euclidean space; convex hull; record times; records
UR - http://eudml.org/doc/219113
ER -

References

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  1. [1] I. Bárany and Z. Füredi, On the shape of the convex hull of random points, Probab. Theory Related Fields 80 (1988), 72-87. Zbl0639.60015
  2. [2] W. Feller, An Introduction to Probability Theory and its Applications, Vol. I, Wiley, New York, 1961. Zbl0039.13201
  3. [3] C. M. Goldie and S. Resnick, Records in a partially ordered set, Ann. Probab. 17 (1989), 678-699. Zbl0678.60001
  4. [4] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1965. Zbl0918.65002
  5. [5] P. Groeneboom, Limit theorems for convex hulls, Probab. Theory Related Fields 79 (1988), 327-368. Zbl0635.60012
  6. [6] M. G. Kendall, and P. A. P. Moran, Geometrical Probability, Griffin's Statist. Monographs Courses 5, Griffin, London, 1963. 
  7. [7] J. F. C. Kingman, Random secants of a convex body, J. Appl. Probab. 6 (1969), 660-672. Zbl0186.51603
  8. [8] V. B. Nevzorov, Records, Teor. Veroyatnost. i Primenen. 32 (2) (1987), 219-252 (in Russian). 
  9. [9] S. Resnick, Extreme Values, Regular Variation, and Point Processes, Springer, Berlin, 1987. Zbl0633.60001
  10. [10] I. M. Yaglom and V. G. Boltyanskiĭ, Convex Bodies, Nauka, Moscow, 1951 (in Russian). Zbl0098.35501

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