# Estimates of some probabilities in multidimensional convex records

Applicationes Mathematicae (1995)

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

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topKałuszka, 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

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

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