Previous |  Up |  Next


Title: Boolean cluster models: mean cluster dilations and spherical contact distances (English)
Author: Rataj, Jan
Author: Saxl, Ivan
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 122
Issue: 1
Year: 1997
Pages: 21-36
Summary lang: English
Category: math
Summary: Boolean cluster point processes with various cluster distributions are examined by means of their spherical contact distribution function. Special attention is paid to clusters with strong independence properties (Poisson clusters) and regular clusters. (English)
Keyword: cluster process
Keyword: Boolean model
Keyword: spherical contact distribution function
Keyword: Poisson process
Keyword: Matérn model
MSC: 60D05
MSC: 60G55
MSC: 62M30
idZBL: Zbl 0892.60015
idMR: MR1446397
DOI: 10.21136/MB.1997.126185
Date available: 2009-09-24T21:22:24Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Affentranger F.: Expected volume of a random polytope in a ball.J. Microscopy 151 (1988), 277-287. 10.1111/j.1365-2818.1988.tb04688.x
Reference: [2] Baddeley A. J., Gill R. D.: Kaplan-Meier estimators of interpoint distance distributions for spatial point processes.Research Report BS-R 9315. CWI, Amsterdam 1993.
Reference: [3] Buchta C: Das Volumen von Zufallpolyedern im Ellipsoid.Anz. Österr. Akad. Wiss. Math.-Natur. Kl. 1 (1984), 1-4. MR 0831270
Reference: [4] Coleman R.: The distance from a given point to the nearest end of one member of a random process of linear segments.Stochastic geometry (Harding E. F., Kendall D. G., eds.). John Wiley, London, 1974, pp. 192-201. Zbl 0289.60007, MR 0358908
Reference: [5] Daley D. J., Vere-Jones D.: An Introduction to the Theory of Point Processes.Springer-Verlag, New York, 1988. Zbl 0657.60069, MR 0950166
Reference: [6] Miles R.E.: Isotropic random simplices.Adv. Appl. Probab. 3 (1971), 353-382. Zbl 0237.60006, MR 0309164, 10.2307/1426176
Reference: [7] Saxl I.: Spherical contact distances in Neyman-Scott process of regular clusters.Acta Stereol. 12 (1993), 115-122.
Reference: [8] Saxl I., Rataj J.: Spherical contact and nearest neighbour distances in Boolean cluster fields.Acta Stereol. 15 (1996). 91-96.
Reference: [9] Stoyan D.: Statistical estimation of model parameters of planar Neyman-Scott cluster processes.Metrika 39 (1992), 67-74. Zbl 0850.62701, MR 1162686, 10.1007/BF02613983
Reference: [10] Stoyan D., Kendall W. S., Mecke J.: Stochastic Geometry and its Applications.J. Wiley, Chichester & Akademie-Verlag, Berlin, 1987. Zbl 0622.60019, MR 0879119


Files Size Format View
MathBohem_122-1997-1_3.pdf 1.030Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo