Boolean cluster models: mean cluster dilations and spherical contact distances

Jan Rataj; Ivan Saxl

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 1, page 21-36
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Rataj, Jan, and Saxl, Ivan. "Boolean cluster models: mean cluster dilations and spherical contact distances." Mathematica Bohemica 122.1 (1997): 21-36. <http://eudml.org/doc/248117>.

@article{Rataj1997,
abstract = {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.},
author = {Rataj, Jan, Saxl, Ivan},
journal = {Mathematica Bohemica},
keywords = {cluster process; Boolean model; spherical contact distribution function; Poisson process; Matérn model; cluster process; Boolean model; spherical contact distribution function},
language = {eng},
number = {1},
pages = {21-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boolean cluster models: mean cluster dilations and spherical contact distances},
url = {http://eudml.org/doc/248117},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Rataj, Jan
AU - Saxl, Ivan
TI - Boolean cluster models: mean cluster dilations and spherical contact distances
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 1
SP - 21
EP - 36
AB - 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.
LA - eng
KW - cluster process; Boolean model; spherical contact distribution function; Poisson process; Matérn model; cluster process; Boolean model; spherical contact distribution function
UR - http://eudml.org/doc/248117
ER -

References

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  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. (1993) 
  3. Buchta C, Das Volumen von Zufallpolyedern im Ellipsoid, Anz. Österr. Akad. Wiss. Math.-Natur. Kl. 1 (1984), 1-4. (1984) MR0831270
  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. (1974) Zbl0289.60007MR0358908
  5. Daley D. J., Vere-Jones D., An Introduction to the Theory of Point Processes, Springer-Verlag, New York, 1988. (1988) Zbl0657.60069MR0950166
  6. Miles R.E., 10.2307/1426176, Adv. Appl. Probab. 3 (1971), 353-382. (1971) Zbl0237.60006MR0309164DOI10.2307/1426176
  7. Saxl I., Spherical contact distances in Neyman-Scott process of regular clusters, Acta Stereol. 12 (1993), 115-122. (1993) 
  8. Saxl I., Rataj J., Spherical contact and nearest neighbour distances in Boolean cluster fields, Acta Stereol. 15 (1996). 91-96. (1996) 
  9. Stoyan D., 10.1007/BF02613983, Metrika 39 (1992), 67-74. (1992) Zbl0850.62701MR1162686DOI10.1007/BF02613983
  10. Stoyan D., Kendall W. S., Mecke J., Stochastic Geometry and its Applications, J. Wiley, Chichester & Akademie-Verlag, Berlin, 1987. (1987) Zbl0622.60019MR0879119

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