| 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:
|
http://hdl.handle.net/10338.dmlcz/126185 |
| . |
| 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 |
| . |
