The volume fraction of a poisson germ model with maximally non-overlapping spherical grains

Advances in Applied Probability

Volumn 31, Issue 3, 1999, Pages 610-624

  Daley, D J ^a,b   Stoyan, H ^a,b   Stoyan, D ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Dynamic lilypond model; Germ grain model; Growth model; Non overlapping spheres; Poisson process; Stienen model; Volume fraction

Indexed keywords

EID: 0033184502     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800009319     Document Type: Article

References (13)

1. DALEY, D. J., STOYAN, D. AND STOYAN, H. (1997). The volume fraction of a Poisson germ model with maximally non-overlapping spherical grains. Statistics research report No. SRR 006-97, Centre for Mathematics and its Applications, Australian National University, Canberra.
2. DALEY, D. J., MALLOWS, C. L. AND SHEPP, L. A. (1999). A one-dimensional Poisson growth model with non-overlapping intervals. To appear in Stock. Proc. Appl.
3. DIGGLE, P. J. (1983). Statistical Analysis of Spatial Point Patterns. Chapman and Hall, London.
4. HÄGGSTRÖM, O. AND MEESTER, R. (1996). Nearest neighbor and hard sphere models in continuum percolation. Rand. Struct. Algorithms 9, 295-315.
5. HERCZYNSKI, R. (1975). Distribution function for random distribution of spheres. Nature 255, 540-541.
6. PICKARD, D. K. (1982). Isolated nearest neighbors. J Appl. Prob. 19, 444-449.
7. QUINE, M. P. AND WATSON, D. F. (1984). Radial simulation of n-dimensional Poisson processes. J. Appl. Prob. 21, 548-557.
8. SCHLATHER, M. AND STOYAN, D. (1997). The covariance of the Stienen model. In Advances in Theory and Applications of Random Sets, ed. D. Jeulin. World Scientific, Singapore, pp. 157-174.
9. STIENEN, J. (1982). Die Vergroeberung von Karbiden in reinen Eisen-Kohlenstoff-Staehlen. Dissertation, RWTH Aachen, Germany.
10. STOYAN, D. (1990). Stereological formulae for a random system of non-overlapping spheres. Statistics 21, 131-136.
11. STOYAN, D. (1998). Random sets: models and statistics. Internat. Statist. Rev. 66, 1-27.
12. STOYAN, D..KENDALL.W.S. AND MECKE.J. (1995). Stochastic Geometry and its Applications.Wiley, Chichesler, UK.
13. YAO, Y-C. AND SIMONS, G. (1996). A large-dimensional independentand identically distributed property for nearest neighbour counts in Poisson processes. Ann. Appl. Prob. 6, 561-571.