On the estimation of distance distribution functions for point processes and random sets

Image Analysis and Stereology

Volumn 20, Issue 1, 2001, Pages 65-69

  Stoyan, Dietrich ^a   Stoyan, Helga ^a   Tscheschel, André ^a   Mattfeldt, Torsten ^b  

^a TU BERGAKADEMIE FREIBERG   (Germany)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

Contact distribution; Estimator; Horvitz Thompson; Minus sampling; Nearest neighbour distance distribution

Indexed keywords

EID: 0012598946     PISSN: 15803139     EISSN: 18545165     Source Type: Journal    
DOI: 10.5566/ias.v20.p65-69     Document Type: Article

References (16)

1. Baddeley AJ, Moyeed RA, Howard CV, Boyde A (1993). Analysis of a three-dimensional point pattern with replication. Appl. Statist. 42:641-68.
2. Baddeley AJ, Gill RD (1997). Kaplan-Meier estimators of distance distribution for spatial point processes. Ann. Statist. 25:263-92.
3. Baddeley AJ (1998). Spatial sampling and censoring. Chapter 2 of Current Trends in Stochastic Geometry and its Applications (ed. Kendall WS, van Lieshout MNM, Barndorff-Nielsen OE), Chapman and Hall, London, New York.
4. Chiu SN, Stoyan D (1998). Estimators of distance distributions for spatial patterns. Statist. Neerl. 52:239- 46.
5. Cressie N (1991). Statistics of Spatial Data. J.Wiley&Sons, New York.
6. Delfiner P (1972). A generalization of the concept of size. J. Microsc. 95:203-16.
7. Diggle PJ (1983). Statistical Analysis of Statistial Point Patterns. Academic Press, London.
8. Hanisch K-H (1984). Some remarks on estimators of the distribution function of nearest-neighbour distance in stationary spatial point patterns. Statistics 15:409-12.
9. Landy SL, Szalay AS (1993). Bias and variance of angular correlation function. Astrophys. J. 412:64-71.
10. Mattfeldt T, Stoyan D (2000). Improved estimation of the pair correlation function of random sets. J. Microsc. 200:158-73.
11. Ohser J, Mücklich F (2000). Statistical Analysis of Microstructures in Materials Science. J. Wiley & Sons, Chichester.
12. Overton WS, Stehman SV (1995). The Horvitz-Thompson theorem as a unifying perspective for probability sampling; with examples from natural resource sampling. Amer. Statist. 49:261-68.
13. Serra J (1982). Image Analysis and Mathematical Morphology. Academic Press, London, New York.
14. Stoyan D, Kendall WS, Mecke J (1995). Stochastic Geometry and its Applications. Chichester: John Wiley & Sons.
15. Stoyan D, Stoyan H (1994). Fractals, Random Shapes and Point Fields. J. Wiley & Sons, Chichester.
16. Stoyan D, Stoyan H (2000). Improving ratio estimators of second order point process characteristics. Scand. J. Statist. 27:641-56.