Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T16:28:27.356Z Has data issue: false hasContentIssue false
  • English
  • Français

On the possible form of size distributions for Gibbsian processes of mutually non-intersecting balls

Published online by Cambridge University Press:  14 July 2016

Shigeru Mase
Shigeru Mase*
Affiliation:
Hiroshima University
*
∗Postal address: Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Senda-Machi, Naka-Ku, Hiroshima, 730 Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a model of mutually non-intersecting balls using a generalized notion of Gibbsian processes and characterize its size, i.e. radius, distribution. The explicit form of this distribution is given in the one-dimensional case, that is, mutually non-intersecting segment processes on the line.

Keywords

RANDOM BALLSNON-INTERSECTIONSTEREOLOGYSEGMENT PROCESS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 646 - 659
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported in part by a Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture under Contract Number 321–6059–59530012.

References

Hadwiger, H. (1957) Vorlesungen Über Inhalt, Oberfläche und Isoperimetrie. Springer-Verlag.Google Scholar
Keiding, N., Jensen, T. S. and Ranek, L. (1972) Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section. Biometrics 28, 813–829.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Mitrinovic, D. S. (1970) Analytic Inequalities. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Mürman, M. G. (1978) Poisson point process with exclusion. Z. Wahrsheinlichkeitsth. 43, 23–37.Google Scholar
Nguyen, X. X. and Zessin, H. (1976) Punktprozesse mit Wechselwirkung. Z. Wahrsheinlichkeitsth. 37, 91–126.Google Scholar
Nguyen, X. X. and Zessin, H. (1979) Integral and differential characterizations of the Gibbs process. Math. Nachr. 88, 105–115.Google Scholar
Petrov, V. V. (1975) Sums of Independent Random Variables. Springer-Verlag, Berlin.Google Scholar
Preston, C. (1976) Random Fields. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Suwa, N. (1977) Quantitative Stereology (in Japanese). Iwanami Publishing Co., Tokyo.Google Scholar
Underwood, E. E. (1970) Quantitative Stereology. Addison-Wesley, Reading, Mass.Google Scholar