Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T21:11:13.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximations to hard-core models and their application to statistical analysis

Published online by Cambridge University Press:  14 July 2016

Mark Westcott
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

Keywords

HARD-CORE MODELINFERENCE FOR POINT PROCESSESNEAREST-NEIGHBOUR DISTANCESPOINTS ON A SPHEREPOISSON PROCESS
Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 281 - 292
Copyright
Copyright © 1982 Applied Probability Trust 

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.)

References

Besag, J. and Diggle, P. J. (1977) Simple Monte Carlo tests for spatial pattern. Appl. Statist. 26, 327–333.CrossRefGoogle Scholar
Cox, D. R. and Hinkley, D. V. (1975) Theoretical Statistics. Chapman and Hall, London.Google Scholar
Diggle, P. J. (1979) On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35, 87–101.CrossRefGoogle Scholar
Diggle, P. J. (1981) Statistical analysis of spatial point patterns. N. Z. Statistician 16, 22–41.Google Scholar
Diggle, P. J., Besag, J. and Gleaves, J. T. (1976) Statistical analysis of spatial point patterns by means of distance methods. Biometrics 32, 659–667.CrossRefGoogle Scholar
Donnelly, K. (1978) Simulations to determine the variance and edge-effect of total nearest neighbour distance. In Simulation Methods in Archaeology , ed. Hodder, I.. Cambridge University Press, London.Google Scholar
Gates, D. J. and Westcott, M. (1980) Further bounds for the distribution of minimum interpoint distance on a sphere. Biometrika 67, 466–469.CrossRefGoogle Scholar
Lieb, ?. (1963) New method in the theory of imperfect gases and liquids. J. Math. Phys. 4, 671–678.CrossRefGoogle Scholar
Moran, P. A. P. (1979) The closest pair of N random points on the surface of a sphere. Biometrika 66, 158–162.CrossRefGoogle Scholar
Ree, F. H. and Hoover, W. G. (1964) Fifth and sixth virial coefficients for hard spheres and hard discs. J. Chem. Phys. 40, 939–950.CrossRefGoogle Scholar
Ripley, B. D. (1977) Modelling spatial pattern (with discussion). J. R. Statist. Soc. B 39, 172–212.Google Scholar
Ripley, B. D. (1979) Tests of ‘randomness’ for spatial point patterns. J. R. Statist. Soc. B 41, 368–374.Google Scholar
Ripley, B. D. and Kelly, F. P. (1977) Markov point processes. J. Lond. Math. Soc. 15, 188–192.CrossRefGoogle Scholar
Ripley, B. D. and Silverman, B. W. (1978) Quick tests for spatial interaction. Biometrika 65, 641–642.CrossRefGoogle Scholar
Ruelle, D. (1969) Statistical Mechanics. Benjamin, New York.Google Scholar