Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-12T11:39:06.179Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum likelihood estimation for random sequential adsorption

Part of: Inference from stochastic processes Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  08 September 2016

M. N. M. van Lieshout
M. N. M. van Lieshout*
Affiliation:
CWI and EURANDOM
*
∗ Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The existence and uniqueness of maximum likelihood estimators for the time and range parameters in random sequential adsorption models are investigated.

Keywords

Maximum likelihood estimationrandom sequential adsorptionsequential spatial processsimple sequential inhibition

MSC classification

Primary: 60G55: Point processes 60D05: Geometric probability and stochastic geometry 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 889 - 898
Copyright
Copyright © Applied Probability Trust 2006 

References

Cressie, N. A. C. (1991). Statistics for Spatial Data. John Wiley, New York.Google Scholar
Daley, D. J. and Vere-Jones, D. (1988). An Introduction to The Theory of Point Processes. Springer, New York.Google Scholar
Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.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
Döge, G. (2001). Perfect simulation for random sequential adsorption of d-dimensional spheres with random radii. J. Statist. Comput. Simul. 69, 141–156.CrossRefGoogle Scholar
Dvoretzky, A. and Robbins, H. (1964). On the ‘parking’ problem. Publ. Math. Res. Inst. Hungar. Acad. Sci. 9, 209–225.Google Scholar
Evans, J. W. (1993). Random and cooperative sequential adsorption. Rev. Modern Phys. 65, 1281–1329.CrossRefGoogle Scholar
Feder, J. (1980). Random sequential adsorption. J. Theoret. Biol. 87, 237–254.CrossRefGoogle Scholar
Feller, W. (1970). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. John Wiley, New York.Google Scholar
Hall, P. G. (1988). Introduction to the Theory of Coverage Processes. John Wiley, New York.Google Scholar
Lotwick, H. W. (1982). Simulations of some spatial hard core models, and the complete packing problem. J. Statist. Comput. Simul. 15, 295–314.CrossRefGoogle Scholar
Mathai, A. M. (1982). Storage capacity of a dam with gamma type inputs. Ann. Inst. Statist. Math. 34, 591–597.CrossRefGoogle Scholar
Penrose, M. D. (2001). Random parking, sequential adsorption, and the Jamming limit. Commun. Math. Phys. 218, 153–176.CrossRefGoogle Scholar
Prékopa, A. (1973). On logarithmic concave measures and functions. Acta Sci. Math. (Szeged) 34, 335–343.Google Scholar
Rényi, A. (1958). On a one-dimensional problem concerning random space filling. Publ. Math. Inst. Hungar. Acad. Sci. 3, 109–125.Google Scholar
Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge University Press.CrossRefGoogle Scholar
Senger, B., Voegel, J.-C. and Schaaf, P. (2000). Irreversible adsorption of colloidal particles on solid substrates. Colloids Surfaces A 165, 255–285.CrossRefGoogle Scholar
Stoyan, D. (1998). Random sets: models and statistics. Internat. Statist. Rev. 66, 1–27.CrossRefGoogle Scholar
Tanemura, M. (1979). On random complete packing by disks. Ann. Inst. Statist. Math. 31, 351–365.CrossRefGoogle Scholar
Upton, G. J. G. and Fingleton, B. (1985). Spatial Data Analysis by Example, Vol. I, Point Pattern and Quantitative Data. John Wiley, Chichester.Google Scholar
Van Lieshout, M. N. M. (2006). Campbell and moment measures for finite sequential spatial processes. In Proc. Prague Stoch. 2006, eds Hušková, M. and Janžura, M., Matfyzpress, Prague, pp. 215–224.Google Scholar
Van Lieshout, M. N. M. (2006). Markovianity in space and time. In Dynamics and Stochastics: Festschrift in Honour of M. S. Keane (Lecture Notes Monogr. Ser. 48), eds Denteneer, D., den Hollander, F. and Verbitskiy, E., Institute for Mathematical Statistics, Beachwood, OH, pp. 154–168.CrossRefGoogle Scholar