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Note on the determination of cluster centers from a realization of a multidimensional Poisson cluster process

Published online by Cambridge University Press:  14 July 2016

Michel Baudin
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Abstract

This is the sequel to a previous paper (Baudin (1981)). The joint probability generating functional of two point processes is introduced as a tool to compute the conditional intensity of the process of cluster centers of a multidimensional Poisson cluster process when a realization is given in a bounded observation window. An explicit formula is derived but it is too complicated for actual use; a linear method for practical estimation is discussed.

Keywords

PROBABILITY GENERATING FUNCTIONALPOINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 136 - 143
Copyright
Copyright © Applied Probability Trust 1983 

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References

Amman, L. P. and Thall, P. F. (1979) Count distributions, orderliness and invariance of Poisson cluster processes. J. Appl. Prob. 16, 261–273.Google Scholar
Baudin, M. (1981) Likelihood and nearest neighbour distance properties of multidimensional Poisson cluster processes. J. Appl. Prob. 18, 879–888.CrossRefGoogle Scholar
Bolshakov, I. A. (1969) Statistical problems in the separation of a signal stream from noise. Soviet Radio, Moscow.Google Scholar
Fisher, L. (1972) A survey of the mathematical theory of multidimensional point processes. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 468–513.Google Scholar
Kagan, Ya. Ya. (1973) On a probabilistic description of the seismic regime. Izv. Acad. Sci. USSR Phys. Solid Earth 9, 213–219.Google Scholar
Kagan, Y. and Knopoff, L. (1976) Statistical search for non-random features of the seismicity of strong earthquakes. Phys. Earth, Planetary Interiors 12, 291–318.Google Scholar
Neyman, J. and Scott, E. L. (1972) Processes of clustering and applications. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 646–681.Google Scholar
Vere-Jones, D. (1970) Stochastic models for earthquake occurrence. J. R. Statist. Soc. B 32, 1–62.Google Scholar
Westcott, M. (1972) The probability generating functional. J. Austral. Math. Soc. 14, 448–466.Google Scholar