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Likelihood and nearest-neighbor distance properties of multidimensional Poisson cluster processes

  • Michel Baudin (a1)
Abstract

The probability generating functional representation of a multidimensional Poisson cluster process is utilized to derive a formula for its likelihood function, but the prohibitive complexity of this formula precludes its practical application to statistical inference. In the case of isotropic processes, it is however feasible to compute functions such as the probability Q(r) of finding no point in a disc of radius r and the probability Q(r | 0) of nearest-neighbor distances greater than r, as well as the expected number C(r | 0) of points at a distance less than r from a given point. Explicit formulas and asymptotic developments are derived for these functions in the n-dimensional case. These can effectively be used as tools for statistical analysis.

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L. P. Ammann and P. F. Thall (1979) Count distributions, orderliness and invariance of Poisson cluster processes. J. Appl. Prob. 16, 261273.

R. B. Davies (1977) Testing the hypothesis that a point process is Poisson. Adv. Appl. Prob. 9, 724746.

Y. Y. Kagan and L. Knopoff (1976a) Statistical search for non-random features of the seismicity of strong earthquakes. Phys. Earth, Planetary Interiors 12, 291318.

Y. Y. Kagan and L. Knopoff (1976b) Earthquake risk prediction as a stochastic process. Phys. Earth, Planetary Interiors 14, 97108.

O. Macchi (1975) The coincidence approach to stochastic point processes. Adv. Appl. Prob. 7, 83122.

J. Mecke (1967) Stationäre zufällige Masse auf lokalkompakten, abelschen Gruppen. Z. Wahrscheinlichkeitsth. 9, 3658.

J. E. Moyal (1962) The general theory of stochastic population processes. Acta Math. 108, 131.

D. Vere-Jones (1978) Space-time correlations for microearthquakes — a pilot study. Suppl. Adv. Appl. Prob. 10, 7387.

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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