Asymptotic Developments of the Solutions of the Translation Equation

1993 ◽  
Vol 12 (3) ◽  
pp. 585-590 ◽  
Author(s):  
Lothar Berg
Keyword(s):  
Translation Equation ◽  
Asymptotic Developments

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

1981 ◽  
Vol 18 (4) ◽  
pp. 879-888 ◽  
Author(s):  
Michel Baudin
Keyword(s):  
Nearest Neighbor ◽  
Likelihood Function ◽  
Practical Application ◽  
Expected Number ◽  
Generating Functional ◽  
Functional Representation ◽  
Distance Properties ◽  
Poisson Cluster ◽  
Nearest Neighbor Distances ◽  
Asymptotic Developments

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.

scholarly journals Γ-Asymptotic Developments, the Cahn–Hilliard Functional, and Curvatures

1996 ◽  
Vol 197 (3) ◽  
pp. 908-924 ◽  
Author(s):  
G. Anzellotti ◽  
S. Baldo ◽  
G. Orlandi
Keyword(s):  
Asymptotic Developments
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