No. 1115

Title:

Remark on spatial point pattern interactions in a Neyman-Scott spacial cluster field and their application to evaluation of a parameter set

Author(s):

Tanaka, Ushio (The Institute of Statistical Mathematics)

Key words:

cluster diameter; Neyman-Scott spatial cluster field; Palm intensity; parameter evaluation; range of correlation; spatial point pattern interactions.

Abstract:

    In the present article we consider the delimitation of the distances of spatial point pattern interactions in a Neyman-Scott spatial cluster field and note its geometrical implication. Its vanishing distance of finiteness is interpreted as the so-called range of correlation. A finite range of correlation for a Neyman-Scott spatial cluster field implies the unobserved diameter per cluster in the spatial cluster field. To investigate the range of correlation, we require the explicit form of a density function with respect to the distances between two arbitrary points per cluster. Due to making it explicit, we can obtain a necessary and sufficient condition for the finite range of correlation. As an application, by evaluating solely a range of correlation of finiteness, we demonstrate that it is feasible to evaluate the parameter set with respect to the distances between each individual cluster centre and its points. The evaluation procedure for such a parameter set might be heuristic in the absence of a conventional parameter sensitivity estimation procedure, namely, a maximum likelihood analysis.