Analysis of Central Place Theory.
INDIANA UNIV AT BLOOMINGTON DEPT OF MATHEMATICS
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Central Place Theory predicts a regular spatial pattern in the plane and it is observed that the Delaunay triangles will be equilateral under the theory. However, when the pattern is random, the asymptotic p.d.f. of the interior angles of a random Delaunay triangle are given. A von Mises-type model is proposed with a concentration parameter K the larger the value of K, the closer one is to the Central Place Theory. The model can be approximated to the Miles density for some value of K. The moment and maximum likelihood estimators of K are provided, and it is recognized that the areas of the Delaunay triangles play an important role. A test of departure from the random pattern is constructed with the alternative of Central Place Theory. As a numerical example, 44 Central Places in Iowa are analyzed where some evidence for the validity of Central Place Theory in that particular region is found.
- Statistics and Probability