Analysis of Central Place Theory.

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 04, 1978
Accession Number
ADA051861

Entities

People

  • K. V. Mardia
  • Madan L. Puri
  • Robert G. Edwards

Organizations

  • Indiana University Bloomington

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Algorithms
  • Bessel Functions
  • Cells
  • Distribution Functions
  • Equations
  • Estimators
  • Frequency
  • Mathematics
  • Maximum Likelihood Estimation
  • Numbers
  • Order Statistics
  • Polygons
  • Security
  • Simulations
  • Statistical Algorithms

Fields of Study

  • Mathematics

Readers

  • Aviation Safety and Air Traffic Management
  • Fluid Dynamics.
  • Statistical inference.