Measuring the Shape Distortions of Retail Market Areas

Existing measures of shape rely upon prespecifying boundaries and have little relationship to theory. Where definite shape boundaries do not exist, these problems can be overcome by use of weighted data points and statistical moments. Measures of various shape properties are identified, including compactness and the degree of distortion from the circular shape underlying central place theory and, the gravity model; a bivariate normal distribution is assumed. Examples are included of the application of the measures to suburban retail market areas, although the measures are applicable to all situations in which the statistical model is a reasonable assumption and only subjective boundaries of shape can be identified.