The objective of this paper is to formulate a statistical method of testing the hypothesis that the distribution of activity points (such as retail stores) is independent of location of ‘surface-like’ infrastructural elements (such as parks). In order to do this, first, the probability density function of a distance from a random point to the nearest surface-like element is derived. Second, through the use of this function, a measure, R, of spatial dependency on the surface-like elements is defined as the ratio of the average nearest-neighbor distance to the expected average nearest-neighbor distance. This measure is an extension of the ordinary nearest-neighbor distance measure frequently referred to in geography and ecology. Third, the statistical use of measure R is shown. Fourth, as this measure is difficult to compute geometrically, the computational method of calculating the value of R is developed. Last, by use of this method, a test is conducted to decide whether or not the distribution of high-class apartment buildings in Setagaya, Tokyo, is affected by the location of big parks.
Manifold-adaptive dimension estimation revisited
