Cite as:

Okabe A, Yoshikawa T, Fujii A, Oikawa K, 1988, "The statistical analysis of a distribution of activity points in relation to surface-like elements" *Environment and Planning A* **20**(5) 609 – 620

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**The statistical analysis of a distribution of activity points in relation to surface-like elements**

**A Okabe, T Yoshikawa, A Fujii, K Oikawa**

Received 1 August 1986; in revised form 14 July 1987

**Abstract. **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 functions 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.

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