Nearest neighbour analysis of random distributions on a sphere

Abstract

The distribution of nearest neighbor separations of points placed randomly on the surface of a sphere is useful in deciding whether objects in real data are random or occur in pairs. In the past, a Poisson distribution has been used. A more natural spherical analysis of this problem, obtaining the probability distribution function and the mean separation of random points, is presented. It is shown that for a large number of points this distribution is equivalent to the Poisson form and can be extended to give the 2nd and Mth nearest neighbor distributions. To illustrate the application to astronomical data, the distribution of X-ray clusters, which are found to occur in pairs, is considered.