The interpoint distance distribution as a descriptor of point patterns, with an application to cluster detection

The topic of this paper is the distribution of the distance between two points distributed independently in space. We illustrate the use of this interpoint distance distribution to describe the characteristics of a set of points within some fixed region. The properties of its sample version, and thus the inference about this function, are discussed both in the discrete and in the continuous setting. We illustrate its use in the detection of spatial clustering by application to a well-known leukaemia data set, and report on the results of a simulation experiment designed to study the power characteristics of the methods within that study region and in an artificial homogenous setting.