Estimation of Density from a Sample of Joint Point and Nearest-Neighbor Distances

Distances are measured from sample points to the nearest member of a population, from that member to its nearest neighbor, and from that neighbor to its nearest neighbor. The point-to-nearest member is used to obtain an estimate of density, which is characteristically unbiased if the population is random, but biased if the population is uniformly or contagiously distributed. The bias is corrected by an exponential function of the sum of the point distances divided by the sum of either the nearest- or second-nearest-neighbor distances. The distances also provide an index of departure from randomness.