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In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, nearest neighbor functions are defined with respect to some point in the point process as being the probability distribution of the distance from this point to its nearest neighboring point in the same point process, hence they are used to describe the probability of another point existing within some distance of a point. A nearest neighbor function can be contrasted with a spherical contact distribution function, which is not defined in reference to some initial point but rather as the probability distribution of the radius of a sphere when it first encounters or makes contact with a point of a point process.
Nearest neighbor function are used in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.