Spherical contact distribution function

rdf:langString Spherical contact distribution function

rdf:langString In probability and statistics, a spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, a spherical contact distribution function is defined as probability distribution of the radius of a sphere when it first encounters or makes contact with a point in a point process. This function can be contrasted with the nearest neighbour function, which is defined in relation to some point in the point process as being the probability distribution of the distance from that point to its nearest neighbouring point in the same point process. The spherical contact function is also referred to as the contact distribution function, but some authors define the contact distribution function in relation to a more general set, and not simply a sphere as in the case of the spherical contact distribution function. Spherical contact distribution functions 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.