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In mathematics, a point process is a random element whose values are "point patterns" on a set S.While in the exact mathematical definition a point pattern is specified as a locally finite counting measure, it is sufficient for more applied purposes to think of a point pattern as a countable subset of S that has no limit points.
The thinning operation entails using some predefined rule to remove points from a point process to form a new point process .These thinning rules may be deterministic, that is, not random, which is the case for one of the simplest rules known as -thinning: [1] each point of is independently removed (or kept) with some probability (or ).
A visual depiction of a Poisson point process starting. In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
A point process is often denoted by a single letter, [1] [7] [8] for example , and if the point process is considered as a random set, then the corresponding notation: [1], is used to denote that a random point is an element of (or belongs to) the point process . The theory of random sets can be applied to point processes owing to this ...
The fact that the spherical distribution function H s (r) and nearest neighbor function D o (r) are identical for the Poisson point process can be used to statistically test if point process data appears to be that of a Poisson point process. For example, in spatial statistics the J-function is defined for all r ≥ 0 as: [4]
2 Examples. 3 Uniqueness. 4 Literature. Toggle the table of contents. Simple point process. ... A simple point process is a special type of point process in ...