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The simplest and most ubiquitous example of a point process is the Poisson point process, which is a spatial generalisation of the Poisson process. A Poisson (counting) process on the line can be characterised by two properties : the number of points (or events) in disjoint intervals are independent and have a Poisson distribution. A Poisson ...
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 ...
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 point process is called simple if no two (or more points) coincide in location with probability one.Given that often point processes are simple and the order of the points does not matter, a collection of random points can be considered as a random set of points [1] [5] The theory of random sets was independently developed by David Kendall and Georges Matheron.
A simple point process is a special type of point process in probability theory. In simple point processes, every point is assigned the weight one. Definition
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Pages in category "Poisson point processes" The following 17 pages are in this category, out of 17 total. ... Mapping theorem (point process) Mixed Poisson process; P.
It describes how a Poisson point process is altered under measurable transformations. This allows construction of more complex Poisson point processes out of homogeneous Poisson point processes and can, for example, be used to simulate these more complex Poisson point processes in a similar manner to inverse transform sampling.