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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 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 ...
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One point process that gives particularly convenient results under random point process operations is the Poisson point process, [2] The Poisson point process often exhibits a type of mathematical closure such that when a point process operation is applied to some Poisson point process, then provided some conditions on the point process ...
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.
The point pattern theory provides a major building block for generation of random object processes, allowing construction of elaborate random spatial patterns. The simplest version, the Boolean model, places a random compact object at each point of a Poisson point process. More complex versions allow interactions based in various ways on the ...
Poisson point processes (17 P) Pages in category "Poisson distribution" The following 14 pages are in this category, out of 14 total. This list may not reflect recent ...
Sometimes the term point process is not preferred, as historically the word process denoted an evolution of some system in time, so a point process is also called a random point field. [229] There are different interpretations of a point process, such a random counting measure or a random set.