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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 ...
This page was last edited on 9 December 2016, at 22:59 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
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 Poisson random measure with intensity measure is a family of random variables {} defined on some probability space (,,) such that i) ∀ A ∈ A , N A {\displaystyle \forall A\in {\mathcal {A}},\quad N_{A}} is a Poisson random variable with rate μ ( A ) {\displaystyle \mu (A)} .
Point Processes; Poisson point process; R. Renewal theory; Residual time; S. Simple point process This page was last edited on 9 October 2023, at 03:00 (UTC). ...
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 ...