Search results
Results From The WOW.Com Content Network
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 ...
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.
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.
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 ...
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 ...
Realization of Boolean model with random-radii discs. For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry.
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.