Matches in DBpedia 2016-04 for { ?s ?p "In probability, statistics and related fields, a Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object known as a point process or point field that consists of randomly located points located on some underlying mathematical space. The process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, physics, image processing, and telecommunications.The Poisson point process is often defined on the real line playing an important role in the field of queueing theory where it is used to model certain random events happening in time such as the arrival of customers at a store or phone calls at an exchange. In the plane, the point process, also known as a spatial Poisson process, may represent scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest. In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. In more abstract spaces, the Poisson point process serves as an object of mathematical study in its own right.In all settings, the Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the points. This has sometimes led to the overuse of the point process in mathematical models, and has inspired other point processes, some of which are constructed via the Poisson point process, that seek to capture this interaction.The process is named after French mathematician Siméon Denis Poisson owing to the fact that if a collection of random points in some space forms a Poisson process, then the number points in a region of finite size is directly related to the Poisson distribution, but Poisson never studied the process, which independently arose in several different settings. The process is defined with a single non-negative mathematical object, which, depending on the context, may be a constant, an integrable function or, in more general settings, a Radon measure. If this object is a constant, then the resulting process is called a homogeneous or stationary Poisson point process. Otherwise, the parameter depends on its location in the underlying space, which leads to the inhomogeneous or nonhomogeneous Poisson point process. The word point is often omitted, but there are other Poisson processes of objects, which, instead of points, consist of more complicated mathematical objects such as lines and polygons, and such processes can be based on the Poisson point process."@en }
Showing triples 1 to 2 of
2
with 100 triples per page.
- Poisson_point_process abstract "In probability, statistics and related fields, a Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object known as a point process or point field that consists of randomly located points located on some underlying mathematical space. The process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, physics, image processing, and telecommunications.The Poisson point process is often defined on the real line playing an important role in the field of queueing theory where it is used to model certain random events happening in time such as the arrival of customers at a store or phone calls at an exchange. In the plane, the point process, also known as a spatial Poisson process, may represent scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest. In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. In more abstract spaces, the Poisson point process serves as an object of mathematical study in its own right.In all settings, the Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the points. This has sometimes led to the overuse of the point process in mathematical models, and has inspired other point processes, some of which are constructed via the Poisson point process, that seek to capture this interaction.The process is named after French mathematician Siméon Denis Poisson owing to the fact that if a collection of random points in some space forms a Poisson process, then the number points in a region of finite size is directly related to the Poisson distribution, but Poisson never studied the process, which independently arose in several different settings. The process is defined with a single non-negative mathematical object, which, depending on the context, may be a constant, an integrable function or, in more general settings, a Radon measure. If this object is a constant, then the resulting process is called a homogeneous or stationary Poisson point process. Otherwise, the parameter depends on its location in the underlying space, which leads to the inhomogeneous or nonhomogeneous Poisson point process. The word point is often omitted, but there are other Poisson processes of objects, which, instead of points, consist of more complicated mathematical objects such as lines and polygons, and such processes can be based on the Poisson point process.".
- Q1145117 abstract "In probability, statistics and related fields, a Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object known as a point process or point field that consists of randomly located points located on some underlying mathematical space. The process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, physics, image processing, and telecommunications.The Poisson point process is often defined on the real line playing an important role in the field of queueing theory where it is used to model certain random events happening in time such as the arrival of customers at a store or phone calls at an exchange. In the plane, the point process, also known as a spatial Poisson process, may represent scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest. In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. In more abstract spaces, the Poisson point process serves as an object of mathematical study in its own right.In all settings, the Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the points. This has sometimes led to the overuse of the point process in mathematical models, and has inspired other point processes, some of which are constructed via the Poisson point process, that seek to capture this interaction.The process is named after French mathematician Siméon Denis Poisson owing to the fact that if a collection of random points in some space forms a Poisson process, then the number points in a region of finite size is directly related to the Poisson distribution, but Poisson never studied the process, which independently arose in several different settings. The process is defined with a single non-negative mathematical object, which, depending on the context, may be a constant, an integrable function or, in more general settings, a Radon measure. If this object is a constant, then the resulting process is called a homogeneous or stationary Poisson point process. Otherwise, the parameter depends on its location in the underlying space, which leads to the inhomogeneous or nonhomogeneous Poisson point process. The word point is often omitted, but there are other Poisson processes of objects, which, instead of points, consist of more complicated mathematical objects such as lines and polygons, and such processes can be based on the Poisson point process.".