The Poisson point process is often defined on the real line, where it can be considered as a stochastic process. The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution. The process is named after French mathematician Siméon Denis Poisson despite Poisson never having studied the process. This point 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, seismology, physics, economics, image processing, and telecommunications. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space. A visual depiction of a Poisson point process starting from 0, in which increments occur continuously and independently at rate λ.
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