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In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
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 ...
This means that aggregate insurance claims and the amount of rainfall accumulated in a reservoir are modelled by a gamma process – much like the exponential distribution generates a Poisson process. The gamma distribution is also used to model errors in multi-level Poisson regression models because a mixture of Poisson distributions with ...
According to his analysis, both Poisson distribution and negative binomial distribution provided an adequate fit to results of football games. The series of ball passing between players during football matches was successfully analyzed using negative binomial distribution by Reep and Benjamin [3] in 1968.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
(The related question of the number of events in a given amount of time is described by the Poisson distribution.) The Erlang distribution, which measures the time between incoming calls, can be used in conjunction with the expected duration of incoming calls to produce information about the traffic load measured in erlangs.
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, [1] nearest-neighbor distribution function [2] or nearest neighbor distribution [3] is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned ...
Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge . Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light.