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  2. Poisson distribution - Wikipedia

    en.wikipedia.org/wiki/Poisson_distribution

    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]

  3. Photon statistics - Wikipedia

    en.wikipedia.org/wiki/Photon_statistics

    Photon statistics is the theoretical and experimental study of the statistical distributions produced in photon counting experiments, which use photodetectors to analyze the intrinsic statistical nature of photons in a light source.

  4. Cumulant - Wikipedia

    en.wikipedia.org/wiki/Cumulant

    The limiting case n −1 = 0 is a Poisson distribution. The negative binomial distributions, (number of failures before r successes with probability p of success on each trial). The special case r = 1 is a geometric distribution. Every cumulant is just r times the corresponding

  5. Shot noise - Wikipedia

    en.wikipedia.org/wiki/Shot_noise

    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.

  6. Poisson regression - Wikipedia

    en.wikipedia.org/wiki/Poisson_regression

    In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. [1] Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters.

  7. Probability theory - Wikipedia

    en.wikipedia.org/wiki/Probability_theory

    Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.

  8. Poisson point process - Wikipedia

    en.wikipedia.org/wiki/Poisson_point_process

    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 ...

  9. (a,b,0) class of distributions - Wikipedia

    en.wikipedia.org/wiki/(a,b,0)_class_of_distributions

    The (a,b,0) class of distributions is also known as the Panjer, [1] [2] the Poisson-type or the Katz family of distributions, [3] [4] and may be retrieved through the Conway–Maxwell–Poisson distribution. Only the Poisson, binomial and negative binomial distributions satisfy the full form of this