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In probability theory, the law of rare events or Poisson limit theorem states that the Poisson distribution may be used as an approximation to the binomial distribution, under certain conditions. [1] The theorem was named after Siméon Denis Poisson (1781–1840). A generalization of this theorem is Le Cam's theorem
Baron Siméon Denis Poisson FRS FRSE (French: [si.me.ɔ̃ də.ni pwa.sɔ̃]; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid ...
Cameron–Martin theorem; Campbell's theorem (probability) Central limit theorem; Characterization of probability distributions; Chung–Erdős inequality; Condorcet's jury theorem; Continuous mapping theorem; Contraction principle (large deviations theory) Coupon collector's problem; Cox's theorem; Cramér–Wold theorem; Cramér's theorem ...
In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /; French pronunciation:) 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]
There is no simple formula for the entropy of a Poisson binomial distribution, but the entropy is bounded above by the entropy of a binomial distribution with the same number parameter and the same mean. Therefore, the entropy is also bounded above by the entropy of a Poisson distribution with the same mean. [7]
Central limit theorem. Central limit theorem (illustration) – redirects to Illustration of the central limit theorem; Central limit theorem for directional statistics; Lyapunov's central limit theorem; Martingale central limit theorem; Central moment; Central tendency; Census; Cepstrum; CHAID – CHi-squared Automatic Interaction Detector
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 ...
First hitting times are central features of many families of stochastic processes, including Poisson processes, Wiener processes, gamma processes, and Markov chains, to name but a few. The state of the stochastic process may represent, for example, the strength of a physical system, the health of an individual, or the financial condition of a ...