Poisson distribution

a limiting form of the binomial probability distribution for small values of the probability of success and for large numbers of trials: particularly useful in industrial qualitycontrol work and in radiation and bacteriological problems.[192025; named after S. D. Poisson (17811840), French mathematician and physicist]
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in statistics, a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space.The French mathematician SiméonDenis Poisson (Poisson, SiméonDenis) developed his function in 1830 to describe the number of times a gambler would win a rarely won game of chance in a large number of tries. Letting p represent the probability of a win on any given try, the mean, or average, number of wins (λ) in n tries will be given by λ = np. Using the Swiss mathematician Jakob Bernoulli (Bernoulli, Jakob)'s binomial distribution, Poisson showed that the probability of obtaining k wins is approximately λ^{k}/e^{λ}k!, where e is the exponential function and k! = (k − 1)(k − 2)⋯2∙1. Noteworthy is the fact that λ equals both the mean and variance (a measure of the dispersal of data away from the mean) for the Poisson distribution.The Poisson distribution is now recognized as a vitally important distribution in its own right. For example, in 1946 the British statistician R.D. Clarke published “An Application of the Poisson Distribution,” in which he disclosed his analysis of the distribution of hits of flying bombs (V1 (V1 missile) and V2 (V2 missile) missiles) in London during World War II. Some areas were hit more often than others (see table—>). The British military wished to know if the Germans were targeting these districts (the hits indicating great technical precision) or if the distribution was due to chance. If the missiles were in fact only randomly targeted (within a more general area), the British could simply disperse important installations to decrease the likelihood of their being hit.Clarke began by dividing an area into thousands of tiny, equally sized plots. Within each of these, it was unlikely that there would be even one hit, let alone more. Furthermore, under the assumption that the missiles fell randomly, the chance of a hit in any one plot would be a constant across all the plots. Therefore, the total number of hits would be much like the number of wins in a large number of repetitions of a game of chance with a very small probability of winning. This sort of reasoning led Clarke to a formal derivation of the Poisson distribution as a model. The observed hit frequencies were very close to the predicted Poisson frequencies. Hence, Clarke reported that the observed variations appeared to have been generated solely by chance.Richard Routledge* * *
Universalium. 2010.
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Poisson distribution — [pwä sōn′, pwäsōn′] n. [after S. D. Poisson (1781 1840), Fr mathematician] Statistics a frequency distribution that may be regarded as an approximation of the binomial distribution when the number of events becomes large and the probability of… … English World dictionary
Poisson Distribution — A statistical distribution showing the frequency probability of specific events when the average probability of a single occurrence is known. The Poisson distribution is a discrete function. For example, if the average number of people that rent… … Investment dictionary
Poisson distribution — * cite journal author=Joachim H. Ahrens, Ulrich Dieter title=Computer Generation of Poisson Deviates journal=ACM Transactions on Mathematical Software year=1982 volume=8 issue=2 pages=163 179 doi=10.1145/355993.355997* cite journal author=Ronald… … Wikipedia
Poisson distribution — see frequency distribution S. D. Poisson (1781 1840), French mathematician * * * the probability distribution that describes counts of events randomly distributed in time or space, such as radioactive decay or blood cell counts. The probability… … Medical dictionary
Poisson distribution — Puasono skirstinys statusas T sritis Standartizacija ir metrologija apibrėžtis Retų įvykių skirstinys. atitikmenys: angl. Poisson distribution vok. Poissonsche Verteilung, f; Poisson Verteilung, f rus. распределение Пуассона, n pranc.… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
Poisson distribution — Puasono skirstinys statusas T sritis fizika atitikmenys: angl. Poisson distribution vok. Poissonsche Verteilung, f; Poisson Verteilung, f rus. распределение Пуассона, n pranc. distribution de Poisson, f … Fizikos terminų žodynas
Poisson distribution — [ pwʌsɒPoisson distribution] noun Statistics a discrete frequency distribution which gives the probability of a number of independent events occurring in a fixed time. Origin named after the French mathematical physicist Siméon Denis Poisson… … English new terms dictionary
Poisson distribution — distribution probability that represents the happening of unusual events in a large number of trials … English contemporary dictionary
Poisson distribution — noun Etymology: Siméon D. Poisson died 1840 French mathematician Date: 1922 a probability density function that is often used as a mathematical model of the number of outcomes obtained in a suitable interval of time and space, that has its mean… … New Collegiate Dictionary
Poisson distribution — Pois•son′ distribu tion [[t]pwɑˈsoʊn, ˈsɔ̃[/t]] n. sta a probability distribution whose mean and variance are identical • Etymology: 1920–25; after S. D. Poisson (1781–1840), French mathematician and physicist … From formal English to slang