Poisson distribution

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Pois·son distribution

n. Statistics
A probability distribution which arises when counting the number of occurrences of a rare event in a long series of trials.

[After Siméon Denis Poisson (1781-1840), French mathematician.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Poisson distribution

(Statistics) statistics a distribution that represents the number of events occurring randomly in a fixed time at an average rate λ; symbol P0(λ). For large n and small p with np = λ it approximates to the binomial distribution Bi(n,p)
[C19: named after S. D. Poisson]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Pois•son′ distribu`tion

(pwɑˈsoʊn, -ˈsɔ̃)
a probability distribution whose mean and variance are identical.
[1920–25; after S. Dutch. Poisson (1781–1840), French mathematician and physicist]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Poisson distribution - a theoretical distribution that is a good approximation to the binomial distribution when the probability is small and the number of trials is large
distribution, statistical distribution - (statistics) an arrangement of values of a variable showing their observed or theoretical frequency of occurrence
statistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
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References in periodicals archive ?
Also, the proposed model produces networks with out-degree distributions that follow exponential and Poisson distributions. This contrasts with the out-degree distributions of several real networks in which the out-degree distribution follows a power-law.
which means that {[M.sup.x.sub.t]; t = 1, ..., [infinity]} follows a compound Poisson process in which both the number of jumps and jump size follow Poisson distributions.
Keeping the math at an algebra level, this handbook explains the probability mass function and distributional parameters for discrete uniform, binomial, multinomial, hypergeometric, geometric, negative binomial, and Poisson distributions. The continuous probability chapter introduces the law of large numbers, MarkovAEs inequality, and ChebyshevAEs theorem, and presents 15 continuous probability distributions useful for the types of problems that arise in the quality field.
Poisson distributions for number of tropical cyclones, number of hurricanes, number of major hurricanes, and number of U.S.
Equation (13) is the mathematical link between the exponential and Poisson distributions. Equation (13) is the Poisson Equation (12) with the number of occurrences, x, set equal to zero.
Since the probability matrix P can become large if the number of buffers is large, together with a large number allowed per buffer, we modified the probability structure to be represented by truncated Poisson distributions. The Poisson distribution is generally defined on the integer range 0, 1, ...
The distribution of the difference, a = s1 - s2, of two statistically independent random variables s1 and s2, each having Poisson distributions with different expected values [m.sub.1] and [m.sub.2], is denoted as the Skellam distribution [23] and can be given as
The authors introduce order statistics and applications, then cover basic distribution theory, including joint distribution of two order statistics, discrete order statistics, including joint probability mass functions and distributions of the range, order statistics from specific distributions, including Bernoulli and Poisson distributions moment relations, bounds, approximations, characterizations using order statistics, order statistics in statistical inference, asymptotic theory, including central and intermediate order statistics and record values.
After the introduction of geometric Brownian motions, much attention was devoted to Poisson distributions as an alternative specification of stock returns.
and it consists of normal, lognormal and Poisson distributions. The last two can be substituted also with some other suitable distributions.
The number of events in the photoelectron peaks is then determined by the sum of these Poisson distributions over the various electron energies and paddle positions where the electrons hit.