Poisson distribution

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Related to Poisson distribution: binomial distribution, Poisson process

Pois·son distribution

(pwä-sôN′)
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.]

Poisson distribution

(ˈpwɑːsən)
n
(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]

Pois•son′ distribu`tion

(pwɑˈsoʊn, -ˈsɔ̃)
n.
a probability distribution whose mean and variance are identical.
[1920–25; after S. Dutch. Poisson (1781–1840), French mathematician and physicist]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 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 largedistribution, statistical distribution - (statistics) an arrangement of values of a variable showing their observed or theoretical frequency of occurrencestatistics - 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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We then modeled the number of mislaid eggs in: (1) one-egg clutches, (2) two-egg clutches, and (3) both one- and two-egg clutches as a function of total available nests using generalized linear mixed models (GLMM) that assumed a Poisson distribution. We included an offset term in each model for the number of breeding females, which allowed us to assess the number of mislaid eggs relative to the number of females at each site.
Note that count data can be modelled for certain distributions using continuous distributions; for example, count data that follows a Poisson distribution and has a high mean can be modelled using a normal distribution.
Traditionally, a macroscopic approach for analysing such networks have been used wherein the users and/or remote radio heads are randomly deployed, often following a homogeneous Poisson distribution such that well established stochastic geometry theory can be applied.
* Conditional on the past [[U.bar].sub.t], variable [Z.sub.t] follows Poisson distribution with parameter [[beta]U.sub.t].
In this paper, we highlight the use of neutrosophic crisp sets theory [3,4] with the classical probability distributions, particularly Poisson distribution, Exponential distribution and Uniform distribution, which opens the way for dealing with issues that follow the classical distributions and at the same time contain data not specified accurately.
In real networks, the degree distribution P(k) , defined as the probability that a node chosen uniformly at random has degree k or, equivalently, as the fraction of nodes in the graph having degree k, significantly deviates from the poisson distribution expected for a random graph  and, in many cases, exhibits a power law (scale-free) tail with an exponent .
The count data of each taxon was checked for fit to a known probability distribution according to the steps in Krebs (1999) and Crawley (2007): Poisson distribution for random pattern (ID = 1), negative binomial distribution for aggregated pattern (ID > 1), and binomial distribution for uniform pattern (ID < 1).
In these cases, the latent variables follow, respectively, a geometric and a zero-truncated Poisson distribution and each of components in risk came from a Weibull baseline distribution.
Examples are as follows: for p = 0 then we have a normal distribution, p = 1, and [THETA] = 1; it is a Poisson distribution, and Gamma distribution for p = 2, while when p = 3 it is Gaussian inverse distribution.
Recently, Porwal  introduced a Poisson distribution series whose coefficients are probabilities of Poisson distribution and established a correlation between Statistics and Geometric Function Theory which opened up a new direction of research.
Regarding the fitting of the binomial distribution, if as n increases, p decreases such that n * p remains constant, then the binomial distribution approaches the Poisson distribution; see Mood, Graybill, and Boes (1974).

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