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Poisson's ratio of a material defines the ratio of transverse strain (x direction) to the axial strain (y direction)In materials science and solid mechanics, Poisson's ratio (symbol: ν ()) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading.
Poisson number can refer to: In mechanics, the reciprocal of Poisson's ratio. 1 / v. In statistics, a number drawn from a Poisson distribution
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Conversely, if the "integrated" Poisson's ratio is constant, which is what you are talking about, then the incremental Poisson's ratio must vary with the amount of deformation. Only when the deformations are very small with respect to the dimensions of the unstressed test object do the two become very nearly the same.
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]
The shift geometric distribution is discrete compound Poisson distribution since it is a trivial case of negative binomial distribution. This distribution can model batch arrivals (such as in a bulk queue [5] [9]). The discrete compound Poisson distribution is also widely used in actuarial science for modelling the distribution of the total ...
A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. Negative binomial regression is a popular generalization of Poisson regression because it loosens the highly restrictive assumption that the variance is equal to the mean made by the Poisson model. The traditional negative ...
The Poisson summation formula was discovered by Siméon Denis Poisson and is sometimes called Poisson resummation. For a smooth, complex valued function s ( x ) {\displaystyle s(x)} on R {\displaystyle \mathbb {R} } which decays at infinity with all derivatives ( Schwartz function ), the Poisson summation formula states that