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Poisson's ratio. In materials science and solid mechanics, Poisson's ratio ν (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain.
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.
A discrete random variable X is said to have a Poisson distribution, with parameter if it has a probability mass function given by: [2]: 60 where k is the number of occurrences ( k = 0 , 1 , 2 , … {\displaystyle k=0,1,2,\ldots } ) e is Euler's number ( e = 2.71828 … {\displaystyle e=2.71828\ldots } ) k! = k (k– 1) ··· (3) (2) (1) is the factorial. The positive real number λ is equal ...
Displaced Poisson distribution. Displaced Poisson distributions for several values of and . At , the Poisson distribution is recovered. The probability mass function is only defined at integer values. In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution.
Conway–Maxwell–Poisson. In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and ...
Compound Poisson distribution. In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. The result can be either a continuous or a discrete distribution.
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A Cox point process, Cox process or doubly stochastic Poisson process is a generalization of the Poisson point process by letting its intensity measure to be also random and independent of the underlying Poisson process.