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List Of Things Named After Siméon Denis Poisson
These are things named after Siméon Denis Poisson (1781 – 1840), a French mathematician. Physics * ''Poisson’s Equations'' (thermodynamics) * ''Poisson’s Equation'' (rotational motion) * Schrödinger–Poisson equation * Vlasov–Poisson equation ;Hamiltonian mechanics * Poisson bracket ;Electrostatics *Poisson equation **Euler–Poisson–Darboux equation **Poisson–Boltzmann equation **Screened Poisson equation ;Optics * Poisson's spot ;Elasticity *Poisson's ratio Mathematics * Dirichlet–Poisson problem *Poisson algebra **Poisson superalgebra * Poisson boundary * Poisson bracket, see Hamiltonian mechanics header * Poisson games *Poisson manifold * Poisson ring ** Poisson supermanifold * Poisson–Charlier polynomials * Poisson-Hopf algebra * Poisson–Mellin–Newton cycle *Poisson–Lie group ;Probability theory * Boolean-Poisson model * Poisson bootstrap *Poisson distribution **Compound Poisson distribution ** Conditional Poisson distribution **Conway–Maxwell– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siméon Denis Poisson
Baron Siméon Denis Poisson FRS FRSE (; 21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid mechanics. Moreover, he predicted the Poisson spot in his attempt to disprove the wave theory of Augustin-Jean Fresnel, which was later confirmed. Biography Poisson was born in Pithiviers, Loiret district in France, the son of Siméon Poisson, an officer in the French army. In 1798, he entered the École Polytechnique in Paris as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to make his own decisions as to what he would study. In his final year of study, less than two years after his entry, he published two memoirs, one on Étienne Bézout's method of elimination, the other on the number of integrals of a finite di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Supermanifold
In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to clarify this: M is not a point set space and so, doesn't "really" exist, and really, this algebra is all we have), C^\infty(M) is equipped with a bilinear map called the Poisson superbracket turning it into a Poisson superalgebra. Every symplectic supermanifold is a Poisson supermanifold but not vice versa. See also * Poisson manifold * Poisson algebra * Noncommutative geometry {{differential-geometry-stub Symplectic geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Binomial Distribution
In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson. In other words, it is the probability distribution of the number of successes in a collection of ''n'' independent yes/no experiments with success probabilities p_1, p_2, \dots , p_n. The ordinary binomial distribution is a special case of the Poisson binomial distribution, when all success probabilities are the same, that is p_1 = p_2 = \cdots = p_n. Definitions Probability Mass Function The probability of having ''k'' successful trials out of a total of ''n'' can be written as the sum :\Pr(K=k) = \sum\limits_ \prod\limits_ p_i \prod\limits_ (1-p_j) where F_k is the set of all subsets of ''k'' integers that can be selected from . For example, if ''n'' = 3, then F_2=\left\. A^c is the complement of A, i.e. A^c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Poisson Distribution
In probability theory and statistics, the geometric Poisson distribution (also called the Pólya–Aeppli distribution) is used for describing objects that come in clusters, where the number of clusters follows a Poisson distribution and the number of objects within a cluster follows a geometric distribution. It is a particular case of the compound Poisson distribution. The probability mass function of a random variable ''N'' distributed according to the geometric Poisson distribution \mathcal(\lambda,\theta) is given by : f_N(n) = \mathrm(N=n)= \begin \sum_^n e^\frac(1-\theta)^\theta^k\binom, & n>0 \\ e^, & n=0 \end where ''λ'' is the parameter of the underlying Poisson distribution and θ is the parameter of the geometric distribution. The distribution was described by George Pólya in 1930. Pólya credited his student Alfred Aeppli's 1924 dissertation as the original source. It was called the geometric Poisson distribution by Sherbrooke in 1968, who gave probability tables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displaced Poisson Distribution
In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function is : P(X=n) = \begin e^\dfrac\cdot\dfrac, \quad n=0,1,2,\ldots &\text r\geq 0\\0pt e^\dfrac\cdot\dfrac,\quad n=s,s+1,s+2,\ldots &\text \end where \lambda>0 and ''r'' is a new parameter; the Poisson distribution is recovered at ''r'' = 0. Here I\left(r,\lambda\right) is the Pearson's incomplete gamma function In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals. Their respective names stem from their integral definitions, which ...: : I(r,\lambda)=\sum^\infty_\frac, where ''s'' is the integral part of ''r''. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is P(X=n)/P(X=n-1)) is given by \lambda/n for n>0 and the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway–Maxwell–Poisson Distribution
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 underdispersion. It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case. Background The CMP distribution was originally proposed by Conway and Maxwell in 1962 as a solution to handling queueing systems with state-dependent service rates. The CMP distribution was introduced into the statistics literature by Boatwright et al. 2003 Boatwright, P., Borle, S. and Kadane, J.B. "A model of the joint distribution of purchase quantity and timing." Journal of the American Statistical Association 98 (2003): 564–572. and Shmueli et al. (2005).Shmueli G., Minka T., Ka ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-truncated Poisson Distribution
In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers. This distribution is also known as the conditional Poisson distribution or the positive Poisson distribution. It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero. Consider for example the random variable of the number of items in a shopper's basket at a supermarket checkout line. Presumably a shopper does not stand in line with nothing to buy (i.e., the minimum purchase is 1 item), so this phenomenon may follow a ZTP distribution. Since the ZTP is a truncated distribution with the truncation stipulated as , one can derive the probability mass function from a standard Poisson distribution ) as follows: : g(k;\lambda) = P(X = k \mid X > 0) = \frac = \frac = \fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Definition Suppose that :N\sim\operatorname(\lambda), i.e., ''N'' is a random variable whose distribution is a Poisson distribution with expected value λ, and that :X_1, X_2, X_3, \dots are identically distributed random variables that are mutually independent and also independent of ''N''. Then the probability distribution of the sum of N i.i.d. random variables :Y = \sum_^N X_n is a compound Poisson distribution. In the case ''N'' = 0, then this is a sum of 0 terms, so the value of ''Y'' is 0. Hence the conditional distribution of ''Y'' given that ''N'' = 0 is a degenerate distribution. The compound Poisson distribution is obtained by marginalising the j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and Statistical independence, independently of the time since the last event. It is named after France, French mathematician Siméon Denis Poisson (; ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bootstrapping (statistics)
Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates.software This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an (such as its ) by measuring those properties when sampling from an approximating distribution. One standard choice for an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Model (probability Theory)
For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson point process of rate \lambda in the plane and make each point be the center of a random set; the resulting union of overlapping sets is a realization of the Boolean model . More precisely, the parameters are \lambda and a probability distribution on compact sets; for each point \xi of the Poisson point process we pick a set C_\xi from the distribution, and then define as the union \cup_\xi (\xi + C_\xi) of translated sets. To illustrate tractability with one simple formula, the mean density of equals 1 - \exp(- \lambda A) where \Gamma denotes the area of C_\xi and A=\operatorname (\Gamma). The classical theory of stochastic geometry In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson–Lie Group
In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of Lie groups. Many quantum groups are quantizations of the Poisson algebra of functions on a Poisson–Lie group. Definition A Poisson–Lie group is a Lie group ''G'' equipped with a Poisson bracket for which the group multiplication \mu:G\times G\to G with \mu(g_1, g_2)=g_1g_2 is a Poisson map, where the manifold G\times G has been given the structure of a product Poisson manifold. Explicitly, the following identity must hold for a Poisson–Lie group: :\ (gg') = \ (g') + \ (g) where f_1 and f_2 are real-valued, smooth functions on the Lie group, while ''g'' and ''g''' are elements of the Lie group. Here, ''L_g'' denotes left-multiplication and ''R_g'' denot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
