| 释义 |
Poisson Math.|pwasɔ̃|
[The name of S. D. Poisson (1781–1840), French mathematician and physicist.]
1. Used, chiefly attrib., with reference to a discrete frequency distribution defined by e-mmx/x!, which gives the probability of x events occurring, m being its only parameter; it has mean m and variance m2, and is appropriate if the events occur independently and there is no upper limit to their number, so that the distribution is the limit of the binomial distribution as the number of trials increases, the probability of success at each decreases, and the average number of successes tends to m; so Poisson('s) approximation, Poisson distribution, Poisson form, Poisson law, etc.; Poisson-distributed adj. Also passing into adj. (= Poissonian) and used predicatively. [Described in Poisson's Recherches sur la Probabilité des Jugements (1837).]
1911Ark. för Matem., Astr. och Fysik VII. xvii. 8, I shall generally understand with Poisson's theorem the expressions..giving the probability for obtaining in s trials with variable chances in all m white and n black balls (where m + n = s). 1914Biometrika X. 36 (heading) On the Poisson law of small numbers. 1919G. U. Yule Theory Statistics (ed. 5) 372 [This] may be termed Poisson's limit to the binomial. 1922Ann. Appl. Biol. IX. 331 When the statistical examination of these data was commenced it was not anticipated that any clear relationship with the Poisson distribution would be obtained. Ibid. 334 The curves strongly suggest that the departures in these data from the Poisson samples were not..systematic. 1928[see normal a. 2 e]. 1931L. H. C. Tippett Meth. Statistics ii. 34 This is known as Poisson's Limit to the Binomial, the Poisson Series, or as the Law of Small Numbers. 1939H. Jeffreys Theory of Probability ii. 75 Put x = r/n and let n tend to infinity; then the law tends to the Poisson form. 1948H. E. Freeman et al. Sampling Inspection xvii. 185 For such small values of n the Poisson approximation is not adequate. 1950W. Feller Introd. Probability Theory I. vi. 119 A radioactive substance emits α-particles, and the number of particles reaching a given portion of space during time t is the best-known example of random events obeying the Poisson law. Ibid. xvii. 367 In the Poisson process the probability of a change during (t, t + h) is independent of the number of changes during (O, t). 1954[see erlang 1]. 1958Condon & Odishaw Handbk. Physics i. xii. 155/2 The discrete distribution..termed the Poisson exponential distribution, is (with the normal, and binomial distributions) one of the three principal distributions of probability theory. 1966McGraw-Hill Encycl. Sci. & Technol. X. 631/2 If p is so small that the mean np is of the order of unity in any given application, Bernoulli's distribution is then approximated by Poisson's law. 1968P. A. P. Moran Introd. Probability Theory iii. 162 We suppose that customers arrive at a servicing counter in a Poisson process with mean λ, i.e. the number arriving in any interval of length T has a Poisson distribution with mean λT, and the numbers arriving in different intervals are independent. 1971J. B. Carroll et al. Word Freq. Bk. p. xxxvi, The remaining entries show that..9,436 [words] would be expected not to appear at all in the AHI Corpus, but that 3,826 would appear once, 776 would appear twice, 105 would appear 3 times, 10 would appear 4 times, and 1 would appear 5 times. (These numbers are predicted by the Poisson distribution.) 1976E. J. Dudewicz Introd. Statistics & Probability iii. 56 Suppose that X is binomial with parameters n and p... Then X is approximately Poisson with λ = np. 1979Nature 15 Feb. 533/1, ni, the number of abberations in the i-th culture, is Poisson-distributed.
b. ellipt. for Poisson distribution.
1962S. R. Calabro Reliability Princ. & Pract. vi. 65 If the expected number of failures..is substituted in the Poisson, then it is possible to calculate the probability of 0, 1, 2, 3, etc., failures. 1975R. M. Bethea et al. Statistical Methods for Scientists & Engineers iii. 57 We can estimate the probability of getting less than two adverse reactions using the Poisson as follows.
2. Special Comb.: Poisson bracket, a function [u, v] of two dynamical variables u(p1, p2,{ddd}pn, q1, q2,{ddd}qn) and v(p1, p2,{ddd}pn, q1, q2,{ddd}qn) equal to {Summ}nr = 1 ⎜ ∂u / ∂qr ∂v / ∂pr - ∂u / ∂pr ∂v / ∂qr ⎟; Poisson's equation [discussed by Poisson in Nouveau Bull. des Sci. par la Soc. philomath. de Paris (1813) III. 390], the generalization of Laplace's equation produced by replacing the zero of the right hand side by a constant or, more generally, by a specified function of position; Poisson's ratio [discussed by Poisson in Ann. de Chim. et de Physique (1827) XXXVI. 385], the ratio of the proportional decrease in a lateral measurement to the proportional increase in length in a sample of material that is elastically stretched.
1904E. T. Whittaker Treat. Analytical Dynamics xi. 309 If ϕ and ψ are two integrals of the system, the Poisson-bracket (ϕ, ψ) is constant throughout the motion. 1960Dicke & Wittke Introd. Quantum Mech. v. 86 The Poisson bracket provides a powerful tool in formulating quantum theory. 1976Mathews & Venkatesan Textbk. Quantum Mech. 351 Canonically conjugate co⁓ordinate-momentum pairs are..characterized by a unit value for the Poisson bracket.
[1872Trans. R. Soc. Edin. XXVI. 71 If ρ be the potential at ρ, and if r be the density of the attracting matter, &c., at ρ, ∇σ = ∇2P = 4πr by Poisson's extension of Laplace's equation.] 1873J. C. Maxwell Treat. Electr. & Magn. I. i. ii. 80 This equation, in the case in which the density is zero, is called Laplace's Equation. In its more general form it was first given by Poisson... We may express Poisson's equation in words by saying that the electric density multiplied by 4π is the concentration of the potential. 1916F. B. Pidduck Treat. Electr. iii. 61 This becomes..△V = -4πρ, which is known as Poisson's equation. 1971C. R. Chester Techniques in Partial Differential Equations iii. 87 The nonhomogeneous potential equation, ∇2u = F(x, y, z) is called Poisson's equation.
1886J. D. Everett Units & Physical Constants (ed. 2) v. 62 The following values of Poisson's ratio have been found. 1930Engineering 11 Apr. 465/1 The modern theory of the elasticity of isotropic materials makes use of a number of physical constants, all of which are definitely related to Young's Modulus E and Poisson's ratio η = 1/m the latter of which is sometimes known as the ‘stretch–squeeze’ ratio. 1966C. R. Tottle Sci. Engin. Materials vii. 153 An orthorhombic crystal can thus be defined by nine independent constants, three elastic moduli, three moduli of rigidity, and three values of Poisson's ratio. |