Poissonn.adj.

Brit.

/ˈpwɑːsɒn/,

/ˈpwasɒn/,

/ˈpwɑːsɒ̃/,

/ˈpwasɒ̃/, U.S.

/pwɑˈsɑn/

Origin: From a proper name. Etymon: proper name Poisson.

Etymology: < the name of Siméon-Denis Poisson (1781–1840), French mathematician and physicist.

Mathematics and Physics.

I. Compounds.

1. attributive and in the genitive. Denoting mathematical and statistical concepts introduced or discussed by Poisson. Also attributive or as adj.: relating to or described by such concepts, esp. the Poisson distribution (see sense 4a).In quot. 1976 used predicatively: cf. Poissonian adj.

ΘΚΠ

the world > relative properties > number > probability or statistics > [adjective] > relating to distribution

multinomial1608

Poisson1839

Poissonian1894

cumulative1950

Weibull1955

1839 Philos. Trans. (Royal Soc.) 129 177 Poisson's theory explains the near equality between the attraction of a sphere or thick shell and that of a thin shell.

1922 Ann. Appl. Biol. 9 334 The curves strongly suggest that the departures in these data from the Poisson samples were not..systematic.

1931 L. H. C. Tippett Methods Statistics ii. 34 This is known as Poisson's Limit to the Binomial, the Poisson Series, or as the Law of Small Numbers.

1939 H. Jeffreys Theory of Probability ii. 75 Put x = r/n and let n tend to infinity; then the law tends to the Poisson form.

1950 W. Feller Introd. Probability Theory I. 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).

1976 E. 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.

1993 Brit. Med. Jrnl. (BNC) 6 Feb. 362 The Poisson model implies that the variance, in the rates of sickness absence between individuals is equal to the expected rate of sickness absence.

2. Poisson's ratio n. [discussed by Poisson in Ann. de chim. et de physique 36 (1827) 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.One of the four elastic constants, the others being the modulus of elasticity (Young's modulus), the bulk modulus, and the rigidity modulus.

ΘΚΠ

the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > alteration of form or dimensions caused by stress > specific alteration of dimensions > specific ratio of dimensions

Poisson's ratio1866

1866 Philos. Trans. (Royal Soc.) 156 189 Poisson's ratio, or the ratio of transverse contraction..to longitudinal extension when a prismatic or cylindric rod is stretched longitudinally.

1930 Engineering 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.

1990 P. Kearey & F. J. Vine Global Tectonics ii. 22 The value of Poisson's ratio for layer 3A, which can be estimated directly from a knowledge of both P and S wave velocities, is much lower than would be expected for serpentinized peridotite.

3. Poisson's equation n. [discussed by Poisson in Nouveau bull. des sci. par la Soc. Philomatique de Paris 3 (1813) 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.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > equation

equation1570

cardanic equation1684

binomial equation1814

simultaneous equation1816

characteristic equation1828

characteristic equation1841

characteristic equation1849

intrinsic equation of a curve1849

complete primitive1859

primitive1862

Poisson's equation1873

Jacobi equation1882

formulaic equation1884

adjoint1889

recursion formula1895

characteristic equation1899

characteristic equation1900

Pell equation1910

Lotka–Volterra equations1937

Langevin equation1943

1872 Trans. Royal Soc. Edinb. 26 71 If R be the potential at ρ, and if r be the density of the attracting matter, &c., at ρ, ∇σ = ∇²R = 4πr by Poisson's extension of Laplace's equation.]

1873 J. C. Maxwell Treat. Electr. & Magnetism I. i. ii. 80 We may express Poisson's equation in words by saying that the electric density multiplied by 4π is the concentration of the potential.

1916 F. B. Pidduck Treat. Electr. iii. 61 This becomes..∆V = −4πρ, which is known as Poisson's equation.

1984 L. Solymar Lect. Electromagn. Theory (BNC) (rev. ed.) 66 We are faced here with an electrostatic problem which may be solved with the aid of Poisson's equation.

a. Poisson distribution n. (also Poisson's distribution) [described by Poisson in Recherches sur la probabilité des jugements (1837)] a frequency distribution which gives the probability of a number of discrete events occurring in a certain time interval, or of a particular number of successes out of a given number of trials.In a Poisson distribution the probability of k events (or successes) occurring is given by the probability mass function λ^ke^−λ/k!, where λ is a positive parameter. The mean and variance of the function are both λ.This distribution applies to random events that are independent of one another, where the events are rare (or the probability of success is low), and where the average rate of occurrence does not change over time.

ΘΚΠ

the world > relative properties > number > probability or statistics > [noun] > distribution

distribution1854

random distribution1882

frequency distribution1895

probability distribution1895

Poisson distribution1898

binomial distribution1911

Student's t-distribution1925

sampling distribution1928

probability density1931

Poisson1940

beta distribution1941

Cauchy distribution1948

geometric distribution1950

1898 Philos. Trans. 1897 (Royal. Soc.) A. 190 233 We have to take account of the effect of a Poisson distribution on the surface of this cavity.

1922 Ann. Appl. Biol. 9 331 When the statistical examination of these data was commenced it was not anticipated that any clear relationship with the Poisson distribution would be obtained.

1954 A. Jensen Distribution Model v. 16 Erlang's distribution corresponds to Poisson's distribution just as that of Pascal corresponds to the binomial distribution.

1994 Computers & Humanities 28 91/1 Damerau's tests were based on the assumption that a word will be independent of context (and therefore a function word) if its occurrences follow a Poisson distribution.

b. Poisson-distributed adj. having a Poisson distribution.

ΚΠ

1945 Ann. Math. Statistics 16 340 The last term of the expression..is precisely the square of the first moment of Y when s is Poisson distributed.

1979 Nature 15 Feb. 533/1 n_i, the number of aberrations in the i-th culture, is Poisson-distributed.

5. Poisson bracket n. a function [u, v] of two dynamical variables u(p₁, p₂,…p_n, q₁, q₂,…q_n) and v(p₁, p₂,…p_n, q₁, q₂,…q_n) equal to ∑nr = 1 ^∂u/ _{∂q_r}^∂v/ _{∂p_r} − ^∂u/ _{∂p_r}^∂v/ _{∂q_r}.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function

function1758

exponential1784

potential function1828

syzygy1850

permutant1852

Green function1863

theta-function1871

Greenian1876

Gudermannian1876

discriminoid1877

Weierstrassian function1878

gradient1887

beta function1888

distribution function1889

Riemann zeta function1899

Airy integral1903

Poisson bracket1904

Stirling approximation1908

functional1915

metric1921

Fourier transform1923

recursive function1934

utility function1934

Airy function1939

transfer function1948

objective function1949

restriction1949

multifunction1954

restriction mapping1956

scalar function1956

Langevin function1960

mass function1961

1904 E. T. Whittaker Treat. Analyt. Dynamics xi. 309 If ϕ and ψ are two integrals of the system, the Poisson-bracket (ϕ, ψ) is constant throughout the motion.

1960 R. H. Dicke & J. P. Wittke Introd. Quantum Mech. v. 86 The Poisson bracket provides a powerful tool in formulating quantum theory.

1995 Nature 9 Feb. 469/2 The test is that the so-called Poisson bracket, called {f,g}, should be equal to 1.

6. Poisson law n. (also Poisson's law) a law expressed by a Poisson distribution.

ΚΠ

1914 Biometrika 10 36 (heading) On the Poisson law of small numbers.

1950 W. 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.

1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) 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.

1989 R. Dryer & G. Lata Exper. Biochem. i. xii. 302 Many well-known variables do not obey the normal error law; instead they obey other distribution laws, including Poisson's law, or the log-normal law.

1994 Computers & Humanities 28 94/2 Yule's conviction of a compound Poisson law was taken up by Sichel (1975) who proposed a new family of compound Poisson distributions as a model for word frequency counts.

II. Simple uses.

7. With the: the Poisson distribution.

ΘΚΠ

the world > relative properties > number > probability or statistics > [noun] > distribution

distribution1854

random distribution1882

frequency distribution1895

probability distribution1895

Poisson distribution1898

binomial distribution1911

Student's t-distribution1925

sampling distribution1928

probability density1931

Poisson1940

beta distribution1941

Cauchy distribution1948

geometric distribution1950

1940 Jrnl. Amer. Statist. Assoc. 35 375 The interval stated is the one where the Poisson is to be rejected.

1959 M. Sasieni & A. Yaspan Operations Res. iii. 58 The next step is to fit some theoretical discrete distribution to the observed relative frequencies... The Poisson is a natural first choice to consider.

1975 R. 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.

2004 Physica E. 21 124/2 The Poisson is a good approximation for the probability distribution function if the number of impurities is small.

This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022).

单词	poisson
释义	Poissonn.adj. Brit. /ˈpwɑːsɒn/, /ˈpwasɒn/, /ˈpwɑːsɒ̃/, /ˈpwasɒ̃/, U.S. /pwɑˈsɑn/ Origin: From a proper name. Etymon: proper name Poisson. Etymology: < the name of Siméon-Denis Poisson (1781–1840), French mathematician and physicist. Mathematics and Physics. I. Compounds. 1. attributive and in the genitive. Denoting mathematical and statistical concepts introduced or discussed by Poisson. Also attributive or as adj.: relating to or described by such concepts, esp. the Poisson distribution (see sense 4a).In quot. 1976 used predicatively: cf. Poissonian adj. ΘΚΠ the world > relative properties > number > probability or statistics > [adjective] > relating to distribution multinomial1608 Poisson1839 Poissonian1894 cumulative1950 Weibull1955 1839 Philos. Trans. (Royal Soc.) 129 177 Poisson's theory explains the near equality between the attraction of a sphere or thick shell and that of a thin shell. 1922 Ann. Appl. Biol. 9 334 The curves strongly suggest that the departures in these data from the Poisson samples were not..systematic. 1931 L. H. C. Tippett Methods Statistics ii. 34 This is known as Poisson's Limit to the Binomial, the Poisson Series, or as the Law of Small Numbers. 1939 H. Jeffreys Theory of Probability ii. 75 Put x = r/n and let n tend to infinity; then the law tends to the Poisson form. 1950 W. Feller Introd. Probability Theory I. 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). 1976 E. 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. 1993 Brit. Med. Jrnl. (BNC) 6 Feb. 362 The Poisson model implies that the variance, in the rates of sickness absence between individuals is equal to the expected rate of sickness absence. 2. Poisson's ratio n. [discussed by Poisson in Ann. de chim. et de physique 36 (1827) 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.One of the four elastic constants, the others being the modulus of elasticity (Young's modulus), the bulk modulus, and the rigidity modulus. ΘΚΠ the world > matter > physics > mechanics > force > stress or force exerted and tending to deform > [noun] > alteration of form or dimensions caused by stress > specific alteration of dimensions > specific ratio of dimensions Poisson's ratio1866 1866 Philos. Trans. (Royal Soc.) 156 189 Poisson's ratio, or the ratio of transverse contraction..to longitudinal extension when a prismatic or cylindric rod is stretched longitudinally. 1930 Engineering 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. 1990 P. Kearey & F. J. Vine Global Tectonics ii. 22 The value of Poisson's ratio for layer 3A, which can be estimated directly from a knowledge of both P and S wave velocities, is much lower than would be expected for serpentinized peridotite. 3. Poisson's equation n. [discussed by Poisson in Nouveau bull. des sci. par la Soc. Philomatique de Paris 3 (1813) 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. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > equation equation1570 cardanic equation1684 binomial equation1814 simultaneous equation1816 characteristic equation1828 characteristic equation1841 characteristic equation1849 intrinsic equation of a curve1849 complete primitive1859 primitive1862 Poisson's equation1873 Jacobi equation1882 formulaic equation1884 adjoint1889 recursion formula1895 characteristic equation1899 characteristic equation1900 Pell equation1910 Lotka–Volterra equations1937 Langevin equation1943 1872 Trans. Royal Soc. Edinb. 26 71 If R be the potential at ρ, and if r be the density of the attracting matter, &c., at ρ, ∇σ = ∇²R = 4πr by Poisson's extension of Laplace's equation.] 1873 J. C. Maxwell Treat. Electr. & Magnetism I. i. ii. 80 We may express Poisson's equation in words by saying that the electric density multiplied by 4π is the concentration of the potential. 1916 F. B. Pidduck Treat. Electr. iii. 61 This becomes..∆V = −4πρ, which is known as Poisson's equation. 1984 L. Solymar Lect. Electromagn. Theory (BNC) (rev. ed.) 66 We are faced here with an electrostatic problem which may be solved with the aid of Poisson's equation. 4. a. Poisson distribution n. (also Poisson's distribution) [described by Poisson in Recherches sur la probabilité des jugements (1837)] a frequency distribution which gives the probability of a number of discrete events occurring in a certain time interval, or of a particular number of successes out of a given number of trials.In a Poisson distribution the probability of k events (or successes) occurring is given by the probability mass function λ^ke^−λ/k!, where λ is a positive parameter. The mean and variance of the function are both λ.This distribution applies to random events that are independent of one another, where the events are rare (or the probability of success is low), and where the average rate of occurrence does not change over time. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > distribution distribution1854 random distribution1882 frequency distribution1895 probability distribution1895 Poisson distribution1898 binomial distribution1911 Student's t-distribution1925 sampling distribution1928 probability density1931 Poisson1940 beta distribution1941 Cauchy distribution1948 geometric distribution1950 1898 Philos. Trans. 1897 (Royal. Soc.) A. 190 233 We have to take account of the effect of a Poisson distribution on the surface of this cavity. 1922 Ann. Appl. Biol. 9 331 When the statistical examination of these data was commenced it was not anticipated that any clear relationship with the Poisson distribution would be obtained. 1954 A. Jensen Distribution Model v. 16 Erlang's distribution corresponds to Poisson's distribution just as that of Pascal corresponds to the binomial distribution. 1994 Computers & Humanities 28 91/1 Damerau's tests were based on the assumption that a word will be independent of context (and therefore a function word) if its occurrences follow a Poisson distribution. b. Poisson-distributed adj. having a Poisson distribution. ΚΠ 1945 Ann. Math. Statistics 16 340 The last term of the expression..is precisely the square of the first moment of Y when s is Poisson distributed. 1979 Nature 15 Feb. 533/1 n_i, the number of aberrations in the i-th culture, is Poisson-distributed. 5. Poisson bracket n. a function [u, v] of two dynamical variables u(p₁, p₂,…p_n, q₁, q₂,…q_n) and v(p₁, p₂,…p_n, q₁, q₂,…q_n) equal to ∑nr = 1 ^∂u/ _{∂q_r}^∂v/ _{∂p_r} − ^∂u/ _{∂p_r}^∂v/ _{∂q_r}. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function function1758 exponential1784 potential function1828 syzygy1850 permutant1852 Green function1863 theta-function1871 Greenian1876 Gudermannian1876 discriminoid1877 Weierstrassian function1878 gradient1887 beta function1888 distribution function1889 Riemann zeta function1899 Airy integral1903 Poisson bracket1904 Stirling approximation1908 functional1915 metric1921 Fourier transform1923 recursive function1934 utility function1934 Airy function1939 transfer function1948 objective function1949 restriction1949 multifunction1954 restriction mapping1956 scalar function1956 Langevin function1960 mass function1961 1904 E. T. Whittaker Treat. Analyt. Dynamics xi. 309 If ϕ and ψ are two integrals of the system, the Poisson-bracket (ϕ, ψ) is constant throughout the motion. 1960 R. H. Dicke & J. P. Wittke Introd. Quantum Mech. v. 86 The Poisson bracket provides a powerful tool in formulating quantum theory. 1995 Nature 9 Feb. 469/2 The test is that the so-called Poisson bracket, called {f,g}, should be equal to 1. 6. Poisson law n. (also Poisson's law) a law expressed by a Poisson distribution. ΚΠ 1914 Biometrika 10 36 (heading) On the Poisson law of small numbers. 1950 W. 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. 1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) 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. 1989 R. Dryer & G. Lata Exper. Biochem. i. xii. 302 Many well-known variables do not obey the normal error law; instead they obey other distribution laws, including Poisson's law, or the log-normal law. 1994 Computers & Humanities 28 94/2 Yule's conviction of a compound Poisson law was taken up by Sichel (1975) who proposed a new family of compound Poisson distributions as a model for word frequency counts. II. Simple uses. 7. With the: the Poisson distribution. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > distribution distribution1854 random distribution1882 frequency distribution1895 probability distribution1895 Poisson distribution1898 binomial distribution1911 Student's t-distribution1925 sampling distribution1928 probability density1931 Poisson1940 beta distribution1941 Cauchy distribution1948 geometric distribution1950 1940 Jrnl. Amer. Statist. Assoc. 35 375 The interval stated is the one where the Poisson is to be rejected. 1959 M. Sasieni & A. Yaspan Operations Res. iii. 58 The next step is to fit some theoretical discrete distribution to the observed relative frequencies... The Poisson is a natural first choice to consider. 1975 R. 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. 2004 Physica E. 21 124/2 The Poisson is a good approximation for the probability distribution function if the number of impurities is small. This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022). < n.adj.1839
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