| 释义 |
semi-inˈvariant Math.
Also seminvariant.
[f. semi- + invariant.]
1. A function of the coefficients of a binary quantic which remains unchanged, except for a constant factor, when x + λ is substituted for x, but not when y + λ is substituted for y.
1860in Cayley Math. Papers (1891) IV. 241 The coefficients of the equation of differences, quâ functions of the differences of the roots of the given equation, are leading coefficients of covariants, or (to use a shorter expression) they are ‘Seminvariants’. [Note, The term ‘Seminvariant’ seems to me preferable to M. Brioschi's term ‘Peninvariant’.] 1882Sylvester in Amer. Jrnl. Math. V. 79 On Sub⁓invariants, i.e. Semi-Invariants to Binary Quantics of an Unlimited Order.
2. Statistics. Any of a set of functions of a statistical distribution, each expressible as a polynomial in the moments.
[1903T. N. Thiele Theory of Observations vi. 24 From the sums of powers we can easily compute also another serviceable collection of symmetrical functions, which for brevity we shall call the half-invariants.] 1922A. Fisher Math. Theory Probabilities (ed. 2) xiv. 191 (heading) Semi-invariants of Thiele. 1930Biometrika XXII. 225 Thiele, in 1889, after defining the semi-invariants, used symmetric functions of the observations of a sample which are the same functions of the sample moment coefficients as the population semi-invariants are of the population moment coefficients. He supplied an expression covering all the semi-invariants of the mean. 1968P. A. P. Moran Introd. Probability Theory vi. 267 The κn (n ⩾ 2) are dependent only on µ2, µ3,..and are the same for all distributions of the form F(x + d) (—∞ ‹ d ‹ ∞). They are therefore sometimes known as ‘semi-invariants’ since they are invariant under translation. |