| 单词 | moment generating function |
| 释义 | > as lemmasmoment generating function moment generating function n. Statistics a function from which each of the moments (sense 8d) of a given random variable can be derived, the kth moment being equal to the kth derivative of the function, evaluated at zero; (formerly also) †a function from which the product moments of a given set of data can be similarly derived (obsolete). ΚΠ 1932 Ann. Math. Statistics 3 198 We shall define a moment-generating function ϕ(α,k) as [etc.]... It is clear that ∂h/ ∂αhϕ(α,k)|α=0 is the product moment. 1932 Biometrika 24 454 The moment generating function M is therefore defined by ∞0ehxdf, since the coefficient of hr/r! in the expansion is μr′(x), the rth moment coefficient about the origin. 1968 P. A. P. Moran Introd. Probability Theory vi. 256 When x is purely imaginary the characteristic function becomes the moment generating function. 1986 G. Grimmett & D. Welsh Probability (1988) vii. 113 A similar argument enables us to find the moment generating function of the sum of independent random variables. < as lemmas |
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