Cumulant - Wikipedia
网页Every cumulant is just r times the corresponding cumulant of the corresponding geometric distribution. The derivative of the cumulant generating function is K′(t) = r·((1 − p) −1 ·e −t −1) −1. The first cumulants are κ 1 = K′(0) = r·(p −1 −1), and κ 2 = K′′(0) = κ 1 ·p −1.
[再论母函数]Moment,Cumulant以及费曼图的那些事 - 知乎
网页2023年5月17日 · Moment. 我们假设拥有一个概率分布 f (x) ，其矩（Moment）被定义为： \langle x^n\rangle=\int dx x^n f (x) （积分区间为 \mathbb {R} ）. 而其中心矩（Central Moment）被定义为： \langle (x-\langle x\rangle)^n\rangle.
累积量 - 维基百科，自由的百科全书
网页在概率论和统计学中，一个概率分布的累积量 κ n (英語： Cumulant)是指一系列能够提供和矩一样的信息的量。累积量和随机变量的矩密切相关。如果两个随机变量的各阶矩都一样，那么它们的累积量也都一样，反之亦然。
网页The term cumulant was coined by Fisher (1929) on account of their behaviour under addition of random variables. Let S = X + Y be the sum of two independent random variables. The moment generating function of the sum is the product MS(ξ) = MX(ξ)MY (ξ), and the cumulant generating function is the sum KS(ξ) = KX(ξ)+KY (ξ).
如何写出累积量（cumulant）和原点矩（moment）的关系式？是 …
网页得到以矩表示的累积量生成函数。. 其中 \sum n p_ {n}=m ，不过这是把矩写为累积量的形式，和你的要求好像不大一样。. 这部分我抄的是Kardar的Statistical Physics of Particles第二章，有兴趣的话可以参阅。. 看见一篇论文写道：特征函数（characteristic function）的展开式 …
网页the term cumulant was suggested by Hotelling in a letter to Fisher, who approved of the coinage. Let S= X+ Y be the sum of two independent random variables. The moment generating function of the sum is the product M S(˘) = E(e˘(X+Y)) = E(e˘Xe˘Y) = M X(˘)M Y(˘); and the cumulant generating function of the sum is the sum of the cumulant
网页For d>1, the nth cumulant is a tensor of rank nwith dn components, related to the moment tensors, m l, for 1 ≤ l≤ n. For example, the second cumulant matrix is given by c(ij) 2 = m (ij) 2 −m (i) 1 m (j) 1. 3 Additivity of Cumulants A crucial feature of random walks with independently identically distributed (IID) steps is that cumulants ...
网页Moments of the random variable can then be generated as terms of the coecients of the Taylor expansion of G( ) around the origin. Another useful quantity is the cumulant generating function which is the logarithm of the moment characteristic function.
Cumulant—Wolfram 语言参考资料
网页一般而言， MomentConvert [Cumulant [r], "Moment"] 用矩给出 . Cumulant [data, r] 有效地使用 MomentConvert 根据数据的其他矩来计算. 对于 x ∈ Arrays [{n 1, n 2, …, n k}] ， Cumulant [x, r] 等价于 ArrayReduce [Cumulant [#, r] &, data, 1]. »
Cumulant -- from Wolfram MathWorld
网页2024年8月22日 · Let phi (t) be the characteristic function, defined as the Fourier transform of the probability density function P (x) using Fourier transform parameters a=b=1, phi (t) = F_x [P (x)] (t) (1) = int_ (-infty)^inftye^ (itx)P (x)dx. (2) The cumulants kappa_n are then defined by lnphi (t)=sum_ (n=1)^inftykappa_n ( (it)^n)/ (n!)
跳至内容