# cumulants

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## cumulants

[′kyü·myə·ləns]
(statistics)
A set of parameters kh (h = 1, … r) of a one-dimensional probability distribution defined by where χx (q) is the characteristic function of the probability distribution of x. Also known as semi-invariants.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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passing instead via the free cumulant [[kappa].sub.2n]([a.sup.*], ...,
The 1st The 3rd The 4th order order order Node cumulant The 2nd order cumulant cumulant cumulant 5 1.0178 0.3181 x [10.sup.-6] 0 0 10 0.9893 0.3482 x [10.sup.-5] 0 0 18 0.9786 0.8142 x [10.sup.-5] 0 0 22 0.9756 0.8796 x [10.sup.-5] 0 0 Table 3: Moment of bus voltage in case 2.
Denote the empirical cumulant generating function and rate function of system i as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively.
Zhao, "4D near-field sourcelocalization using cumulant," EURASIP Journal on Advances in Signal Processing, vol.
Here [K.sub.4] is the fourth cumulant of [y.sub.1] and [y.sub.2] calculated by their marginal distribution
We prepared three types of examples: I) third-order partially symmetric tensors, II) fourth-order fully symmetric tensors, and III) a fourth-order cumulant tensor in a blind source separation problem.
Equivalently, if [mathematical expression not reproducible] (...) means a free cumulant in terms of the linear functional [mathematical expression not reproducible] of (9.3.5) on [mathematical expression not reproducible], then
1 shows the relationship between bi-spectrum and the 3rd order cumulant. Considering the characteristics of symmetry and periodicity, bi-spectrum estimation can be performed around the triangle area where contains all required information.
Similarly, Yan and Zhou  combined relevant cumulant with StOMP algorithm for feature extraction of the weak impulse signal.
Morton, "Cumulant component analysis: a simultaneous generalization of PCA and ICA," Computational Algebraic Statistics, Theories and Applications, 2008.
Mansour, "Automatic modulation recognition of MPSK signals using constellation rotation and its 4th order cumulant," Digital Signal Processing: A Review Journal, vol.

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