Signal detection or modulation recognition methods based on higher order cumulants
(HOCs) are popular currently, not only for their favorable recognition capability, but also they are immune to AWGN as the HOCs of Gaussian functions are equal to zero, which is the main reason why these methods are not suitable for detecting quasi-Gaussian signals.
Lee, "Probabilistic load flow computation using the method of combined cumulants
and Gram-Charlier expansion", IEEE Trans.
The dimension reduction integration method has been used in  to efficiently calculate the statistical moments needed to calculate the first four cumulants
for estimating the cumulant
generating function (CGF) in SA.
Probabilistic power flow studies for transmission systems with photovoltaic generation using cumulants
," IEEE Trans.
The related coefficients C3 and C4 are the third-order (skewness) and fourth-order (kurtosis) cumulants
of the random envelope.
This might be explained by the fact that the robust instruments used in this study are built on higher moments and cumulants
of the observed data.
Further, the skewness and kurtosis are obtained from the third and fourth standardized cumulants
hand concern the moments and free cumulants
of familiar random variables
Higher order cumulants
(HOC) can describe the higher order statistical characteristic of random process.
The maximum likelihood function , the equivalence of theoretical and experimental statistical moments  and the second-kind cumulants
 are commonly used for the parameter estimation of the clutter models.
It follows that the cumulants
of the stochastic variable X([theta]) are given by
34] provided an interesting algebraic approach to overcomplete ICA of three sources and two mixtures by solving a system of linear equations in the third and fourth-order cumulants
, and Bofill and Zibulevsky  treated a special case ('delta-like' source distributions) of source signals after Fourier transformation.