Higher-order statistics (spectra) and their application in signal processing

Most real-world signals are non-Gaussian. If they were Gaussian then they could be completely characterized by their first- and second-order statistics, because the probability density function (p.d.f.) for a Gaussian signal is completely described by these statistics. Because most real-world signals are not Gaussian, we need to use more than just first- and second-order statistics, i.e., we need to use "higher-order statistics." We could use higher-order moments, e.g., triplecorrelations, quadruple-correlations, etc., or we could use cumulants. Cumulants are related to higher-order moments, but do not necessarily always equal these moments. Reasons for preferring cumulants over moments are explained below.