  The basic goal of computer engineering is the analysis of data. Such data are
often large data sets distributed according to various distribution models. In
this manuscript we focus on the analysis of non-Gaussian distributed data. In
the case of univariate data analysis we discuss stochastic processes with
auto-correlated increments and univariate distributions derived from specific
stochastic processes, i.e. Levy and Tsallis distributions. Deep investigation
of multivariate non-Gaussian distributions requires the copula approach. A
copula is an component of multivariate distribution that models the mutual
interdependence between marginals. There are many copula families characterised
by various measures of the dependence between marginals. Importantly, one of
those are `tail' dependencies that model the simultaneous appearance of extreme
values in many marginals. Those extreme events may reflect a crisis given
financial data, outliers in machine learning, or a traffic congestion. Next we
discuss higher order multivariate cumulants that are non-zero if multivariate
distribution is non-Gaussian. However, the relation between cumulants and
copulas is not straight forward and rather complicated. We discuss the
application of those cumulants to extract information about non-Gaussian
multivariate distributions, such that information about non-Gaussian copulas.
The use of higher order multivariate cumulants in computer science is inspired
by financial data analysis, especially by the safe investment portfolio
evaluation. There are many other applications of higher order multivariate
cumulants in data engineering, especially in: signal processing, non-linear
system identification, blind sources separation, and direction finding
algorithms of multi-source signals.
