A modern way to model the petrophysical dependence structure between random variables is using copulas.
In this paper, the statistical dependence between random variables is quantified by mutual information and estimated using a k nearest neighbor based approximation.
In structural reliability the dependence structure between random variables is almost exclusively modeled by Gauss (normal or Gaussian) copula; however, this implicit assumption is typically not corroborated.
Normally, the variation between random variables is estimated by the distance variation of each random variable from their mean in units of standard deviation.
Analyzing and estimating covariances between random variables is an important and interesting problem with manifold applications to Economics, Finance, Actuarial Science, Engineering, Statistics, and other areas (see, e.g., Egozcue et al. [1], Furman and Zitikis [2 5], Zitikis [6], and references therein).
Since the relationship between random variables is not based on the distribution, but rather constructed from mathematical structures between random variables, dependence can be evaluated using non-parametric correlation statistics (Spearman's ρs and Kendall's τ), which are independent on marginal distributions.
Then, we present the generalized Cauchy distribution, and a relation between GGD and GCD random variables is introduced.
Statistical correlation, a measurement between two random variables, is used to detect a jamming attack [3].
Scatter plot, which is able to reveal the relationship between two random variables, is applied here for the copula selection.
This type of dependence between two random variables is called here a rotational or correlation type dependence.
