In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by computing Pearson’s correlation coefficient. In practice, we often have a copula instead of a full...

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating thus needs to be addressed based on correlations. This paper first demonstrates capture by fitting various bivariate non-Gau...

empirical studies show that there is stronger dependency between large losses than large profit in financial market, which undermine the performance of using symmetric distribution for modeling these asymmetric. that is why the assuming normal joint distribution of returns is not suitable because of considering the linier dependence, and can be lead to inappropriate estimate of var. copula theo...

A dependence relation between two data references is linear if it generates dependence vectors that are linear functions of the loop indices. A linear dependence relation often induces a large number of dependence vectors. Empirical studies also show that linear dependencies often intermix with uniform dependencies in loops [5, 6]. These factors make it difficult to analyze such loops and extra...

Wide Area Measurement Systems (WAMS) enable real time monitoring and control of smart grids by combining digital measurement devices, communication and control systems. As WAMS consist of various infrastructures, they imply complex dependencies among their underlying systems and components of different types, such as cyber, physical and geographical dependencies. Although several works exist in...