Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the...

We show that all multivariate Extreme Value distributions, which are the possible weak limits of the K largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through exact expressions for its density and distribution functions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation...

Vine copula models have proven themselves as a very flexible class of multivariate copula models with regard to symmetry and tail dependence for pairs of variables. The full specification of a vine model requires the choice of vine tree structure, copula families for each pair copula term and their corresponding parameters. In this survey we discuss the different approaches, both frequentist as...

In information theory, mutual information (MI) is a difference concept with entropy.[1] In this paper, we prove with copula [2] that they are essentially same – mutual information is also a kind of entropy, called copula entropy. Based on this insightful result, We propose a simple method for estimating mutual information. Copula is a theory on dependence and measurement of association.[2] Skla...

We consider the problem of accurately measuring the credit risk of a portfolio consisting of loans, bonds and other financial assets. One particular performance measure of interest is the probability of large portfolio losses over a fixed time horizon. We revisit the so-called t-copula that generalizes the popular normal copula to allow for extremal dependence among defaults. By utilizing the a...

In this paper, a lexical functional grammar for an automatic classification of Urdu copula verb hO (be/become) is presented according to linguistic theories. A test suite of sentences containing almost all different conjugation forms of copula verb is extracted from a raw corpus. It is tried to keep only the cases of copular construction because the copula verb hO is very much dynamic in nature...

This paper presents algorithms for generating random variables for exponential/Rayleigh/ Weibull, Nakagami-m and Rician copulas with any desired copula parameter(s), using the direct conditional cumulative distribution function method and the complex Gaussian distribution method. Moreover, a novel method for optimal copula selection is also proposed, based on the criterion that for a given seri...

Copula as an effective way of modeling dependence has become more or less a standard tool in risk management, and a wide range of applications of copula models appear in the literature of economics, econometrics, insurance, finance, etc. How to estimate and test a copula plays an important role in practice, and both parametric and nonparametric methods have been studied in the literature. In th...

This paper presents the use of graphical models and copula functions in Estimation of Distribution Algorithms (EDAs) for solving multivariate optimization problems. It is shown in this work how the incorporation of copula functions and graphical models for modeling the dependencies among variables provides some theoretical advantages over traditional EDAs. By means of copula functions and two w...

We propose a parametric version of Independent Component Analysis (ICA) via Copulas families of multivariate distributions that join univariate margins to multivariate distributions. Our procedure exploits the role for copula models in information theory and in measures of association, specifically: the use of copulae densities as parametric mutual information, and as measures of association on...