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...

Vine copula provides a flexible tool to capture asymmetry in modelling multivariate distributions. Nevertheless, its flexibility is achieved at the expense of exponentially increasing complexity of the model. To alleviate this issue, the simplifying assumption (SA) is commonly adapted in specific applications of vine copula models. In this paper, generalized linear models (GLMs) are proposed fo...

In this paper, we consider nonparametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large number of estimators of the distribution function, and therefore for a large number of bivariate censoring frameworks. Under so...

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to statistical modelling proceeds by specifying distributions for each margin and a copula function. In this paper, a number of families of copula functions are given, with attentio...

We consider the problem of dividing a resource among a group of agents who have conflicting claims on it. A typical situation is when a firm goes bankrupt and its liquidation value has to be divided among its creditors. We follow the axiomatic approach. Our main axioms are inequality preservation in gains and inequality preservation in losses (Hougaard and Thorlund-Petersen, 2001; Hougaard and ...

this study presents a new method for interpolation by use of copula for groundwater quality zoning. in this regard, the data of the concentration of bicarbonate in 87 piezometric wells on the plains of kerman and ravar in september 2013 were examined. for this purpose, four archimedean copula including clayton, frank, gumbel and joe have been used. then, the obtained results were compared to th...

The copula–entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) ha...

The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function (df) in a continuous manner. A multivariate extension was established by Aulbach et al. (2011a): The upper tail of a given copula C was cut off and substituted by the upper tail of a multivariate GPD-copula in a continuous manner. The result is...

Copula constructions are problematic in the syntax of most languages. The paper describes three different dependency syntactic methods for handling copula constructions: function head, content head and complex label analysis. Furthermore, we also propose a POS-based approach to copula detection. We evaluate the impact of these approaches in computational parsing, in two parsing experiments for ...

Considering two different metrics on the space of two-dimensional copulas C we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, w...