Correlations between spike counts are often used to analyze neural coding. The noise is typically assumed to be Gaussian. Yet, this assumption is often inappropriate, especially for low spike counts. In this study, we present copulas as an alternative approach. With copulas it is possible to use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for mod...

This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the ...

Input modeling software tries to fit standard probability distributions to data assuming that the data are independent. However, the input environment can generate correlated data. Ignoring the correlations might lead to serious inaccuracies in the performance measures. In the past few years, several dependence modeling packages with different properties have been developed. In our dissertation...

Although bivariate imprecise copulas have recently attracted substantial attention, the multivariate case seems still to be open. So, it is natural test first on shock model induced copulas, a family which might most useful in various applications. We investigate some of shocks are assumed and develop corresponding set copulas. In Marshall's we get coherent distributions where bounds naturally ...

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution, to the distribution whose Laplace trans...

Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the larges...

Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions tha...

This study after reviewing  construction methods of generators in Archimedean copulas (AC),  proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.

Copulas are becoming an essential tool in analyzing data thus encouraging interest related questions. In the early stage of exploratory analysis, say, it is helpful to know local copula bounds with a fixed value given measure association. These have been computed for Spearman’s rho, Kendall’s tau, and Blomqvist’s beta. The importance another two measures association, footrule Gini’s gamma, has ...