The joint-distribution function between variables plays an important role in reliability analysis. A method is proposed for constructing the using a neural network, which used to construct copula model under arbitrarily measured data, including input and output values of network empirical cumulative distribution. Three traditional models are constructed based on Kendall rank-correlation coeffic...

We present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence. Moreover, we present the tail concentration function (which depends on the diagonal section of a copula) as a tool to give a description of tail dependence at finite scale. The tail concentration function is hence used to introduce...

This paper presents an introduction to the stochastic concepts of coupling and copula. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distribution to its one-dimensional margins. Their role in stochastic modeling is illustrated by exam...

It is very important for bank to control the credit risk of guarantee loan or combinational loan by evaluating the joint default risk of different enterprises. Firstly we apply a combinational copula function to measure the joint default risk of two enterprises with credit rating information; secondly the default intensity model is intended to analyze the default time distribution; thirdly we u...

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies indicate that the existence of the lower tail dependence function of the survival copula is necessary and ...

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, standardized marginal distributions are standard normal. The copula itself depends on familiar skewing construction based normal function. This concerned with two topics. First, number extensions Notably these include case in Student’s t, different degrees freedom allowed for each margin. I...

Since the emergence of power market, the target of power generating utilities has mainly switched from cost minimization to revenue maximization. They dispatch their power energy generation units in the uncertain environment of power market. As a result, multi-stage stochastic programming has been applied widely by many power generating agents as a suitable tool for dealing with self-scheduling...

A copula is a function which joins (or 'couples') a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

Copulas are a general tool for assessing the dependence structure of random variables. Important properties as well as a number of examples are discussed, including Archimedean copulas and the Marshall-Olkin copula. As measures of the dependence we consider linear correlation, rank correlation, the coefficients of tail dependence and association. Copulas are a tool for modeling and capturing th...