A New Trivariate Semicopula Using Rüschendorf Method
M. M. E. Abd EL-Monsef *
Faculty of Science, Tanta University, Egypt.
M. M. Seyam
Faculty of Science, Tanta University, Egypt.
S. M. Elsobky
Faculty of Science, Tanta University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper we have introduced semicopula function by using Rüschendorf method, semicopula which is related to correlation between one or more random variables and this way is more flexible than traditional correlation approaches and dependency among variables. Every semicopula has density associated with it, which is similar to the probability density of a multivariate distribution. Our purpose is developing a new trivariate semicopula under conditions which is a trivariate cumulative distribution with uniform marginal distribution on the interval [0,1]. In order to choose a random function under specific conditions, we rely on utilizing Rüschendorf method. As a result, we will discuss that in this paper. In this theme we select an arbitrary trivariate function which adopts the Rüschendorf conditions to acquire anew function; which supposed to be a density of copula with dependence parameter. According to the evidence, we have got a semicopula function. Therefore, we can say that a semicopula is a copula function despite of missing increasing property.
Keywords: Copula, semicopula, rüschendorf technique, superharmonic, subharmonic, concave