CONSTRUCTION OF SOME ARCHIMEDEAN COPULAS

Abstract

We propose an approach allowing to manage the statistical data. At the same time, starting from the copulas of Gumbel,of Ali-Michael and Haq., we propose some copulas of the Archimedean family that we estimate contribute to the resolution of the problems related to the choice of the maximum or the optimal values for a group of random variables united within d random vectors of size n, independent and identifically distributed, suitably normalized as n tends to infinity. To our knowledge, there exists, in this case, the copula of Ali-Michael and Haq, Which goes in the same direction, however, the copula that we propose takes into account on the one hand the dependence parameters of the marginals and on the other hand the size of the samples including the dependence parameter of the joint distribution function