Archimedean copula and its application

Archimedean copula and its application

. In many statistical models, assumption of independence among data or components in multivariate data is not valid and even wrong in some cases, which results in incorrect inference of observation. In this paper, we shall attempt appeared in several papers to se Archimedean Copilas for modeling dependency in practical situations. Residual and past lifetime of an (n - k + 1)-out-of-n system with non-identical and dependent components is investigated using some extension of usual stochastie ordering in multivariate case. We also consider multivariate aging notions for a vector X of lifetimes based on stochastic comparisons between X and X, where X is the multivariate residual lifetime after time t > 0. under the assumption that the dependence structure in X is described by an Archimedean survival copula. We also obtain the density and distribution functions of progressively Type-II censored order statistics (PCOS)-II arising from dependent variables distributed according to an Archimedean copula, and an example of a special case of PCOS-II from dependent variables is provided for illustration.