Ordering properties of generalized aggregation with applications

The generalized aggregation n-ary sumation i=1nWi phi(Xi,ai)arises in many research fields including applied probability, actuarial science, and reliability theory, where phi is a bivariate kernel function andais a parameter vector. One of its remarkable features is that bothXandWare dependent in many practical situations. Therefore, studying the stochastic properties of generalized aggregations under various dependence structures is an interesting and meaningful problem. In this paper, by using left tail weakly stochastic arrangement increasing, right tail weakly stochastic arrangement increasing, and comonotonicity to characterize the dependent structures amongXorW, we establish the increasing convex ordering and the expectation ordering of generalized aggregations to investigate the effects of the arrangement and heterogeneity amonga(i)'s. Numerical examples and three practical applications are presented to illustrate our results as well.