Ordering properties of the smallest and largest claim amounts in a general scale model

Suppose is a set of non-negative random variables with having the distribution function , for and are independent Bernoulli random variables, independent of the ’s, with , . Let , for . It is of interest to note that in actuarial science, corresponds to the claim amount in a portfolio of risks. In this paper, under certain conditions, by using the concept of vector majorization and related orders, we discuss stochastic comparison between the …