Stochastic comparisons of the largest and smallest claim amounts with heterogeneous survival exponentiated location-scale distributed claim severities

Suppose X-1,...,X-n are independent survival exponentiated location-scale random variables, and Ip(1),...,Ip(n) are independent Bernoulli random variables, independently of X-i's, i=1, horizontal ellipsis ,n. Let Y-i=Ip(i)X(i), for i=1,...,n. Then, in actuarial context, Yi corresponds to the claim amount in a portfolio of heterogeneous risks. In this work, we compare the largest and smallest order statistics arising from two heterogeneous portfolios in the sense of usual stochastic order. The results obtained here are based on multivariate chain majorization with heterogeneity in different parameters, and generalize some of the results known in the literature. Some examples and counterexamples are also presented for illustrating the results established here.