Supermodular stochastic orders and positive dependence of random vectors
Journal of Multivariate Analysis
Stochastic Convexity on General Space
Mathematics of Operations Research
Stochastic comparisons for multivariate shock models
Journal of Multivariate Analysis
Probability in the Engineering and Informational Sciences
Stochastic comparisons for rooted butterfly networks and tree networks, with random environments
Information Sciences: an International Journal
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Recently, Belzunce, Ortega, Pellerey, and Ruiz [3] have obtained stochastic comparisons in increasing componentwise convex order sense for vectors of random sums when the summands and number of summands depend on a common random environment, which prove how the dependence among the random environmental parameters influences the variability of vectors of random sums. The main results presented here generalize the results in Belzunce et al. [3] by considering vectors of parameters instead of a couple of parameters and the increasing directionally convex order. Results on stochastic directional convexity of families of random sums under appropriate conditions on the families of summands and number of summands are obtained, which lead to the convex comparisons between random sums mentioned earlier. Different applications in actuarial science, reliability, and population growth are also provided to illustrate the main results.