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Building on the seminal work by Shaked and Shanthikumar (Adv Appl Probab 20:427–446, 1988a; Stoch Process Appl 27:1–20, 1988b), Denuit et al. (Eng Inf Sci 13:275–291, 1999; Methodol Comput Appl Probab 2:231–254, 2000; 2001) studied the stochastic s-increasing convexity properties of standard parametric families of distributions. However, the analysis is restricted there to a single parameter. As many...