their components in the senses of the convex order and tail convex order respectively. In the first part, we extend the … convex order if and only if they are counter-monotonic. Three simple and illuminating proofs are provided. In the second part …, we investigate upper comonotonicity by means of the tail convex order. By establishing some useful properties of this …

, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then … the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the … the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result …