Connections among various variability orderings

Recently, a new variability ordering, called right spread ordering or excess wealth ordering has been introduced. This new ordering is weaker than dispersive ordering. We show in this note that if X is less variable than Y in the sense of right spread ordering or convex ordering, then it implies that X1 - X2 is less variable than Y1 - Y2 according to increasing convex ordering. Here X1 and X2 (Y1 and Y2) are two independent copies of X (Y). An application of the right spread ordering in the study of spacings from an increasing mean residual life distribution is given.