New order preserving properties of geometric compounds

We show that randomly stopped partial sums of nonnegative i.i.d. sequences with a geometric stopping variable, inherit some nonparametric class properties defined via the Laplace ordering and that the corresponding converses also hold. Our findings extend earlier results in this direction available in the literature, and are stronger in the sense of reciprocity of closure under the weaker nonparametric assumptions. © 2003 Elsevier B.V. All rights reserved.