EQUALITY IN DISTRIBUTION IN A CONVEX ORDERING FAMILY

J. S. HUANG^{1} AND G. D. LIN^{2}

1Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1

2Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, R.O.C.

(Received March 7, 1996; revised October 23, 1997)

Abstract. Let F and G be the respective distributions of nonnegative random variables X and Y satisfying the convex ordering. We investigate the class of functions h for which the equality E[h(X)] = E[h(Y)] guarantees F = G. It leads to extensions of some existing results and at the same time offers a somewhat simpler proof.

Key words and phrases: Characterization of distribution, convex ordering, concave ordering, moment, Laplace-Stieltjes transform, moment generating function, probability generating function, order statistics.