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EQUALITY IN DISTRIBUTION IN

A CONVEX ORDERING FAMILY

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

^{1} *Department of Mathematics and Statistics, University of Guelph,*

Guelph, Ontario, Canada N1G 2W1

^{2} *Institute 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.

**Source**
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