International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 639-664
Stochastic orderings induced by star-shaped functions
Department of Mathematics, Harvey Mudd College, Claremont 91711, CA, USA
Received 18 September 1990
Copyright © 1991 Henry A. Krieger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The non-decreasing functions whicl are star-shaped and supported above at each point
of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution
functions with finite first moments, that is strictly weaker than first degree stochastic
dominance and strictly stronger than second degree stochastic dominance. Several characterizations
of this ordering are developed, both joint distribution criteria and those involving
only marginals. Tle latter are deduced from a decomposition theorem, which reduces the
problem to consideration of certain functions which are star-shaped on the complement of
an open interval.