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Dispersive ordering of distributions

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked
Moshe Shaked*
Affiliation:
Indiana University
*
∗ Present address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A.
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Abstract

Two distributions, F and G, are said be ordered in dispersion if F-1(β)-F-1(α)≦G-1(β)-G-1(α) whenever 0<α <β <1. This relation has been studied by Saunders and Moran (1978). The purpose of this paper is to study this partial ordering in detail. Few characterizations of this concept are given. These characterizations are then used to show that some particular pairs of distributions are ordered by dispersion. In addition to it some proofs of results of Saunders and Moran (1978) are simplified. Furthermore, the characterizations of this paper can be used to throw a new light on the meaning of the underlying partial ordering and also to derive various inequalities. Several examples illustrate the methods of this paper.

Keywords

ORDERED IN DISPERSIONSTOCHASTIC ORDERINGNUMBER OF SIGN CHANGESINEQUALITIESTOTAL POSITIVITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 310 - 320
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported by NSF Grant MCS-79-27150.

References

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