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Stochastic orderings for discrete random variables

Giovagnoli, Alessandra and Wynn, Henry P. (2008) Stochastic orderings for discrete random variables. Statistics & Probability Letters, 78 (16). pp. 2827-2835. ISSN 0167-7152

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Abstract

A number of application areas of statistics make direct use of stochastic orderings. Here the special case of discrete distributions is covered. For a given partial ordering ⪯⪯ one can define the class of all ⪯⪯-order preserving functions x⪯y⇒g(x)≤g(y)x⪯y⇒g(x)≤g(y). Stochastic orderings may be defined in terms of ⪯:X⪯stY⇔EXg(X)≤EYg(Y)⪯:X⪯stY⇔EXg(X)≤EYg(Y) for all order-preserving gg. Alternatively they may be defined directly in terms of a class of functions F:X⪯stY⇔EXg(X)≤EYg(Y)F:X⪯stY⇔EXg(X)≤EYg(Y) for all f∈Ff∈F. For discrete distributions Möbius inversions plays a useful part in the theory and there are algebraic representations for the standard ordering ≤≤ for integer grids. In the general case, based on FF, the notion of a dual cone is useful. Several examples are presented.

Item Type: Article
Official URL: http://www.sciencedirect.com/science/journal/01677...
Additional Information: © 2008 Elsevier
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Centre for the Analysis of Time Series (CATS)
Research centres and groups > Decision Support and Risk Group (DSRG)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 26 Feb 2014 11:32
URL: http://eprints.lse.ac.uk/55872/

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