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Stochastic orderings for discrete random variables

Giovagnoli, Alessandra and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2008) Stochastic orderings for discrete random variables. Statistics and Probability Letters, 78 (16). pp. 2827-2835. ISSN 0167-7152

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Identification Number: 10.1016/j.spl.2008.04.002


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
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Additional Information: © 2008 Elsevier
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Feb 2014 11:32
Last Modified: 16 May 2024 00:50

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