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
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 |
| Divisions: | Centre for Analysis of Time Series |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 26 Feb 2014 11:32 |
| Last Modified: | 04 Mar 2024 03:27 |
| URI: | http://eprints.lse.ac.uk/id/eprint/55872 |
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