Giovagnoli, Alessandra and Wynn, Henry P. (2008) Stochastic orderings for discrete random variables. Statistics & 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 |
| 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) |
| Date Deposited: | 26 Feb 2014 11:32 |
| URL: | http://eprints.lse.ac.uk/55872/ |
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