Giovagnoli, Alessandra and Wynn, Henry P.
(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 |
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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 |

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 |

Last Modified: | 20 Jan 2020 03:47 |

URI: | http://eprints.lse.ac.uk/id/eprint/55872 |

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