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Reversing Conditional Orderings

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Stochastic Orders in Reliability and Risk

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

Abstract

We analyze some specific aspects concerning conditional orderings and relations among them. To this purpose we define a suitable concept of reversed conditional ordering and prove some related results. In particular we aim to compare the univariate stochastic orderings ≤ st, ≤ hr, and ≤ lr in terms of differences among different notions of conditional orderings. Some applications of our result to the analysis of positive dependence will be detailed. We concentrate attention to the case of a pair of scalar random variables X, Y ​. Suitable extensions to multivariate cases are possible.

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Acknowledgements

We thank the editors for inviting us to contribute to this volume in honor of Moshe Shaked.

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Authors and Affiliations

  1. Laboratory of Innovation Management and Economics, IMT Advanced Studies Lucca, Piazza S. Ponziano 6, 55100, Lucca, Italy

    Rachele Foschi

  2. Dipartimento di Matematica G. Castelnuovo, Università degli Studi di Roma La Sapienza, Piazzale Aldo Moro 5, 00185, Roma, Italy

    Fabio Spizzichino

Authors
  1. Rachele Foschi
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  2. Fabio Spizzichino
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Corresponding author

Correspondence to Rachele Foschi .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

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Foschi, R., Spizzichino, F. (2013). Reversing Conditional Orderings. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_3

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