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Non-Comparability with respect to the convex transform order with applications

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  23 November 2020

Idir Arab ,
Milto Hadjikyriakou  and
Paulo Eduardo Oliveira Open the ORCID record for Paulo Eduardo Oliveira [Opens in a new window]
Idir Arab*
Affiliation:
University of Coimbra
Milto Hadjikyriakou*
Affiliation:
University of Central Lancashire
Paulo Eduardo Oliveira*
Affiliation:
University of Coimbra
*
*Postal address: CMUC, Department of Mathematics, University of Coimbra, PO Box 3008, EC Santa Cruz, Coimbra, Portugal. Email address: paulo@mat.uc.pt
**Postal address: School of Sciences, 12–14 University Avenue, Pyla, 7080 Larnaka, Cyprus.
*Postal address: CMUC, Department of Mathematics, University of Coimbra, PO Box 3008, EC Santa Cruz, Coimbra, Portugal. Email address: paulo@mat.uc.pt
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Abstract

In the literature of stochastic orders, one rarely finds results characterizing non-comparability of random variables. We prove simple tools implying the non-comparability with respect to the convex transform order. The criteria are used, among other applications, to provide a negative answer for a conjecture about comparability in a much broader scope than its initial statement.

Keywords

Convex transform orderfailure raterapidly varying functions

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60E05: Distributions 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1339 - 1348
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Copyright
© Applied Probability Trust 2020

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References

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