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Star-shaped order for distributions characterized by several parameters and some applications

Published online by Cambridge University Press:  28 September 2021

Idir Arab ,
Milto Hadjikyriakou ,
Paulo Eduardo Oliveira Open the ORCID record for Paulo Eduardo Oliveira [Opens in a new window]  and
Beatriz Santos Open the ORCID record for Beatriz Santos [Opens in a new window]
Idir Arab
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal
Milto Hadjikyriakou
Affiliation:
School of Sciences, University of Central Lancashire, Pyla, Cyprus
Paulo Eduardo Oliveira
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal
Beatriz Santos*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal
*
*Corresponding author. E-mail: b14796@gmail.com
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Abstract

The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.

Keywords

Parallel systemsPHR modelsPRHR modelsSeries systemsStar-shaped order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 49 - 59
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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