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On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes.

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Title: On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes.
Authors: Bezgina, E.1, Burkschat, M.1,2 marco.burkschat@rwth-aachen.de
Source: Journal of Multivariate Analysis. Jan2019, Vol. 169, p95-109. 15p.
Subjects: Random variables, Mathematical symmetry, Multivariate analysis, Distribution (Probability theory), Exponential functions
Abstract: Abstract Necessary and sufficient conditions for multivariate total positivity of order 2 (MTP 2) for density functions of some class of exchangeable random variables are obtained. The considered densities occur via symmetrization of particular ordered random variables. As an example, a characterization of the MTP 2 property for the Freund–Weinman multivariate exponential distribution is given. Furthermore, the results are applied to general failure-dependent component lifetimes in systems based on sequential order statistics. In the latter setting, the hazard rate increasing upon failure (HIF) property is also characterized. In particular, the case of underlying distributions satisfying the proportional hazards assumption is considered. The results are supplemented by an analysis of the covariances of the above multivariate exponential distribution. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes.
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  Data: <searchLink fieldCode="AR" term="%22Bezgina%2C+E%2E%22">Bezgina, E.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Burkschat%2C+M%2E%22">Burkschat, M.</searchLink><relatesTo>1,2</relatesTo><i> marco.burkschat@rwth-aachen.de</i>
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  Data: <searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+symmetry%22">Mathematical symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Multivariate+analysis%22">Multivariate analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink>
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  Data: Abstract Necessary and sufficient conditions for multivariate total positivity of order 2 (MTP 2) for density functions of some class of exchangeable random variables are obtained. The considered densities occur via symmetrization of particular ordered random variables. As an example, a characterization of the MTP 2 property for the Freund–Weinman multivariate exponential distribution is given. Furthermore, the results are applied to general failure-dependent component lifetimes in systems based on sequential order statistics. In the latter setting, the hazard rate increasing upon failure (HIF) property is also characterized. In particular, the case of underlying distributions satisfying the proportional hazards assumption is considered. The results are supplemented by an analysis of the covariances of the above multivariate exponential distribution. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Multivariate Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmva.2018.08.015
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 95
    Subjects:
      – SubjectFull: Random variables
        Type: general
      – SubjectFull: Mathematical symmetry
        Type: general
      – SubjectFull: Multivariate analysis
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Exponential functions
        Type: general
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      – TitleFull: On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes.
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              Text: Jan2019
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              Y: 2019
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              Value: 169
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            – TitleFull: Journal of Multivariate Analysis
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