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A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes

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  • Luigi-Ionut Catana

    (S.C. Synergetix Educational S.R.L., No. 51, Dogăriei Street, 1st Floor, 800225 Galati, Romania
    Secondary School No. 56, University of Bucharest, 030018 Bucharest, Romania)

  • Vasile Preda

    (Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Costin C. Kiritescu National Institute for Economic Research, Romanian Academy, 050711 Bucharest, Romania
    Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania
    Current address: Mathematics and Computer Science Department, University of Bucharest, 010014 Bucharest, Romania.)

Abstract

In this article, we introduce and study a new stochastic order of multivariate distributions, namely, the conditional likelihood ratio order. The proposed order and other stochastic orders are analyzed in the case of a bivariate exponential distributions family. The theoretical results obtained are applied for studying the reliability of bridges affected by earthquakes. The conditional likelihood ratio order involves the multivariate stochastic ordering; it resembles the likelihood ratio order in the univariate case but is much easier to verify than the likelihood ratio order in the multivariate case. Additionally, the likelihood ratio order in the multivariate case implies this ordering. However, the conditional likelihood ratio order does not imply the weak hard rate order, and it is not an order relation on the multivariate distributions set. The new conditional likelihood ratio order, together with the likelihood ratio order and the weak hazard rate order, were studied in the case of the bivariate Marshall–Olkin exponential distributions family, which has a lack of memory type property. At the end of the paper, we also presented an application of the analyzed orderings for this bivariate distributions family to the study of the effects of earthquakes on bridges.

Suggested Citation

  • Luigi-Ionut Catana & Vasile Preda, 2022. "A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:102-:d:1015420
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    References listed on IDEAS

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