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**Mean residual life functions of finite mixtures, order statistics and coherent systems.**
*(English)*
Zbl 1357.62304

Summary: We study properties of the mean residual life functions of finite mixtures. Specifically, we study ordering properties, monotonicity and the limiting behaviour. We show, under some mild conditions, that the limiting behaviour is similar to that of the strongest member (in the mean residual life order) of the mixture. We also consider the case of negative mixtures (i.e., mixtures with some negative coefficients) which is applied to study the behaviour of the mean residual life of order statistics and coherent systems with possibly dependent components.

### Keywords:

finite mixtures; mean residual life; failure rate; order statistics; coherent system; \(k\)-out-of-\(n\) system
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\textit{J. Navarro} and \textit{P. J. Hernandez}, Metrika 67, No. 3, 277--298 (2008; Zbl 1357.62304)

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