Stochastic comparisons of distorted distributions,coherent systems and mixtures with ordered components |
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Authors: | Jorge Navarro Yolanda del Águila |
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Affiliation: | 1.Facultad de Matemáticas,Universidad de Murcia,Murcia,Spain;2.Departamento de Matemáticas,Universidad de Almería,Almería,Spain |
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Abstract: | A distribution function F is a generalized distorted distribution of the distribution functions (F_1,ldots ,F_n) if (F=Q(F_1,ldots ,F_n)) for an increasing continuous distortion function Q such that (Q(0,ldots ,0)=0) and (Q(1,ldots ,1)=1). In this paper, necessary and sufficient conditions for the stochastic (ST) and the hazard rate (HR) orderings of generalized distorted distributions are provided when the distributions (F_1,ldots ,F_n) are ordered. These results are used to obtain distribution-free ordering properties for coherent systems with heterogeneous components. In particular, we determine all the ST and HR orderings for coherent systems with 1–3 independent components. We also compare systems with dependent components. The results on distorted distributions are also used to get comparisons of finite mixtures. |
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