Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components

Jorge Navarro () and Yolanda Águila
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Jorge Navarro: Universidad de Murcia
Yolanda Águila: Universidad de Almería

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 2, 627-648

Abstract: Abstract A distribution function F is a generalized distorted distribution of the distribution functions $$F_1,\ldots ,F_n$$ F 1 , … , F n if $$F=Q(F_1,\ldots ,F_n)$$ F = Q ( F 1 , … , F n ) for an increasing continuous distortion function Q such that $$Q(0,\ldots ,0)=0$$ Q ( 0 , … , 0 ) = 0 and $$Q(1,\ldots ,1)=1$$ Q ( 1 , … , 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 $$F_1,\ldots ,F_n$$ F 1 , … , 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.

Keywords: Stochastic orders; Coherent systems; Order statistics; Copulas; Mixtures; 62K10; 60E15; 90B25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s00184-017-0619-y

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