Stochastic comparison of parallel systems with Pareto components

Naqvi, Sameen and Ding, Weiyong and Zhao, Peng (2021) Stochastic comparison of parallel systems with Pareto components. Probability in the Engineering and Informational Sciences. pp. 1-13. ISSN 0269-9648

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Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686-687] from support to general supports, (a), 0. As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering. © 2021 The Author(s). Published by Cambridge University Press.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Article
Uncontrolled Keywords: Convex transform order; Dispersive order; Parallel system; Pareto distribution; Star order
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 30 Sep 2022 12:20
Last Modified: 30 Sep 2022 12:20
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