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Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  04 September 2020

Lu Li ,
Qinyu Wu  and
Tiantian Mao
Lu Li*
Affiliation:
University of Science and Technology of China
Qinyu Wu*
Affiliation:
University of Science and Technology of China
Tiantian Mao*
Affiliation:
University of Science and Technology of China
*
*Postal address: Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, China. Email address: [email protected]
**Email address: [email protected]
***Email address: [email protected]
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Abstract

We investigate stochastic comparisons of parallel systems (corresponding to the largest-order statistics) with respect to the reversed hazard rate and likelihood ratio orders for the proportional reversed hazard rate (PRHR) model. As applications of the main results, we obtain the equivalent characterizations of stochastic comparisons with respect to the reversed hazard rate and likelihood rate orders for the exponentiated generalized gamma and exponentiated Pareto distributions. Our results recover and strengthen some recent results in the literature.

Keywords

Reversed hazard rate orderlikelihood ratio orderusual stochastic orderexponentiated generalized gamma distributionexponentiated Pareto distributionoptimal reinsurance

MSC classification

Primary: 60E05: Distributions
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 3 , September 2020 , pp. 832 - 852
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Copyright
© Applied Probability Trust 2020

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