Stochastic Comparison for Extreme Order Statistics Arising from PHR, PRHR or Location Model

Abstract

We have considered series and parallel systems with independent set of random variables belonging from PHR, PRHR family of distributions to study dispersive and star ordering between two systems such that the number of components in both the system are different. This will help us in identifying the deviation of lifetime of a product from the warranty of the product. Moreover, we have also considered series and parallel systems with dependent set of random variables each belonging from location based models, such that the baseline distribution for both the sets are different. The Archimedean copula generators used here are ψ1 and ψ2 such that the condition “ϕ1 ・ ψ2 or ϕ2 ・ψ1 is super-additive” holds. Earlier researchers have studied location-scaled or resilience-scaled models for independent or dependent set of random variables. Our study is an addition to the existing research.

Keywords

• Archimedean copula
• dispersive order
• proportional hazard rate distribution
• proportional reversed hazard rate distribution
• star order