Stochastic Ordering of Dependent Systems under Transformation Models and Archimedean Copulas
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911630360576000 |
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| author | Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo |
| author_facet | Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo |
| contents | We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean copulas, allowing for a unified treatment of several transformation-based models, including proportional hazard, proportional reversed hazard rate and proportional odds families. For parallel, series and $(n-k)$-out-of-$n$ systems, we derive conditions for stochastic dominance based on monotonicity of the transformation and structural properties of the copula generators, formulated through super-additivity and Schur-type arguments.
The results provide tractable criteria that extend existing comparisons beyond independence and illustrate the combined effect of dependence and parameter heterogeneity on system reliability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Ordering of Dependent Systems under Transformation Models and Archimedean Copulas Arab, Idir Hadjikyriakou, Milto Oliveira, Paulo Eduardo Probability 60E15, 60E05, 62N05 We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean copulas, allowing for a unified treatment of several transformation-based models, including proportional hazard, proportional reversed hazard rate and proportional odds families. For parallel, series and $(n-k)$-out-of-$n$ systems, we derive conditions for stochastic dominance based on monotonicity of the transformation and structural properties of the copula generators, formulated through super-additivity and Schur-type arguments. The results provide tractable criteria that extend existing comparisons beyond independence and illustrate the combined effect of dependence and parameter heterogeneity on system reliability. |
| title | Stochastic Ordering of Dependent Systems under Transformation Models and Archimedean Copulas |
| topic | Probability 60E15, 60E05, 62N05 |
| url | https://arxiv.org/abs/2604.26026 |