发表机构
University of Zaragoza（萨拉戈萨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出风险率序和逆风险率序的一般刻画，统一处理连续、离散与混合分布，给出双变量刻画的直接证明，引入加法群上的新分布类并推广随机和下的保序结果。
AI 中文摘要
我们提出了对随机变量的风险率序和逆风险率序的一般刻画，这些随机变量关于一个共同的支配测度是绝对连续的。该框架有助于统一处理连续、离散和混合分布，而无需采用特设的近似技术或限制性的可积性假设。利用这一结果，我们给出了两种序的双变量刻画的直接证明。此外，我们在加法群上引入了$\overline{G}$-IFR和$\overline{G}$-DRHR分布类，统一了不同领域的老化性质，并证明了它们在卷积下的封闭性。最后，我们重新审视并推广了Shanthikumar和Yao（1991）关于随机和下风险率序保持的经典结果，简化了潜在条件，并允许离散和混合的和分量。
英文摘要
We propose a general characterization of the hazard rate and reversed hazard rate stochastic orders for random variables that are absolutely continuous with respect to a common dominating measure. This framework is useful in giving a unified treatment of continuous, discrete, and mixed distributions without requiring ad hoc approximation techniques or restrictive integrability assumptions. Using this result, we provide direct proofs of the bivariate characterizations of both orders. Additionally, we introduce the class of $\overline{G}$-IFR and $\overline{G}$-DRHR distributions on additive groups, unifying aging properties across different domains and proving their closure under convolution. Finally, we revisit and extend the classic results of Shanthikumar and Yao (1991) on the preservation of hazard rate orders under random sums, simplifying the underlying conditions and accommodating discrete and mixed sum components.
