论文标题
多元分布的失真表示
Distortion Representations of Multivariate Distributions
论文作者
论文摘要
在风险理论中引入了单变量扭曲的分布，以表示某些风险的预期分布中的变化（扭曲）。后来，它们还用于代表订单统计，相干系统，比例危害率（PHR）和比例反向危险率（PRHR）模型等分布。在本文中，我们将此概念扩展到多元设置。我们表明，在某些情况下，它们是Copula表示形式的有效替代方法，尤其是当边缘分布不易处理时。几个相关示例说明了此类表示在统计建模中的应用。它们包括对配对（依赖）有序数据，关节剩余寿命，订单统计和相干系统的研究。
The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent systems, proportional hazard rate (PHR) and proportional reversed hazard rate (PRHR) models, etc. In this paper we extend this concept to the multivariate setup. We show that, in some cases, they are a valid alternative to the copula representations especially when the marginal distributions may not be easily handled. Several relevant examples illustrate the applications of such representations in statistical modeling. They include the study of paired (dependent) ordered data, joint residual lifetimes, order statistics and coherent systems.
