We first review some main results for phase-type distributions, including a discussion of Coxian distributions and their canonical representations. We then consider the extension of phase-type modeling to cover competing risks. This extension involves the consideration of finite state Markov chains with more than one absorbing state, letting each absorbing state correspond to a particular risk. The non-uniqueness of Markov chain representations of phase-type distributions is well known. In the paper we study corresponding issues for the competing risks case with the aim of obtaining identifiable parameterizations. Statistical inference for the Coxian competing risks model is briefly discussed and some real data are analyzed for illustration.

我们首先回顾了相型分布的一些主要结果，包括对 Coxian 分布及其规范表示的讨论。然后，我们考虑扩展阶段型建模以涵盖竞争风险。此扩展涉及考虑具有多个吸收状态的有限状态马尔可夫链，让每个吸收状态对应于特定风险。相型分布的马尔可夫链表示的非唯一性是众所周知的。在本文中，我们研究了竞争风险案例的相应问题，目的是获得可识别的参数化。简要讨论了 Coxian 竞争风险模型的统计推断，并分析了一些实际数据以供说明。