Whereas discrimination methods and their error probabilities were broadly investigated for common data distributions such as the multivariate normal or t-distributions, this paper considers the case when the recorded data are assumed to be observations from sequential order statistics. Random vectors of sequential order statistics describe, e.g., successive failures in a k-out-of-n system or in other coherent and load sharing systems allowing for changes of underlying lifetime distributions caused by component failures. Within this framework, the Bayesian two-class discrimination approach with known prior probabilities and class parameters is considered, and exact and asymptotic formulas for the error probabilities in terms of Erlang and hypoexponential distributions are derived. Since the Bayesian classifier is closely related to Kullback–Leibler’s information distance, this approach is extended by invoking other divergence measures such as Jeffreys and Rényi’s distance. While exact formulas for the misclassification rates of the resulting distance-based classifiers are not available, inequalities among the corresponding error probabilities are derived. The performance of the applied classifiers is illustrated by some simulation results.

中文翻译：

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使用顺序订单统计进行分类

尽管针对通用数据分布（例如多元正态分布或t分布）广泛地研究了判别方法及其错误概率，但本文考虑了假设记录的数据是来自顺序统计的观察结果的情况。顺序统计量的随机向量描述了例如n出k的系统或其他相干和负载分担系统中的连续故障，从而允许由组件故障引起的底层寿命分布发生变化。在此框架内，考虑了具有已知先验概率和类参数的贝叶斯两类判别方法，并根据Erlang和低指数分布推导了误差概率的精确和渐近公式。由于贝叶斯分类器与Kullback-Leibler的信息距离密切相关，因此通过调用其他差异度量（例如Jeffreys和Rényi的距离）来扩展此方法。虽然无法获得针对基于距离的分类器的误分类率的精确公式，但可以得出相应错误概率之间的不等式。一些仿真结果说明了应用分类器的性能。