论文标题
审查数据的Weibull分布的后属性
Posterior properties of the Weibull distribution for censored data
论文作者
论文摘要
Weibull分布是可靠性分析中最常用的工具之一。在本文中，假设采用贝叶斯方法，我们提出了必要和足够的条件，以验证何时不正确的先验会导致在存在完整或右审核数据的情况下为Weibull分布的参数提供适当的后代。此外，我们提出了足够的条件来验证获得的后矩是否有限。这些结果可以通过检查不当先验的行为来实现，这些先验是在不同的客观先验中应用的，以说明新结果的有用性。作为我们定理的应用，我们证明，如果不正确的先验导致适当的后部，则后均值以及量表参数的其他较高矩，则不是有限的，因此不应使用。
The Weibull distribution is one of the most used tools in reliability analysis. In this paper, assuming a Bayesian approach, we propose necessary and sufficient conditions to verify when improper priors lead to proper posteriors for the parameters of the Weibull distribution in the presence of complete or right-censored data. Additionally, we proposed sufficient conditions to verify if the obtained posterior moments are finite. These results can be achieved by checking the behavior of the improper priors, which are applied in different objective priors to illustrate the usefulness of the new results. As an application of our theorem, we prove that if the improper prior leads to a proper posterior, the posterior mean, as well as other higher moments of the scale parameter, are not finite and, therefore, should not be used.
