论文标题
Weibull分布的最小消息长度推断，并具有完整和审查的数据
Minimum message length inference of the Weibull distribution with complete and censored data
论文作者
论文摘要
带有形状参数$ k> 0 $和比例参数$λ> 0 $的Weibull分布是生存分析中最受欢迎的参数分布之一，具有完整或审查的数据。尽管通常通过最大可能性进行了威布尔分布参数的推断，但由于相关的大偏见很小，或者审查数据的比例很大，因此形状参数的最大似然估计值不足。该手稿说明了贝叶斯信息理论最小消息长度原理如何以及适当的弱信息性先前分布的选择，可用于在给定完整的数据或使用I型审查的数据的情况下推断Weibull分布参数。经验实验表明，所提出的最小消息长度估计值优于最大似然估计值，并且在Kullback-Leibler风险方面，似乎优于其他最近提出的修改后的最大似然估计。最后，我们将所提出方法的扩展扩展到具有II型审查的数据。
The Weibull distribution, with shape parameter $k>0$ and scale parameter $λ>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the Weibull distribution is commonly done through maximum likelihood, it is well established that the maximum likelihood estimate of the shape parameter is inadequate due to the associated large bias when the sample size is small or the proportion of censored data is large. This manuscript demonstrates how the Bayesian information-theoretic minimum message length principle coupled with a suitable choice of weakly informative prior distributions, can be used to infer Weibull distribution parameters given complete data or data with type I censoring. Empirical experiments show that the proposed minimum message length estimate of the shape parameter is superior to the maximum likelihood estimate and appears superior to other recently proposed modified maximum likelihood estimates in terms of Kullback-Leibler risk. Lastly, we derive an extension of the proposed method to data with type II censoring.
