The Weibull distribution, with shape parameter $k>0$ and scale parameter $\lambda>0$, 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.
翻译:Weibull 分布, 包括形状参数 $k>0$和比例参数 $\lambda>0$, 是存续分析中最流行的参数分布, 包括完整或检查过的数据。 虽然对 Weibull 分布参数的推论通常是通过最大可能性进行的, 但人们已经清楚地确定, 在样本大小小或受审查数据比例大的情况下, 形状参数的最大估计概率并不足够, 原因是相关的大偏差。 此手稿展示了Bayesian 信息- 理论最小信息长度原则, 以及适当选择信息不足的先前分布方法, 可以用来推导 Weibull 分布参数, 提供完整的数据或数据, 并使用I型审查 。 经验实验显示, 对形状参数的拟议最小信息长度估计优于最大可能性估计, 似乎优于最近提出的其他以 Kullback- Leiber 风险 修改过的最大概率估计。