威布尔分布组与删失数据下最大似然估计的存在性

摘要

In this paper we consider the estimation problem in the situation where the lifetime of some products follows a Weibull distribution, and the observed data are grouped and right-censored. All possible cases are discussed, and a necessary and sufficient condition for the existence of the maximum likelihood estimate of the unknown pararneters is given. The paper is concluded with a short discussion about one failure situation and about the calculation of the maximum likelihood estimate with a true data set.%本文研究寿命服从威布尔分布，观测数据分组与可能删失的情况下，最大似然估计的存在性。针对所有数据类型，我们给出了最大似然估计存在性的一个充分必要条件。文章结尾讨论了仅一个失效数据时最大似然估计的计算。