Stochastic analysis of an age‐dependent mixture truncation model
提出一种新混合模型处理随机左截断数据，证明原始随机变量的递增失效率性质在排序条件下可传递至结果变量，并应用于上记录值和老化过程分析。
Abstract In this article, a new mixture model is introduced to model randomly left truncated data. The likelihood ratio ordering of original random variable and resultant random variable in the model is established. It is shown that the increasing failure rate (IFR) property of the original random variable translates into the IFR property of the resultant random variable under an ordering property. In addition, the resultant random variable in the random truncation model is proved to be less than the resultant random variable in our model with respect to the likelihood ratio order. Possible extensions of the model to the multivariate case are considered. Finally, the model is applied to model the upper record values of a sequence of random variables and as another application the lifetime of a unit under burn‐in process is scrutinized.