Stochastic analysis of an age‐dependent mixture truncation model

Abstract

AbstractIn 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.