Further results involving percentile inactivity time order and its inference

摘要

This paper studies a family of stochastic orders of random variables defined via the comparison of their percentile inactivity time functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. The estimator of the percentile inactivity time is introduced. Finally, some applications in reliability theory and finance are described.