In recent years, interest has grown in the study of the residual lifetime . Residual lifetime at time t is defned as the remaining lifetime of a subject or a unit who has already survived at least t. This concept is widely used in many technical systems and life analyses. For example, in medicine, the patients, especially those who su?er from a chronic disease like cancer, are interested in knowing their remaining lifetime. Besides, in a randomized Phase III breast cancer clinical trial, the physician needs to use the obtained residual life to advise whether a patient should participate in the study to take a di?erent type of therapy. Residual lifetime function also has a tremendous range of applications in many other studies, such as to model the duration of strikes, length of wars, job mobility in social science and analysis in the recidivism The mean residual life function and the median residual life function
