The problem of analyzing time to event data arises in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. Let X be the time until some specified event. More precisely, in this work, X is a nonnegative random variable (r. v.) from a homogeneous population. Four functions characterize the distribution of X, namely, the survival function, which is the probability of an individual surviving to time x; the hazard rate (function), sometimes termed risk function, which is the chance an individual of age x experiences the event in the next instant in time; the probability density (or probability mass) function, which is the unconditional probability of the event’s occurring at time x; and the mean residual life at time x, which is the mean time to the event of interest, given the event has not occurred at x. If we know any one of these four functions, then the other three can be uniquely determined. We prove asymptotic results for estimators of mean residual life function both in independent and dependent random right censoring models. Dependence is described by Archimedean copula function.

Survival Function, Mean Residual Life Function, Random Censoring, Copulas