Survival time ($T$)

A survival time is the elapsed time to an event of interest, which may be death, failure, recovery or completion of a task. Its survival function and hazard function describe the event-time law. Right censoring records only that the event time exceeds the observed follow-up time.

A survival distribution is the probability distribution of an event or failure time, commonly summarized by its survivor function, hazard function or cumulative hazard function. It may contain atoms or a positive probability of an event never occurring; an ordinary density-based hazard therefore need not describe every survival distribution.