Failure-rate functions for doubly-truncated random variables

The failure rate function is generalized for doubly-truncated random variables. This generalized function is used to characterize the distribution function and to obtain the properties that any function must have to be a generalized failure rate function, both for continuous and discrete random variables. From the theoretical results are constructed nonparametric estimators of the Kaplan-Meier type and cumulative-hazard type.