A new class of distribution functions for lifetime data

This paper deals with the issue of building a parametric model from the empirical and/or qualitative information about the hazard rate. We propose a new class of models for survival data analysis. This class is characterized by a distribution function which includes, in its expression, a function that defines the sign of the first derivative of a monotonic transformation of the hazard rate. We show that certain parametric models used in survival analysis belong to the proposed class. Finally, by using the proposed method, we build two new distributions which allow us to achieve a highly flexible hazard rate. The first one is based on an m-degree polynomial and allows us to get BT, IFR and UBT-BT hazard rates, while the second, based on trigonometric functions, enables us to obtain monotonically increasing or decreasing hazard rates or hazard rates with a non-monotonic behavior. The usefulness of the new method is illustrated through two applications to real data.