So far we have exclusively studied nonparametric methods for survival analysis. This is a tradition that has its roots in medical (cancer) research. In technical applications, on the other hand, parametric models dominate; of special interest is the Weibull model (Weibull 1951). The textbook by (Lawless 2003) is a good source for the study of parametric survival models. More technical detail about parametric distributions is found in Appendix B.
In eha three kinds of parametric models are available; the proportional hazards, the accelerated failure time in continuous time, and the discrete time proportional hazards models.
A proportional hazards family of distributions ...