Single Sample Data
This chapter introduces the basic model descriptions of survival data. Basically, the distribution of survival data may be either continuous or discrete, but the nonparametric estimators of the distributions of survival time are discrete in any case. Therefore, when introducing the estimators, the discrete models are necessary to know. Traditional statistical model descriptions are based on the density and the cumulative distribution functions. The chapter discusses discrete time survival models. For instance, life lengths may be measured in full years, introducing tied data. The cumulative hazard function is important because it is fairly easy to estimate nonparametrically, in contrast to the hazard and density functions. In the estimation of the hazard atoms, the concept of risk set is of vital importance. The property of constant hazard implies no aging. It is important to realize that in practice all data are discrete.