The routines described in this chapter compute estimates for smoothing parameters and estimates in models for estimating density and hazard functions. For density estimation, the penalized likelihood method of Scott (1976) may be used to obtain smooth estimates for arbitrary (smooth) densities. Alternatively, the routines DESKN and DNFFT obtain density estimates by the kernel method for a given window width and kernel function. Routine DNFFT uses a Gaussian kernel, while for routine DESKN, the kernel is provided by the user. Finally, routine DESPT finds linear or quasi‑cubic interpolated estimates of a density. Tapia and Thompson (1978) discuss all of these methods.

For hazard estimation, the methods of Tanner and Wong (1984) are used to obtain estimates of the smoothing parameters in a modified likelihood. These methods are implemented in routines HAZRD and HAZEZ, the difference between the routines is in the ease of use and the options offered. For given smoothing parameters, the routine HAZST may be used to obtain estimates for the hazard function.