Statistical Methods in Customer Relationship Management

Appendix I

Proportional Hazards Model

(Sources: Kalbfleisch and Prentice [1], Franses and Paap [2])

A second way to include explanatory variables in a duration model is to scale the hazard function by the function , that is,

(I.1)

where denotes an arbitrary, unspecified, baseline hazard function for continuous . Again, because the hazard function has to be non-negative, one usually specifies as

(I.2)

If the intercept is unequal to 0, the baseline hazard is identified upon a scalar. Here, if one opts for a Weibull or an exponential baseline hazard one again has to restrict to 1 to identify the parameters.

The conditional density function of given covariates is

(I.3)

The conditional survivor ...