ABSTRACT
Gjessing et al. (2003) have given a very nice introduction of frailty models based on Levy processes. We present some of their results in this chapter. The failure rate is theoretical and descriptive technique which plays a fundamental role in survival and event history analysis. Basic methods in these elds, such as the counting process approach and the Cox model, focus on failure rates. The purpose of the failure rate is to measure, locally, the risk of an event given the nonoccurrence of the event up to that time. It is an intuitive and attractive concept, and is also closely related to incidence rate in epidemiology. In a context of probability, the failure rate is a special case of an intensity process or the derivative of a Doob-Meyer compensator; see Andersen et al. (1994).
