Often, we are interested in modeling the duration or time between two events. For example, we may be interested in the time between the start and the end of a strike, the time it takes an unemployed person to find a job, the time to failure of a machine component, or the recidivism duration of an ex-convict. In each of these examples, the data set consists of a response variable that records the time or duration between the events of interest. Due to the nature of the study, the data set usually consists of a mixture of complete and censored observations. For example, in the recidivism study conducted by Chung, Schmidt, and Witte (1991), a random sample of 1,445 former inmates released from prison between July 1, 1977 and June 30, 1978 was collected using April 1, 1984 as the end point of the study. The study found that 552 former inmates were arrested again for different violations. Their duration or time response was therefore recorded. Duration measurements for the remaining 893 individuals were not recorded and were censored. That is, at the time the study concluded, these individuals had not been arrested for any violation since their release. Note that the censored times for these individuals will vary due to the staggered entry of the subjects into the study.
As another example, consider an auto and home insurance company that may be interested in the time between a policy holder’s start and termination date. The company’s objective ...