ABSTRACT
The parameter θ for the exponential distribution is a scale parameter. Intuitively, it is easier to think about modifying a location parameter. When there is no censoring, so all complete life lengths are available, it is straight-forward to write down the likelihood. The large sample theory of the maximum likelihood estimators and likelihood ratio statistics follow from the standard results for regression. However, in many applications of exponential regression, the observations are censored. When all of the observations are either complete or order statistic censored, exact distribution theory is possible, at least for the inverse power law. In other instances, approximate large sample distribution theory must be applied. Exact inference procedures have only been developed for special cases and those pertain to the inverse power law model. The chapter considers two examples to illustrate a variety of issues in estimation and exploring goodness-of-fit to the exponential regression model.
