Parameter Estimation and Censored Lives

The usual likelihood used to make inferences about parameters of lifetime distributions when lives may be censored consists of the product of probability densities for completed lives and reliabilities for the censored lives. This works well in many situations. We consider two special cases of a model which assumes a Poisson birth process for the items: in one case the usual method works well, but in the other case it does not, and better estimates are found.