Extinctions are difficult to observe and typically are inferred from the timing and reliability of field observations and collections. Recent advances in approaches to estimating extinction probability consider the type, timing and certainty of records, the timing, scope and severity of threats, and the timing, extent and reliability of surveys. Here we describe a new approach to inference of extinction that uses survival theory, an approach that has a long history of effective use in other disciplines that confront similar problems. The model takes into account uncertainties in input parameter estimates and provides bounds on estimates of the extinction probability for the case in which a species has not been detected following some specified time. We illustrate application of the model using information for dodos and Aldabra snails. This approach provides an alternative perspective on the models underlying the techniques for inferring extinction. It should provide reliable estimates of recent extinction rates.