Predicting the Number of Future Events

This article describes prediction methods for the number of future events from a population units associated with an on-going time-to-event process. Examples include warranty returns and product failures that could cause serious threats to property or life. Important decisions such as whether recall should be mandated are often based on predictions. Data, generally right-censored (and sometimes left truncated right-censored), used estimate parameters distribution. distribution can then predict over periods time. Such predictions called within-sample differ other problems considered in most literature. shows plug-in (also known estimative naive) method is not asymptotically correct (i.e., large amounts data, coverage probability always fails converge nominal confidence level). However, commonly calibration shown predictions, two alternative predictive-distribution-based perform better than presented justified. Supplementary materials this available online.