Predicting a future median life through a power transformation

A simple and unified prediction interval (PI) for the median of a future lifetime can be obtained through a power transformation. This interval usually possesses the correct coverage, at least asymptotically, when the transformation is known. However, when the transformation is unknown and is estimated from the data, a correction is required. A simple correction factor is derived based on large sample theory. Simulation shows that the unified PI after correction performs well. When compared with the existing frequentist PI's, it shows an equivalent or a better performance in terms of coverage probability and average length of the interval. Its nonparametric aspect and the ease of usage make it very attractive to practitioners. Real data examples are provided for illustration.