Estimating the critical time of the inverse Gaussian hazard rate

Methods for estimating the critical time of the hazard rate for an inverse Gaussian lifetime distribution are discussed. The critical time is the point at which (1) the hazard rate starts to decrease, and (2) the mean residual lifetime starts to increase. An algorithm for estimating this critical time is developed. Six methods of estimating parameters are compared in terms of their bias and RMS (root-mean-square) error; two of them are recommended. A table of constants is provided to help estimate the critical time. The jackknife procedure for estimating the bias and standard deviation of the recommended estimators is also considered. A numerical example is included