Power-Law Adjusted Survival Models

A simple adjustment to parametric failure-time distributions, which allows for much greater flexibility in the shape of the hazard-rate function, is considered. Analytical expressions for the distributions of the power-law adjusted Weibull, gamma, log-gamma, generalized gamma, lognormal, and Pareto distributions are given. Most of these allow for bathtub-shaped and other multi-modal forms of the hazard rate. The new distributions are fitted to real failure-time data which exhibit a multi-modal hazard-rate function and the fits are compared.