Mortality Models based on the Transform $\log(-\log x)$

Abstract

A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years. These common structures are gathered by a representation based on age-constants and time-stochastic processes. From the projection of the time-processes the mortality forecasting is straigthforward. Comparisons of the new model with the well-known Lee-Carter and Cairns-Blake-Dowd models employing sex-based mortality data of some countries are provided. Some in-sample and out-of-sample goodness-of-fit criteria show that in some situations the new model performs better than the ones mentioned above. Assessments of the performance of these models using rates of mortality improvement are discussed.