An R Package for Discrete Beta Kernel Graduation of Probabilities of Dying

Probabilities of dying are indicators commonly used in demography and actuarial practice. They are usually referred to one or more variables, the most common being age, calendar years and duration; for ease of presentation, we will start focusing on age only, while bivariate extensions will be addressed afterward. To be specific, the dx deaths at age x can be seen as arising from a population, initially exposed to the risk of death, of size ex. This can be summarized via the model dx Bin (ex, qx), where qx represents the true, but unknown, mortality rate at age x. The crude rate °qx is the observed counterpart of qx. Graduation is necessary because crude data usually presents abrupt changes, which do not agree with the dependence structure supposedly characterizing the true rates (London, 1985). Nonparametric models are the natural choice if the aim is to reflect this belief. Furthermore, a nonparametric approach can be used to choose the simplest suitable parametric model, to provide a diagnostic check of a