DBKGrad: An R Package for Mortality Rates Graduation by Discrete Beta Kernel Techniques

We introduce the R package DBKGrad, conceived to facilitate the use of kernel smoothing in graduating mortality rates. The package implements univariate and bivariate adaptive discrete beta kernel estimators. Discrete kernels have been preferred because, in this context, variables such as age, calendar year and duration, are pragmatically considered as discrete and the use of beta kernels is motivated since it reduces boundary bias. Furthermore, when data on exposures to the risk of death are available, the use of adaptive bandwidth, that may be selected by cross-validation, can provide additional benets. To exemplify the use of the package, an application to Italian mortality rates, for dierent ages and calendar years, is presented.