Discrete approximations of continuous and mixed measures on a compact interval

When considering a mixed probability measure on [0, 1] with atoms in zero and one, the frontier points have to be treated (and “weighted”) differently and separately with respect to the interior points. In order to avoid the troublesome consequences of a mixed model, an easily interpretable discretization of [0, 1] on uniformly spaced atoms is here proposed. This “homogeneous support” is used to define two discrete models, a parametric and a nonparametric one. An application to real data on recovery risk of the Bank of Italy’s loans is here considered to exemplify both discretization and proposed models. Finally, a simulation study is performed to analyze the behavior of the nonparametric proposal in terms of goodness-of-fit.