Deconvolution of Arbitrary Distribution Functions and Densities

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in mathematics. We show that the model under consideration always can be transformed to a model with a symmetric error variable, whose characteristic function has its values in the unit interval. As a consequence, the characteristic function of the target variable turns out as the limit of a geometric series. By truncation of this series, an approximation for the associated distribution function (and density) is established. The convergence properties of these approximations are examined in detail across diverse setups.