Deconvolution of arbitrary distribution functions and densities

Abstract

In this article we propose a novel approach for the deconvolution of the distribution function associated with an arbitrary probability measure (and possibly existing density). We first show that the initial convolution equation always can be transformed to a convolution equation that involves a symmetric distribution function, whose characteristic function has its values in the unit interval. As a consequence, the characteristic function of the target measure turns out as the limit of a geometric series. By truncation of this series, approximations for distribution function and density are established. The convergence properties of these approximations are examined in detail across diverse setups.