The numerical integration of the fourier inversion formula for distribution functions

Abstract

Given a characteristic function f(t) there are several so-called inversion formulas giving F(x) as a function of f(t). These formulas are, however, mostly unfit for numerical integration. Either the formula will lead to such voluminous calculations that they will be too burdensome even for an electronic computer, or, there are no rules how the formula could be used to produce an approximate value of F(x) of a prescribed precision.