For calculating the inverse Fourier transform of characteristic functions, to obtain the corresponding probability density function and cumulative density function.

Based on: Viktor Witkovský (2016) - Numerical inversion of a characteristic function: An alternative tool to form the probability distribution of output quantity in linear measurement models https://github.com/witkovsky/CharFunTool

written by: Tomás Lobão de Almeida, 2022-2023

Returns the pdf of the provided characteristic function Φ as the result of performing an inverse Fourier transform using fft and a discretized grid. The function returned is a linear interpolation of the resulting grid.

Returns a tuple (xmin, xmax) with the boundaries for the integration interval. Approximated by using finite differences for calculating moments from the characteristic function.

Returns integration objects of the provided characteristic function Φ as the result of applying the fft algorithm to a discretized grid. These are used to obtain either the pdf or cdf by performing some transformations.

Returns the pdf of the provided characteristic function Φ as the result of performing an inverse Fourier transform using fft and a discretized grid. The function returned is a linear interpolation of the resulting grid.