# Math Help - Characteristic function to pdf

1. ## Characteristic function to pdf

Can someone give me an example of solving an integral of an inverse characteristic function? For example, let's say we have the characteristic function of a gaussian. How would I recover the probability distribution from that? I can't seem to solve the integral.

Ultimately, I'm trying to use a moment generating function to recover some probability distribution from that. I want to create an arbitrary series of moments (subject to some constraints) and then get a pdf from that. I just can't remember enough complex maths to solve the integrals! Thanks.

(I'm cross-posting the question to the Advanced Topics forum...)

2. Originally Posted by langweilig
Can someone give me an example of solving an integral of an inverse characteristic function? For example, let's say we have the characteristic function of a gaussian. How would I recover the probability distribution from that? I can't seem to solve the integral.

[snip]
You would find the inverse Fourier transform of the characteristic function.