# Characteristic function to pdf

• May 29th 2008, 10:01 AM
langweilig
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...)
• May 29th 2008, 08:46 PM
mr fantastic
Quote:

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.