# Calculating the mode of a distribution from the characteristic function

1. Jan 17, 2009

### natski

Is it possible to exactly derive the mode of a probability distribution if you have the characteristic function? I cannot get the pdf of the distribution because the inverse Fourier transform of the characteristic function cannot be found analytically.

Any thoughts would be appreciated!

natski

2. Jan 17, 2009

### mathman

Although I'm not absolutely certain, I'm pretty sure you can't get the mode. I presume you know that you can get the moments by expanding the char. funct. in a power series.

3. Jan 19, 2009

### natski

Yes, so I can compute the mean, variance, skewness, kurtosis.... but I can't find an equation for computing the mode...

Natski

4. Oct 7, 2009

### bpet

Hi Natski (found this old thread while looking for a solution to another problem)

To solve df/dx=0, what if you differentiate the inverse Fourier transform (with suitable assumptions on the pdf and c.f.) - if p(t) is the c.f. then the modes would be the zero-amplitude frequencies of (t*p(t)) ?