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Calculating the mode of a distribution from the characteristic function

  1. Jan 17, 2009 #1
    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!

  2. jcsd
  3. Jan 17, 2009 #2


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    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.
  4. Jan 19, 2009 #3
    Yes, so I can compute the mean, variance, skewness, kurtosis.... but I can't find an equation for computing the mode...

  5. Oct 7, 2009 #4
    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)) ?
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