Talk:Characteristic function (probability theory)

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I think the formula for calculating the n-th moment based on the characteristic function was not correct. It was:

E(X^n)=-i^n \varphi^{(n)}_X(0).

I changed it to

E(X^n)=(-i)^n \varphi^{(n)}_X(0).

Please compare with [1].

[edit] Inversion theorem

I have a bit of a different definition for the inversion theorem that seems to contradict the one in this article. From "probability and random processes" by Grimmet I have:

\overline{F}(x) = \frac{1}{2}[F(x) + \lim_{y \to x^-}F(y)]

then

\overline{F}_X(y) - \overline{F}_X(x) = \lim_{\tau \to +\infty} \frac{1} {2\pi} \int_{-\tau}^{+\tau} \frac{e^{-itx} - e^{-ity}} {it}\, \varphi_X(t)\, dt.

--Faisel Gulamhussein 22:17, 20 October 2006 (UTC)

Probably you're correct. I don't think there is a contradiction exactly. Just many authors assume their random variables have a density, if this is the case the statements would be the same. Thenub314 13:07, 21 October 2006 (UTC)

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