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Positivity of exponentially bounded characteristic functions
I've noticed that for the classical examples of exponentially bounded, symmetrical distributions (Gaussian, Laplace, Double Exponential, Uniform), their characteristic functions are positive for all ...
- 73
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General Fourier inversion formula (Gil-Pelaez)
Gil-Pelaez (1951) proves the Fourier inversion formula
\begin{align*}
F(x) &= \frac{1}{2} + \frac{1}{2\pi} \int_0^\infty \frac{e^{itx}\phi(-t)-e^{-itx}\phi(t)}{it}dt \\
&= \frac{1}{2} - \frac{...
- 255