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 Incoming links: Standard Cauchy distribution

Characteristic function of the Cauchy distribution 2026-10-03

For

X \sim Cauchy (x_{0}, γ)

,

E [e^{i tX}] = e^{i x_{0} t - γ ∣ t ∣} .

In particular, the Standard Cauchy distribution has characteristic function

e^{- ∣ t ∣}

.

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