Lévy distribution

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CDF

erfc ( c 2 ( x − μ ) ) {\displaystyle {\textrm {erfc}}\left({\sqrt {\frac {c}{2(x-\mu )}}}\right)}

CF

e i μ t − − 2 i c t {\displaystyle e^{i\mu t-{\sqrt {-2ict}}}}

Entropy

1 + 3 γ + ln ⁡ ( 16 π c 2 ) 2 {\displaystyle {\frac {1+3\gamma +\ln(16\pi c^{2})}{2}}} where γ {\displaystyle \gamma } is the Euler-Mascheroni constant

Excess kurtosis

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Mean

∞ {\displaystyle \infty }

Median

μ + c / 2 ( erfc − 1 ( 1 / 2 ) ) 2 {\displaystyle \mu +c/2({\textrm {erfc}}^{-1}(1/2))^{2}\,}