라플라스분포 (Laplace Distribution)

$$ x \in ( \ -\infty \ , \ \infty \ ) $$

$$ f(x) = \frac{1}{2b} \exp \left[ \frac{- | \ x - \mu \ | }{b} \right] $$

$$ F(x) = \frac{1}{2} \left\{ 1 + sgn (x - \mu) \left( 1 - \exp \left[ \frac{- | \ x - \mu \ | }{b} \right] \right) \right\} $$

$$ E(X) = \mu $$

$$ Var(X) = 2 b^{2} $$

$$ \gamma_{1} = 0 $$

$$ \gamma_{2} = 3 $$

$$ \phi \ (t) = \frac{e^{i \mu t}}{1 + b^{2} t^{2}} $$