# Laplace cdf

The Laplace cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $b>0$ and is given by $$F(x) = \left\{ \begin{array}{ll} \dfrac{1}{2} \exp \left(\dfrac{x-\mu}{b} \right), & \quad x \leq \mu \\ 1 - \dfrac{1}{2} \exp \left( -\dfrac{x-\mu}{b} \right), & \quad x>\mu, \end{array} \right.$$ where $\exp$ denotes the exponential function.