The Asymmetric Laplace distribution is given by the two-sided exponential
distribution given by the function:
$$f(x;a_l,a_r,m) =
\frac{1}{A} e^{-|\frac{x-m}{a_l}| }, x < m
$$
$$f(x;a_l,a_r,m) =
\frac{1}{A} e^{-|\frac{x-m}{a_r}| }, x > m
$$
with:
$$A = a_l + a_r$$
The random sampling is done by inverse transform sampling.