Infinite divisibility of skew Gaussian and Laplace laws

We study infinite divisibility of skew distributions given by the density function gλ(x)=2f(x)F(λx)gλ(x)=2f(x)F(λx), λ∈Rλ∈R, where f and F   are the density and distribution functions of (symmetric) normal or Laplace laws. It turns out that although the symmetric laws are both infinitely divisible (ID), the skew normal is not ID but the skew Laplace is ID. A new stochastic representation for skewed Laplace distributions is given, which is independently useful for simulation. We also show that the skew Laplace laws are self-decomposable only for |λ||λ| below a specified threshold.