If xi, omega^2 and alpha are not specified they assume the default values of 0, 1 and 0, respectively.
The Skew Normal distribution with parameters xi = \(\xi\), omega^2 = \(\omega^2\) and alpha = \(\alpha\) has density:
$$ \left(\frac{2}{\omega}\right)\phi\left(\frac{x-\xi}{\omega}\right)\Phi\left(\alpha\left(\frac{x-\xi}{\omega}\right)\right) $$
where \(\phi(x)\) is the standard normal probability density function and \(\Phi(x)\) is its cumulative distribution function.