The Skew Normal Density Function
The skew normal distribution is an extention of the normal distribution. The difference is the presence of skewness, determined by the parameter (for we have the normal distribution).
The skew normal density function is given by
where is the probability density function of the standard normal distribution and is its distribution function.
A. Azzalini, "A Class of Distributions Which Includes the Normal Ones," Scandinavian Journal of Statistics, 12(2), 1985 pp. 171–178.