Skew normal distribution

In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Let ϕ ( x ) {displaystyle phi (x)} denote the standard normal probability density function with the cumulative distribution function given by where 'erf' is the error function. Then the probability density function (pdf) of the skew-normal distribution with parameter α {displaystyle alpha } is given by