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. == Definition == Let ϕ ( x ) {\displaystyle \phi (x)} denote the standard normal probability density function ϕ ( x ) = 1 2 π e − x 2 2 {\displaystyle \phi (x)={\frac {1}{\sqrt {2\pi }}}e^{-{\frac {x^{2}}{2}}}} with the cumulative distribution function given by Φ ( x ) = ∫ − ∞ x ϕ ( t ) d t = 1 2 [ 1 + erf ( x 2 ) ] , {\displaystyle \Phi (x)=\int _{-\infty }^{x}\phi (t)\ \mathrm {d} t={\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x}{\sqrt {2}}}\right)\right],} where "erf" is the error function.