Skew normal distribution with location m scale s and shape a
SkewNormalDistribution[μ, σ, α]
Mean[SkewNormalDistribution[μ, σ, α]]
→ μ + (Sqrt[2/Pi]*α*σ)/Sqrt[1 + α^2]PDF[SkewNormalDistribution[μ, σ, α], x]
→ Erfc[-((α*(x - μ))/(Sqrt[2]*σ))]/(E^((x - μ)^2/(2*σ^2))*Sqrt[2*Pi]*σ)CDF[SkewNormalDistribution[μ, σ, α], x]
→ -2*OwenT[(x - μ)/σ, α] + Erfc[(-x + μ)/(Sqrt[2]*σ)]/2