Skewed Normal Distribution
X ~ SkewNormal(ξ, ω, α)
Skewed / Asymmetric-Extension Family • Published July 22, 2026
Azzalini's one-parameter skew extension of the already-published Normal, exactly recovered at α=0: PDF/CDF verified against scipy.stats.skewnorm, and the delta-decomposition construction (which reuses the already-published Half-Normal via its |Z₀| term) confirmed via 3-million-draw simulation. Skewness is bounded, unlike the unbounded skewness of the already-published Weibull or Gamma. Maximum-likelihood fit has no closed form, verified via joint numerical optimization.
This reference sheet is part of an Analyze subscription.
Subscribe to read the full Skewed Normal Distribution reference sheet, along with every other resource in the library.
See plansPrefer a saved copy?
About This Reference Sheet
Azzalini's one-parameter skew extension of the already-published Normal, exactly recovered at α=0: PDF/CDF verified against scipy.stats.skewnorm, and the delta-decomposition construction (which reuses the already-published Half-Normal via its |Z₀| term) confirmed via 3-million-draw simulation. Skewness is bounded, unlike the unbounded skewness of the already-published Weibull or Gamma. Maximum-likelihood fit has no closed form, verified via joint numerical optimization.
Support
x ∈ (-∞, ∞)
Parameters
ξ ∈ ℝ (location), ω > 0 (scale), α ∈ ℝ (shape)