Skew Normal Distribution

Skew Normal Distribution

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where 𝜙(𝑥) and Φ(𝑥) are respectively the PDF and CDF of the standard normal distribution, and cdfbvn is the cumulative standardized bivariate normal distribution.

Range -∞ < 𝑥 < ∞

Location parameter, 𝜇

Scale parameter 𝜎 > 0

Skew parameter 𝛼, negative for left skew, positive for right skew