Skew Normal distribution | Vose Software

Skew Normal distribution

Format: SkewNormal(


The Skew Normal (SkewNormal) distribution is a continuous unbounded distribution developed as a deviation to the Normal distribution to allow for skewness by altering the α parameter, as illustrated in the plot below. When α=0 the distribution reduces to a Normal(μ,σ).



The Skew Normal distribution is mostly used by fitting to data that are approximately Normal but have some skewness. The Skew Normal can readily be compared to a Normal since they share the same mean μ and standard deviation σ parameters.


The range of possible skewness values lies within [-0.9952717,0.9952717]. The relationship between the parameter α and the distribution’s skewness is given in the following plot (negative α gives the equivalent negative skewness):


ModelRisk functions added to Microsoft Excel for the Skew Normal distribution

VoseSkewNormal generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseSkewNormalObject constructs a distribution object for this distribution.

VoseSkewNormalProb returns the probability density or cumulative distribution function for this distribution.

VoseSkewNormalProb10 returns the log10 of the probability density or cumulative distribution function.

VoseSkewNormalFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseSkewNormalFitObject constructs a distribution object of this distribution fitted to data.

VoseSkewNormalFitP returns the parameters of this distribution fitted to data.


Skew Normal distribution equations