Skew Normal Distribution

The “classic” normal distribution is symmetric around it's mean. But many distributions in nature are not symmetric, having a distribution that allows for skewness can be of great use. The skew normal is one such distributions allowing for non zero skweness.

Let \( \phi(x) = \frac{1}{\sqrt(2\pi)} e^{-x^2/2} \) be the standard normal probability function.

With cumulative distribution function given by \( \Phi(x) = \int_{-\infty}^x \phi(t)\,dt = \frac{1}{2}[1+erf(\frac{x}{\sqrt(2)})] \), where erf is the error function.

Then the probability density function of the skew normal distribution with parameter \( \alpha \) is given by:

\( f(x)= 2\phi(x)\Phi(\alpha x) \).

The purpose of this app is to play around with the parameters of this distribution to see what the pdf looks like, especially to see how a skew distribution looks like.

Keep in mind that the parameters affected in the app are not mean, variance and skweness, but location scale and shape. The app “starts” from the neutral position of a normal (0,1). The shape parameter has been reescaled from it's original definition to match the usual definitions of positive/negative skew.