I am looking at the wikipedia page for the skewed Gaussian distribution, and am interested in quantifying the skewness. From the first subsection, I gather that the theoretical maximum skewness $\gamma_1$ can only be $.9952717...$. I am working with these skewed Gaussians and need a model that accounts for skewnesses for which $\gamma_1$ is greater than $.9952717$. So I have two questions: first, why is the skewed Gaussian set up like this - a skewness of $.9952717$ is still somewhat normal? Second, how can I find a distribution model with some skewness parameter that I can quantify for $\gamma_1 > .9952717$?
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