[…] For each (s,k) value in the moment-ratio diagram, you can find the corresponding (a,b) parameter value for the Beta distribution that has the specified skewness and kurtosis. You can do this by solving for the root of the vector-valued function M(a,b) - (s,k), where M(a,b) is the transformation that maps parameter values to the corresponding (s,k) values. This can be done by using the SAS IML language, which enables you to define the vector-valued mapping and solve nonlinear equations in a least-square sense. …