Parameters obtained from Moments using the Johnson Distribution System

When simulating random numbers from correspondingly parameterized statistical probability distributions, the pertaining statistical moments (if they exist and are finite) can be determined numerically at least approximately. The reverse approach, i.e. specifying statistical moments for determining the parameters, is generally more complex. The aim of this analysis is to numerically compute the corresponding parameterization of a suitable continuous probability distribution type from given moments via the programming language R.