Before revision:  The method developed here may also be regarded as providing  analytical and numerical bases for doing a more precise form of Cornish-Fisher expansion . Examples are given of equations for converting normal samples to Student t, and converting exponential to hyperbolic and variance gamma .
After revision:  The method developed here may also be regarded as providing analytical and numerical bases for doing a more precise form of Cornish-Fisher expansion . Examples are given of equations for converting normal samples to Student t, and converting exponential to hyperbolic , variance gamma and normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of the sample space. The avoidance of any branching statement may be of use in optimal GPU computations .