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 transformations . Examples are given of equations for converting normal samples to Student t, and converting exponential to hyperbolic and variance gamma .