  This note considers the applicability of Gauss-Hermite quadrature and direct
numerical quadrature for computation of moment generating function (mgf) and
the derivatives. A preprocessing using the asymptotic technique is employed
while computing the characteristic function (chf) using Gauss Hermite
quadrature while this is optional for mgf. The mgf of the low and high
amplitude regions of a single lognormal variable and the derivatives is
examined and attention is drawn to the effect of variance. The problem of
inversion of the mgf/chf of a sum of lognormals to obtain the CDF/pdf is
considered with special reference to methods related to Post Widder technique,
Gaussian quadrature and the Fourier series method. The method based on the
complex exponential integral which makes use of the derivative of the cumulant
is an alternative. Segmentation of the mgf/chf on the basis of the derivative
structure which indicates activity rate is shown to be useful.
