The computation of one-sided probability density functions (PDFs) from their cumulants using Laplace transform is proposed by following paper:
M.N. Berberan-Santos, Journal of Mathematical Chemistry, Vol. 41, No. 1, January 2007 (© 2006)71-77. a link!
I need similar computation for two-sided PDF.
Expansion of the method for two-tailed PDF is developed in the following paper:
"Expressing a probability density function in terms of another PDF: A generalized Gram-Charlier expansion" M.N. Berberan-Santos, Journal of Mathematical Chemistry, Vol. 42, No. 3, October 2007 (© 2006) a link!