Journal of Mathematical Chemistry

, Volume 42, Issue 3, pp 585–594 | Cite as

Expressing a Probability Density Function in Terms of another PDF: A Generalized Gram-Charlier Expansion


An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the Gram-Charlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained.


probability density function cumulant Gram-Charlier expansion Hermite polynomials 

AMS subject classification

60E10 characteristic functions; other transforms 62E17 approximations to distributions (non-asymptotic) 62E20 asymptotic distribution theory 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Centro de Química-Física MolecularInstituto Superior TécnicoLisboaPortugal

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