The Gram–Charlier A series (named in honor of Jørgen Pedersen Gram and Carl Charlier), and the Edgeworth series (named in honor of Francis Ysidro Edgeworth) are series that approximate a probability distribution in terms of its cumulants.[1] The series are the same; but, the arrangement of terms (and thus the accuracy of truncating the series) differ.[2] The key idea of these expansions is to write the characteristic function of the distribution whose probability density function f is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover f through the inverse Fourier transform.
- ^ Stuart, A., & Kendall, M. G. (1968). The advanced theory of statistics. Hafner Publishing Company.
- ^ Kolassa, John E. (2006). Series approximation methods in statistics (3rd ed.). Springer. ISBN 0387322272.