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Gram-Charlier Series

Approximates a distribution in terms of a Normal Distribution. Let

\begin{displaymath}
\phi(t)\equiv {1\over\sqrt{2\pi}} e^{-t^2/2},
\end{displaymath}

then

\begin{displaymath}
f(t)=\phi(t)+{\textstyle{1\over 6}}\gamma_1 \phi^{(3)}(t)+{\textstyle{1\over 24}}\gamma_2\phi^{(4)}(t)+\ldots.
\end{displaymath}

See also Edgeworth Series


References

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 107-108, 1951.




© 1996-9 Eric W. Weisstein
1999-05-25