Gram-Charlier Series

Approximates a distribution in terms of a Normal Distribution. Let

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

then

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

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.