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A Gram-Charlier series involves the expansion of one probability density function in terms of the derivatives of another density function. This paper generalizes the original series introduced by Gram, an expansion that minimizes a weighted square error. Two new Gram-Charlier expansions for the density of a finite variate are derived and recursion formulas for series coefficients are given.
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Roy S. Freedman (1981) studied this question.
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