The early history of the cumulants and the Gram-Charlier series

The early history of the Gram-Charlier series is discussed from three point s of view: (1) a generalization of Laplace's central limit theorem, (2) a l east squares approximation to a continuous function by means of Chebyshev-H ermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions, Thiele defined the cumulants in terms of th e moments, first by a recursion formula and later by an expansion of the lo garithm of the moment generating function. He devised a differential operat or which adjusts any cumulant to a desired value, His little known 1899 pap er in Danish on the properties of the cumulants is translated into English in the Appendix.