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Medientyp:
E-Artikel
Titel:
The Early History of the Cumulants and the Gram‐Charlier Series
Beteiligte:
Hald, Anders
Erschienen:
Wiley, 2000
Erschienen in:
International Statistical Review, 68 (2000) 2, Seite 137-153
Sprache:
Englisch
DOI:
10.1111/j.1751-5823.2000.tb00318.x
ISSN:
0306-7734;
1751-5823
Entstehung:
Anmerkungen:
Beschreibung:
SummaryThe early history of the Gram‐Charlier series is discussed from three points of view: (1) a generalization of Laplace's central limit theorem, (2) a least squares approximation to a continuous function by means of Chebyshev‐Hermite polynomials, (3) a generalization of Gauss's normal distribution to a system of skew distributions. Thiele defined the cumulants in terms of the moments, first by a recursion formula and later by an expansion of the logarithm of the moment generating function. He devised a differential operator which adjusts any cumulant to a desired value. His little known 1899 paper in Danish on the properties of the cumulants is translated into English in the Appendix.