• 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
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  • 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.