Calculation of a formal moment generating function by using a differential operator

• Autores: Hiroki Hashiguchi, Toshiya Iwashita
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 6-7, 2008, págs. 508-514
• Idioma: inglés
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• Resumen

  • A differential form in a formal moment generating function is given by the decomposition of powers in terms of the Hermite polynomials. This paper shows that this differential form for calculating the expectation of normal and ?2 distributions has the benefit of avoiding divergence for Edgeworth type approximations from the viewpoint of a formal power series ring. A symbolic computational algorithm is also discussed, within the distribution theory of statistics.