Cornish-Fisher Asymptotic Expansion
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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1-4-2021
4000
Cornish-Fisher Asymptotic Expansion
 |
(1)
|
where
where
and combinations of Hermite polynomials.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 935, 1972.
Cornish, E. A. and Fisher, R. A. "Moments and Cumulants in the Specification of Distributions." Extrait de la Revue de l'Institute International de Statistique 4, 1-14, 1937. Reprinted in Fisher, R. A. Contributions to Mathematical Statistics. New York: Wiley, 1950.
Wallace, D. L. "Asymptotic Approximations to Distributions." Ann. Math. Stat. 29, 635-654, 1958.
Wasow, W. "On the Asymptotic Transformation of Certain Distributions into the Normal Distribution." Proceedings of Symposia in Applied Mathematica VI, Numerical Analysis. New York: McGraw-Hill, pp. 251-259, 1956.
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