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Edgeworth Expansion

  1. Peter Hall

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15031

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Hall, P. 2005. Edgeworth Expansion. Encyclopedia of Biostatistics. 4.

Author Information

  1. Australian National University, Canberra, Australia

Publication History

  1. Published Online: 15 JUL 2005

Abstract

The Edgeworth expansion expresses one probability density in terms of another by the use of cumulants, and is particularly important when the reference distribution is the standard normal. There are applications to the distributions of statistics including the sample mean, sample variance, variance ratio and correlation coefficient, and to the coverage of confidence intervals.

Keywords:

  • cumulant;
  • Chebyshev–Hermite;
  • polynomial;
  • Cornish–Fisher;
  • Gram–Charlier;
  • central limit