Edgeworth expansion

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An expansion, derived by Edgeworth in 1905, that relates the probability density function, f, of a random variable, X, having expectation 0 and variance 1, to ϕ, the probability density function of a standard normal distribution, using the Chebyshev–Hermite polynomials. The first terms of the expansion are , where κr is the rth cumulant of X, and Hr(x) is the rth Chebyshev–Hermite polynomial. See also Cornish–Fisher expansion.

Subjects: Probability and Statistics.

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