# Edgeworth Expansion for Near-Normal Data

Edgeworth Expansion for Near-Normal Data

This Demonstration shows how you can use the Edgeworth expansion to describe standardized near-normal data. In order to do so, you can apply Mathematica's built-in function RandomVariate to data obtained from either (1) a gamma distribution, with shape parameter and scale parameter , or (2) a chi distribution with degrees of freedom. The built-in command Standardize shifts and rescales the elements of the generated list of data to have a zero mean and a unit sample variance. The Edgeworth expansion uses the third and fourth central moments ( and ) and is given by .

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f(x)=1+(-3x)6+(-120+360-120+8)576+(12-24+4)(-3)96

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