Edgeworth Expansion for Near-Normal Data
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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 α and scale parameter β, or (2) a chi distribution with ν 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 (SubscriptBox["μ", "3"] and SubscriptBox["μ", "4"]) and is given by .
Contributed by: Housam Binous, Mamdouh Al-Harthi, and Brian G. Higgins (November 2011)
Open content licensed under CC BY-NC-SA