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 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 .