Statistical Moments and Generating Functions

A variety of moments or combinations of moments are used to summarize a distribution or data. Mean is used to indicate a center location, variance and standard deviation are used to indicate dispersion and covariance, and correlation to indicate dependence. The Wolfram Language fully supports moments of any order, univariate or multivariate, for symbolic distributions and data. You can automatically convert between different moment representations as well as automatically derive unbiased moment estimators.

Special Moments

General Moments

(RefLink[Moment, paclet:ref/Moment]) — moments of distributions and data

(RefLink[CentralMoment, paclet:ref/CentralMoment]) — central moments of distributions and data

Moment-Generating Functions

(RefLink[MomentGeneratingFunction, paclet:ref/MomentGeneratingFunction]) — moment-generating function (MGF) of distributions

(RefLink[CharacteristicFunction, paclet:ref/CharacteristicFunction]) — characteristic function (CF) of distributions

Moments and Estimators

(RefLink[MomentConvert, paclet:ref/MomentConvert]) — convert between different types of moments and sample moments

(RefLink[MomentEvaluate, paclet:ref/MomentEvaluate]) — evaluate moments and sample moments on distributions and data