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.

ReferenceReference

Special Moments

Mean  ▪  Variance  ▪  StandardDeviation  ▪  Skewness  ▪  Kurtosis

Covariance  ▪  Correlation

General Moments

Moment moments of distributions and data

CentralMoment central moments of distributions and data

FactorialMoment  ▪  Cumulant

Moment-Generating Functions

MomentGeneratingFunction moment-generating function (MGF) of distributions

CharacteristicFunction characteristic function (CF) of distributions

CumulantGeneratingFunction  ▪  CentralMomentGeneratingFunction  ▪  FactorialMomentGeneratingFunction

Moments and Estimators

MomentConvert convert between different types of moments and sample moments

MomentEvaluate evaluate moments and sample moments on distributions and data

PowerSymmetricPolynomial  ▪  AugmentedSymmetricPolynomial