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based on an earlier version of the Wolfram Language.
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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. Mathematica 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
Mean  ▪ Variance  ▪ StandardDeviation  ▪ Skewness  ▪ Kurtosis
General Moments
Moment moments of distributions and data
CentralMoment central moments of distributions and data
Moment Generating Functions
MomentGeneratingFunction moment generating function (MGF) of distributions
CharacteristicFunction characteristic function (CF) of distributions
Moments and Estimators
MomentConvert convert between different types of moments and sample moments
MomentEvaluate evaluate moments and sample moments on distributions and data