Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Random Variables > Statistical Moments and Generating Functions > MomentEvaluate
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Random Variables > Statistical Moments and Generating Functions > MomentEvaluate
Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Random Variables > Statistical Distribution Functions > Statistical Moments and Generating Functions > MomentEvaluate
BUILT-IN MATHEMATICA SYMBOL

MomentEvaluate

MomentEvaluate[mexpr, dist]
evaluates formal moments in the moment expression mexpr on the distribution dist.

MomentEvaluate[mexpr, list]
evaluates formal moments and formal sample moments in mexpr on the data list.

MomentEvaluate[mexpr, dist, list]
evaluates formal moments on the distribution dist and formal sample moments on the data list.

DetailsDetails

  • A moment expression is an expression involving formal moments and formal sample moments.
  • A formal moment is an expression of the form:
  • Moment[r]formal r^(th) moment
    CentralMoment[r]formal r^(th) central moment
    FactorialMoment[r]formal r^(th) factorial moment
    Cumulant[r]formal r^(th) cumulant
  • A formal sample moment is an expression of the form:
  • PowerSymmetricPolynomial[r]formal r^(th) power symmetric polynomial
    AugmentedSymmetricPolynomial[{r1,r2,...}]formal augmented symmetric polynomial
  • For a sample moment expression PowerSymmetricPolynomial[0] is taken to be the length of the list of data.
  • MomentEvaluate[mexpr, ..., n] assumes that n is taken to be the length of the list of data.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Evaluate formal moments for a univariate distribution:

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Evaluate formal moments for a multivariate distribution:

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Evaluate sample formal moments for data:

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Evaluate formal moments for data:

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Scope (6)Scope (6)

Generalizations & Extensions (1)Generalizations & Extensions (1)

Applications (1)Applications (1)

Properties & Relations (1)Properties & Relations (1)

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