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.

Details

  • 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 {r1,r2,} 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.

Examples

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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)

Generalizations & Extensions  (1)

Applications  (2)

Properties & Relations  (1)

See Also

MomentConvert  Moment  CentralMoment  FactorialMoment  Cumulant  PowerSymmetricPolynomial  AugmentedSymmetricPolynomial

Introduced in 2010
(8.0)