# 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 moment CentralMoment[r] formal r central moment FactorialMoment[r] formal r factorial moment Cumulant[r] formal r cumulant
• A formal sample moment is an expression of the form:
•  PowerSymmetricPolynomial[r] formal r power symmetric polynomial AugmentedSymmetricPolynomial[{r1,r2,…}] formal {r1,r2,…} augmented symmetric polynomial
• For a sample moment expression 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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