Moment

Moment[list, r]
gives the r^(th) sample moment of the elements in list.

Moment[dist, r]
gives the r^(th) moment of the symbolic distribution dist.

Moment[..., {r1, r2, ...}]
gives the ^(th) multivariate moment.

Moment[r]
represents the r^(th) formal moment.

DetailsDetails

  • Moment is also known as a raw moment.
  • Moment handles both numerical and symbolic data.
  • For the list , the r^(th) moment is given by .
  • Moment[{{x1, y1, ...}, ..., {xn, yn, ...}}, {rx, ry, ...}] gives .
  • Moment works with SparseArray objects.
  • For a symbolic distribution dist, the r^(th) moment is given by Expectation[xr, xDistributeddist].
  • For a multivariate symbolic distribution dist, the ^(th) moment is given by Expectation[x1r1x2r2..., {x1, x2, ...}Distributeddist].
  • Moment[r] can be used in functions such as MomentConvert and MomentEvaluate, etc.

ExamplesExamplesopen allclose all

Basic Examples (5)Basic Examples (5)

Compute moments from data:

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Use symbolic data:

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Compute the second moment of a continuous univariate distribution:

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The moment for a discrete univariate distribution:

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The moment for a multivariate distribution:

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Convert a formal moment to central moments:

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Evaluate for a particular distribution:

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