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Statistics[Moment] - compute moments
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Calling Sequence
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Moment(A, n, ds_options)
Moment(X, n, rv_options)
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Parameters
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A
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Array or Matrix data set; data sample
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X
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algebraic; random variable or distribution
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n
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algebraic; order
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ds_options
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(optional) equation(s) of the form option=value where option is one of ignore, origin, or weights; specify options for computing the moment of a data set
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rv_options
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(optional) equation(s) of the form option=value where option is one of numeric or origin; specifies options for computing the moment of a random variable
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Description
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The Moment function computes the moment of order n of the specified random variable or data set.
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The second parameter can be any Maple expression.
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Computation
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All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.
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By default, all computations involving random variables are performed symbolically (see option numeric below).
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Data Set Options
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The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.
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ignore=truefalse -- This option controls how missing data is handled by the Moment command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Moment command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.
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weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight  .
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origin=algebraic -- By default, the moment is computed about 0. If this option is present, the moment will be calculated about the specified point. If A is a Matrix data set, then you can specify several origins instead, one for each column of the matrix. This is accomplished by passing a list or Vector as the value of the origin option.
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Random Variable Options
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The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
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numeric=truefalse -- By default, the moment is computed symbolically. To compute the moment numerically, specify the numeric or numeric = true option.
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origin=algebraic -- By default, the moment is computed about 0. If this option is present, the moment will be calculated about the specified point.
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Compatibility
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The A parameter was updated in Maple 16.
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Examples
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Compute the third moment of the beta distribution with parameters 3 and 5.
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Generate a random sample of size 100000 drawn from the above distribution and compute the third moment.
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Compute the standard error of the third moment for the normal distribution with parameters 5 and 2.
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]](/support/helpjp/helpview.aspx?si=4685/file02900/math307.png)
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![[185, (1/500)*9465^(1/2)]](/support/helpjp/helpview.aspx?si=4685/file02900/math310.png)
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]](/support/helpjp/helpview.aspx?si=4685/file02900/math314.png)
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![[185., .1945764631]](/support/helpjp/helpview.aspx?si=4685/file02900/math317.png)
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![[Moment(B, 3), StandardError(Moment, B, 3, origin = 0)]](/support/helpjp/helpview.aspx?si=4685/file02900/math321.png)
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![[184.739612197642, .194581255981410461]](/support/helpjp/helpview.aspx?si=4685/file02900/math324.png)
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Create a beta-distributed random variable  and compute the third moment of  .
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Verify this using simulation.
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Compute the average moment of a weighted data set.
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Consider the following Matrix data set.
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![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4685/file02900/math387.png)
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![M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])](/support/helpjp/helpview.aspx?si=4685/file02900/math390.png)
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We compute the second moment of each of the columns.
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](/support/helpjp/helpview.aspx?si=4685/file02900/math399.png)
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We compute the second moment of each column with origin 3.
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](/support/helpjp/helpview.aspx?si=4685/file02900/math408.png)
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We compute the second moment of each column with three different origins.
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![Moment(M, 2, 'origin = [3, 1000, 100000]')](/support/helpjp/helpview.aspx?si=4685/file02900/math414.png)
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](/support/helpjp/helpview.aspx?si=4685/file02900/math417.png)
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References
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Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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