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Statistics[Moment] - compute moments
Calling Sequence
Moment(A, n, ds_options)
Moment(X, n, rv_options)
Parameters
A
-
Array or Matrix data set; data sample
X
algebraic; random variable or distribution
n
algebraic; order
ds_options
(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
rv_options
(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
Description
The Moment function computes the moment of order n of the specified random variable or data set.
The first parameter can be a data set (represented as an Array or a Matrix data set), a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
The second parameter can be any Maple expression.
Computation
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.
By default, all computations involving random variables are performed symbolically (see option numeric below).
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
Data Set Options
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.
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.
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 .
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.
Random Variable Options
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.
numeric=truefalse -- By default, the moment is computed symbolically. To compute the moment numerically, specify the numeric or numeric = true option.
origin=algebraic -- By default, the moment is computed about 0. If this option is present, the moment will be calculated about the specified point.
Compatibility
The A parameter was updated in Maple 16.
Examples
Compute the third moment of the beta distribution with parameters 3 and 5.
Generate a random sample of size 100000 drawn from the above distribution and compute the third moment.
Compute the standard error of the third moment for the normal distribution with parameters 5 and 2.
Create a beta-distributed random variable and compute the third moment of .
Verify this using simulation.
Compute the average moment of a weighted data set.
Consider the following Matrix data set.
We compute the second moment of each of the columns.
We compute the second moment of each column with origin 3.
We compute the second moment of each column with three different origins.
See Also
Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[RandomVariables], Statistics[StandardError]
References
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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