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Statistics[Cumulant] - compute cumulants
Calling Sequence
Cumulant(A, n, ds_options)
Cumulant(M, n, ds_options)
Cumulant(X, n, rv_options)
Parameters
A
-
Array; data sample
M
Matrix data set
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, or weights; specify options for computing the cumulant of a data set
rv_options
(optional) equation of the form numeric=value; specifies options for computing the cumulant of a random variable
Description
The Cumulant function computes the cumulant 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 Cumulant command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Cumulant 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 .
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 cumulant is computed symbolically. To compute the cumulant numerically, specify the numeric or numeric = true option.
Compatibility
The M parameter was introduced in Maple 16.
For more information on Maple 16 changes, see Updates in Maple 16.
Examples
Compute the third cumulant 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 cumulant.
Create a beta-distributed random variable Y and compute the third cumulant of 1/(Y+2).
Verify this using simulation.
Compute the cumulant of a weighted data set.
Consider the following Matrix data set.
We compute the second cumulant of each column.
See Also
Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[RandomVariables]
References
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
Download Help Document
