Statistics
Variation
compute the coefficient of variation
Calling Sequence
Parameters
Description
Computation
Data Set Options
Random Variable Options
Examples
References
Compatibility
Variation(A, ds_options)
Variation(X, rv_options)
A
-
data set or Matrix data set
X
algebraic; random variable or distribution
ds_options
(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the coefficient of variation of a data set
rv_options
(optional) equation of the form numeric=value; specifies options for computing the coefficient of variation of a random variable
The Variation function computes the coefficient of variation of the specified random variable or data set.
The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
By default, all computations involving random variables are performed symbolically (see option numeric below).
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.
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
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 Variation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Variation 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 1.
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 coefficient of variation is computed using exact arithmetic. To compute the coefficient of variation numerically, specify the numeric or numeric = true option.
with(Statistics):
Compute the coefficient of variation of the beta distribution with parameters p and q.
Variation('Beta'(p, q));
p⁢qp+q+1p
Use numeric parameters.
Variation('Beta'(3, 5));
159
Variation('Beta'(3, 5), numeric);
0.4303314828
Generate a random sample of size 100000 drawn from the above distribution and compute the sample variation.
A := Sample('Beta'(3, 5), 10^5):
Variation(A);
0.432422803985375
Compute the standard error of the sample variation for the normal distribution with parameters 5 and 2.
X := RandomVariable(Normal(5, 2)):
B := Sample(X, 10^6):
[Variation(X), StandardError[10^6](Variation, X)];
25,2912500
Variation(B);
0.400136408914884
Compute the coefficient of variation of a weighted data set.
V := <seq(i, i = 57..77), undefined>:
W := <2, 4, 14, 41, 83, 169, 394, 669, 990, 1223, 1329, 1230, 1063, 646, 392, 202, 79, 32, 16, 5, 2, 5>:
Variation(V, weights = W);
Float⁡undefined
Variation(V, weights = W, ignore = true);
0.0406951177946295
Consider the following Matrix data set.
M := Matrix([[3,1130,114694],[4,1527,127368],[3,907,88464],[2,878,96484],[4,995,128007]]);
M≔31130114694415271273683907884642878964844995128007
We compute the coefficient of variation of each of the columns.
Variation(M);
0.2614562582918990.2433068957043710.161742551310824
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
The A parameter was updated in Maple 16.
See Also
Statistics[Computation]
Statistics[DescriptiveStatistics]
Statistics[Distributions]
Statistics[ExpectedValue]
Statistics[RandomVariables]
Statistics[StandardError]
Download Help Document
What kind of issue would you like to report? (Optional)