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Statistics

  

Variation

  

compute the coefficient of variation

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

Variation(A, ds_options)

Variation(X, rv_options)

Parameters

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

Description

• 

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]).

Computation

• 

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.

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 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.

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 coefficient of variation is computed using exact arithmetic. To compute the coefficient of variation numerically, specify the numeric or numeric = true option.

Examples

with(Statistics):

Compute the coefficient of variation of the beta distribution with parameters p and q.

Variation('Beta'(p, q));

pqp+q+1p

(1)

Use numeric parameters.

Variation('Beta'(3, 5));

159

(2)

Variation('Beta'(3, 5), numeric);

0.4303314828

(3)

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

(4)

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

(5)

Variation(B);

0.400136408914884

(6)

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);

Floatundefined

(7)

Variation(V, weights = W, ignore = true);

0.0406951177946295

(8)

Consider the following Matrix data set.

M := Matrix([[3,1130,114694],[4,1527,127368],[3,907,88464],[2,878,96484],[4,995,128007]]);

M31130114694415271273683907884642878964844995128007

(9)

We compute the coefficient of variation of each of the columns.

Variation(M);

0.2614562582918990.2433068957043710.161742551310824

(10)

References

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

• 

The A parameter was updated in Maple 16.

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[ExpectedValue]

Statistics[RandomVariables]

Statistics[StandardError]