Student[Statistics] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Package : Statistics : Student/Statistics/Skewness

Student[Statistics]

  

Skewness

  

compute the coefficient of skewness

 

Calling Sequence

Parameters

Description

Computation

Examples

References

Compatibility

Calling Sequence

Skewness(A, numeric_option)

Skewness(M, numeric_option)

Skewness(X, numeric_option, inert_option)

Parameters

A

-

data sample

M

-

Matrix data sample

X

-

algebraic; random variable

numeric_option

-

(optional) equation of the form numeric=value where value is true or false

inert_option

-

(optional) equation of the form inert=value where value is true or false

Description

• 

The Skewness function computes the coefficient of skewness of the specified random variable or data set. In the data set case the following formula for computing the coefficient of skewness is used:

SkewnessA=NMomentA,3,origin=MeanAN1StandardDeviationA3,

  

where N is the number of elements in A.

• 

The first parameter can be a data sample (e.g., a Vector), a Matrix data sample, a random variable, or an algebraic expression involving random variables (see Student[Statistics][RandomVariable]).

• 

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

• 

By default, the skewness is computed according to the rules mentioned above. To always compute the skewness numerically, specify the numeric or numeric = true option.

Examples

withStudent[Statistics]:

Compute the coefficient of skewness of the log normal random variable with parameters μ and σ.

SkewnessLogNormalRandomVariableμ,σ

ⅇ3μ+92σ23ⅇ3μ+52σ2+2ⅇ3μ+32σ2ⅇσ2+2μⅇσ213/2

(1)

Use numeric parameters for the beta random variable.

SkewnessBetaRandomVariable2,7

107735

(2)

SkewnessBetaRandomVariable2,7,numeric

0.7683220505

(3)

Use the inert option.

SkewnessBetaRandomVariable2,7,inert

∫0156_t2+∫0156_t121+_t16ⅆ_t13_t21+_t26ⅆ_t2∫0156_t0+∫0156_t21+_t6ⅆ_t2_t01+_t06ⅆ_t03/2

(4)

evalfSkewnessBetaRandomVariable2,7,inert

0.7683220503

(5)

Consider the following list of data.

A1,2,3,3.0,2,π

A1,2,3,3.0,2,π

(6)

SkewnessA

1.22868166495079

(7)

Consider the following Matrix data sample.

MMatrix3.0,3.8,114,4,ln7,128,π,97,200

M3.03.81144ln7128π97200

(8)

Compute the skewness of each of the columns.

SkewnessM

0.5331979491509490.576594538650996572751530245463883

(9)

References

  

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

Compatibility

• 

The Student[Statistics][Skewness] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

skewness

Statistics[Skewness]

Student

Student[Statistics]

Student[Statistics][RandomVariable]