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stats[describe]

  

moment

  

Moments of a Statistical List

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

stats[describe, moment[which, origin, Nconstraint]](data)

describe[moment[which, origin, Nconstraint]](data)

Parameters

data

-

statistical list

which

-

integer that specifies the required moment

origin

-

(optional, default=0) the quantity about which the moment is computed.

Nconstraint

-

(optional, default=0) number of constraints, 1 for sample, 0 for full population

Description

• 

Important: The stats package has been deprecated. Use the superseding package Statistics instead.

• 

The function moment of the subpackage stats[describe, ...] computes the various moments  of the given data about any origin.

• 

The r-th moment about an origin R is computed as follows: M_R:=(1/(N-Nconstraints))*sum( (X-R)^r ), where N is the total weight of the data.

• 

The value of origin can be either a number, or the various descriptive statistic functions that can be specified via stats[describe, descriptive statistic function].

• 

The function moment is closely related to the function sumdata.

• 

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

• 

The definition of the moment varies according to whether it is computed for the whole population, or only for a sample. The parameter Nconstraint provides for this. Refer to describe[standarddeviation] for more information about this.

• 

The command with(stats[describe],moment) allows the use of the abbreviated form of this command.

Examples

Important: The stats package has been deprecated. Use the superseding package Statistics instead.

withstats:

data1,3,5

data:=1,3,5

(1)

Third moment about 0:

describe[moment[3]]data=113+33+533

51=51

(2)

Fourth moment about 1:

describe[moment[4,1]]data=1114+314+5143

2723=2723

(3)

Fifth moment about the mean, for a sample population:

describe[moment[5,mean,1]]data=1135+335+5352

0=0

(4)

See Also

describe(deprecated)[kurtosis]

describe(deprecated)[standarddeviation]

describe(deprecated)[sumdata]

describe(deprecated)[variance]

Statistics

Statistics[Moment]

stats(deprecated)[data]

transform(deprecated)[classmark]

 


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