Moments of a Statistical List

stats[describe,moment] - Moments of a Statistical List

	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.

(1)

Third moment about 0:

describe[moment[3]](data) = (1^3+3^3+5^3)*(1/3)

(2)

Fourth moment about 1:

describe[moment[4, 1]](data) = ((1-1)^4+(3-1)^4+(5-1)^4)*(1/3)

(3)

Fifth moment about the mean, for a sample population:

describe[moment[5, mean, 1]](data) = ((1-3)^5+(3-3)^5+(5-3)^5)*(1/2)

(4)

	See Also
	describe(deprecated)[kurtosis], describe(deprecated)[standarddeviation], describe(deprecated)[sumdata], describe(deprecated)[variance], Statistics, Statistics[Moment], stats(deprecated)[data], transform(deprecated)[classmark]