Third: Third multivariate moment of a data matrix

In MultiSkew: Measures, Tests and Removes Multivariate Skewness

Description

It contains all moments of order three which can be obtained from the variables.

Usage

Third(data, type)

Arguments

data	data matrix
type	type="raw" is the third raw moment type="central" is the third central moment type="standardized" is the third standardized moment

Details

Some general information about the third multivariate moment of both theoretical and emprical distributions are reviewed in Loperfido, N. (2015).

Value

Third moment: all moments of order three which can be obtained from the variables in "data".

Author(s)

Cinzia Franceschini and Nicola Loperfido

References

Loperfido, N. (2015). Singular Value Decomposition of the Third Multivariate Moment. Linear Algebra and its Applications 473, 202-216.

Examples

data(PM10_2006)
PM10_2006_matrix<-data.matrix(PM10_2006)
Third(PM10_2006_matrix[,2:5], "raw")

Example output

Loading required package: MaxSkew
[1] "Third moment"
           [,1]      [,2]      [,3]      [,4]
 [1,]  58790.47  50622.91  152272.5  207709.2
 [2,]  50622.91  44180.63  129610.7  176976.6
 [3,] 152272.48 129610.68  405977.8  553636.9
 [4,] 207709.18 176976.55  553636.9  766832.0
 [5,]  50622.91  44180.63  129610.7  176976.6
 [6,]  44180.63  39351.54  111763.1  152833.4
 [7,] 129610.68 111763.13  341825.6  466640.9
 [8,] 176976.55 152833.38  466640.9  647181.2
 [9,] 152272.48 129610.68  405977.8  553636.9
[10,] 129610.68 111763.13  341825.6  466640.9
[11,] 405977.84 341825.61 1111445.9 1515262.9
[12,] 553636.88 466640.85 1515262.9 2097043.4
[13,] 207709.18 176976.55  553636.9  766832.0
[14,] 176976.55 152833.38  466640.9  647181.2
[15,] 553636.88 466640.85 1515262.9 2097043.4
[16,] 766832.03 647181.21 2097043.4 2955156.4

MultiSkew documentation built on May 2, 2019, 9:36 a.m.