SampleSkew {MultiStatM}

Estimation of Sample Skewness (Mardia, MRSz)

Description

Estimates the sample skewness index based on the specified method: Mardia or MRSz.

Usage

SampleSkew(x, Type = c("Mardia", "MRSz"))

Arguments

x

A matrix of multivariate data.

Type

A character string specifying the type of skewness index to estimate. Use "Mardia" for Mardia's skewness index or "MRSz" for the Mori-Rohatgi-Szekely skewness vector and index.

Value

A list containing the estimated skewness index or vector and the associated p-value under the Gaussian hypothesis.

Mardia.Skewness

The skewness index when Type is "Mardia".

MRSz.Skewness.Vector

The skewness vector when Type is "MRSz".

MRSz.Skewness.Index

The skewness index when Type is "MRSz".

p.value

The p-value under the Gaussian hypothesis for the estimated skewness.

References

Gy.Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Example 6.1 and 6.2.

S. R. Jammalamadaka, E. Taufer, Gy. Terdik. On multivariate skewness and kurtosis. Sankhya A, 83(2), 607-644.

See Also

Other Estimation: SampleEVSK(), SampleKurt(), SampleMomCum(), VarianceKurt(), VarianceSkew()

Examples

# Mardia's skewness example
x <- matrix(rnorm(100*5), ncol=5)
SampleSkew(x, Type = "Mardia")

# MRSz's skewness example
SampleSkew(x, Type = "MRSz")