SampleKurt {MultiStatM}

Estimation of Sample Kurtosis (Mardia, MRSz, Total)

Description

Estimates the sample kurtosis index based on the specified method: Mardia, MRSz, or Total.

Usage

SampleKurt(x, Type = c("Mardia", "MRSz", "Total"))

Arguments

x

A matrix of multivariate data.

Type

A character string specifying the type of kurtosis index to estimate. Use "Mardia" for Mardia's kurtosis index, "MRSz" for the Mori-Rohatgi-Szekely kurtosis matrix, or "Total" for the total kurtosis index.

Value

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

Mardia.Kurtosis

The kurtosis index when Type is "Mardia".

MRSz.Kurtosis

The kurtosis matrix when Type is "MRSz".

Total.Kurtosis

The total kurtosis index when Type is "Total".

p.value

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

References

Gy.Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Example 6.1 and 6.9.

See Also

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

Examples

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

# MRSz's kurtosis example
SampleKurt(x, Type = "MRSz")

# Total kurtosis example
SampleKurt(x, Type = "Total")