MultiStatM (version 2.0.0)

EVSKUniS: EVSK of the Uniform distribution on the sphere or its modulus

Description

Cumulants (up to the 4th order), skewness, and kurtosis of the d-variate Uniform distribution on the sphere or the modulus of the d-variate Uniform distribution on the sphere.

Usage

EVSKUniS(d, nCum = TRUE, Type = c("Standard", "Modulus"))

Value

A list of computed moments and cumulants.

When Type is "Standard":

EU1

Mean vector

varU

Covariance matrix

Skew.U

Skewness vector (always zero)

Skew.tot

Total skewness (always zero)

Kurt.U

Kurtosis vector

Kurt.tot

Total kurtosis

When Type is "Modulus":

EU1

Mean vector

varU

Covariance matrix

EU.k

List of moments up to 4th order

cumU.k

List of cumulants up to 4th order

skew.U

Skewness vector

kurt.U

Kurtosis vector

Arguments

d

dimensions

nCum

if it is FALSE then moments (up to the 4th order) are calculated.

Type

specify the type of distribution: "Standard" for the Uniform distribution on the sphere, or "Modulus" for the modulus of the Uniform distribution on the sphere.

References

Gy. Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021 Proposition 5.3 p.297

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

Gy. Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021, Lemma 5.12 p.298

See Also

Other Moments and cumulants: Cum2Mom(), EVSKSkewNorm(), Mom2Cum(), MomCumCFUSN(), MomCumSkewNorm(), MomCumUniS(), MomCumZabs()

Examples

# Example for Standard type
EVSKUniS(d=3, Type="Standard")

# Example for Modulus type
EVSKUniS(d=3, Type="Modulus")