| EVSKUniS {MultiStatM} | R Documentation |
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"))
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. |
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 |
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")