distr_SkewNorm_EVSK_Th {MultiStatM}

EVSK multivariate Skew Normal

Description

Computes the theoretical values of the mean vector, covariance, skewness vector, total skenwness, kurtosis vector and total kurtosis for the multivariate Skew Normal distribution

Usage

distr_SkewNorm_EVSK_Th(omega, alpha)

Arguments

omega

A d \times d correlation matrix

alpha

shape parameter d-vector

Value

A list of theoretical values for the mean vector, covariance, skewness vector, total skenwness, kurtosis vector and total kurtosis

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021 (5.5) p.247

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

See Also

Other Theoretical Moments and Cumulants: distr_CFUSN_MomCum_Th(), distr_SkewNorm_MomCum_Th(), distr_UniAbs_EVSK_Th(), distr_Uni_EVSK_Th(), distr_Uni_MomCum_Th(), distr_ZabsM_MomCum_Th(), distr_Zabs_MomCum_Th()

Other Multivariate distributions: distr_CFUSN_MomCum_Th(), distr_CFUSN_Rand(), distr_CFUSSD_Rand(), distr_SkewNorm_MomCum_Th(), distr_SkewNorm_Rand(), distr_UniAbs_EVSK_Th(), distr_Uni_EVSK_Th(), distr_Uni_MomCum_Th(), distr_Uni_Rand(), distr_ZabsM_MomCum_Th(), distr_Zabs_MomCum_Th()

Examples

alpha<-c(10,5,0)
omega<-diag(3)
distr_SkewNorm_EVSK_Th(omega,alpha)