distr_SkewNorm_MomCum_Th {MultiStatM}R Documentation

Moments and cumulants d-variate Skew Normal

Description

Computes the theoretical values of moments and cumulants up to the r-th order. Warning: if nMu = TRUE it can be very slow

Usage

distr_SkewNorm_MomCum_Th(r = 4, omega, alpha, nMu = FALSE)

Arguments

r

the highest moment and cumulant order

omega

A d \times d correlation matrix

alpha

shape parameter d-vector

nMu

if it is TRUE then moments are calculated as well

Value

A list of theoretical moments and cumulants

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021 (5.5) p.247, Lemma 5.1 p. 246

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_EVSK_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_EVSK_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_MomCum_Th(r=4,omega,alpha)

[Package MultiStatM version 1.2.1 Index]