distr_CFUSN_MomCum_Th {MultiStatM}

Moments and cumulants CFUSN

Description

Provides the theoretical cumulants of the multivariate Canonical Fundamental Skew Normal distribution

Usage

distr_CFUSN_MomCum_Th(r, d, p, Delta, nMu = FALSE)

Arguments

r

The highest cumulant order

d

The multivariate dimension and number of rows of the skewness matrix Delta

p

The number of cols of the skewness matrix Delta

Delta

The skewness matrix

nMu

If set to TRUE, the list of the first r d-variate moments is provided

Value

The list of theoretical cumulants in vector form

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021, Lemma 5.3 p.251

See Also

Other Theoretical Moments and Cumulants: distr_SkewNorm_EVSK_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_Rand(), distr_CFUSSD_Rand(), distr_SkewNorm_EVSK_Th(), 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

r <- 4; d <- 2; p <- 3
Lamd <-  matrix(sample(1:50-25, d*p), nrow=d)
ieg<- eigen(diag(p)+t(Lamd)%*%Lamd)
V <- ieg$vectors
Delta <-Lamd %*% V %*% diag(1/sqrt(ieg$values)) %*% t(V)
MomCum_CFUSN <- distr_CFUSN_MomCum_Th (r,d,p,Delta)