distr_CFUSSD_Rand {MultiStatM}

Random multivariate CFUSSD

Description

Generate random d-vectors from the multivariate Canonical Fundamental Skew-Spherical distribution (CFUSSD) with Gamma generator

Usage

distr_CFUSSD_Rand(n, d, p, a, b, Delta)

Arguments

n

sample size

d

dimension

p

dimension of the first term of (5.5)

a

shape parameter of the Gamma generator

b

scale parameter of the Gamma generator

Delta

skewness matrix

Value

A matrix of n \times d random numbers

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021, (5.36) p. 266, (see p.247 for Delta)

See Also

Other Random generation: distr_CFUSN_Rand(), distr_SkewNorm_Rand(), distr_Uni_Rand()

Other Multivariate distributions: distr_CFUSN_MomCum_Th(), distr_CFUSN_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

n <- 10^3; d <- 2; p <- 3 ; a <- 1; b <- 1
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)
distr_CFUSSD_Rand(20,d,p,1,1,Delta)