MVNMIX: Random Generation for the Normal Mixture Distribution
In mvnormalTest: Powerful Tests for Multivariate Normality

Description Usage Arguments Value References Examples

Generate univariate or multivariate random sample for the normal mixture distribution with density λ N(0,∑_1)+(1-λ)N(bl, ∑_2), where l is the column vector with all elements being 1, ∑_i=(1-ρ_i)I+ρ_ill^T for i=1,2. ρ has to satisfy ρ > -1/(p-1) in order to make the covariance matrix meaningful.

1	MVNMIX(n, p, lambda, mu2, rho1 = 0, rho2 = 0)

`n`	number of rows (observations).
`p`	total number of columns (variables).
`lambda`	weight parameter to allocate the proportions of the mixture, 0<λ<1.
`mu2`	is bl of N(bl, ∑_2).
`rho1`	parameter in ∑_1.
`rho2`	parameter in ∑_2.

Returns univariate (p=1) or multivariate (p>1) random sample matrix.

Zhou, M., & Shao, Y. (2014). A powerful test for multivariate normality. Journal of applied statistics, 41(2), 351-363.

set.seed(12345)

## Generate 5X2 random sample matrix from MVNMIX(0.5,4,0,0) ##
MVNMIX(n=5, p=2, lambda=0.5, mu2=4, rho1=0, rho2=0)


## Power calculation against bivariate (p=2) MVNMIX(0.5,4,0,0) distribution ##
## at sample size n=50 at one-sided alpha = 0.05 ##

# Zhou-Shao's test #
power.mvnTest(a=0.05, n=50, p=2, B=100, FUN=MVNMIX, lambda=0.5, mu2=4, rho1=0, rho2=0)