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)
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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.
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## 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)
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